Research ArticleEstimatingSolar InsolationandPowerGenerationofPhotovoltaicSystems Using Previous Day Weather Data

Min Hee Chung

School of Architecture and Building Science Chung-Ang University Seoul 06974 Republic of Korea

Correspondence should be addressed to Min Hee Chung mhloveucauackr

Received 22 October 2019 Revised 2 January 2020 Accepted 16 January 2020 Published 18 February 2020

Academic Editor Emanuele Brunesi

Copyright copy 2020 Min Hee Chung (is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Day-ahead predictions of solar insolation are useful for forecasting the energy production of photovoltaic (PV) systems attachedto buildings and accurate forecasts are essential for operational efficiency and trading markets In this study a multilayer feed-forward neural network-based model that predicts the next dayrsquos solar insolation by taking into consideration the weatherconditions of the present day was proposed (e proposed insolation model was employed to estimate the energy production of areal PV system located in South Korea Validation research was performed by comparing themodelrsquos estimated energy productionwith the measured energy production data collected during the PV system operation(e accuracy indices for the optimal modelwhich included the root mean squared error mean bias error and mean absolute error were 143 kWhm2day minus 009 kWhm2day and 115 kWhm2day respectively (ese values indicate that the proposed model is capable of producing reasonableinsolation predictions however additional work is needed to achieve accurate estimates for energy trading

1 Introduction

Electricity consumption has been rapidly increasing aroundthe world despite efforts to improve energy conservation In2013 in Korea the electricity consumption in the commercialand public sectors increased by 10 to 658 compared tovalues in 2001 Moreover the electrification of energy con-sumption has further intensified [1] Since natural gas andelectricity have emerged as primary energy sources in thehousehold sector this share of electricity consumption hasbeen steadily increasing (is is because households preferclean energy sources to maintain comfort and the convenienceof living (e Korean government is promoting buildings inwhich renewable energy systems are used to save on primaryenergy consumption and to realize energy independence

Solar energy is known to be a good substitute for fossilfuels which currently account for more than 80 of theprimary energy supply [2] Photovoltaic (PV) systems are themost suitable replacements for fossil fuels because they do notproduce CO2 emissions and do not pose the same risks asthose associated with other alternative energy supplies such asnuclear power generation It may be more desirable to install

PV systems in the city rather than in the rural or forested areasbecause of land conservation concerns Indeed PV systemsare more likely than other types of renewable energy systemsto be constructed in urban built environments

(e Korean government intends to introduce a smartgrid to promote the embracement of renewable energy [3]As part of these efforts the government announced a secondbasic plan for an intelligent power grid in 2018 Accordinglythe government has set up policies on smart grid complexconstruction infrastructure and facility expansion It wasreported that in 2019 a distributed energy resource marketwould be allowed in Korea As a result significant changesare expected in the electric trading market which has beenfocused on centralized power generation companies (eexpansion of distributed generation will accelerate directenergy trading among individuals and groups that canproduce and consume energy simultaneously [3 4] Suchpeer-to-peer (P2P) energy trading has been demonstrated invarious forms in the United States United KingdomNetherlands and Germany [5ndash7] P2P energy trading isbeneficial because it reduces the need for expensive andinefficient energy transportation with substantial losses [8]

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8701368 13 pageshttpsdoiorg10115520208701368

thus improving the reliability of energy supply [9] and al-leviating transmission and distribution congestion problems[10] Forecasting solar insolation in advance is essential inthe management of the PV systemrsquos generated output in adistributed grid It is necessary to provide information onthe energy production through the system to the prosumerwho conducts the small-scale electricity trading as a weatherforecast in advance Time-based predictions may need to beprovided according to the individualrsquos characteristicsHowever it is necessary to provide daily production forecastinformation to a large number of prosumers In small-scaleenergy trading the provision of daily energy productionforecast information is more effective than providing de-tailed hourly energy generation forecast information Dailyenergy production by PV systems can be predicted simplybased on daily irradiation

Many researchers are presently directing their efforts onsolar insolation forecasting techniques Soares et al [11]examined the intrahour solar insolation predictions basedon hourly weather data for a period of 4 years (ey esti-mated the hourly values of the diffuse solar radiation byusing multilayer perceptron neural networks Howevertheir model could not reflect the present-day weatherchange Mathiesen and Kleissl [12] compared five fore-casting models for the intraday solar insolation by usingground-based weather measurement data and these effortsresulted in the production of an accurate database to validatenumerical weather predictions (e accuracy of each modelin predicting insolation varied in accordance with theweather conditions However it was difficult to considermultiple models simultaneously Sun et al [13] proposed arandom forest algorithm for estimating the daily solar ra-diation based on meteorological data solar radiation andthree air pollution indexes for SO2 NO2 and PM10 (eyoptimized the proposed estimation model depending on theinput variables In a city with a high degree of air pollutionthis model can be used to estimate the exact amount of solarradiation however the number of input variables increasesSharma and Kakkar [14] also proposed an hourly global solarirradiance model for different forecasting horizons rangingfrom a few hours ahead to 48 hours ahead by using machinelearning (e model with 1 hour ahead predictions was themost accurate however there was not enough time toprovide information to users Gutierrez-Corea et al [15]modeled the spatial-temporal short-term global solar in-solation by using artificial neural networks (is model gaveaccurate data predictions over time but increased thecomplexity of the prediction model with more than 900input parameters Huang and Davy [16] proposed a linearregression model for the intrahour solar irradiance that usesthe hourly clear sky index and geopotential thickness (emodel predicted hourly solar irradiance only for summer(erefore there were limitations in applying this model toother seasons Vakili et al [17] designed a prediction modelfor the total daily solar insolation for Iran by using amultilayer perceptron artificial neural network (e limi-tation of this model was that the solar insolation was esti-mated based on the weather observation information ratherthan the future value Qing and Niu [18] presented a novel

solar irradiance prediction method for hourly day-aheadforecasts by using hourly weather forecast data (e pro-posed model contained structured long- and short-termmemory networks and it was compared with other algo-rithms By using weather forecasting data as input variablesit is possible to reflect the change in solar radiation in ac-cordance with the weather changes However the accuracyof the solar radiation prediction changes based on theprediction accuracy of the weather forecast data Amroucheand Le Pivert [19] proposed a solar radiation forecastingmodel using artificial neural networks (ANNs) and specialmodelling In cases where there were no meteorological datafrom the predicted area the solar radiation was estimatedusing meteorological data from the nearby areas (is modelpredicted daily values which were used to estimate powergeneration by PV systems Long et al [20] proposed aprediction model for the daily PV energy production bymeteorological parameters (e efficiency of the predictionalgorithm was improved by classifying the weather databased on importance and with reduced input variables usedas input data

(e prediction accuracy varied in accordance with theaccuracy of the weather forecasts In addition there havebeen many studies on various solar insolation predictionmodels with different prediction horizons and differentprediction methods (e previous solar forecasting modelsmade predictions based on the time or day However a largeamount of input data was needed for accuracy within thepredicted time scale (e limitation of the prediction modelis that the training and prediction time increases as thenumber of input variables increases (is study aims todevelop a simple solar insolation prediction model by usingfewer weather data variables which make it easy to acquireinformation Typically weather forecast data may be used topredict the next dayrsquos solar insolation However predictingthe next dayrsquos solar insolation using weather forecast data ischaracterized by a lot of uncertainty due to the uncertaintyin the weather forecast data

(e objective of this paper is to propose a simple pre-diction model for day-ahead solar insolation using weatherobservation data (e predicted solar insolation would beused for estimating energy production in advance (e es-timated energy production would give information for thedetermination of optimal operating conditions such as self-consumption or feed-in into the grid mode for PV systemslocated in a distributed grid (e day-ahead solar insolationprediction model forecasts the solar radiation of the next daybased on the weather data of the current day It is assumedthat the predicted model cannot be applied to systems in-stalled in a specific condition however it can predict in-formation applicable to a wide range of conditions(erefore the weather difference due to the differences inthe meteorological observation site and the installation lo-cation of the PV system was ignored (e input variables usemeteorological data that can be easily obtained from themeteorological administration (e prediction model couldprovide building users with useful information to plan theirenergy use in advance (is paper is organized as follows InSection 2 the data used for training and checking the

2 Advances in Civil Engineering

prediction model are described Section 3 explains thepredictionmodel and the verificationmethod(emeasuredenergy production for a PV system located in South Koreawas compared to the energy production prediction obtainedthrough the solar insolation prediction model Section 4presents the results and Section 5 presents the conclusions

2 Meteorological Data

(emeteorological data used in this study were provided bythe Korea Meteorological Administration Ground obser-vations were carried out by manual and automatic obser-vations for the automated synoptic observing system (etemperature humidity wind direction wind velocity airpressure precipitation sunshine solar radiation surfacetemperature grass temperature and ground temperaturewere automatically obtained by the use of synoptic weatherobservation equipment which report atmospheric condi-tions near the ground in real-time Snowfall clouds andother daily phenomena were observed manually every houror every three hours

(e air temperature which varied with the measuredheight was measured at a height of about 12 to 15m abovethe ground (e wind direction was represented by a vectorquantity with a direction and magnitude However since thehorizontal component was much larger than the verticalcomponent generally only the horizontal component wasobserved Air flow at a height of 10m from the ground wasalso observed Precipitation refers to rain snow and hailie liquid and solid precipitation In the case of solidprecipitation the depth of the precipitation was measuredSolar insolation was automatically observed by a pyran-ometer every hour Data on sunshine hours and sunshineduration were collected (ese data were then used tocompute the continued sunshine duration which is ameasure of the duration of continuous reflection of sunshineon the ground surface without blockage by clouds or fogClouds were manually observed in terms of their shapeheight and cover Other meteorological phenomena such asthe visibility ground surface minimum grass surface andground temperatures were observed (e solar insolationwas determined by the Sunrsquos altitude and azimuth withrespect to the season and time However the solar insolationreaching the Earthrsquos surface varied depending on the at-mospheric weather conditions

(e weather data for the prediction model were recordedin Seoul South Korea and the station specifications aregiven in Table 1 (e dataset collection period lasted for 4years (2014ndash2017) Data that had some elements missingwere excluded from the dataset (e dataset was divided intotraining and testing datasets For the training dataset dataranging from 2014 to 2016 were used For testing the 2017data were used (e total training and testing datasetsconsisted of 1084 and 357 days respectively (e variableswere selected based on the results of a previous study [21]which analyzed the correlation between solar insolation andweather data Temperature humidity precipitation pre-cipitation duration wind speed sunshine duration con-tinued sunshine duration and cloud cover were selected as

initial input variables that could affect the solar radiation asdepicted in Table 2 Visibility can especially be influenced byaerosols in the air According to Chung [22] there is a lowcorrelation between the ratio of the horizontal global ra-diation to the extraterrestrial radiation and particulatematter in Korea In this study the effects of wind directioncloud shapes heights of clouds visibility ground temper-atures and surface ground temperature were excluded

In the next step all the data were normalized to a scalebetween zero and one based on equation (1) normalizationof the input reduces estimation errors and makes learningfast and efficient [23]

yi xi minus MIN(x)

MAX(x) minus MIN(x) (1)

where xi is the observed data at time i yi is the normalizeddata at time i and MIN(x) and MAX(x) are the minimumand maximum values during the observation periodrespectively

3 Model Methods and Evaluation Indices

A forecast model based on the weather data is presented inthis section along with the model verification procedures(e solar insolation presented through the predictive modelis the value of the horizontal plane insolation therefore theinsolation on the inclined PV module is calculated (issolar insolation of the inclined plane will be used to calculatethe energy output of the PV system and compare it with theenergy output of the PV system beingmonitored Finally theerror verification method used in this paper is presented

31 Forecast Method (is study used a type of artificialneural network (ANN) architecture known as a multilayerfeed-forward neural network (MLF) for the modelling (emultilayer feed-forward neural network is also referred to asa multilayer perceptron (MLP) (is model is similar to thepersistence model in that the previous dayrsquos data are used asthe input variables (e persistence model assumes that theconditions are unchanged between the current time and thefuture time [24] However because the sunrsquos position andweather conditions change from day to day it cannot beassumed that data on weather conditions are the same asthose of the previous day In particular it is difficult to applya persistence model in the case of a 1-day forecast horizonFor ANN models the magnitudes of weights and biases arechanged in a time series which makes them more appro-priate [25] Diagne et al suggested an appropriate model by

Table 1 Station specifications

Item SpecificationLocation Seoul South KoreaLatitude 375714degNLongitude 1269658degEElevation 8567mClimate type Humid continentalObserved period 2014ndash2017

Advances in Civil Engineering 3

forecasting the horizon [26] (e persistence model is ap-propriate when the forecasting horizon is within an hourbut the ANNmodel is suitable when the forecasting horizonis longer than an hour Trained with a backpropagationlearning algorithm MLF is one of the most popular types ofANN architectures used to forecast solar insolation[15 27ndash30] (e MLF was implemented in MATLAB (eMLF consists of activation functions bias and neurons [31](e neurons were ordered into input and hidden and outputlayers as shown in Figure 1 (e number of hidden layers(NHLs) was set to be between 1 and 5(is was done becausethe forecast model was supposed to forecast the output ofnonlinear relationships between input data Moreover themodel was complicated (e range of the number of hiddenneurons was determined by the initial number of hiddenneurons which was calculated based on equation (2) byusing the number of input neurons [32] Each layer consistsof the same number of neurons

NHN 2NIN + 1 (2)

where NHN is the number of hidden neurons and NIN is thenumber of input neurons

(e LevenbergndashMarquardt method for training was usedin this study (e LevenbergndashMarquardt method is the mostrepresentative method for solving nonlinear least squaresproblems [33 34](e sliding-windowmethod that providesa higher accuracy was used for controlling the trainingdataset [32 35 36]

(e initial input variables were obtained by predicting thesolar radiation using the nine input variables presented in theprevious study and then refining the predicted values byadjusting the number of input variables (is prediction pre-vented a fitting problem by using normalized data and drop-out method (e training parameters are as shown in Table 3

32 Insolation on an Inclined Plane (e inclined insolationwas calculated by Lid and Jordanrsquos equation [37]

KT H

Ho

Ho 24π

middot Isc 1 + 0033 cos360n

3651113874 1113875

middot cosϕ cos δ sinωs +πωs

180sinϕ sin δ1113874 1113875

(3)

where Isc is the solar constant (1367Wm2) n is the daynumber of year ϕ is the latitude δ is the solar declination andωs is the sunset hour angle (e values of δ and ωs can beapproximately expressed by equations (4) and (5) respectively

δ 2345 sin360(n + 284)

3651113890 1113891 (4)

ωs arccos(minus tan δ tanϕ) (5)

(e daily solar insolation on an inclined plane Ht canbe expressed as

Ht R middot H (6)

where R is defined to be the ratio of the daily mean insolationon an inclined plane to the mean insolation in a horizontalplane

R 1 minusHd

H1113874 1113875Rb + Hd

1 + cos(s)

2H1113888 1113889 + ρ

1 minus cos(s)

d1113888 1113889

(7)

where Rb is the ratio of the average beam insolation on theinclined plane to that on a horizontal surface s is the tiltedangle and ρ is the ground reflectance Rb is a function of theatmospherersquos transmittance and is calculated by

Rb cos(ϕ minus s)cos(δ)sin ωsprime( 1113857 + ωsprime(π180)sin(ϕ minus s)sin(δ)

cos(ϕ)cos(δ)sin ωs( 1113857 + ωs(π180)sin(ϕ)sin(δ)

(8)

where ωsprime is the sunset hour angle for the inclined plane andis estimated by equation (9) Hd is the daily diffuse solarinsolation given by Page [38] as equation (10)

1

2

3

N

SI

Input layer One or more hidden layer Output layer

Figure 1 MLF architecture

Table 2 (e weather variables at initial time

Variables Min MaxLowest temperature (Tlow degC) minus 180 287Highest temperature (Thigh degC) minus 105 366Precipitation (PR mm) 0 1445Precipitation duration (PD hr) 0 24Minimum humidity (RH ) 7 94Daily wind speed (DWS ms) 09 64Sunshine duration (SD hr) 96 148Continued sunshine duration (CSD hr) 0 137Cloud cover (CC minus ) 0 10

Table 3 Training parameters

Parameters ValueMaximum number of epochs to train 1000Performance goal 001Minimum performance gradient 1e minus 7Initial mu 0001Maximum mu 1e+ 10Maximum validation failures 6Epochs between displays 50

4 Advances in Civil Engineering

ωsprime min ωs arccons[minus tan(ϕ minus s)tan(δ)]1113864 1113865 (9)

Hd H 100 minus 113KT( 1113857 (10)

33 Estimation Model and Monitoring the PhotovoltaicSystem Energy Production For the evaluation of the ap-plicability of the proposed solar radiation predictionmodel the PV production obtained by using the estimatedsolar insolation was compared to the actual energy pro-duction (e PV system was assumed to be of the grid-connected type for the distributed generation (e gen-erated energy was not stored in batteries Energy pro-duction by the photovoltaic system was obtained byapplying equations (11) and (12) [39ndash42]

EPV Aa middot Ht middot ηcon (11)

ηcon ηSTC 1 minus β Tc minus TSTC( 1113857( 1113857 middot ηinv (12)

Tc Ta +SI

SINOCTTNOCT minus TaNOCT( 1113857 (13)

where EPV is the energy delivered by photovoltaics (kWh)Aa is the area of the array (m2) Ht is the insolation on theplane for the photovoltaics array (kWhm2) ηcon representsthe conversion efficiency () ηSTC is themodule efficiency atSTC () β is the temperature coefficient at the maximalpower of the module (degC) Tc is the PV cell temperature(degC) TSTC is the standard test condition temperature (25degC)ηinv is the inverter efficiency () Ta is the ambient tem-perature (degC) SI is the incident solar irradiance on the PVplane PV (Wm2) SINOCT is the incident solar irradiance of800Wm2 TNOCT is the nominal operating cell temperature(degC) and TaNOCT is the ambient temperature for the nominaloperating cell temperature (20degC)

(e PV system was installed in Seoul South Korea (ePV system was connected to the electrical system of abuilding with a grid connected type inverter Values suchas the current voltage and produced power measured bythe inverter were sent to the monitoring system by thesensor box And the produced energy was monitored on apersonal computer (PC) as displayed in Figure 2 (ecapacity of the PV system was 1750W and the efficienciesof the modules and the inverter at standard test conditionswere 1534 and 96 respectively (e generated PVoutputs were monitored from August 2018 to July 2019(e actual generated PV system specifications are listed inTable 4

34 ErrorMetrics In this study the mean bias error (MBE)mean absolute error (MAE) root mean square error(RMSE) and NASH-Sutcliffe efficiency (NSE) wereemployed to evaluate the performance of the model (eMBE MAE RMSE and NSE were calculated using equa-tions (14)ndash(17) respectively (e verification values of eachMBE MAE and RMSE were close to zero which means thatthe observed values were similar to the predicted values (e

MBE was used to measure the typical average model de-viation (e MBE can provide useful information includingwhether the predictive model overestimated or under-estimated the real values However the MBE should beinterpreted carefully because positive and negative errorswill cancel out (erefore the MAE and MBE must beevaluated together Willmott and Matsuura [43] pointed outthat the MAE is a more natural and unambiguous measureof the average error magnitude (e RMSE is often used todetermine the success of a prediction model and it issuitable for determining model precision [44] If the per-formance of the prediction model is improved based on theRMSE when evaluating the accuracy of the predictionmodel where the RMSE is based on the standard deviationlearning can be used to reduce large errors (eMAE on thecontrary is sensitive to small errors Hence in this study theRMSE was used during the evaluation of the predictionmodel to reduce the maximum error of the predicted solarinsolation NSE on the contrary is a normalized measurethat compares the mean square error estimated by a par-ticular model simulation to the variance of the observedvalue during the period under investigation [45] (e rangeof NSE is between 1 and minus infin An NSE value of 1 represents acomplete match between the observations and the forecastswhile a smaller NSE value implies that there is less con-sistency between the measured value and the model valueAdditionally the MAE MBE and NSE were evaluatedtogether

Utility grid

Sensor box

Grid connected type inverter

PC monitoring

PV module

~Building

load

I VSolar insolation

Moduletemperature

Air temperature

~

Power

Figure 2 Schematic of the PV and monitoring systems

Table 4 PV system specifications

Parameters SpecificationSite location Seoul South KoreaSite longitude 37deg30prime128PrimeNSite latitude 126deg57prime253PrimeEType of installation Rooftop installation (elevated)Orientation and tilt South 35degModule type Multicrystalline siliconModule size 1640times 992mmNumber of modules 7Maximum power 250WType of PV system Grid connectedEfficiency of module at STC 1543Efficiency of inverter (EU) 96

Advances in Civil Engineering 5

MBE 1n

1113944

n

i1( 1113954H minus H) (14)

MAE 1n

1113944

n

i1| 1113954H minus H| (15)

RMSE

1n

1113944

n

i1( 1113954H minus H)

2

11139741113972

(16)

NSE 1 minusΣ(H minus 1113954H)2

1113936(H minus H)2 (17)

where 1113954H H and H are the predicted actual and averageactual solar insolation values respectively

(e error ranges of the daily prediction models pre-sented in the previous studies were RMSE 2304ndash3624 kWhm2day MBE 0120ndash2400 kWhm2day and MAE1488ndash2592 kWhm2day [12 46 47]

4 Results and Discussion

41 Prediction Performance of the Solar Insolation Model(e solar insolation on any day can be predicted by theweather data of the previous day (e prediction model usedin this research was an MLF (e initial number of hiddenneurons for the initial 9 inputs in the hidden layer wasdetermined to be 19 based on equation (2) In order toincrease the accuracy of the prediction model the number ofhidden neurons was extended from 10 to 20 with referenceto the initial number of neurons considering the reductionof inputs (e initial model was predicted using the fol-lowing initial input valuables highest and lowest temper-ature minimum humidity precipitation precipitationduration wind speed sunshine duration continued sun-shine duration and cloud cover In the second modelprecipitation and precipitation duration which were poorpredictors were removed (en the less correlated cloudcover was excluded from the input variables Cloud cover isthe weather factor that has the most significant influence onthe solar insolation in the present or near future however ithas a low effect on the next dayrsquos solar insolation

(e accuracy of the predicted model with various NHNand NHL is shown in Table 5 (e range of predicted resultsvaried according to the range of input variables A highernumber of input variables does not increase the accuracy ofpredictions In particular when the input variables werereduced from 8 to 7 the prediction accuracy decreasedHowever the prediction accuracy was at its highest when theinput variables were further reduced to six highly correlatedinput variables (is can be attributed to the correlationbetween the predicted value and the input value and therelationship between the input variables

(e optimal prediction model was that with the smallestRMSE among the 55 prediction result values with 6 inputvariables namely highest and lowest temperature mini-mum humidity wind speed sunshine duration and

continued sunshine duration (e calculated RMSE valuesranged from a minimum of 1421 kWhm2day to a maxi-mum of 1720 kWhm2day depending on the number ofhidden neurons and hidden layers (e optimal model fromthe RMSE consisted of 3 hidden layers and 11 hiddenneurons (e RMSE MBE and MAE of the optimal pre-diction model were 1421 kWhm2day minus 0227 kWhm2day and 1133 kWhm2day respectively For this model theaverage of the errors and the predicted values with largeerrors were smaller than those of the other models[11 20 46] (e RMSE limit presented in this model waslower than the RMSE mentioned in Section 34 which isbetter than the existing model According to the MBE thepredicted values tended to be underestimated In Table 6 theoptimal prediction model of 3 hidden layers and 11 hiddenneurons was compared to the regression model derived inthe previous study [21] Similar results were obtained fromthe RMSE MBE and MAE of the predicted values derivedby these two models however the NSE values showed betterpredictive models by the optimal MLF model (is meansthat the MLF with fewer input variables reflects the dailyfluctuation better than the regression model

Figure 3 presents the daily solar insolation over a yearwhich was predicted and observed by the meteorologicaladministration (e number of days when the predictedvalue was lesser than the observed value was 198 in total andthe number of days when the predicted value was higherthan the observed value was 159 in total Generally thepredicted value is lesser than the observed value in springwhen the solar insolation increases (is is because theweather data do not reflect the solar insolation increase dueto the movement of the Sun and the Earth (e sunshineduration was used to reflect the change in the orbits of theSun and the Earth (e average solar insolation changepattern was reflected According to Sun et al [48] a non-linear approach to a prediction model should be considereddue to the nonlinear variation in meteorological variablesHowever the daily fluctuation was not reflected fully be-cause a nonlinear approach was not utilized in this model

With regard to the monthly accuracy of the optimalprediction model (see Table 7) the error from April toSeptember was larger than that of the other months (esemonthsrsquo RMSE andMAE values were greater than the yearlyRMSE and MAE As shown in Table 7 the standard devi-ation of the measured solar insolation was greater than thatof the other months In particular from April to Septemberthe solar insolation was abundant but it varied greatly inresponse to sudden changes in the weather such as heavyrainfall Table 8 and Figure 4 show the range of measuredsolar insolation in each month (e difference in themaximum and minimum measured insolation for a monthwas at least 57 kWhm2day during the spring and summerseasons (ere were 29 days out of 357 days when thedifference between the predicted and measured values wasover 25 kWhm2day (ese days occurred between Marchand October but mostly between May and September As aresult of analyzing the changes in meteorological factors onthe day before and days with a large error the change incontinued sunshine duration and average cloud cover was

6 Advances in Civil Engineering

found to be largely as a result of rainfall humidity variationsand changes in suspended matter concentrations In 24 outof the 29 days the previous dayrsquos rain came to a halt or itrained on the estimation day

(e RMSE and MAE patterns exhibited similar ten-dencies to the patterns of the monthly solar insolationaccording to the Sunrsquos trajectory (e RMSE and MAEvalues were smallest in December during the winter solstice(e RMSE and MAE values then increased with the increasein solar radiation until June(e solar insolation RMSE andMAE values decreased after June (e predicted values forthe period between October and December where the MBEvalues showed positive values were overestimated On thecontrary the predicted values for January to March wereunderestimated compared to the measured values (epredicted values between October and December wereoverestimated because of the learning effect of the summerdata Conversely the predicted values between January andMarch did not reflect the increase in solar insolation becauseof the influence of the winter data

42 Application of the Optimal Prediction Model toPV Output Estimations In order to compare the PVproduction forecast the energy production of the 175 kWPV system was monitored for 364 days from August 2018 toJuly 2019 (e weather conditions during the monitoringperiod are listed in Table 9 Conditions were generally clearhowever there were some rainy days due to the effects oftyphoons(ere was a precipitation period of 97 days in totalduring the entire monitoring period During this period theaverage daily cloud cover fluctuated greatly As a result thevariation in solar insolation was larger than that for the otherperiods (e power generation range for the PV system was01ndash108 kWhday depending on the weather conditions

(e predicted solar insolation was estimated by using theoptimal solar insolation prediction model (e predictedsolar insolation was then used to calculate the PV

production by using equation (11) To check the validity ofthe approach the energy production was calculated from themeasured insolation and compared with the actual energyproduced by the PV system Table 10 presents the accuracyresults for the energy production estimations (e predictedpower generation calculated from the measured insolationwas similar to the actual power generation as shown inFigure 5 (ere was a difference between the power gen-eration calculated by the measured insolation and the actualproduction values Detailed meteorological observationscannot be performed at all PV installation sites As a result itis determined that an error occurred due to the positionaldifference It is also possible that a difference occurred due tothe limitation of the numerical calculations However theRMSE MAE and MBE of the energy generation calculatedfrom the measured insolation and the actual productionwere 085 kWhday 038 kWhday and 066 kWhday re-spectively indicating that the calculation procedure could beused for estimating the energy production of a PV system(e energy production was calculated using the estimatedsolar insolation using the proposed procedure (e powergeneration obtained by the predicted insolation fluctuatedless than the actual energy production Some errors were dueto the insufficient predictions of the daily weather conditionchanges Although the forecast model reflected the dailyvariation it did not predict the actual magnitude of thechange In the spring and summer observation there was awide variation in the day to day solar radiation (is wasbecause unlike previous studies in which the prediction wasby hours the forecast horizon was long and did not reflect allof the variability during that forecast periods (e predictionmodel proposed in this study predicts the next dayrsquos solarinsolation by using the weather conditions of the previousday However the weather conditions of the monitoringperiod changed extensively each day which made it difficultto predict the insolation (e energy production error wasespecially significant on days when the solar radiationsuddenly changed due to rain or snow In order to provide

Table 5 Accuracies of predicted value ranges according to the input variables NHN and NHL

Input variables Number of hidden layerslowast RMSE(kWhm2day)

MBE(kWhm2day)

MAE(kWhm2day) NSE

Thigh Tlow RH DWS PRPD SD CSD CC

1 1764ndash2000 minus 0891 to minus 0787 1368ndash1529 minus 0503 to minus 01692 1763ndash2023 minus 0811 to minus 0649 1355ndash1552 minus 0920 to minus 02103 1760ndash2015 minus 0840 to minus 0568 1373ndash1506 minus 1092 to minus 01644 1799ndash2015 minus 0903 to minus 0711 1382ndash1559 minus 0937 to minus 02165 1793ndash2102 minus 0853 to minus 0589 1366ndash1631 minus 1068 to minus 0207

Thigh Tlow RH DWSSD CSD CC

1 1975ndash2227 minus 1301 to minus 0969 1515ndash1692 minus 0292 to minus 00162 1975ndash2138 minus 1076 to minus 0714 1550ndash1635 minus 0162 to minus 00163 1792ndash2318 minus 1221 to minus 0567 1432ndash1773 minus 0391 to 01644 1889ndash2187 minus 1005 to minus 0547 1436ndash1632 minus 0245 to 00715 1807ndash2338 minus 1227 to minus 0419 1444ndash1773 minus 0423 to 0150

Thigh Tlow RH DWS SD CSD

1 1425ndash1506 minus 0272 to minus 0129 1157ndash1204 0411ndash04732 1423ndash1597 minus 0400 to minus 0090 1131ndash1297 0337ndash04743 1421ndash1660 minus 0376 to minus 0114 1131ndash1342 0284ndash04824 1444ndash1692 minus 0464 to minus 0121 1148ndash1372 0256ndash04585 1450ndash1720 minus 0291 to minus 0118 1153ndash1405 minus 0338 to 0454

lowast(e NHN for each layer was conducted by changing both to 10ndash20a

Advances in Civil Engineering 7

Table 6 Comparison of the regression and optimal models of MLF

Model RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day) NSERegression model 1428 minus 0074 1179 minus 0771Optimal model of MLF 1421 minus 0227 1133 0482

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

1-Fe

b

1-M

ar

1-Ap

r

1-Ju

n

1-D

ec

1-Ja

n

1-Au

g

1-Se

p

1-O

ct

1-Ju

l

1-N

ov

1-M

ay

Date

(a)

Observed valuePredicted value

Sola

r ins

olat

ion

(kW

hm

2 day

)

0123456789

8-M

ar

15-M

ar

22-M

ar

29-M

ar

5-Ap

r

12-A

pr

19-A

pr

26-A

pr

1-M

ar

10-M

ay

24-M

ay

31-M

ay

17-M

ay

3-M

ay

Date

(b)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

8-Ju

n

15-Ju

n

22-Ju

n

29-Ju

n

17-A

ug

10-A

ug

20-Ju

l

27-Ju

l

3-Au

g

24-A

ug

31-A

ug

6-Ju

l

13-Ju

l

1-Ju

n

Date

(c)

Sola

r ins

olat

ion

(kW

hm

2 day

)

0

1

2

3

4

5

6

7

Observed valuePredicted value

24-N

ov

20-O

ct

6-O

ct

8-Se

p

1-Se

p

3-N

ov

10-N

ov

29-S

ep

22-S

ep

13-O

ct

17-N

ov

15-S

ep

27-O

ct

Date

(d)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

545

435

325

215

105

7-Ja

n

24-F

eb

19-Ja

n

12-F

eb

1-D

ec

1-Ja

n

6-Fe

b

25-D

ec19

-Dec

7-D

ec

31-D

ec

31-Ja

n

13-Ja

n

25-Ja

n

18-F

eb

13-D

ec

Date

(e)

Figure 3 Comparison between the predicted and observed values of daily solar insolation (a) over one year (b) spring (c) summer (d) fall(e) winter

8 Advances in Civil Engineering

accurate forecasts of the energy production according toweather condition changes as basic information for energytrading it will be necessary to compensate for dramaticfluctuations in weather conditions (e error magnitude wassmaller in the fall and winter periods with less precipitationbut these seasons were predicted to be less than the actualenergy production In regions with distinct characteristics ofseasons it is necessary to present the solar insolation pre-diction model by season

P2P energy trading should also take into account theenergy price and the energy consumption of buildings

according to weather conditions and operating schedules Ingeneral the summer and winter energy consumption inbuildings is related to the external weather conditions Ondays where energy consumption is expected to be high inbuildings the energy produced by PV systems will beconsumed preferentially in buildings even if less or moreenergy is produced through PV systems On the contrary ifthe prosumer is planning to sell the produced energy to thegrid because the projected energy consumption is low in thebuilding the energy trade profits may be less than expected ifthe system actually produces less power than expected Inorder to propose the optimal operations for P2P energytrading it is necessary to predict the energy consumption ofthe building the price of energy and the amount of energy

Table 7 Accuracies of the optimal predicted values as compared to the measured values

Month Number of valid days RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day)January 31 0717 minus 0376 0580February 28 1133 minus 0246 1003March 31 1112 minus 0356 0917April 28 1742 minus 0595 1581May 31 1753 minus 0797 1536June 30 2034 minus 0901 1744July 31 1760 0029 1485August 31 1753 minus 0439 1491September 29 1650 minus 0432 1455October 30 0925 0559 0643November 26 0668 0609 0481December 31 0767 0521 0595

Table 8 Range of measured solar insolation (unit kWhm2day)

Month Maximum value Minimum value Mean value Difference between maximum and minimum values Standard deviationJanuary 334 054 237 280 070February 442 061 304 380 120March 505 135 407 370 097April 710 091 494 619 187May 770 155 577 615 165June 793 096 572 697 181July 629 056 342 573 176August 679 083 373 596 174September 600 001 395 600 172October 311 062 214 249 070November 231 034 159 196 060December 195 019 136 175 058

Average

Month

Sola

r ins

olat

ion

(kW

hm

2 day

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

9876543210

Figure 4 Range of monthly solar insolation bymeasured data fromthe meteorological administration

Table 9 Weather conditions during the monitoring period

Weather elements Value

Monitoring period 2 August 2018 to 31 July 2019 (364days)

(e dayrsquos highesttemperature minus 66ndash396degC

Minimum humidity 10ndash91Daily wind speed 08ndash38msNumber of rainy days 97 daysSunshine duration 96ndash148 hours

Advances in Civil Engineering 9

Table 10 Accuracies of the energy production estimations

RMSE (kWhday) MBE (kWhday) MAE (kWhday)Energy production by measured insolation 085 038 066Energy production by predicted insolationYear 270 minus 036 228Spring (Mar Apr and May) 325 005 260Summer (Jun Jul and Aug) 257 042 217Fall (Sep Oct and Nov) 243 minus 008 214Winter (Dec Jan and Feb) 245 minus 113 220

1-A

ug-1

8

1-Se

p-18

1-O

ct-1

8

1-N

ov-1

8

1-D

ec-1

8

1-Ja

n-19

1-Fe

b-19

1-M

ar-1

9

1-A

pr-1

9

1-M

ay-1

9

1-Ju

n-19

1-Ju

l-19

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(a)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-M

ar-1

9

11-M

ar-1

9

21-M

ar-1

9

31-M

ar-1

9

10-A

pr-1

9

20-A

pr-1

9

30-A

pr-1

9

10-M

ay-1

9

20-M

ay-1

9

30-M

ay-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(b)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-A

ug-1

8

11-A

ug-1

8

21-A

ug-1

8

31-A

ug-1

8

9-Ju

n-19

19-J

un-1

9

29-J

un-1

9

9-Ju

l-19

19-J

ul-1

9

29-J

ul-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(c)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-Se

p-18

11-S

ep-1

8

21-S

ep-1

8

1-O

ct-1

8

11-O

ct-1

8

21-O

ct-1

8

31-O

ct-1

8

10-N

ov-1

8

20-N

ov-1

8

30-N

ov-1

8

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(d)

Figure 5 Continued

10 Advances in Civil Engineering

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

prediction model are described Section 3 explains thepredictionmodel and the verificationmethod(emeasuredenergy production for a PV system located in South Koreawas compared to the energy production prediction obtainedthrough the solar insolation prediction model Section 4presents the results and Section 5 presents the conclusions

2 Meteorological Data

(emeteorological data used in this study were provided bythe Korea Meteorological Administration Ground obser-vations were carried out by manual and automatic obser-vations for the automated synoptic observing system (etemperature humidity wind direction wind velocity airpressure precipitation sunshine solar radiation surfacetemperature grass temperature and ground temperaturewere automatically obtained by the use of synoptic weatherobservation equipment which report atmospheric condi-tions near the ground in real-time Snowfall clouds andother daily phenomena were observed manually every houror every three hours

(e air temperature which varied with the measuredheight was measured at a height of about 12 to 15m abovethe ground (e wind direction was represented by a vectorquantity with a direction and magnitude However since thehorizontal component was much larger than the verticalcomponent generally only the horizontal component wasobserved Air flow at a height of 10m from the ground wasalso observed Precipitation refers to rain snow and hailie liquid and solid precipitation In the case of solidprecipitation the depth of the precipitation was measuredSolar insolation was automatically observed by a pyran-ometer every hour Data on sunshine hours and sunshineduration were collected (ese data were then used tocompute the continued sunshine duration which is ameasure of the duration of continuous reflection of sunshineon the ground surface without blockage by clouds or fogClouds were manually observed in terms of their shapeheight and cover Other meteorological phenomena such asthe visibility ground surface minimum grass surface andground temperatures were observed (e solar insolationwas determined by the Sunrsquos altitude and azimuth withrespect to the season and time However the solar insolationreaching the Earthrsquos surface varied depending on the at-mospheric weather conditions

(e weather data for the prediction model were recordedin Seoul South Korea and the station specifications aregiven in Table 1 (e dataset collection period lasted for 4years (2014ndash2017) Data that had some elements missingwere excluded from the dataset (e dataset was divided intotraining and testing datasets For the training dataset dataranging from 2014 to 2016 were used For testing the 2017data were used (e total training and testing datasetsconsisted of 1084 and 357 days respectively (e variableswere selected based on the results of a previous study [21]which analyzed the correlation between solar insolation andweather data Temperature humidity precipitation pre-cipitation duration wind speed sunshine duration con-tinued sunshine duration and cloud cover were selected as

initial input variables that could affect the solar radiation asdepicted in Table 2 Visibility can especially be influenced byaerosols in the air According to Chung [22] there is a lowcorrelation between the ratio of the horizontal global ra-diation to the extraterrestrial radiation and particulatematter in Korea In this study the effects of wind directioncloud shapes heights of clouds visibility ground temper-atures and surface ground temperature were excluded

In the next step all the data were normalized to a scalebetween zero and one based on equation (1) normalizationof the input reduces estimation errors and makes learningfast and efficient [23]

yi xi minus MIN(x)

MAX(x) minus MIN(x) (1)

where xi is the observed data at time i yi is the normalizeddata at time i and MIN(x) and MAX(x) are the minimumand maximum values during the observation periodrespectively

3 Model Methods and Evaluation Indices

A forecast model based on the weather data is presented inthis section along with the model verification procedures(e solar insolation presented through the predictive modelis the value of the horizontal plane insolation therefore theinsolation on the inclined PV module is calculated (issolar insolation of the inclined plane will be used to calculatethe energy output of the PV system and compare it with theenergy output of the PV system beingmonitored Finally theerror verification method used in this paper is presented

31 Forecast Method (is study used a type of artificialneural network (ANN) architecture known as a multilayerfeed-forward neural network (MLF) for the modelling (emultilayer feed-forward neural network is also referred to asa multilayer perceptron (MLP) (is model is similar to thepersistence model in that the previous dayrsquos data are used asthe input variables (e persistence model assumes that theconditions are unchanged between the current time and thefuture time [24] However because the sunrsquos position andweather conditions change from day to day it cannot beassumed that data on weather conditions are the same asthose of the previous day In particular it is difficult to applya persistence model in the case of a 1-day forecast horizonFor ANN models the magnitudes of weights and biases arechanged in a time series which makes them more appro-priate [25] Diagne et al suggested an appropriate model by

Table 1 Station specifications

Item SpecificationLocation Seoul South KoreaLatitude 375714degNLongitude 1269658degEElevation 8567mClimate type Humid continentalObserved period 2014ndash2017

Advances in Civil Engineering 3

forecasting the horizon [26] (e persistence model is ap-propriate when the forecasting horizon is within an hourbut the ANNmodel is suitable when the forecasting horizonis longer than an hour Trained with a backpropagationlearning algorithm MLF is one of the most popular types ofANN architectures used to forecast solar insolation[15 27ndash30] (e MLF was implemented in MATLAB (eMLF consists of activation functions bias and neurons [31](e neurons were ordered into input and hidden and outputlayers as shown in Figure 1 (e number of hidden layers(NHLs) was set to be between 1 and 5(is was done becausethe forecast model was supposed to forecast the output ofnonlinear relationships between input data Moreover themodel was complicated (e range of the number of hiddenneurons was determined by the initial number of hiddenneurons which was calculated based on equation (2) byusing the number of input neurons [32] Each layer consistsof the same number of neurons

NHN 2NIN + 1 (2)

where NHN is the number of hidden neurons and NIN is thenumber of input neurons

(e LevenbergndashMarquardt method for training was usedin this study (e LevenbergndashMarquardt method is the mostrepresentative method for solving nonlinear least squaresproblems [33 34](e sliding-windowmethod that providesa higher accuracy was used for controlling the trainingdataset [32 35 36]

(e initial input variables were obtained by predicting thesolar radiation using the nine input variables presented in theprevious study and then refining the predicted values byadjusting the number of input variables (is prediction pre-vented a fitting problem by using normalized data and drop-out method (e training parameters are as shown in Table 3

32 Insolation on an Inclined Plane (e inclined insolationwas calculated by Lid and Jordanrsquos equation [37]

KT H

Ho

Ho 24π

middot Isc 1 + 0033 cos360n

3651113874 1113875

middot cosϕ cos δ sinωs +πωs

180sinϕ sin δ1113874 1113875

(3)

where Isc is the solar constant (1367Wm2) n is the daynumber of year ϕ is the latitude δ is the solar declination andωs is the sunset hour angle (e values of δ and ωs can beapproximately expressed by equations (4) and (5) respectively

δ 2345 sin360(n + 284)

3651113890 1113891 (4)

ωs arccos(minus tan δ tanϕ) (5)

(e daily solar insolation on an inclined plane Ht canbe expressed as

Ht R middot H (6)

where R is defined to be the ratio of the daily mean insolationon an inclined plane to the mean insolation in a horizontalplane

R 1 minusHd

H1113874 1113875Rb + Hd

1 + cos(s)

2H1113888 1113889 + ρ

1 minus cos(s)

d1113888 1113889

(7)

where Rb is the ratio of the average beam insolation on theinclined plane to that on a horizontal surface s is the tiltedangle and ρ is the ground reflectance Rb is a function of theatmospherersquos transmittance and is calculated by

Rb cos(ϕ minus s)cos(δ)sin ωsprime( 1113857 + ωsprime(π180)sin(ϕ minus s)sin(δ)

cos(ϕ)cos(δ)sin ωs( 1113857 + ωs(π180)sin(ϕ)sin(δ)

(8)

where ωsprime is the sunset hour angle for the inclined plane andis estimated by equation (9) Hd is the daily diffuse solarinsolation given by Page [38] as equation (10)

1

2

3

N

SI

Input layer One or more hidden layer Output layer

Figure 1 MLF architecture

Table 2 (e weather variables at initial time

Variables Min MaxLowest temperature (Tlow degC) minus 180 287Highest temperature (Thigh degC) minus 105 366Precipitation (PR mm) 0 1445Precipitation duration (PD hr) 0 24Minimum humidity (RH ) 7 94Daily wind speed (DWS ms) 09 64Sunshine duration (SD hr) 96 148Continued sunshine duration (CSD hr) 0 137Cloud cover (CC minus ) 0 10

Table 3 Training parameters

Parameters ValueMaximum number of epochs to train 1000Performance goal 001Minimum performance gradient 1e minus 7Initial mu 0001Maximum mu 1e+ 10Maximum validation failures 6Epochs between displays 50

4 Advances in Civil Engineering

ωsprime min ωs arccons[minus tan(ϕ minus s)tan(δ)]1113864 1113865 (9)

Hd H 100 minus 113KT( 1113857 (10)

33 Estimation Model and Monitoring the PhotovoltaicSystem Energy Production For the evaluation of the ap-plicability of the proposed solar radiation predictionmodel the PV production obtained by using the estimatedsolar insolation was compared to the actual energy pro-duction (e PV system was assumed to be of the grid-connected type for the distributed generation (e gen-erated energy was not stored in batteries Energy pro-duction by the photovoltaic system was obtained byapplying equations (11) and (12) [39ndash42]

EPV Aa middot Ht middot ηcon (11)

ηcon ηSTC 1 minus β Tc minus TSTC( 1113857( 1113857 middot ηinv (12)

Tc Ta +SI

SINOCTTNOCT minus TaNOCT( 1113857 (13)

where EPV is the energy delivered by photovoltaics (kWh)Aa is the area of the array (m2) Ht is the insolation on theplane for the photovoltaics array (kWhm2) ηcon representsthe conversion efficiency () ηSTC is themodule efficiency atSTC () β is the temperature coefficient at the maximalpower of the module (degC) Tc is the PV cell temperature(degC) TSTC is the standard test condition temperature (25degC)ηinv is the inverter efficiency () Ta is the ambient tem-perature (degC) SI is the incident solar irradiance on the PVplane PV (Wm2) SINOCT is the incident solar irradiance of800Wm2 TNOCT is the nominal operating cell temperature(degC) and TaNOCT is the ambient temperature for the nominaloperating cell temperature (20degC)

(e PV system was installed in Seoul South Korea (ePV system was connected to the electrical system of abuilding with a grid connected type inverter Values suchas the current voltage and produced power measured bythe inverter were sent to the monitoring system by thesensor box And the produced energy was monitored on apersonal computer (PC) as displayed in Figure 2 (ecapacity of the PV system was 1750W and the efficienciesof the modules and the inverter at standard test conditionswere 1534 and 96 respectively (e generated PVoutputs were monitored from August 2018 to July 2019(e actual generated PV system specifications are listed inTable 4

34 ErrorMetrics In this study the mean bias error (MBE)mean absolute error (MAE) root mean square error(RMSE) and NASH-Sutcliffe efficiency (NSE) wereemployed to evaluate the performance of the model (eMBE MAE RMSE and NSE were calculated using equa-tions (14)ndash(17) respectively (e verification values of eachMBE MAE and RMSE were close to zero which means thatthe observed values were similar to the predicted values (e

MBE was used to measure the typical average model de-viation (e MBE can provide useful information includingwhether the predictive model overestimated or under-estimated the real values However the MBE should beinterpreted carefully because positive and negative errorswill cancel out (erefore the MAE and MBE must beevaluated together Willmott and Matsuura [43] pointed outthat the MAE is a more natural and unambiguous measureof the average error magnitude (e RMSE is often used todetermine the success of a prediction model and it issuitable for determining model precision [44] If the per-formance of the prediction model is improved based on theRMSE when evaluating the accuracy of the predictionmodel where the RMSE is based on the standard deviationlearning can be used to reduce large errors (eMAE on thecontrary is sensitive to small errors Hence in this study theRMSE was used during the evaluation of the predictionmodel to reduce the maximum error of the predicted solarinsolation NSE on the contrary is a normalized measurethat compares the mean square error estimated by a par-ticular model simulation to the variance of the observedvalue during the period under investigation [45] (e rangeof NSE is between 1 and minus infin An NSE value of 1 represents acomplete match between the observations and the forecastswhile a smaller NSE value implies that there is less con-sistency between the measured value and the model valueAdditionally the MAE MBE and NSE were evaluatedtogether

Utility grid

Sensor box

Grid connected type inverter

PC monitoring

PV module

~Building

load

I VSolar insolation

Moduletemperature

Air temperature

~

Power

Figure 2 Schematic of the PV and monitoring systems

Table 4 PV system specifications

Parameters SpecificationSite location Seoul South KoreaSite longitude 37deg30prime128PrimeNSite latitude 126deg57prime253PrimeEType of installation Rooftop installation (elevated)Orientation and tilt South 35degModule type Multicrystalline siliconModule size 1640times 992mmNumber of modules 7Maximum power 250WType of PV system Grid connectedEfficiency of module at STC 1543Efficiency of inverter (EU) 96

Advances in Civil Engineering 5

MBE 1n

1113944

n

i1( 1113954H minus H) (14)

MAE 1n

1113944

n

i1| 1113954H minus H| (15)

RMSE

1n

1113944

n

i1( 1113954H minus H)

2

11139741113972

(16)

NSE 1 minusΣ(H minus 1113954H)2

1113936(H minus H)2 (17)

where 1113954H H and H are the predicted actual and averageactual solar insolation values respectively

(e error ranges of the daily prediction models pre-sented in the previous studies were RMSE 2304ndash3624 kWhm2day MBE 0120ndash2400 kWhm2day and MAE1488ndash2592 kWhm2day [12 46 47]

4 Results and Discussion

41 Prediction Performance of the Solar Insolation Model(e solar insolation on any day can be predicted by theweather data of the previous day (e prediction model usedin this research was an MLF (e initial number of hiddenneurons for the initial 9 inputs in the hidden layer wasdetermined to be 19 based on equation (2) In order toincrease the accuracy of the prediction model the number ofhidden neurons was extended from 10 to 20 with referenceto the initial number of neurons considering the reductionof inputs (e initial model was predicted using the fol-lowing initial input valuables highest and lowest temper-ature minimum humidity precipitation precipitationduration wind speed sunshine duration continued sun-shine duration and cloud cover In the second modelprecipitation and precipitation duration which were poorpredictors were removed (en the less correlated cloudcover was excluded from the input variables Cloud cover isthe weather factor that has the most significant influence onthe solar insolation in the present or near future however ithas a low effect on the next dayrsquos solar insolation

(e accuracy of the predicted model with various NHNand NHL is shown in Table 5 (e range of predicted resultsvaried according to the range of input variables A highernumber of input variables does not increase the accuracy ofpredictions In particular when the input variables werereduced from 8 to 7 the prediction accuracy decreasedHowever the prediction accuracy was at its highest when theinput variables were further reduced to six highly correlatedinput variables (is can be attributed to the correlationbetween the predicted value and the input value and therelationship between the input variables

(e optimal prediction model was that with the smallestRMSE among the 55 prediction result values with 6 inputvariables namely highest and lowest temperature mini-mum humidity wind speed sunshine duration and

continued sunshine duration (e calculated RMSE valuesranged from a minimum of 1421 kWhm2day to a maxi-mum of 1720 kWhm2day depending on the number ofhidden neurons and hidden layers (e optimal model fromthe RMSE consisted of 3 hidden layers and 11 hiddenneurons (e RMSE MBE and MAE of the optimal pre-diction model were 1421 kWhm2day minus 0227 kWhm2day and 1133 kWhm2day respectively For this model theaverage of the errors and the predicted values with largeerrors were smaller than those of the other models[11 20 46] (e RMSE limit presented in this model waslower than the RMSE mentioned in Section 34 which isbetter than the existing model According to the MBE thepredicted values tended to be underestimated In Table 6 theoptimal prediction model of 3 hidden layers and 11 hiddenneurons was compared to the regression model derived inthe previous study [21] Similar results were obtained fromthe RMSE MBE and MAE of the predicted values derivedby these two models however the NSE values showed betterpredictive models by the optimal MLF model (is meansthat the MLF with fewer input variables reflects the dailyfluctuation better than the regression model

Figure 3 presents the daily solar insolation over a yearwhich was predicted and observed by the meteorologicaladministration (e number of days when the predictedvalue was lesser than the observed value was 198 in total andthe number of days when the predicted value was higherthan the observed value was 159 in total Generally thepredicted value is lesser than the observed value in springwhen the solar insolation increases (is is because theweather data do not reflect the solar insolation increase dueto the movement of the Sun and the Earth (e sunshineduration was used to reflect the change in the orbits of theSun and the Earth (e average solar insolation changepattern was reflected According to Sun et al [48] a non-linear approach to a prediction model should be considereddue to the nonlinear variation in meteorological variablesHowever the daily fluctuation was not reflected fully be-cause a nonlinear approach was not utilized in this model

With regard to the monthly accuracy of the optimalprediction model (see Table 7) the error from April toSeptember was larger than that of the other months (esemonthsrsquo RMSE andMAE values were greater than the yearlyRMSE and MAE As shown in Table 7 the standard devi-ation of the measured solar insolation was greater than thatof the other months In particular from April to Septemberthe solar insolation was abundant but it varied greatly inresponse to sudden changes in the weather such as heavyrainfall Table 8 and Figure 4 show the range of measuredsolar insolation in each month (e difference in themaximum and minimum measured insolation for a monthwas at least 57 kWhm2day during the spring and summerseasons (ere were 29 days out of 357 days when thedifference between the predicted and measured values wasover 25 kWhm2day (ese days occurred between Marchand October but mostly between May and September As aresult of analyzing the changes in meteorological factors onthe day before and days with a large error the change incontinued sunshine duration and average cloud cover was

6 Advances in Civil Engineering

found to be largely as a result of rainfall humidity variationsand changes in suspended matter concentrations In 24 outof the 29 days the previous dayrsquos rain came to a halt or itrained on the estimation day

(e RMSE and MAE patterns exhibited similar ten-dencies to the patterns of the monthly solar insolationaccording to the Sunrsquos trajectory (e RMSE and MAEvalues were smallest in December during the winter solstice(e RMSE and MAE values then increased with the increasein solar radiation until June(e solar insolation RMSE andMAE values decreased after June (e predicted values forthe period between October and December where the MBEvalues showed positive values were overestimated On thecontrary the predicted values for January to March wereunderestimated compared to the measured values (epredicted values between October and December wereoverestimated because of the learning effect of the summerdata Conversely the predicted values between January andMarch did not reflect the increase in solar insolation becauseof the influence of the winter data

42 Application of the Optimal Prediction Model toPV Output Estimations In order to compare the PVproduction forecast the energy production of the 175 kWPV system was monitored for 364 days from August 2018 toJuly 2019 (e weather conditions during the monitoringperiod are listed in Table 9 Conditions were generally clearhowever there were some rainy days due to the effects oftyphoons(ere was a precipitation period of 97 days in totalduring the entire monitoring period During this period theaverage daily cloud cover fluctuated greatly As a result thevariation in solar insolation was larger than that for the otherperiods (e power generation range for the PV system was01ndash108 kWhday depending on the weather conditions

(e predicted solar insolation was estimated by using theoptimal solar insolation prediction model (e predictedsolar insolation was then used to calculate the PV

production by using equation (11) To check the validity ofthe approach the energy production was calculated from themeasured insolation and compared with the actual energyproduced by the PV system Table 10 presents the accuracyresults for the energy production estimations (e predictedpower generation calculated from the measured insolationwas similar to the actual power generation as shown inFigure 5 (ere was a difference between the power gen-eration calculated by the measured insolation and the actualproduction values Detailed meteorological observationscannot be performed at all PV installation sites As a result itis determined that an error occurred due to the positionaldifference It is also possible that a difference occurred due tothe limitation of the numerical calculations However theRMSE MAE and MBE of the energy generation calculatedfrom the measured insolation and the actual productionwere 085 kWhday 038 kWhday and 066 kWhday re-spectively indicating that the calculation procedure could beused for estimating the energy production of a PV system(e energy production was calculated using the estimatedsolar insolation using the proposed procedure (e powergeneration obtained by the predicted insolation fluctuatedless than the actual energy production Some errors were dueto the insufficient predictions of the daily weather conditionchanges Although the forecast model reflected the dailyvariation it did not predict the actual magnitude of thechange In the spring and summer observation there was awide variation in the day to day solar radiation (is wasbecause unlike previous studies in which the prediction wasby hours the forecast horizon was long and did not reflect allof the variability during that forecast periods (e predictionmodel proposed in this study predicts the next dayrsquos solarinsolation by using the weather conditions of the previousday However the weather conditions of the monitoringperiod changed extensively each day which made it difficultto predict the insolation (e energy production error wasespecially significant on days when the solar radiationsuddenly changed due to rain or snow In order to provide

Table 5 Accuracies of predicted value ranges according to the input variables NHN and NHL

Input variables Number of hidden layerslowast RMSE(kWhm2day)

MBE(kWhm2day)

MAE(kWhm2day) NSE

Thigh Tlow RH DWS PRPD SD CSD CC

1 1764ndash2000 minus 0891 to minus 0787 1368ndash1529 minus 0503 to minus 01692 1763ndash2023 minus 0811 to minus 0649 1355ndash1552 minus 0920 to minus 02103 1760ndash2015 minus 0840 to minus 0568 1373ndash1506 minus 1092 to minus 01644 1799ndash2015 minus 0903 to minus 0711 1382ndash1559 minus 0937 to minus 02165 1793ndash2102 minus 0853 to minus 0589 1366ndash1631 minus 1068 to minus 0207

Thigh Tlow RH DWSSD CSD CC

1 1975ndash2227 minus 1301 to minus 0969 1515ndash1692 minus 0292 to minus 00162 1975ndash2138 minus 1076 to minus 0714 1550ndash1635 minus 0162 to minus 00163 1792ndash2318 minus 1221 to minus 0567 1432ndash1773 minus 0391 to 01644 1889ndash2187 minus 1005 to minus 0547 1436ndash1632 minus 0245 to 00715 1807ndash2338 minus 1227 to minus 0419 1444ndash1773 minus 0423 to 0150

Thigh Tlow RH DWS SD CSD

1 1425ndash1506 minus 0272 to minus 0129 1157ndash1204 0411ndash04732 1423ndash1597 minus 0400 to minus 0090 1131ndash1297 0337ndash04743 1421ndash1660 minus 0376 to minus 0114 1131ndash1342 0284ndash04824 1444ndash1692 minus 0464 to minus 0121 1148ndash1372 0256ndash04585 1450ndash1720 minus 0291 to minus 0118 1153ndash1405 minus 0338 to 0454

lowast(e NHN for each layer was conducted by changing both to 10ndash20a

Advances in Civil Engineering 7

Table 6 Comparison of the regression and optimal models of MLF

Model RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day) NSERegression model 1428 minus 0074 1179 minus 0771Optimal model of MLF 1421 minus 0227 1133 0482

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

1-Fe

b

1-M

ar

1-Ap

r

1-Ju

n

1-D

ec

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n

1-Au

g

1-Se

p

1-O

ct

1-Ju

l

1-N

ov

1-M

ay

Date

(a)

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Sola

r ins

olat

ion

(kW

hm

2 day

)

0123456789

8-M

ar

15-M

ar

22-M

ar

29-M

ar

5-Ap

r

12-A

pr

19-A

pr

26-A

pr

1-M

ar

10-M

ay

24-M

ay

31-M

ay

17-M

ay

3-M

ay

Date

(b)

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r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

8-Ju

n

15-Ju

n

22-Ju

n

29-Ju

n

17-A

ug

10-A

ug

20-Ju

l

27-Ju

l

3-Au

g

24-A

ug

31-A

ug

6-Ju

l

13-Ju

l

1-Ju

n

Date

(c)

Sola

r ins

olat

ion

(kW

hm

2 day

)

0

1

2

3

4

5

6

7

Observed valuePredicted value

24-N

ov

20-O

ct

6-O

ct

8-Se

p

1-Se

p

3-N

ov

10-N

ov

29-S

ep

22-S

ep

13-O

ct

17-N

ov

15-S

ep

27-O

ct

Date

(d)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

545

435

325

215

105

7-Ja

n

24-F

eb

19-Ja

n

12-F

eb

1-D

ec

1-Ja

n

6-Fe

b

25-D

ec19

-Dec

7-D

ec

31-D

ec

31-Ja

n

13-Ja

n

25-Ja

n

18-F

eb

13-D

ec

Date

(e)

Figure 3 Comparison between the predicted and observed values of daily solar insolation (a) over one year (b) spring (c) summer (d) fall(e) winter

8 Advances in Civil Engineering

accurate forecasts of the energy production according toweather condition changes as basic information for energytrading it will be necessary to compensate for dramaticfluctuations in weather conditions (e error magnitude wassmaller in the fall and winter periods with less precipitationbut these seasons were predicted to be less than the actualenergy production In regions with distinct characteristics ofseasons it is necessary to present the solar insolation pre-diction model by season

P2P energy trading should also take into account theenergy price and the energy consumption of buildings

according to weather conditions and operating schedules Ingeneral the summer and winter energy consumption inbuildings is related to the external weather conditions Ondays where energy consumption is expected to be high inbuildings the energy produced by PV systems will beconsumed preferentially in buildings even if less or moreenergy is produced through PV systems On the contrary ifthe prosumer is planning to sell the produced energy to thegrid because the projected energy consumption is low in thebuilding the energy trade profits may be less than expected ifthe system actually produces less power than expected Inorder to propose the optimal operations for P2P energytrading it is necessary to predict the energy consumption ofthe building the price of energy and the amount of energy

Table 7 Accuracies of the optimal predicted values as compared to the measured values

Month Number of valid days RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day)January 31 0717 minus 0376 0580February 28 1133 minus 0246 1003March 31 1112 minus 0356 0917April 28 1742 minus 0595 1581May 31 1753 minus 0797 1536June 30 2034 minus 0901 1744July 31 1760 0029 1485August 31 1753 minus 0439 1491September 29 1650 minus 0432 1455October 30 0925 0559 0643November 26 0668 0609 0481December 31 0767 0521 0595

Table 8 Range of measured solar insolation (unit kWhm2day)

Month Maximum value Minimum value Mean value Difference between maximum and minimum values Standard deviationJanuary 334 054 237 280 070February 442 061 304 380 120March 505 135 407 370 097April 710 091 494 619 187May 770 155 577 615 165June 793 096 572 697 181July 629 056 342 573 176August 679 083 373 596 174September 600 001 395 600 172October 311 062 214 249 070November 231 034 159 196 060December 195 019 136 175 058

Average

Month

Sola

r ins

olat

ion

(kW

hm

2 day

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

9876543210

Figure 4 Range of monthly solar insolation bymeasured data fromthe meteorological administration

Table 9 Weather conditions during the monitoring period

Weather elements Value

Monitoring period 2 August 2018 to 31 July 2019 (364days)

(e dayrsquos highesttemperature minus 66ndash396degC

Minimum humidity 10ndash91Daily wind speed 08ndash38msNumber of rainy days 97 daysSunshine duration 96ndash148 hours

Advances in Civil Engineering 9

Table 10 Accuracies of the energy production estimations

RMSE (kWhday) MBE (kWhday) MAE (kWhday)Energy production by measured insolation 085 038 066Energy production by predicted insolationYear 270 minus 036 228Spring (Mar Apr and May) 325 005 260Summer (Jun Jul and Aug) 257 042 217Fall (Sep Oct and Nov) 243 minus 008 214Winter (Dec Jan and Feb) 245 minus 113 220

1-A

ug-1

8

1-Se

p-18

1-O

ct-1

8

1-N

ov-1

8

1-D

ec-1

8

1-Ja

n-19

1-Fe

b-19

1-M

ar-1

9

1-A

pr-1

9

1-M

ay-1

9

1-Ju

n-19

1-Ju

l-19

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(a)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-M

ar-1

9

11-M

ar-1

9

21-M

ar-1

9

31-M

ar-1

9

10-A

pr-1

9

20-A

pr-1

9

30-A

pr-1

9

10-M

ay-1

9

20-M

ay-1

9

30-M

ay-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(b)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-A

ug-1

8

11-A

ug-1

8

21-A

ug-1

8

31-A

ug-1

8

9-Ju

n-19

19-J

un-1

9

29-J

un-1

9

9-Ju

l-19

19-J

ul-1

9

29-J

ul-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(c)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-Se

p-18

11-S

ep-1

8

21-S

ep-1

8

1-O

ct-1

8

11-O

ct-1

8

21-O

ct-1

8

31-O

ct-1

8

10-N

ov-1

8

20-N

ov-1

8

30-N

ov-1

8

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(d)

Figure 5 Continued

10 Advances in Civil Engineering

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

forecasting the horizon [26] (e persistence model is ap-propriate when the forecasting horizon is within an hourbut the ANNmodel is suitable when the forecasting horizonis longer than an hour Trained with a backpropagationlearning algorithm MLF is one of the most popular types ofANN architectures used to forecast solar insolation[15 27ndash30] (e MLF was implemented in MATLAB (eMLF consists of activation functions bias and neurons [31](e neurons were ordered into input and hidden and outputlayers as shown in Figure 1 (e number of hidden layers(NHLs) was set to be between 1 and 5(is was done becausethe forecast model was supposed to forecast the output ofnonlinear relationships between input data Moreover themodel was complicated (e range of the number of hiddenneurons was determined by the initial number of hiddenneurons which was calculated based on equation (2) byusing the number of input neurons [32] Each layer consistsof the same number of neurons

NHN 2NIN + 1 (2)

where NHN is the number of hidden neurons and NIN is thenumber of input neurons

(e LevenbergndashMarquardt method for training was usedin this study (e LevenbergndashMarquardt method is the mostrepresentative method for solving nonlinear least squaresproblems [33 34](e sliding-windowmethod that providesa higher accuracy was used for controlling the trainingdataset [32 35 36]

(e initial input variables were obtained by predicting thesolar radiation using the nine input variables presented in theprevious study and then refining the predicted values byadjusting the number of input variables (is prediction pre-vented a fitting problem by using normalized data and drop-out method (e training parameters are as shown in Table 3

32 Insolation on an Inclined Plane (e inclined insolationwas calculated by Lid and Jordanrsquos equation [37]

KT H

Ho

Ho 24π

middot Isc 1 + 0033 cos360n

3651113874 1113875

middot cosϕ cos δ sinωs +πωs

180sinϕ sin δ1113874 1113875

(3)

where Isc is the solar constant (1367Wm2) n is the daynumber of year ϕ is the latitude δ is the solar declination andωs is the sunset hour angle (e values of δ and ωs can beapproximately expressed by equations (4) and (5) respectively

δ 2345 sin360(n + 284)

3651113890 1113891 (4)

ωs arccos(minus tan δ tanϕ) (5)

(e daily solar insolation on an inclined plane Ht canbe expressed as

Ht R middot H (6)

where R is defined to be the ratio of the daily mean insolationon an inclined plane to the mean insolation in a horizontalplane

R 1 minusHd

H1113874 1113875Rb + Hd

1 + cos(s)

2H1113888 1113889 + ρ

1 minus cos(s)

d1113888 1113889

(7)

where Rb is the ratio of the average beam insolation on theinclined plane to that on a horizontal surface s is the tiltedangle and ρ is the ground reflectance Rb is a function of theatmospherersquos transmittance and is calculated by

Rb cos(ϕ minus s)cos(δ)sin ωsprime( 1113857 + ωsprime(π180)sin(ϕ minus s)sin(δ)

cos(ϕ)cos(δ)sin ωs( 1113857 + ωs(π180)sin(ϕ)sin(δ)

(8)

where ωsprime is the sunset hour angle for the inclined plane andis estimated by equation (9) Hd is the daily diffuse solarinsolation given by Page [38] as equation (10)

1

2

3

N

SI

Input layer One or more hidden layer Output layer

Figure 1 MLF architecture

Table 2 (e weather variables at initial time

Variables Min MaxLowest temperature (Tlow degC) minus 180 287Highest temperature (Thigh degC) minus 105 366Precipitation (PR mm) 0 1445Precipitation duration (PD hr) 0 24Minimum humidity (RH ) 7 94Daily wind speed (DWS ms) 09 64Sunshine duration (SD hr) 96 148Continued sunshine duration (CSD hr) 0 137Cloud cover (CC minus ) 0 10

Table 3 Training parameters

Parameters ValueMaximum number of epochs to train 1000Performance goal 001Minimum performance gradient 1e minus 7Initial mu 0001Maximum mu 1e+ 10Maximum validation failures 6Epochs between displays 50

4 Advances in Civil Engineering

ωsprime min ωs arccons[minus tan(ϕ minus s)tan(δ)]1113864 1113865 (9)

Hd H 100 minus 113KT( 1113857 (10)

33 Estimation Model and Monitoring the PhotovoltaicSystem Energy Production For the evaluation of the ap-plicability of the proposed solar radiation predictionmodel the PV production obtained by using the estimatedsolar insolation was compared to the actual energy pro-duction (e PV system was assumed to be of the grid-connected type for the distributed generation (e gen-erated energy was not stored in batteries Energy pro-duction by the photovoltaic system was obtained byapplying equations (11) and (12) [39ndash42]

EPV Aa middot Ht middot ηcon (11)

ηcon ηSTC 1 minus β Tc minus TSTC( 1113857( 1113857 middot ηinv (12)

Tc Ta +SI

SINOCTTNOCT minus TaNOCT( 1113857 (13)

where EPV is the energy delivered by photovoltaics (kWh)Aa is the area of the array (m2) Ht is the insolation on theplane for the photovoltaics array (kWhm2) ηcon representsthe conversion efficiency () ηSTC is themodule efficiency atSTC () β is the temperature coefficient at the maximalpower of the module (degC) Tc is the PV cell temperature(degC) TSTC is the standard test condition temperature (25degC)ηinv is the inverter efficiency () Ta is the ambient tem-perature (degC) SI is the incident solar irradiance on the PVplane PV (Wm2) SINOCT is the incident solar irradiance of800Wm2 TNOCT is the nominal operating cell temperature(degC) and TaNOCT is the ambient temperature for the nominaloperating cell temperature (20degC)

(e PV system was installed in Seoul South Korea (ePV system was connected to the electrical system of abuilding with a grid connected type inverter Values suchas the current voltage and produced power measured bythe inverter were sent to the monitoring system by thesensor box And the produced energy was monitored on apersonal computer (PC) as displayed in Figure 2 (ecapacity of the PV system was 1750W and the efficienciesof the modules and the inverter at standard test conditionswere 1534 and 96 respectively (e generated PVoutputs were monitored from August 2018 to July 2019(e actual generated PV system specifications are listed inTable 4

34 ErrorMetrics In this study the mean bias error (MBE)mean absolute error (MAE) root mean square error(RMSE) and NASH-Sutcliffe efficiency (NSE) wereemployed to evaluate the performance of the model (eMBE MAE RMSE and NSE were calculated using equa-tions (14)ndash(17) respectively (e verification values of eachMBE MAE and RMSE were close to zero which means thatthe observed values were similar to the predicted values (e

MBE was used to measure the typical average model de-viation (e MBE can provide useful information includingwhether the predictive model overestimated or under-estimated the real values However the MBE should beinterpreted carefully because positive and negative errorswill cancel out (erefore the MAE and MBE must beevaluated together Willmott and Matsuura [43] pointed outthat the MAE is a more natural and unambiguous measureof the average error magnitude (e RMSE is often used todetermine the success of a prediction model and it issuitable for determining model precision [44] If the per-formance of the prediction model is improved based on theRMSE when evaluating the accuracy of the predictionmodel where the RMSE is based on the standard deviationlearning can be used to reduce large errors (eMAE on thecontrary is sensitive to small errors Hence in this study theRMSE was used during the evaluation of the predictionmodel to reduce the maximum error of the predicted solarinsolation NSE on the contrary is a normalized measurethat compares the mean square error estimated by a par-ticular model simulation to the variance of the observedvalue during the period under investigation [45] (e rangeof NSE is between 1 and minus infin An NSE value of 1 represents acomplete match between the observations and the forecastswhile a smaller NSE value implies that there is less con-sistency between the measured value and the model valueAdditionally the MAE MBE and NSE were evaluatedtogether

Utility grid

Sensor box

Grid connected type inverter

PC monitoring

PV module

~Building

load

I VSolar insolation

Moduletemperature

Air temperature

~

Power

Figure 2 Schematic of the PV and monitoring systems

Table 4 PV system specifications

Parameters SpecificationSite location Seoul South KoreaSite longitude 37deg30prime128PrimeNSite latitude 126deg57prime253PrimeEType of installation Rooftop installation (elevated)Orientation and tilt South 35degModule type Multicrystalline siliconModule size 1640times 992mmNumber of modules 7Maximum power 250WType of PV system Grid connectedEfficiency of module at STC 1543Efficiency of inverter (EU) 96

Advances in Civil Engineering 5

MBE 1n

1113944

n

i1( 1113954H minus H) (14)

MAE 1n

1113944

n

i1| 1113954H minus H| (15)

RMSE

1n

1113944

n

i1( 1113954H minus H)

2

11139741113972

(16)

NSE 1 minusΣ(H minus 1113954H)2

1113936(H minus H)2 (17)

where 1113954H H and H are the predicted actual and averageactual solar insolation values respectively

(e error ranges of the daily prediction models pre-sented in the previous studies were RMSE 2304ndash3624 kWhm2day MBE 0120ndash2400 kWhm2day and MAE1488ndash2592 kWhm2day [12 46 47]

4 Results and Discussion

41 Prediction Performance of the Solar Insolation Model(e solar insolation on any day can be predicted by theweather data of the previous day (e prediction model usedin this research was an MLF (e initial number of hiddenneurons for the initial 9 inputs in the hidden layer wasdetermined to be 19 based on equation (2) In order toincrease the accuracy of the prediction model the number ofhidden neurons was extended from 10 to 20 with referenceto the initial number of neurons considering the reductionof inputs (e initial model was predicted using the fol-lowing initial input valuables highest and lowest temper-ature minimum humidity precipitation precipitationduration wind speed sunshine duration continued sun-shine duration and cloud cover In the second modelprecipitation and precipitation duration which were poorpredictors were removed (en the less correlated cloudcover was excluded from the input variables Cloud cover isthe weather factor that has the most significant influence onthe solar insolation in the present or near future however ithas a low effect on the next dayrsquos solar insolation

(e accuracy of the predicted model with various NHNand NHL is shown in Table 5 (e range of predicted resultsvaried according to the range of input variables A highernumber of input variables does not increase the accuracy ofpredictions In particular when the input variables werereduced from 8 to 7 the prediction accuracy decreasedHowever the prediction accuracy was at its highest when theinput variables were further reduced to six highly correlatedinput variables (is can be attributed to the correlationbetween the predicted value and the input value and therelationship between the input variables

(e optimal prediction model was that with the smallestRMSE among the 55 prediction result values with 6 inputvariables namely highest and lowest temperature mini-mum humidity wind speed sunshine duration and

continued sunshine duration (e calculated RMSE valuesranged from a minimum of 1421 kWhm2day to a maxi-mum of 1720 kWhm2day depending on the number ofhidden neurons and hidden layers (e optimal model fromthe RMSE consisted of 3 hidden layers and 11 hiddenneurons (e RMSE MBE and MAE of the optimal pre-diction model were 1421 kWhm2day minus 0227 kWhm2day and 1133 kWhm2day respectively For this model theaverage of the errors and the predicted values with largeerrors were smaller than those of the other models[11 20 46] (e RMSE limit presented in this model waslower than the RMSE mentioned in Section 34 which isbetter than the existing model According to the MBE thepredicted values tended to be underestimated In Table 6 theoptimal prediction model of 3 hidden layers and 11 hiddenneurons was compared to the regression model derived inthe previous study [21] Similar results were obtained fromthe RMSE MBE and MAE of the predicted values derivedby these two models however the NSE values showed betterpredictive models by the optimal MLF model (is meansthat the MLF with fewer input variables reflects the dailyfluctuation better than the regression model

Figure 3 presents the daily solar insolation over a yearwhich was predicted and observed by the meteorologicaladministration (e number of days when the predictedvalue was lesser than the observed value was 198 in total andthe number of days when the predicted value was higherthan the observed value was 159 in total Generally thepredicted value is lesser than the observed value in springwhen the solar insolation increases (is is because theweather data do not reflect the solar insolation increase dueto the movement of the Sun and the Earth (e sunshineduration was used to reflect the change in the orbits of theSun and the Earth (e average solar insolation changepattern was reflected According to Sun et al [48] a non-linear approach to a prediction model should be considereddue to the nonlinear variation in meteorological variablesHowever the daily fluctuation was not reflected fully be-cause a nonlinear approach was not utilized in this model

With regard to the monthly accuracy of the optimalprediction model (see Table 7) the error from April toSeptember was larger than that of the other months (esemonthsrsquo RMSE andMAE values were greater than the yearlyRMSE and MAE As shown in Table 7 the standard devi-ation of the measured solar insolation was greater than thatof the other months In particular from April to Septemberthe solar insolation was abundant but it varied greatly inresponse to sudden changes in the weather such as heavyrainfall Table 8 and Figure 4 show the range of measuredsolar insolation in each month (e difference in themaximum and minimum measured insolation for a monthwas at least 57 kWhm2day during the spring and summerseasons (ere were 29 days out of 357 days when thedifference between the predicted and measured values wasover 25 kWhm2day (ese days occurred between Marchand October but mostly between May and September As aresult of analyzing the changes in meteorological factors onthe day before and days with a large error the change incontinued sunshine duration and average cloud cover was

6 Advances in Civil Engineering

found to be largely as a result of rainfall humidity variationsand changes in suspended matter concentrations In 24 outof the 29 days the previous dayrsquos rain came to a halt or itrained on the estimation day

(e RMSE and MAE patterns exhibited similar ten-dencies to the patterns of the monthly solar insolationaccording to the Sunrsquos trajectory (e RMSE and MAEvalues were smallest in December during the winter solstice(e RMSE and MAE values then increased with the increasein solar radiation until June(e solar insolation RMSE andMAE values decreased after June (e predicted values forthe period between October and December where the MBEvalues showed positive values were overestimated On thecontrary the predicted values for January to March wereunderestimated compared to the measured values (epredicted values between October and December wereoverestimated because of the learning effect of the summerdata Conversely the predicted values between January andMarch did not reflect the increase in solar insolation becauseof the influence of the winter data

42 Application of the Optimal Prediction Model toPV Output Estimations In order to compare the PVproduction forecast the energy production of the 175 kWPV system was monitored for 364 days from August 2018 toJuly 2019 (e weather conditions during the monitoringperiod are listed in Table 9 Conditions were generally clearhowever there were some rainy days due to the effects oftyphoons(ere was a precipitation period of 97 days in totalduring the entire monitoring period During this period theaverage daily cloud cover fluctuated greatly As a result thevariation in solar insolation was larger than that for the otherperiods (e power generation range for the PV system was01ndash108 kWhday depending on the weather conditions

(e predicted solar insolation was estimated by using theoptimal solar insolation prediction model (e predictedsolar insolation was then used to calculate the PV

production by using equation (11) To check the validity ofthe approach the energy production was calculated from themeasured insolation and compared with the actual energyproduced by the PV system Table 10 presents the accuracyresults for the energy production estimations (e predictedpower generation calculated from the measured insolationwas similar to the actual power generation as shown inFigure 5 (ere was a difference between the power gen-eration calculated by the measured insolation and the actualproduction values Detailed meteorological observationscannot be performed at all PV installation sites As a result itis determined that an error occurred due to the positionaldifference It is also possible that a difference occurred due tothe limitation of the numerical calculations However theRMSE MAE and MBE of the energy generation calculatedfrom the measured insolation and the actual productionwere 085 kWhday 038 kWhday and 066 kWhday re-spectively indicating that the calculation procedure could beused for estimating the energy production of a PV system(e energy production was calculated using the estimatedsolar insolation using the proposed procedure (e powergeneration obtained by the predicted insolation fluctuatedless than the actual energy production Some errors were dueto the insufficient predictions of the daily weather conditionchanges Although the forecast model reflected the dailyvariation it did not predict the actual magnitude of thechange In the spring and summer observation there was awide variation in the day to day solar radiation (is wasbecause unlike previous studies in which the prediction wasby hours the forecast horizon was long and did not reflect allof the variability during that forecast periods (e predictionmodel proposed in this study predicts the next dayrsquos solarinsolation by using the weather conditions of the previousday However the weather conditions of the monitoringperiod changed extensively each day which made it difficultto predict the insolation (e energy production error wasespecially significant on days when the solar radiationsuddenly changed due to rain or snow In order to provide

Table 5 Accuracies of predicted value ranges according to the input variables NHN and NHL

Input variables Number of hidden layerslowast RMSE(kWhm2day)

MBE(kWhm2day)

MAE(kWhm2day) NSE

Thigh Tlow RH DWS PRPD SD CSD CC

1 1764ndash2000 minus 0891 to minus 0787 1368ndash1529 minus 0503 to minus 01692 1763ndash2023 minus 0811 to minus 0649 1355ndash1552 minus 0920 to minus 02103 1760ndash2015 minus 0840 to minus 0568 1373ndash1506 minus 1092 to minus 01644 1799ndash2015 minus 0903 to minus 0711 1382ndash1559 minus 0937 to minus 02165 1793ndash2102 minus 0853 to minus 0589 1366ndash1631 minus 1068 to minus 0207

Thigh Tlow RH DWSSD CSD CC

1 1975ndash2227 minus 1301 to minus 0969 1515ndash1692 minus 0292 to minus 00162 1975ndash2138 minus 1076 to minus 0714 1550ndash1635 minus 0162 to minus 00163 1792ndash2318 minus 1221 to minus 0567 1432ndash1773 minus 0391 to 01644 1889ndash2187 minus 1005 to minus 0547 1436ndash1632 minus 0245 to 00715 1807ndash2338 minus 1227 to minus 0419 1444ndash1773 minus 0423 to 0150

Thigh Tlow RH DWS SD CSD

1 1425ndash1506 minus 0272 to minus 0129 1157ndash1204 0411ndash04732 1423ndash1597 minus 0400 to minus 0090 1131ndash1297 0337ndash04743 1421ndash1660 minus 0376 to minus 0114 1131ndash1342 0284ndash04824 1444ndash1692 minus 0464 to minus 0121 1148ndash1372 0256ndash04585 1450ndash1720 minus 0291 to minus 0118 1153ndash1405 minus 0338 to 0454

lowast(e NHN for each layer was conducted by changing both to 10ndash20a

Advances in Civil Engineering 7

Table 6 Comparison of the regression and optimal models of MLF

Model RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day) NSERegression model 1428 minus 0074 1179 minus 0771Optimal model of MLF 1421 minus 0227 1133 0482

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

1-Fe

b

1-M

ar

1-Ap

r

1-Ju

n

1-D

ec

1-Ja

n

1-Au

g

1-Se

p

1-O

ct

1-Ju

l

1-N

ov

1-M

ay

Date

(a)

Observed valuePredicted value

Sola

r ins

olat

ion

(kW

hm

2 day

)

0123456789

8-M

ar

15-M

ar

22-M

ar

29-M

ar

5-Ap

r

12-A

pr

19-A

pr

26-A

pr

1-M

ar

10-M

ay

24-M

ay

31-M

ay

17-M

ay

3-M

ay

Date

(b)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

8-Ju

n

15-Ju

n

22-Ju

n

29-Ju

n

17-A

ug

10-A

ug

20-Ju

l

27-Ju

l

3-Au

g

24-A

ug

31-A

ug

6-Ju

l

13-Ju

l

1-Ju

n

Date

(c)

Sola

r ins

olat

ion

(kW

hm

2 day

)

0

1

2

3

4

5

6

7

Observed valuePredicted value

24-N

ov

20-O

ct

6-O

ct

8-Se

p

1-Se

p

3-N

ov

10-N

ov

29-S

ep

22-S

ep

13-O

ct

17-N

ov

15-S

ep

27-O

ct

Date

(d)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

545

435

325

215

105

7-Ja

n

24-F

eb

19-Ja

n

12-F

eb

1-D

ec

1-Ja

n

6-Fe

b

25-D

ec19

-Dec

7-D

ec

31-D

ec

31-Ja

n

13-Ja

n

25-Ja

n

18-F

eb

13-D

ec

Date

(e)

Figure 3 Comparison between the predicted and observed values of daily solar insolation (a) over one year (b) spring (c) summer (d) fall(e) winter

8 Advances in Civil Engineering

accurate forecasts of the energy production according toweather condition changes as basic information for energytrading it will be necessary to compensate for dramaticfluctuations in weather conditions (e error magnitude wassmaller in the fall and winter periods with less precipitationbut these seasons were predicted to be less than the actualenergy production In regions with distinct characteristics ofseasons it is necessary to present the solar insolation pre-diction model by season

P2P energy trading should also take into account theenergy price and the energy consumption of buildings

according to weather conditions and operating schedules Ingeneral the summer and winter energy consumption inbuildings is related to the external weather conditions Ondays where energy consumption is expected to be high inbuildings the energy produced by PV systems will beconsumed preferentially in buildings even if less or moreenergy is produced through PV systems On the contrary ifthe prosumer is planning to sell the produced energy to thegrid because the projected energy consumption is low in thebuilding the energy trade profits may be less than expected ifthe system actually produces less power than expected Inorder to propose the optimal operations for P2P energytrading it is necessary to predict the energy consumption ofthe building the price of energy and the amount of energy

Table 7 Accuracies of the optimal predicted values as compared to the measured values

Month Number of valid days RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day)January 31 0717 minus 0376 0580February 28 1133 minus 0246 1003March 31 1112 minus 0356 0917April 28 1742 minus 0595 1581May 31 1753 minus 0797 1536June 30 2034 minus 0901 1744July 31 1760 0029 1485August 31 1753 minus 0439 1491September 29 1650 minus 0432 1455October 30 0925 0559 0643November 26 0668 0609 0481December 31 0767 0521 0595

Table 8 Range of measured solar insolation (unit kWhm2day)

Month Maximum value Minimum value Mean value Difference between maximum and minimum values Standard deviationJanuary 334 054 237 280 070February 442 061 304 380 120March 505 135 407 370 097April 710 091 494 619 187May 770 155 577 615 165June 793 096 572 697 181July 629 056 342 573 176August 679 083 373 596 174September 600 001 395 600 172October 311 062 214 249 070November 231 034 159 196 060December 195 019 136 175 058

Average

Month

Sola

r ins

olat

ion

(kW

hm

2 day

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

9876543210

Figure 4 Range of monthly solar insolation bymeasured data fromthe meteorological administration

Table 9 Weather conditions during the monitoring period

Weather elements Value

Monitoring period 2 August 2018 to 31 July 2019 (364days)

(e dayrsquos highesttemperature minus 66ndash396degC

Minimum humidity 10ndash91Daily wind speed 08ndash38msNumber of rainy days 97 daysSunshine duration 96ndash148 hours

Advances in Civil Engineering 9

Table 10 Accuracies of the energy production estimations

RMSE (kWhday) MBE (kWhday) MAE (kWhday)Energy production by measured insolation 085 038 066Energy production by predicted insolationYear 270 minus 036 228Spring (Mar Apr and May) 325 005 260Summer (Jun Jul and Aug) 257 042 217Fall (Sep Oct and Nov) 243 minus 008 214Winter (Dec Jan and Feb) 245 minus 113 220

1-A

ug-1

8

1-Se

p-18

1-O

ct-1

8

1-N

ov-1

8

1-D

ec-1

8

1-Ja

n-19

1-Fe

b-19

1-M

ar-1

9

1-A

pr-1

9

1-M

ay-1

9

1-Ju

n-19

1-Ju

l-19

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(a)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-M

ar-1

9

11-M

ar-1

9

21-M

ar-1

9

31-M

ar-1

9

10-A

pr-1

9

20-A

pr-1

9

30-A

pr-1

9

10-M

ay-1

9

20-M

ay-1

9

30-M

ay-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(b)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-A

ug-1

8

11-A

ug-1

8

21-A

ug-1

8

31-A

ug-1

8

9-Ju

n-19

19-J

un-1

9

29-J

un-1

9

9-Ju

l-19

19-J

ul-1

9

29-J

ul-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(c)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-Se

p-18

11-S

ep-1

8

21-S

ep-1

8

1-O

ct-1

8

11-O

ct-1

8

21-O

ct-1

8

31-O

ct-1

8

10-N

ov-1

8

20-N

ov-1

8

30-N

ov-1

8

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(d)

Figure 5 Continued

10 Advances in Civil Engineering

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

ωsprime min ωs arccons[minus tan(ϕ minus s)tan(δ)]1113864 1113865 (9)

Hd H 100 minus 113KT( 1113857 (10)

33 Estimation Model and Monitoring the PhotovoltaicSystem Energy Production For the evaluation of the ap-plicability of the proposed solar radiation predictionmodel the PV production obtained by using the estimatedsolar insolation was compared to the actual energy pro-duction (e PV system was assumed to be of the grid-connected type for the distributed generation (e gen-erated energy was not stored in batteries Energy pro-duction by the photovoltaic system was obtained byapplying equations (11) and (12) [39ndash42]

EPV Aa middot Ht middot ηcon (11)

ηcon ηSTC 1 minus β Tc minus TSTC( 1113857( 1113857 middot ηinv (12)

Tc Ta +SI

SINOCTTNOCT minus TaNOCT( 1113857 (13)

where EPV is the energy delivered by photovoltaics (kWh)Aa is the area of the array (m2) Ht is the insolation on theplane for the photovoltaics array (kWhm2) ηcon representsthe conversion efficiency () ηSTC is themodule efficiency atSTC () β is the temperature coefficient at the maximalpower of the module (degC) Tc is the PV cell temperature(degC) TSTC is the standard test condition temperature (25degC)ηinv is the inverter efficiency () Ta is the ambient tem-perature (degC) SI is the incident solar irradiance on the PVplane PV (Wm2) SINOCT is the incident solar irradiance of800Wm2 TNOCT is the nominal operating cell temperature(degC) and TaNOCT is the ambient temperature for the nominaloperating cell temperature (20degC)

(e PV system was installed in Seoul South Korea (ePV system was connected to the electrical system of abuilding with a grid connected type inverter Values suchas the current voltage and produced power measured bythe inverter were sent to the monitoring system by thesensor box And the produced energy was monitored on apersonal computer (PC) as displayed in Figure 2 (ecapacity of the PV system was 1750W and the efficienciesof the modules and the inverter at standard test conditionswere 1534 and 96 respectively (e generated PVoutputs were monitored from August 2018 to July 2019(e actual generated PV system specifications are listed inTable 4

34 ErrorMetrics In this study the mean bias error (MBE)mean absolute error (MAE) root mean square error(RMSE) and NASH-Sutcliffe efficiency (NSE) wereemployed to evaluate the performance of the model (eMBE MAE RMSE and NSE were calculated using equa-tions (14)ndash(17) respectively (e verification values of eachMBE MAE and RMSE were close to zero which means thatthe observed values were similar to the predicted values (e

MBE was used to measure the typical average model de-viation (e MBE can provide useful information includingwhether the predictive model overestimated or under-estimated the real values However the MBE should beinterpreted carefully because positive and negative errorswill cancel out (erefore the MAE and MBE must beevaluated together Willmott and Matsuura [43] pointed outthat the MAE is a more natural and unambiguous measureof the average error magnitude (e RMSE is often used todetermine the success of a prediction model and it issuitable for determining model precision [44] If the per-formance of the prediction model is improved based on theRMSE when evaluating the accuracy of the predictionmodel where the RMSE is based on the standard deviationlearning can be used to reduce large errors (eMAE on thecontrary is sensitive to small errors Hence in this study theRMSE was used during the evaluation of the predictionmodel to reduce the maximum error of the predicted solarinsolation NSE on the contrary is a normalized measurethat compares the mean square error estimated by a par-ticular model simulation to the variance of the observedvalue during the period under investigation [45] (e rangeof NSE is between 1 and minus infin An NSE value of 1 represents acomplete match between the observations and the forecastswhile a smaller NSE value implies that there is less con-sistency between the measured value and the model valueAdditionally the MAE MBE and NSE were evaluatedtogether

Utility grid

Sensor box

Grid connected type inverter

PC monitoring

PV module

~Building

load

I VSolar insolation

Moduletemperature

Air temperature

~

Power

Figure 2 Schematic of the PV and monitoring systems

Table 4 PV system specifications

Parameters SpecificationSite location Seoul South KoreaSite longitude 37deg30prime128PrimeNSite latitude 126deg57prime253PrimeEType of installation Rooftop installation (elevated)Orientation and tilt South 35degModule type Multicrystalline siliconModule size 1640times 992mmNumber of modules 7Maximum power 250WType of PV system Grid connectedEfficiency of module at STC 1543Efficiency of inverter (EU) 96

Advances in Civil Engineering 5

MBE 1n

1113944

n

i1( 1113954H minus H) (14)

MAE 1n

1113944

n

i1| 1113954H minus H| (15)

RMSE

1n

1113944

n

i1( 1113954H minus H)

2

11139741113972

(16)

NSE 1 minusΣ(H minus 1113954H)2

1113936(H minus H)2 (17)

where 1113954H H and H are the predicted actual and averageactual solar insolation values respectively

(e error ranges of the daily prediction models pre-sented in the previous studies were RMSE 2304ndash3624 kWhm2day MBE 0120ndash2400 kWhm2day and MAE1488ndash2592 kWhm2day [12 46 47]

4 Results and Discussion

41 Prediction Performance of the Solar Insolation Model(e solar insolation on any day can be predicted by theweather data of the previous day (e prediction model usedin this research was an MLF (e initial number of hiddenneurons for the initial 9 inputs in the hidden layer wasdetermined to be 19 based on equation (2) In order toincrease the accuracy of the prediction model the number ofhidden neurons was extended from 10 to 20 with referenceto the initial number of neurons considering the reductionof inputs (e initial model was predicted using the fol-lowing initial input valuables highest and lowest temper-ature minimum humidity precipitation precipitationduration wind speed sunshine duration continued sun-shine duration and cloud cover In the second modelprecipitation and precipitation duration which were poorpredictors were removed (en the less correlated cloudcover was excluded from the input variables Cloud cover isthe weather factor that has the most significant influence onthe solar insolation in the present or near future however ithas a low effect on the next dayrsquos solar insolation

(e accuracy of the predicted model with various NHNand NHL is shown in Table 5 (e range of predicted resultsvaried according to the range of input variables A highernumber of input variables does not increase the accuracy ofpredictions In particular when the input variables werereduced from 8 to 7 the prediction accuracy decreasedHowever the prediction accuracy was at its highest when theinput variables were further reduced to six highly correlatedinput variables (is can be attributed to the correlationbetween the predicted value and the input value and therelationship between the input variables

(e optimal prediction model was that with the smallestRMSE among the 55 prediction result values with 6 inputvariables namely highest and lowest temperature mini-mum humidity wind speed sunshine duration and

continued sunshine duration (e calculated RMSE valuesranged from a minimum of 1421 kWhm2day to a maxi-mum of 1720 kWhm2day depending on the number ofhidden neurons and hidden layers (e optimal model fromthe RMSE consisted of 3 hidden layers and 11 hiddenneurons (e RMSE MBE and MAE of the optimal pre-diction model were 1421 kWhm2day minus 0227 kWhm2day and 1133 kWhm2day respectively For this model theaverage of the errors and the predicted values with largeerrors were smaller than those of the other models[11 20 46] (e RMSE limit presented in this model waslower than the RMSE mentioned in Section 34 which isbetter than the existing model According to the MBE thepredicted values tended to be underestimated In Table 6 theoptimal prediction model of 3 hidden layers and 11 hiddenneurons was compared to the regression model derived inthe previous study [21] Similar results were obtained fromthe RMSE MBE and MAE of the predicted values derivedby these two models however the NSE values showed betterpredictive models by the optimal MLF model (is meansthat the MLF with fewer input variables reflects the dailyfluctuation better than the regression model

Figure 3 presents the daily solar insolation over a yearwhich was predicted and observed by the meteorologicaladministration (e number of days when the predictedvalue was lesser than the observed value was 198 in total andthe number of days when the predicted value was higherthan the observed value was 159 in total Generally thepredicted value is lesser than the observed value in springwhen the solar insolation increases (is is because theweather data do not reflect the solar insolation increase dueto the movement of the Sun and the Earth (e sunshineduration was used to reflect the change in the orbits of theSun and the Earth (e average solar insolation changepattern was reflected According to Sun et al [48] a non-linear approach to a prediction model should be considereddue to the nonlinear variation in meteorological variablesHowever the daily fluctuation was not reflected fully be-cause a nonlinear approach was not utilized in this model

With regard to the monthly accuracy of the optimalprediction model (see Table 7) the error from April toSeptember was larger than that of the other months (esemonthsrsquo RMSE andMAE values were greater than the yearlyRMSE and MAE As shown in Table 7 the standard devi-ation of the measured solar insolation was greater than thatof the other months In particular from April to Septemberthe solar insolation was abundant but it varied greatly inresponse to sudden changes in the weather such as heavyrainfall Table 8 and Figure 4 show the range of measuredsolar insolation in each month (e difference in themaximum and minimum measured insolation for a monthwas at least 57 kWhm2day during the spring and summerseasons (ere were 29 days out of 357 days when thedifference between the predicted and measured values wasover 25 kWhm2day (ese days occurred between Marchand October but mostly between May and September As aresult of analyzing the changes in meteorological factors onthe day before and days with a large error the change incontinued sunshine duration and average cloud cover was

6 Advances in Civil Engineering

found to be largely as a result of rainfall humidity variationsand changes in suspended matter concentrations In 24 outof the 29 days the previous dayrsquos rain came to a halt or itrained on the estimation day

(e RMSE and MAE patterns exhibited similar ten-dencies to the patterns of the monthly solar insolationaccording to the Sunrsquos trajectory (e RMSE and MAEvalues were smallest in December during the winter solstice(e RMSE and MAE values then increased with the increasein solar radiation until June(e solar insolation RMSE andMAE values decreased after June (e predicted values forthe period between October and December where the MBEvalues showed positive values were overestimated On thecontrary the predicted values for January to March wereunderestimated compared to the measured values (epredicted values between October and December wereoverestimated because of the learning effect of the summerdata Conversely the predicted values between January andMarch did not reflect the increase in solar insolation becauseof the influence of the winter data

42 Application of the Optimal Prediction Model toPV Output Estimations In order to compare the PVproduction forecast the energy production of the 175 kWPV system was monitored for 364 days from August 2018 toJuly 2019 (e weather conditions during the monitoringperiod are listed in Table 9 Conditions were generally clearhowever there were some rainy days due to the effects oftyphoons(ere was a precipitation period of 97 days in totalduring the entire monitoring period During this period theaverage daily cloud cover fluctuated greatly As a result thevariation in solar insolation was larger than that for the otherperiods (e power generation range for the PV system was01ndash108 kWhday depending on the weather conditions

(e predicted solar insolation was estimated by using theoptimal solar insolation prediction model (e predictedsolar insolation was then used to calculate the PV

production by using equation (11) To check the validity ofthe approach the energy production was calculated from themeasured insolation and compared with the actual energyproduced by the PV system Table 10 presents the accuracyresults for the energy production estimations (e predictedpower generation calculated from the measured insolationwas similar to the actual power generation as shown inFigure 5 (ere was a difference between the power gen-eration calculated by the measured insolation and the actualproduction values Detailed meteorological observationscannot be performed at all PV installation sites As a result itis determined that an error occurred due to the positionaldifference It is also possible that a difference occurred due tothe limitation of the numerical calculations However theRMSE MAE and MBE of the energy generation calculatedfrom the measured insolation and the actual productionwere 085 kWhday 038 kWhday and 066 kWhday re-spectively indicating that the calculation procedure could beused for estimating the energy production of a PV system(e energy production was calculated using the estimatedsolar insolation using the proposed procedure (e powergeneration obtained by the predicted insolation fluctuatedless than the actual energy production Some errors were dueto the insufficient predictions of the daily weather conditionchanges Although the forecast model reflected the dailyvariation it did not predict the actual magnitude of thechange In the spring and summer observation there was awide variation in the day to day solar radiation (is wasbecause unlike previous studies in which the prediction wasby hours the forecast horizon was long and did not reflect allof the variability during that forecast periods (e predictionmodel proposed in this study predicts the next dayrsquos solarinsolation by using the weather conditions of the previousday However the weather conditions of the monitoringperiod changed extensively each day which made it difficultto predict the insolation (e energy production error wasespecially significant on days when the solar radiationsuddenly changed due to rain or snow In order to provide

Table 5 Accuracies of predicted value ranges according to the input variables NHN and NHL

Input variables Number of hidden layerslowast RMSE(kWhm2day)

MBE(kWhm2day)

MAE(kWhm2day) NSE

Thigh Tlow RH DWS PRPD SD CSD CC

1 1764ndash2000 minus 0891 to minus 0787 1368ndash1529 minus 0503 to minus 01692 1763ndash2023 minus 0811 to minus 0649 1355ndash1552 minus 0920 to minus 02103 1760ndash2015 minus 0840 to minus 0568 1373ndash1506 minus 1092 to minus 01644 1799ndash2015 minus 0903 to minus 0711 1382ndash1559 minus 0937 to minus 02165 1793ndash2102 minus 0853 to minus 0589 1366ndash1631 minus 1068 to minus 0207

Thigh Tlow RH DWSSD CSD CC

1 1975ndash2227 minus 1301 to minus 0969 1515ndash1692 minus 0292 to minus 00162 1975ndash2138 minus 1076 to minus 0714 1550ndash1635 minus 0162 to minus 00163 1792ndash2318 minus 1221 to minus 0567 1432ndash1773 minus 0391 to 01644 1889ndash2187 minus 1005 to minus 0547 1436ndash1632 minus 0245 to 00715 1807ndash2338 minus 1227 to minus 0419 1444ndash1773 minus 0423 to 0150

Thigh Tlow RH DWS SD CSD

1 1425ndash1506 minus 0272 to minus 0129 1157ndash1204 0411ndash04732 1423ndash1597 minus 0400 to minus 0090 1131ndash1297 0337ndash04743 1421ndash1660 minus 0376 to minus 0114 1131ndash1342 0284ndash04824 1444ndash1692 minus 0464 to minus 0121 1148ndash1372 0256ndash04585 1450ndash1720 minus 0291 to minus 0118 1153ndash1405 minus 0338 to 0454

lowast(e NHN for each layer was conducted by changing both to 10ndash20a

Advances in Civil Engineering 7

Table 6 Comparison of the regression and optimal models of MLF

Model RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day) NSERegression model 1428 minus 0074 1179 minus 0771Optimal model of MLF 1421 minus 0227 1133 0482

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

1-Fe

b

1-M

ar

1-Ap

r

1-Ju

n

1-D

ec

1-Ja

n

1-Au

g

1-Se

p

1-O

ct

1-Ju

l

1-N

ov

1-M

ay

Date

(a)

Observed valuePredicted value

Sola

r ins

olat

ion

(kW

hm

2 day

)

0123456789

8-M

ar

15-M

ar

22-M

ar

29-M

ar

5-Ap

r

12-A

pr

19-A

pr

26-A

pr

1-M

ar

10-M

ay

24-M

ay

31-M

ay

17-M

ay

3-M

ay

Date

(b)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

8-Ju

n

15-Ju

n

22-Ju

n

29-Ju

n

17-A

ug

10-A

ug

20-Ju

l

27-Ju

l

3-Au

g

24-A

ug

31-A

ug

6-Ju

l

13-Ju

l

1-Ju

n

Date

(c)

Sola

r ins

olat

ion

(kW

hm

2 day

)

0

1

2

3

4

5

6

7

Observed valuePredicted value

24-N

ov

20-O

ct

6-O

ct

8-Se

p

1-Se

p

3-N

ov

10-N

ov

29-S

ep

22-S

ep

13-O

ct

17-N

ov

15-S

ep

27-O

ct

Date

(d)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

545

435

325

215

105

7-Ja

n

24-F

eb

19-Ja

n

12-F

eb

1-D

ec

1-Ja

n

6-Fe

b

25-D

ec19

-Dec

7-D

ec

31-D

ec

31-Ja

n

13-Ja

n

25-Ja

n

18-F

eb

13-D

ec

Date

(e)

Figure 3 Comparison between the predicted and observed values of daily solar insolation (a) over one year (b) spring (c) summer (d) fall(e) winter

8 Advances in Civil Engineering

accurate forecasts of the energy production according toweather condition changes as basic information for energytrading it will be necessary to compensate for dramaticfluctuations in weather conditions (e error magnitude wassmaller in the fall and winter periods with less precipitationbut these seasons were predicted to be less than the actualenergy production In regions with distinct characteristics ofseasons it is necessary to present the solar insolation pre-diction model by season

P2P energy trading should also take into account theenergy price and the energy consumption of buildings

according to weather conditions and operating schedules Ingeneral the summer and winter energy consumption inbuildings is related to the external weather conditions Ondays where energy consumption is expected to be high inbuildings the energy produced by PV systems will beconsumed preferentially in buildings even if less or moreenergy is produced through PV systems On the contrary ifthe prosumer is planning to sell the produced energy to thegrid because the projected energy consumption is low in thebuilding the energy trade profits may be less than expected ifthe system actually produces less power than expected Inorder to propose the optimal operations for P2P energytrading it is necessary to predict the energy consumption ofthe building the price of energy and the amount of energy

Table 7 Accuracies of the optimal predicted values as compared to the measured values

Month Number of valid days RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day)January 31 0717 minus 0376 0580February 28 1133 minus 0246 1003March 31 1112 minus 0356 0917April 28 1742 minus 0595 1581May 31 1753 minus 0797 1536June 30 2034 minus 0901 1744July 31 1760 0029 1485August 31 1753 minus 0439 1491September 29 1650 minus 0432 1455October 30 0925 0559 0643November 26 0668 0609 0481December 31 0767 0521 0595

Table 8 Range of measured solar insolation (unit kWhm2day)

Month Maximum value Minimum value Mean value Difference between maximum and minimum values Standard deviationJanuary 334 054 237 280 070February 442 061 304 380 120March 505 135 407 370 097April 710 091 494 619 187May 770 155 577 615 165June 793 096 572 697 181July 629 056 342 573 176August 679 083 373 596 174September 600 001 395 600 172October 311 062 214 249 070November 231 034 159 196 060December 195 019 136 175 058

Average

Month

Sola

r ins

olat

ion

(kW

hm

2 day

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

9876543210

Figure 4 Range of monthly solar insolation bymeasured data fromthe meteorological administration

Table 9 Weather conditions during the monitoring period

Weather elements Value

Monitoring period 2 August 2018 to 31 July 2019 (364days)

(e dayrsquos highesttemperature minus 66ndash396degC

Minimum humidity 10ndash91Daily wind speed 08ndash38msNumber of rainy days 97 daysSunshine duration 96ndash148 hours

Advances in Civil Engineering 9

Table 10 Accuracies of the energy production estimations

RMSE (kWhday) MBE (kWhday) MAE (kWhday)Energy production by measured insolation 085 038 066Energy production by predicted insolationYear 270 minus 036 228Spring (Mar Apr and May) 325 005 260Summer (Jun Jul and Aug) 257 042 217Fall (Sep Oct and Nov) 243 minus 008 214Winter (Dec Jan and Feb) 245 minus 113 220

1-A

ug-1

8

1-Se

p-18

1-O

ct-1

8

1-N

ov-1

8

1-D

ec-1

8

1-Ja

n-19

1-Fe

b-19

1-M

ar-1

9

1-A

pr-1

9

1-M

ay-1

9

1-Ju

n-19

1-Ju

l-19

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(a)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-M

ar-1

9

11-M

ar-1

9

21-M

ar-1

9

31-M

ar-1

9

10-A

pr-1

9

20-A

pr-1

9

30-A

pr-1

9

10-M

ay-1

9

20-M

ay-1

9

30-M

ay-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(b)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-A

ug-1

8

11-A

ug-1

8

21-A

ug-1

8

31-A

ug-1

8

9-Ju

n-19

19-J

un-1

9

29-J

un-1

9

9-Ju

l-19

19-J

ul-1

9

29-J

ul-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(c)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-Se

p-18

11-S

ep-1

8

21-S

ep-1

8

1-O

ct-1

8

11-O

ct-1

8

21-O

ct-1

8

31-O

ct-1

8

10-N

ov-1

8

20-N

ov-1

8

30-N

ov-1

8

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(d)

Figure 5 Continued

10 Advances in Civil Engineering

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

MBE 1n

1113944

n

i1( 1113954H minus H) (14)

MAE 1n

1113944

n

i1| 1113954H minus H| (15)

RMSE

1n

1113944

n

i1( 1113954H minus H)

2

11139741113972

(16)

NSE 1 minusΣ(H minus 1113954H)2

1113936(H minus H)2 (17)

where 1113954H H and H are the predicted actual and averageactual solar insolation values respectively

(e error ranges of the daily prediction models pre-sented in the previous studies were RMSE 2304ndash3624 kWhm2day MBE 0120ndash2400 kWhm2day and MAE1488ndash2592 kWhm2day [12 46 47]

4 Results and Discussion

41 Prediction Performance of the Solar Insolation Model(e solar insolation on any day can be predicted by theweather data of the previous day (e prediction model usedin this research was an MLF (e initial number of hiddenneurons for the initial 9 inputs in the hidden layer wasdetermined to be 19 based on equation (2) In order toincrease the accuracy of the prediction model the number ofhidden neurons was extended from 10 to 20 with referenceto the initial number of neurons considering the reductionof inputs (e initial model was predicted using the fol-lowing initial input valuables highest and lowest temper-ature minimum humidity precipitation precipitationduration wind speed sunshine duration continued sun-shine duration and cloud cover In the second modelprecipitation and precipitation duration which were poorpredictors were removed (en the less correlated cloudcover was excluded from the input variables Cloud cover isthe weather factor that has the most significant influence onthe solar insolation in the present or near future however ithas a low effect on the next dayrsquos solar insolation

(e accuracy of the predicted model with various NHNand NHL is shown in Table 5 (e range of predicted resultsvaried according to the range of input variables A highernumber of input variables does not increase the accuracy ofpredictions In particular when the input variables werereduced from 8 to 7 the prediction accuracy decreasedHowever the prediction accuracy was at its highest when theinput variables were further reduced to six highly correlatedinput variables (is can be attributed to the correlationbetween the predicted value and the input value and therelationship between the input variables

(e optimal prediction model was that with the smallestRMSE among the 55 prediction result values with 6 inputvariables namely highest and lowest temperature mini-mum humidity wind speed sunshine duration and

continued sunshine duration (e calculated RMSE valuesranged from a minimum of 1421 kWhm2day to a maxi-mum of 1720 kWhm2day depending on the number ofhidden neurons and hidden layers (e optimal model fromthe RMSE consisted of 3 hidden layers and 11 hiddenneurons (e RMSE MBE and MAE of the optimal pre-diction model were 1421 kWhm2day minus 0227 kWhm2day and 1133 kWhm2day respectively For this model theaverage of the errors and the predicted values with largeerrors were smaller than those of the other models[11 20 46] (e RMSE limit presented in this model waslower than the RMSE mentioned in Section 34 which isbetter than the existing model According to the MBE thepredicted values tended to be underestimated In Table 6 theoptimal prediction model of 3 hidden layers and 11 hiddenneurons was compared to the regression model derived inthe previous study [21] Similar results were obtained fromthe RMSE MBE and MAE of the predicted values derivedby these two models however the NSE values showed betterpredictive models by the optimal MLF model (is meansthat the MLF with fewer input variables reflects the dailyfluctuation better than the regression model

Figure 3 presents the daily solar insolation over a yearwhich was predicted and observed by the meteorologicaladministration (e number of days when the predictedvalue was lesser than the observed value was 198 in total andthe number of days when the predicted value was higherthan the observed value was 159 in total Generally thepredicted value is lesser than the observed value in springwhen the solar insolation increases (is is because theweather data do not reflect the solar insolation increase dueto the movement of the Sun and the Earth (e sunshineduration was used to reflect the change in the orbits of theSun and the Earth (e average solar insolation changepattern was reflected According to Sun et al [48] a non-linear approach to a prediction model should be considereddue to the nonlinear variation in meteorological variablesHowever the daily fluctuation was not reflected fully be-cause a nonlinear approach was not utilized in this model

With regard to the monthly accuracy of the optimalprediction model (see Table 7) the error from April toSeptember was larger than that of the other months (esemonthsrsquo RMSE andMAE values were greater than the yearlyRMSE and MAE As shown in Table 7 the standard devi-ation of the measured solar insolation was greater than thatof the other months In particular from April to Septemberthe solar insolation was abundant but it varied greatly inresponse to sudden changes in the weather such as heavyrainfall Table 8 and Figure 4 show the range of measuredsolar insolation in each month (e difference in themaximum and minimum measured insolation for a monthwas at least 57 kWhm2day during the spring and summerseasons (ere were 29 days out of 357 days when thedifference between the predicted and measured values wasover 25 kWhm2day (ese days occurred between Marchand October but mostly between May and September As aresult of analyzing the changes in meteorological factors onthe day before and days with a large error the change incontinued sunshine duration and average cloud cover was

6 Advances in Civil Engineering

found to be largely as a result of rainfall humidity variationsand changes in suspended matter concentrations In 24 outof the 29 days the previous dayrsquos rain came to a halt or itrained on the estimation day

(e RMSE and MAE patterns exhibited similar ten-dencies to the patterns of the monthly solar insolationaccording to the Sunrsquos trajectory (e RMSE and MAEvalues were smallest in December during the winter solstice(e RMSE and MAE values then increased with the increasein solar radiation until June(e solar insolation RMSE andMAE values decreased after June (e predicted values forthe period between October and December where the MBEvalues showed positive values were overestimated On thecontrary the predicted values for January to March wereunderestimated compared to the measured values (epredicted values between October and December wereoverestimated because of the learning effect of the summerdata Conversely the predicted values between January andMarch did not reflect the increase in solar insolation becauseof the influence of the winter data

42 Application of the Optimal Prediction Model toPV Output Estimations In order to compare the PVproduction forecast the energy production of the 175 kWPV system was monitored for 364 days from August 2018 toJuly 2019 (e weather conditions during the monitoringperiod are listed in Table 9 Conditions were generally clearhowever there were some rainy days due to the effects oftyphoons(ere was a precipitation period of 97 days in totalduring the entire monitoring period During this period theaverage daily cloud cover fluctuated greatly As a result thevariation in solar insolation was larger than that for the otherperiods (e power generation range for the PV system was01ndash108 kWhday depending on the weather conditions

(e predicted solar insolation was estimated by using theoptimal solar insolation prediction model (e predictedsolar insolation was then used to calculate the PV

production by using equation (11) To check the validity ofthe approach the energy production was calculated from themeasured insolation and compared with the actual energyproduced by the PV system Table 10 presents the accuracyresults for the energy production estimations (e predictedpower generation calculated from the measured insolationwas similar to the actual power generation as shown inFigure 5 (ere was a difference between the power gen-eration calculated by the measured insolation and the actualproduction values Detailed meteorological observationscannot be performed at all PV installation sites As a result itis determined that an error occurred due to the positionaldifference It is also possible that a difference occurred due tothe limitation of the numerical calculations However theRMSE MAE and MBE of the energy generation calculatedfrom the measured insolation and the actual productionwere 085 kWhday 038 kWhday and 066 kWhday re-spectively indicating that the calculation procedure could beused for estimating the energy production of a PV system(e energy production was calculated using the estimatedsolar insolation using the proposed procedure (e powergeneration obtained by the predicted insolation fluctuatedless than the actual energy production Some errors were dueto the insufficient predictions of the daily weather conditionchanges Although the forecast model reflected the dailyvariation it did not predict the actual magnitude of thechange In the spring and summer observation there was awide variation in the day to day solar radiation (is wasbecause unlike previous studies in which the prediction wasby hours the forecast horizon was long and did not reflect allof the variability during that forecast periods (e predictionmodel proposed in this study predicts the next dayrsquos solarinsolation by using the weather conditions of the previousday However the weather conditions of the monitoringperiod changed extensively each day which made it difficultto predict the insolation (e energy production error wasespecially significant on days when the solar radiationsuddenly changed due to rain or snow In order to provide

Table 5 Accuracies of predicted value ranges according to the input variables NHN and NHL

Input variables Number of hidden layerslowast RMSE(kWhm2day)

MBE(kWhm2day)

MAE(kWhm2day) NSE

Thigh Tlow RH DWS PRPD SD CSD CC

1 1764ndash2000 minus 0891 to minus 0787 1368ndash1529 minus 0503 to minus 01692 1763ndash2023 minus 0811 to minus 0649 1355ndash1552 minus 0920 to minus 02103 1760ndash2015 minus 0840 to minus 0568 1373ndash1506 minus 1092 to minus 01644 1799ndash2015 minus 0903 to minus 0711 1382ndash1559 minus 0937 to minus 02165 1793ndash2102 minus 0853 to minus 0589 1366ndash1631 minus 1068 to minus 0207

Thigh Tlow RH DWSSD CSD CC

1 1975ndash2227 minus 1301 to minus 0969 1515ndash1692 minus 0292 to minus 00162 1975ndash2138 minus 1076 to minus 0714 1550ndash1635 minus 0162 to minus 00163 1792ndash2318 minus 1221 to minus 0567 1432ndash1773 minus 0391 to 01644 1889ndash2187 minus 1005 to minus 0547 1436ndash1632 minus 0245 to 00715 1807ndash2338 minus 1227 to minus 0419 1444ndash1773 minus 0423 to 0150

Thigh Tlow RH DWS SD CSD

1 1425ndash1506 minus 0272 to minus 0129 1157ndash1204 0411ndash04732 1423ndash1597 minus 0400 to minus 0090 1131ndash1297 0337ndash04743 1421ndash1660 minus 0376 to minus 0114 1131ndash1342 0284ndash04824 1444ndash1692 minus 0464 to minus 0121 1148ndash1372 0256ndash04585 1450ndash1720 minus 0291 to minus 0118 1153ndash1405 minus 0338 to 0454

lowast(e NHN for each layer was conducted by changing both to 10ndash20a

Advances in Civil Engineering 7

Table 6 Comparison of the regression and optimal models of MLF

Model RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day) NSERegression model 1428 minus 0074 1179 minus 0771Optimal model of MLF 1421 minus 0227 1133 0482

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

1-Fe

b

1-M

ar

1-Ap

r

1-Ju

n

1-D

ec

1-Ja

n

1-Au

g

1-Se

p

1-O

ct

1-Ju

l

1-N

ov

1-M

ay

Date

(a)

Observed valuePredicted value

Sola

r ins

olat

ion

(kW

hm

2 day

)

0123456789

8-M

ar

15-M

ar

22-M

ar

29-M

ar

5-Ap

r

12-A

pr

19-A

pr

26-A

pr

1-M

ar

10-M

ay

24-M

ay

31-M

ay

17-M

ay

3-M

ay

Date

(b)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

8-Ju

n

15-Ju

n

22-Ju

n

29-Ju

n

17-A

ug

10-A

ug

20-Ju

l

27-Ju

l

3-Au

g

24-A

ug

31-A

ug

6-Ju

l

13-Ju

l

1-Ju

n

Date

(c)

Sola

r ins

olat

ion

(kW

hm

2 day

)

0

1

2

3

4

5

6

7

Observed valuePredicted value

24-N

ov

20-O

ct

6-O

ct

8-Se

p

1-Se

p

3-N

ov

10-N

ov

29-S

ep

22-S

ep

13-O

ct

17-N

ov

15-S

ep

27-O

ct

Date

(d)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

545

435

325

215

105

7-Ja

n

24-F

eb

19-Ja

n

12-F

eb

1-D

ec

1-Ja

n

6-Fe

b

25-D

ec19

-Dec

7-D

ec

31-D

ec

31-Ja

n

13-Ja

n

25-Ja

n

18-F

eb

13-D

ec

Date

(e)

Figure 3 Comparison between the predicted and observed values of daily solar insolation (a) over one year (b) spring (c) summer (d) fall(e) winter

8 Advances in Civil Engineering

accurate forecasts of the energy production according toweather condition changes as basic information for energytrading it will be necessary to compensate for dramaticfluctuations in weather conditions (e error magnitude wassmaller in the fall and winter periods with less precipitationbut these seasons were predicted to be less than the actualenergy production In regions with distinct characteristics ofseasons it is necessary to present the solar insolation pre-diction model by season

P2P energy trading should also take into account theenergy price and the energy consumption of buildings

according to weather conditions and operating schedules Ingeneral the summer and winter energy consumption inbuildings is related to the external weather conditions Ondays where energy consumption is expected to be high inbuildings the energy produced by PV systems will beconsumed preferentially in buildings even if less or moreenergy is produced through PV systems On the contrary ifthe prosumer is planning to sell the produced energy to thegrid because the projected energy consumption is low in thebuilding the energy trade profits may be less than expected ifthe system actually produces less power than expected Inorder to propose the optimal operations for P2P energytrading it is necessary to predict the energy consumption ofthe building the price of energy and the amount of energy

Table 7 Accuracies of the optimal predicted values as compared to the measured values

Month Number of valid days RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day)January 31 0717 minus 0376 0580February 28 1133 minus 0246 1003March 31 1112 minus 0356 0917April 28 1742 minus 0595 1581May 31 1753 minus 0797 1536June 30 2034 minus 0901 1744July 31 1760 0029 1485August 31 1753 minus 0439 1491September 29 1650 minus 0432 1455October 30 0925 0559 0643November 26 0668 0609 0481December 31 0767 0521 0595

Table 8 Range of measured solar insolation (unit kWhm2day)

Month Maximum value Minimum value Mean value Difference between maximum and minimum values Standard deviationJanuary 334 054 237 280 070February 442 061 304 380 120March 505 135 407 370 097April 710 091 494 619 187May 770 155 577 615 165June 793 096 572 697 181July 629 056 342 573 176August 679 083 373 596 174September 600 001 395 600 172October 311 062 214 249 070November 231 034 159 196 060December 195 019 136 175 058

Average

Month

Sola

r ins

olat

ion

(kW

hm

2 day

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

9876543210

Figure 4 Range of monthly solar insolation bymeasured data fromthe meteorological administration

Table 9 Weather conditions during the monitoring period

Weather elements Value

Monitoring period 2 August 2018 to 31 July 2019 (364days)

(e dayrsquos highesttemperature minus 66ndash396degC

Minimum humidity 10ndash91Daily wind speed 08ndash38msNumber of rainy days 97 daysSunshine duration 96ndash148 hours

Advances in Civil Engineering 9

Table 10 Accuracies of the energy production estimations

RMSE (kWhday) MBE (kWhday) MAE (kWhday)Energy production by measured insolation 085 038 066Energy production by predicted insolationYear 270 minus 036 228Spring (Mar Apr and May) 325 005 260Summer (Jun Jul and Aug) 257 042 217Fall (Sep Oct and Nov) 243 minus 008 214Winter (Dec Jan and Feb) 245 minus 113 220

1-A

ug-1

8

1-Se

p-18

1-O

ct-1

8

1-N

ov-1

8

1-D

ec-1

8

1-Ja

n-19

1-Fe

b-19

1-M

ar-1

9

1-A

pr-1

9

1-M

ay-1

9

1-Ju

n-19

1-Ju

l-19

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(a)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-M

ar-1

9

11-M

ar-1

9

21-M

ar-1

9

31-M

ar-1

9

10-A

pr-1

9

20-A

pr-1

9

30-A

pr-1

9

10-M

ay-1

9

20-M

ay-1

9

30-M

ay-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(b)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-A

ug-1

8

11-A

ug-1

8

21-A

ug-1

8

31-A

ug-1

8

9-Ju

n-19

19-J

un-1

9

29-J

un-1

9

9-Ju

l-19

19-J

ul-1

9

29-J

ul-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(c)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-Se

p-18

11-S

ep-1

8

21-S

ep-1

8

1-O

ct-1

8

11-O

ct-1

8

21-O

ct-1

8

31-O

ct-1

8

10-N

ov-1

8

20-N

ov-1

8

30-N

ov-1

8

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(d)

Figure 5 Continued

10 Advances in Civil Engineering

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

found to be largely as a result of rainfall humidity variationsand changes in suspended matter concentrations In 24 outof the 29 days the previous dayrsquos rain came to a halt or itrained on the estimation day

(e RMSE and MAE patterns exhibited similar ten-dencies to the patterns of the monthly solar insolationaccording to the Sunrsquos trajectory (e RMSE and MAEvalues were smallest in December during the winter solstice(e RMSE and MAE values then increased with the increasein solar radiation until June(e solar insolation RMSE andMAE values decreased after June (e predicted values forthe period between October and December where the MBEvalues showed positive values were overestimated On thecontrary the predicted values for January to March wereunderestimated compared to the measured values (epredicted values between October and December wereoverestimated because of the learning effect of the summerdata Conversely the predicted values between January andMarch did not reflect the increase in solar insolation becauseof the influence of the winter data

42 Application of the Optimal Prediction Model toPV Output Estimations In order to compare the PVproduction forecast the energy production of the 175 kWPV system was monitored for 364 days from August 2018 toJuly 2019 (e weather conditions during the monitoringperiod are listed in Table 9 Conditions were generally clearhowever there were some rainy days due to the effects oftyphoons(ere was a precipitation period of 97 days in totalduring the entire monitoring period During this period theaverage daily cloud cover fluctuated greatly As a result thevariation in solar insolation was larger than that for the otherperiods (e power generation range for the PV system was01ndash108 kWhday depending on the weather conditions

(e predicted solar insolation was estimated by using theoptimal solar insolation prediction model (e predictedsolar insolation was then used to calculate the PV

production by using equation (11) To check the validity ofthe approach the energy production was calculated from themeasured insolation and compared with the actual energyproduced by the PV system Table 10 presents the accuracyresults for the energy production estimations (e predictedpower generation calculated from the measured insolationwas similar to the actual power generation as shown inFigure 5 (ere was a difference between the power gen-eration calculated by the measured insolation and the actualproduction values Detailed meteorological observationscannot be performed at all PV installation sites As a result itis determined that an error occurred due to the positionaldifference It is also possible that a difference occurred due tothe limitation of the numerical calculations However theRMSE MAE and MBE of the energy generation calculatedfrom the measured insolation and the actual productionwere 085 kWhday 038 kWhday and 066 kWhday re-spectively indicating that the calculation procedure could beused for estimating the energy production of a PV system(e energy production was calculated using the estimatedsolar insolation using the proposed procedure (e powergeneration obtained by the predicted insolation fluctuatedless than the actual energy production Some errors were dueto the insufficient predictions of the daily weather conditionchanges Although the forecast model reflected the dailyvariation it did not predict the actual magnitude of thechange In the spring and summer observation there was awide variation in the day to day solar radiation (is wasbecause unlike previous studies in which the prediction wasby hours the forecast horizon was long and did not reflect allof the variability during that forecast periods (e predictionmodel proposed in this study predicts the next dayrsquos solarinsolation by using the weather conditions of the previousday However the weather conditions of the monitoringperiod changed extensively each day which made it difficultto predict the insolation (e energy production error wasespecially significant on days when the solar radiationsuddenly changed due to rain or snow In order to provide

Table 5 Accuracies of predicted value ranges according to the input variables NHN and NHL

Input variables Number of hidden layerslowast RMSE(kWhm2day)

MBE(kWhm2day)

MAE(kWhm2day) NSE

Thigh Tlow RH DWS PRPD SD CSD CC

1 1764ndash2000 minus 0891 to minus 0787 1368ndash1529 minus 0503 to minus 01692 1763ndash2023 minus 0811 to minus 0649 1355ndash1552 minus 0920 to minus 02103 1760ndash2015 minus 0840 to minus 0568 1373ndash1506 minus 1092 to minus 01644 1799ndash2015 minus 0903 to minus 0711 1382ndash1559 minus 0937 to minus 02165 1793ndash2102 minus 0853 to minus 0589 1366ndash1631 minus 1068 to minus 0207

Thigh Tlow RH DWSSD CSD CC

1 1975ndash2227 minus 1301 to minus 0969 1515ndash1692 minus 0292 to minus 00162 1975ndash2138 minus 1076 to minus 0714 1550ndash1635 minus 0162 to minus 00163 1792ndash2318 minus 1221 to minus 0567 1432ndash1773 minus 0391 to 01644 1889ndash2187 minus 1005 to minus 0547 1436ndash1632 minus 0245 to 00715 1807ndash2338 minus 1227 to minus 0419 1444ndash1773 minus 0423 to 0150

Thigh Tlow RH DWS SD CSD

1 1425ndash1506 minus 0272 to minus 0129 1157ndash1204 0411ndash04732 1423ndash1597 minus 0400 to minus 0090 1131ndash1297 0337ndash04743 1421ndash1660 minus 0376 to minus 0114 1131ndash1342 0284ndash04824 1444ndash1692 minus 0464 to minus 0121 1148ndash1372 0256ndash04585 1450ndash1720 minus 0291 to minus 0118 1153ndash1405 minus 0338 to 0454

lowast(e NHN for each layer was conducted by changing both to 10ndash20a

Advances in Civil Engineering 7

Table 6 Comparison of the regression and optimal models of MLF

Model RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day) NSERegression model 1428 minus 0074 1179 minus 0771Optimal model of MLF 1421 minus 0227 1133 0482

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

1-Fe

b

1-M

ar

1-Ap

r

1-Ju

n

1-D

ec

1-Ja

n

1-Au

g

1-Se

p

1-O

ct

1-Ju

l

1-N

ov

1-M

ay

Date

(a)

Observed valuePredicted value

Sola

r ins

olat

ion

(kW

hm

2 day

)

0123456789

8-M

ar

15-M

ar

22-M

ar

29-M

ar

5-Ap

r

12-A

pr

19-A

pr

26-A

pr

1-M

ar

10-M

ay

24-M

ay

31-M

ay

17-M

ay

3-M

ay

Date

(b)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

8-Ju

n

15-Ju

n

22-Ju

n

29-Ju

n

17-A

ug

10-A

ug

20-Ju

l

27-Ju

l

3-Au

g

24-A

ug

31-A

ug

6-Ju

l

13-Ju

l

1-Ju

n

Date

(c)

Sola

r ins

olat

ion

(kW

hm

2 day

)

0

1

2

3

4

5

6

7

Observed valuePredicted value

24-N

ov

20-O

ct

6-O

ct

8-Se

p

1-Se

p

3-N

ov

10-N

ov

29-S

ep

22-S

ep

13-O

ct

17-N

ov

15-S

ep

27-O

ct

Date

(d)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

545

435

325

215

105

7-Ja

n

24-F

eb

19-Ja

n

12-F

eb

1-D

ec

1-Ja

n

6-Fe

b

25-D

ec19

-Dec

7-D

ec

31-D

ec

31-Ja

n

13-Ja

n

25-Ja

n

18-F

eb

13-D

ec

Date

(e)

Figure 3 Comparison between the predicted and observed values of daily solar insolation (a) over one year (b) spring (c) summer (d) fall(e) winter

8 Advances in Civil Engineering

accurate forecasts of the energy production according toweather condition changes as basic information for energytrading it will be necessary to compensate for dramaticfluctuations in weather conditions (e error magnitude wassmaller in the fall and winter periods with less precipitationbut these seasons were predicted to be less than the actualenergy production In regions with distinct characteristics ofseasons it is necessary to present the solar insolation pre-diction model by season

P2P energy trading should also take into account theenergy price and the energy consumption of buildings

according to weather conditions and operating schedules Ingeneral the summer and winter energy consumption inbuildings is related to the external weather conditions Ondays where energy consumption is expected to be high inbuildings the energy produced by PV systems will beconsumed preferentially in buildings even if less or moreenergy is produced through PV systems On the contrary ifthe prosumer is planning to sell the produced energy to thegrid because the projected energy consumption is low in thebuilding the energy trade profits may be less than expected ifthe system actually produces less power than expected Inorder to propose the optimal operations for P2P energytrading it is necessary to predict the energy consumption ofthe building the price of energy and the amount of energy

Table 7 Accuracies of the optimal predicted values as compared to the measured values

Month Number of valid days RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day)January 31 0717 minus 0376 0580February 28 1133 minus 0246 1003March 31 1112 minus 0356 0917April 28 1742 minus 0595 1581May 31 1753 minus 0797 1536June 30 2034 minus 0901 1744July 31 1760 0029 1485August 31 1753 minus 0439 1491September 29 1650 minus 0432 1455October 30 0925 0559 0643November 26 0668 0609 0481December 31 0767 0521 0595

Table 8 Range of measured solar insolation (unit kWhm2day)

Month Maximum value Minimum value Mean value Difference between maximum and minimum values Standard deviationJanuary 334 054 237 280 070February 442 061 304 380 120March 505 135 407 370 097April 710 091 494 619 187May 770 155 577 615 165June 793 096 572 697 181July 629 056 342 573 176August 679 083 373 596 174September 600 001 395 600 172October 311 062 214 249 070November 231 034 159 196 060December 195 019 136 175 058

Average

Month

Sola

r ins

olat

ion

(kW

hm

2 day

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

9876543210

Figure 4 Range of monthly solar insolation bymeasured data fromthe meteorological administration

Table 9 Weather conditions during the monitoring period

Weather elements Value

Monitoring period 2 August 2018 to 31 July 2019 (364days)

(e dayrsquos highesttemperature minus 66ndash396degC

Minimum humidity 10ndash91Daily wind speed 08ndash38msNumber of rainy days 97 daysSunshine duration 96ndash148 hours

Advances in Civil Engineering 9

Table 10 Accuracies of the energy production estimations

RMSE (kWhday) MBE (kWhday) MAE (kWhday)Energy production by measured insolation 085 038 066Energy production by predicted insolationYear 270 minus 036 228Spring (Mar Apr and May) 325 005 260Summer (Jun Jul and Aug) 257 042 217Fall (Sep Oct and Nov) 243 minus 008 214Winter (Dec Jan and Feb) 245 minus 113 220

1-A

ug-1

8

1-Se

p-18

1-O

ct-1

8

1-N

ov-1

8

1-D

ec-1

8

1-Ja

n-19

1-Fe

b-19

1-M

ar-1

9

1-A

pr-1

9

1-M

ay-1

9

1-Ju

n-19

1-Ju

l-19

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(a)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-M

ar-1

9

11-M

ar-1

9

21-M

ar-1

9

31-M

ar-1

9

10-A

pr-1

9

20-A

pr-1

9

30-A

pr-1

9

10-M

ay-1

9

20-M

ay-1

9

30-M

ay-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(b)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-A

ug-1

8

11-A

ug-1

8

21-A

ug-1

8

31-A

ug-1

8

9-Ju

n-19

19-J

un-1

9

29-J

un-1

9

9-Ju

l-19

19-J

ul-1

9

29-J

ul-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(c)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-Se

p-18

11-S

ep-1

8

21-S

ep-1

8

1-O

ct-1

8

11-O

ct-1

8

21-O

ct-1

8

31-O

ct-1

8

10-N

ov-1

8

20-N

ov-1

8

30-N

ov-1

8

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(d)

Figure 5 Continued

10 Advances in Civil Engineering

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

Table 6 Comparison of the regression and optimal models of MLF

Model RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day) NSERegression model 1428 minus 0074 1179 minus 0771Optimal model of MLF 1421 minus 0227 1133 0482

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

1-Fe

b

1-M

ar

1-Ap

r

1-Ju

n

1-D

ec

1-Ja

n

1-Au

g

1-Se

p

1-O

ct

1-Ju

l

1-N

ov

1-M

ay

Date

(a)

Observed valuePredicted value

Sola

r ins

olat

ion

(kW

hm

2 day

)

0123456789

8-M

ar

15-M

ar

22-M

ar

29-M

ar

5-Ap

r

12-A

pr

19-A

pr

26-A

pr

1-M

ar

10-M

ay

24-M

ay

31-M

ay

17-M

ay

3-M

ay

Date

(b)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

0123456789

8-Ju

n

15-Ju

n

22-Ju

n

29-Ju

n

17-A

ug

10-A

ug

20-Ju

l

27-Ju

l

3-Au

g

24-A

ug

31-A

ug

6-Ju

l

13-Ju

l

1-Ju

n

Date

(c)

Sola

r ins

olat

ion

(kW

hm

2 day

)

0

1

2

3

4

5

6

7

Observed valuePredicted value

24-N

ov

20-O

ct

6-O

ct

8-Se

p

1-Se

p

3-N

ov

10-N

ov

29-S

ep

22-S

ep

13-O

ct

17-N

ov

15-S

ep

27-O

ct

Date

(d)

Sola

r ins

olat

ion

(kW

hm

2 day

)

Observed valuePredicted value

545

435

325

215

105

7-Ja

n

24-F

eb

19-Ja

n

12-F

eb

1-D

ec

1-Ja

n

6-Fe

b

25-D

ec19

-Dec

7-D

ec

31-D

ec

31-Ja

n

13-Ja

n

25-Ja

n

18-F

eb

13-D

ec

Date

(e)

Figure 3 Comparison between the predicted and observed values of daily solar insolation (a) over one year (b) spring (c) summer (d) fall(e) winter

8 Advances in Civil Engineering

accurate forecasts of the energy production according toweather condition changes as basic information for energytrading it will be necessary to compensate for dramaticfluctuations in weather conditions (e error magnitude wassmaller in the fall and winter periods with less precipitationbut these seasons were predicted to be less than the actualenergy production In regions with distinct characteristics ofseasons it is necessary to present the solar insolation pre-diction model by season

P2P energy trading should also take into account theenergy price and the energy consumption of buildings

according to weather conditions and operating schedules Ingeneral the summer and winter energy consumption inbuildings is related to the external weather conditions Ondays where energy consumption is expected to be high inbuildings the energy produced by PV systems will beconsumed preferentially in buildings even if less or moreenergy is produced through PV systems On the contrary ifthe prosumer is planning to sell the produced energy to thegrid because the projected energy consumption is low in thebuilding the energy trade profits may be less than expected ifthe system actually produces less power than expected Inorder to propose the optimal operations for P2P energytrading it is necessary to predict the energy consumption ofthe building the price of energy and the amount of energy

Table 7 Accuracies of the optimal predicted values as compared to the measured values

Month Number of valid days RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day)January 31 0717 minus 0376 0580February 28 1133 minus 0246 1003March 31 1112 minus 0356 0917April 28 1742 minus 0595 1581May 31 1753 minus 0797 1536June 30 2034 minus 0901 1744July 31 1760 0029 1485August 31 1753 minus 0439 1491September 29 1650 minus 0432 1455October 30 0925 0559 0643November 26 0668 0609 0481December 31 0767 0521 0595

Table 8 Range of measured solar insolation (unit kWhm2day)

Month Maximum value Minimum value Mean value Difference between maximum and minimum values Standard deviationJanuary 334 054 237 280 070February 442 061 304 380 120March 505 135 407 370 097April 710 091 494 619 187May 770 155 577 615 165June 793 096 572 697 181July 629 056 342 573 176August 679 083 373 596 174September 600 001 395 600 172October 311 062 214 249 070November 231 034 159 196 060December 195 019 136 175 058

Average

Month

Sola

r ins

olat

ion

(kW

hm

2 day

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

9876543210

Figure 4 Range of monthly solar insolation bymeasured data fromthe meteorological administration

Table 9 Weather conditions during the monitoring period

Weather elements Value

Monitoring period 2 August 2018 to 31 July 2019 (364days)

(e dayrsquos highesttemperature minus 66ndash396degC

Minimum humidity 10ndash91Daily wind speed 08ndash38msNumber of rainy days 97 daysSunshine duration 96ndash148 hours

Advances in Civil Engineering 9

Table 10 Accuracies of the energy production estimations

RMSE (kWhday) MBE (kWhday) MAE (kWhday)Energy production by measured insolation 085 038 066Energy production by predicted insolationYear 270 minus 036 228Spring (Mar Apr and May) 325 005 260Summer (Jun Jul and Aug) 257 042 217Fall (Sep Oct and Nov) 243 minus 008 214Winter (Dec Jan and Feb) 245 minus 113 220

1-A

ug-1

8

1-Se

p-18

1-O

ct-1

8

1-N

ov-1

8

1-D

ec-1

8

1-Ja

n-19

1-Fe

b-19

1-M

ar-1

9

1-A

pr-1

9

1-M

ay-1

9

1-Ju

n-19

1-Ju

l-19

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(a)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-M

ar-1

9

11-M

ar-1

9

21-M

ar-1

9

31-M

ar-1

9

10-A

pr-1

9

20-A

pr-1

9

30-A

pr-1

9

10-M

ay-1

9

20-M

ay-1

9

30-M

ay-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(b)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-A

ug-1

8

11-A

ug-1

8

21-A

ug-1

8

31-A

ug-1

8

9-Ju

n-19

19-J

un-1

9

29-J

un-1

9

9-Ju

l-19

19-J

ul-1

9

29-J

ul-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(c)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-Se

p-18

11-S

ep-1

8

21-S

ep-1

8

1-O

ct-1

8

11-O

ct-1

8

21-O

ct-1

8

31-O

ct-1

8

10-N

ov-1

8

20-N

ov-1

8

30-N

ov-1

8

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(d)

Figure 5 Continued

10 Advances in Civil Engineering

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

accurate forecasts of the energy production according toweather condition changes as basic information for energytrading it will be necessary to compensate for dramaticfluctuations in weather conditions (e error magnitude wassmaller in the fall and winter periods with less precipitationbut these seasons were predicted to be less than the actualenergy production In regions with distinct characteristics ofseasons it is necessary to present the solar insolation pre-diction model by season

P2P energy trading should also take into account theenergy price and the energy consumption of buildings

according to weather conditions and operating schedules Ingeneral the summer and winter energy consumption inbuildings is related to the external weather conditions Ondays where energy consumption is expected to be high inbuildings the energy produced by PV systems will beconsumed preferentially in buildings even if less or moreenergy is produced through PV systems On the contrary ifthe prosumer is planning to sell the produced energy to thegrid because the projected energy consumption is low in thebuilding the energy trade profits may be less than expected ifthe system actually produces less power than expected Inorder to propose the optimal operations for P2P energytrading it is necessary to predict the energy consumption ofthe building the price of energy and the amount of energy

Table 7 Accuracies of the optimal predicted values as compared to the measured values

Month Number of valid days RMSE (kWhm2day) MBE (kWhm2day) MAE (kWhm2day)January 31 0717 minus 0376 0580February 28 1133 minus 0246 1003March 31 1112 minus 0356 0917April 28 1742 minus 0595 1581May 31 1753 minus 0797 1536June 30 2034 minus 0901 1744July 31 1760 0029 1485August 31 1753 minus 0439 1491September 29 1650 minus 0432 1455October 30 0925 0559 0643November 26 0668 0609 0481December 31 0767 0521 0595

Table 8 Range of measured solar insolation (unit kWhm2day)

Month Maximum value Minimum value Mean value Difference between maximum and minimum values Standard deviationJanuary 334 054 237 280 070February 442 061 304 380 120March 505 135 407 370 097April 710 091 494 619 187May 770 155 577 615 165June 793 096 572 697 181July 629 056 342 573 176August 679 083 373 596 174September 600 001 395 600 172October 311 062 214 249 070November 231 034 159 196 060December 195 019 136 175 058

Average

Month

Sola

r ins

olat

ion

(kW

hm

2 day

)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

9876543210

Figure 4 Range of monthly solar insolation bymeasured data fromthe meteorological administration

Table 9 Weather conditions during the monitoring period

Weather elements Value

Monitoring period 2 August 2018 to 31 July 2019 (364days)

(e dayrsquos highesttemperature minus 66ndash396degC

Minimum humidity 10ndash91Daily wind speed 08ndash38msNumber of rainy days 97 daysSunshine duration 96ndash148 hours

Advances in Civil Engineering 9

Table 10 Accuracies of the energy production estimations

RMSE (kWhday) MBE (kWhday) MAE (kWhday)Energy production by measured insolation 085 038 066Energy production by predicted insolationYear 270 minus 036 228Spring (Mar Apr and May) 325 005 260Summer (Jun Jul and Aug) 257 042 217Fall (Sep Oct and Nov) 243 minus 008 214Winter (Dec Jan and Feb) 245 minus 113 220

1-A

ug-1

8

1-Se

p-18

1-O

ct-1

8

1-N

ov-1

8

1-D

ec-1

8

1-Ja

n-19

1-Fe

b-19

1-M

ar-1

9

1-A

pr-1

9

1-M

ay-1

9

1-Ju

n-19

1-Ju

l-19

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(a)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-M

ar-1

9

11-M

ar-1

9

21-M

ar-1

9

31-M

ar-1

9

10-A

pr-1

9

20-A

pr-1

9

30-A

pr-1

9

10-M

ay-1

9

20-M

ay-1

9

30-M

ay-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(b)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-A

ug-1

8

11-A

ug-1

8

21-A

ug-1

8

31-A

ug-1

8

9-Ju

n-19

19-J

un-1

9

29-J

un-1

9

9-Ju

l-19

19-J

ul-1

9

29-J

ul-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(c)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-Se

p-18

11-S

ep-1

8

21-S

ep-1

8

1-O

ct-1

8

11-O

ct-1

8

21-O

ct-1

8

31-O

ct-1

8

10-N

ov-1

8

20-N

ov-1

8

30-N

ov-1

8

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(d)

Figure 5 Continued

10 Advances in Civil Engineering

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

Table 10 Accuracies of the energy production estimations

RMSE (kWhday) MBE (kWhday) MAE (kWhday)Energy production by measured insolation 085 038 066Energy production by predicted insolationYear 270 minus 036 228Spring (Mar Apr and May) 325 005 260Summer (Jun Jul and Aug) 257 042 217Fall (Sep Oct and Nov) 243 minus 008 214Winter (Dec Jan and Feb) 245 minus 113 220

1-A

ug-1

8

1-Se

p-18

1-O

ct-1

8

1-N

ov-1

8

1-D

ec-1

8

1-Ja

n-19

1-Fe

b-19

1-M

ar-1

9

1-A

pr-1

9

1-M

ay-1

9

1-Ju

n-19

1-Ju

l-19

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(a)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-M

ar-1

9

11-M

ar-1

9

21-M

ar-1

9

31-M

ar-1

9

10-A

pr-1

9

20-A

pr-1

9

30-A

pr-1

9

10-M

ay-1

9

20-M

ay-1

9

30-M

ay-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(b)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-A

ug-1

8

11-A

ug-1

8

21-A

ug-1

8

31-A

ug-1

8

9-Ju

n-19

19-J

un-1

9

29-J

un-1

9

9-Ju

l-19

19-J

ul-1

9

29-J

ul-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(c)

0

2

4

6

8

10

12

The p

rodu

ced

ener

gy (k

Wh

day)

1-Se

p-18

11-S

ep-1

8

21-S

ep-1

8

1-O

ct-1

8

11-O

ct-1

8

21-O

ct-1

8

31-O

ct-1

8

10-N

ov-1

8

20-N

ov-1

8

30-N

ov-1

8

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(d)

Figure 5 Continued

10 Advances in Civil Engineering

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

to be produced by PV systems together to suggest the op-timal use method

5 Conclusions

(e recent energy-saving building policies enacted in SouthKorea are expected to lead to the realization of distributedenergy generation in a smart grid P2P trading of the energyproduced in buildings will soon take place Predicting energyproduction is essential for P2P energy trading planning andthe energy produced through PV systems will be mainlytraded In this study the potential applicability of the energyproduction prediction of PV systems was investigated byusing the predicted solar insolation derived from a simplemodel to provide information to prosumers engaging insmall-scale electricity trading (e predictive model pro-posed by the existing researchers attempted to accuratelypredict the hourly or daily radiation by using a large amountof information However in this study the amount of solarradiation the next day was predicted by using a smallamount of weather information(e results are summarizedas follows

(1) (e prediction model for solar insolation was builtby using an MLF and the proposed model uses thedaily weather conditions (e predicted solar inso-lation was based on the estimated weather conditionson the day before the prediction To find the optimalarchitecture the number of input variables thenumber of hidden neurons and the number ofhidden layers were changed

(2) (e input variables of the optimal model includedthe highest and lowest temperature minimum hu-midity wind speed sunshine duration and con-tinued sunshine duration (e optimal modelconsisted of 3 hidden layers and 11 hidden neurons

(3) (e energy output of the PV system was calculatedfrom the solar insolation estimated by the optimalmodel (e calculated energy output was compared

to the actual PV systemrsquos output (e accuracy in-dexes for the PV systemrsquos energy output using theoptimal model which included the root meansquared error mean bias error and mean absoluteerror were 270 kWhm2day minus 036 kWhm2dayand 228 kWhm2day respectively

(e error of the predicted values for solar insolationvaried from season to season For instance in the summerwhen the difference between the maximum and minimuminsolation was large results did not fully reflect insolationchanges in response to weather changes (e predicted valuestended to represent the median value Although this providesstable values data were less predictable in the summer whenenergy production was high On the contrary in winter theaccuracy of the forecasted insolation was high for high solarinsolation days However the predictions were higher thanthe actual solar insolation for the low solar insolation days(e proposed model did not reflect sudden weather changeson any day because it used the daily weather conditions of theday before the forecast To further improve the predictionmodel it is necessary to execute the prediction model in themorning or on an hourly basis rather than the day before theforecast and to further optimize the prediction model inaccordance with the variations in seasonal characteristics

(e prediction of the PV system energy productionthrough solar insolation predictions showed a pattern similarto the solar insolation prediction results (e energy pro-duction estimation by the predicted insolation tended to yieldunderestimates compared to the real produced energy (emonitoring period was characterized by severe weatherfluctuations To accommodate such weather fluctuations inthe future it may be necessary to compensate for climatechange (e accuracy of the prediction model presented inthis study is much lower on sunny days or cloudy days withprecipitation(ere was a limit to predicting the exact amountof solar radiation including various weather variables in therelationship between the weather conditions of the previousday and the weather conditions of the next day (ere was nouncertainty about this change in weather In this research the

0

2

4

6

8

10

The p

rodu

ced

ener

gy (k

Wh

day)

1-D

ec-1

8

11-D

ec-1

8

21-D

ec-1

8

31-D

ec-1

8

10-J

an-1

9

20-J

an-1

9

30-J

an-1

9

9-Fe

b-19

19-F

eb-1

9

Month

Monitored power generation by the PV system

Estimated power generation by measured irradianceEstimated power generation by predicted irradiance

(e)

Figure 5 Comparison of the predicted and measured energy production insolations (a) over one year (b) spring (c) summer (d) fall (e)winter

Advances in Civil Engineering 11

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

solar insolation of the horizontal plane was predicted whilethat of the inclined insolation was calculated by the equationsand added to the solar power generation equation In thisprocess there was a difference between the actual value andthe predicted value obtained using the equation In the futureit may be necessary to distinguish the predictionmodel resultsaccording to weather conditions or to increase the accuracy byshortening the prediction horizon

If P2P energy trading becomes active in the future it willbe necessary to predict the energy production based on theweather conditions of the forecast day (erefore an ac-curate insolation prediction model will be needed to predictthe energy production of the PV systems involved in P2Penergy trading (e model described here represents a goodpotential model for such purposes and future optimizationwork will be forthcoming

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e author declares that there are no conflicts of interest

Acknowledgments

(is research was supported by the Basic Science ResearchProgram through the National Research Foundation ofKorea (NRF) funded by the Ministry of Science ICT ampFuture Planning (NRF-2017R1C1B20117911)

References

[1] Korea Energy Economic Institute Energy ConsumptionSurvey Ministry of Trade Industry and Energy Sejong CitySouth Korea 2015

[2] International Energy Agency Key World Energy StatisticsInternational Energy Agency Paris France 2017

[3] I S Bayram M Z Shakir M Abdallah and K Qaraqe ldquoAsurvey on energy trading in smart gridrdquo in Proceedings of the2014 IEEE Global Conference on Signal and InformationProcessing (GlobalSIP) pp 258ndash262 IEEE Atlanta GA USADecember 2014

[4] S-V Oprea A Bara A Uta A Pırjan and G CarutasuldquoAnalyses of distributed generation and storage effect on theelectricity consumption curve in the smart grid contextrdquoSustainability vol 10 no 7 p 2264 2018

[5] E Mengelkamp J Garttner K Rock S Kessler L Orsini andC Weinhardt ldquoDesigning microgrid energy marketsrdquo Ap-plied Energy vol 210 pp 870ndash880 2018

[6] C Park and T Yong ldquoComparative review and discussion onP2P electricity tradingrdquo Energy Procedia vol 128 no 3ndash92017

[7] C Zhang J Wu C Long and M Cheng ldquoReview of existingpeer-to-peer energy trading projectsrdquo Energy Procediavol 105 pp 2563ndash2568 2017

[8] J Jimeno J Anduaga J Oyarzabal and A G de MuroldquoArchitecture of a microgrid energy management systemrdquoEuropean Transactions on Electrical Power vol 21 no 2pp 1142ndash1158 2011

[9] K Alanne and A Saari ldquoDistributed energy generation andsustainable developmentrdquo Renewable and Sustainable EnergyReviews vol 10 no 6 pp 539ndash558 2006

[10] J (omsen N S Hussein C Senkpiel N Hartmann andT Schlegl ldquoAn optimized energy system planning and op-eration on distribution grid levelmdashthe decentralized marketagent as a novel approachrdquo Sustainable Energy Grids andNetworks vol 12 pp 40ndash56 2017

[11] J Soares A P Oliveira M Z Boznar P MlakarJ F Escobedo and A J Machado ldquoModeling hourly diffusesolar-radiation in the city of Satildeo Paulo using a neural-networktechniquerdquo Applied Energy vol 79 no 2 pp 201ndash214 2004

[12] P Mathiesen and J Kleissl ldquoEvaluation of numerical weatherprediction for intra-day solar forecasting in the continentalUnited Statesrdquo Solar Energy vol 85 no 5 pp 967ndash977 2011

[13] H Sun D Gui B Yan et al ldquoAssessing the potential ofrandom forest method for estimating solar radiation using airpollution indexrdquo Energy Conversion and Managementvol 119 pp 121ndash129 2016

[14] A Sharma and A Kakkar ldquoForecasting daily global solarirradiance generation using machine learningrdquo Renewableand Sustainable Energy Reviews vol 82 no 3 pp 2254ndash22692018

[15] F-V Gutierrez-Corea M-A Manso-Callejo M-P Moreno-Regidor and M-T Manrique-Sancho ldquoForecasting short-term solar irradiance based on artificial neural networks anddata from neighboring meteorological stationsrdquo Solar Energyvol 134 pp 119ndash131 2016

[16] J Huang and R J Davy ldquoPredicting intra-hour variability ofsolar irradiance using hourly local weather forecastsrdquo SolarEnergy vol 139 pp 633ndash639 2016

[17] M Vakili S R Sabbagh-Yazdi S Khosrojerdi and K KalhorldquoEvaluating the effect of particulate matter pollution on es-timation of daily global solar radiation using artificial neuralnetwork modeling based on meteorological datardquo Journal ofCleaner Production vol 141 pp 1275ndash1285 2017

[18] X Qing and Y Niu ldquoHourly day-ahead solar irradianceprediction using weather forecasts by LSTMrdquo Energy vol 148pp 461ndash468 2018

[19] B Amrouche and X Le Pivert ldquoArtificial neural networkbased daily local forecasting for global solar radiationrdquo Ap-plied Energy vol 130 pp 333ndash341 2014

[20] H Long Z Zhang and Y Su ldquoAnalysis of daily solar powerprediction with data-driven approachesrdquo Applied Energyvol 126 pp 29ndash37 2014

[21] M H Chung ldquoModelling of solar irradiance forecasting usinglocal meteorological datardquo KIEAE Journal vol 17 no 6pp 273ndash278 2017

[22] M H Chung ldquo(e correlation of solar radiation and at-mospheric elements including air pollutionrdquo KIEAE Journalvol 19 no 1 pp 69ndash74 2019

[23] J Sola and J Sevilla ldquoImportance of input data normalizationfor the application of neural networks to complex industrialproblemsrdquo IEEE Transactions on Nuclear Science vol 44no 3 pp 1464ndash1468 1997

[24] C F M Coimbra H T C Pedro and J Kleissl ldquoStochastic-learning methodsrdquo in Solar Energy Forecasting and ResourceAssessment pp 383ndash406 Academic Press Oxford UK 1stedition 2013

[25] E W Law A A Prasad M Kay and R A Taylor ldquoDirectnormal irradiance forecasting and its application to con-centrated solar thermal output forecastingmdasha reviewrdquo SolarEnergy vol 108 pp 287ndash307 2014

12 Advances in Civil Engineering

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13

[26] M Daigne M David P Lauret J Boland and N SchmutzldquoReview of solar irradiance forecasting methods and aproposition for small-scale insular gridsrdquo Renewable andSustainable Energy Reviews vol 27 pp 65ndash76 2013

[27] A Mellit and A M Pavan ldquoA 24-h forecast of solar irradianceusing artificial neural network application for performanceprediction of a grid-connected PV plant at Trieste Italyrdquo SolarEnergy vol 84 no 5 pp 807ndash821 2010

[28] P Lauret E Fock R N Randrianarivony and J-F Manicom-Ramsamy ldquoBayesian neural network approach to short timeload forecastingrdquo Energy Conversion and Managementvol 49 no 5 pp 1156ndash1166 2008

[29] R Marquez and C F M Coimbra ldquoForecasting of global anddirect solar irradiance using stochastic learning methodsground experiments and the NWS databaserdquo Solar Energyvol 85 no 5 pp 746ndash756 2011

[30] F S Tymvios C P Jacovides S C Michaelides andC Scouteli ldquoComparative study of Angstromrsquos and artificialneural networksrsquo methodologies in estimating global solarradiationrdquo Solar Energy vol 78 no 6 pp 752ndash762 2005

[31] S Haykin Neural NetworksmdashA Comprehensive FoundationPearson Prentice Hall New York USA 3rd edition 2008

[32] J Yang H Rivard and R Zmeureanu ldquoOn-line buildingenergy prediction using adaptive artificial neural networksrdquoEnergy and Buildings vol 37 no 12 pp 1250ndash1259 2005

[33] J-L Zhang ldquoOn the convergence properties of the Levenberg-Marquardt methodrdquo Optimization vol 52 no 6 pp 739ndash756 2003

[34] L S H Ngia and J Sjoberg ldquoEfficient training of neural netsfor nonlinear adaptive filtering using a recursive Levenberg-Marquardt algorithmrdquo IEEE Transactions on Signal Process-ing vol 48 no 7 pp 1915ndash1927 2000

[35] F M Dias A Antunes J Vieira and A M Mota ldquoOn-linetraining of neural networks a sliding window approach forthe levenberg-marquardt algorithmrdquo in Proceedings of theInternational Work-Conference on the Interplay betweenNatural and Artificial Computation pp 577ndash585 SpringerLas Palmas Spain June 2005

[36] J W Moon ldquoPerformance of ANN-based predictive andadaptive thermal-control methods for disturbances in andaround residential buildingsrdquo Building and Environmentvol 48 pp 15ndash26 2012

[37] B Liu and R Jordan ldquoDaily insolation on surfaces tiltedtowards equatorrdquoASHRAE Transactions vol 67 pp 526ndash5411962

[38] J K Page ldquo(e estimation of monthly mean values of dailytotal short wave radiation on vertical and inclined surfacefrom sunshine records for latitude 40degNndash40degSrdquo in Proceedingsof the UN Conference on New Sources of Energy vol 4pp 378ndash390 Rome Italy August 1961

[39] J V Paatero and P D Lund ldquoEffects of large-scale photo-voltaic power integration on electricity distribution net-worksrdquo Renewable Energy vol 32 no 2 pp 216ndash234 2007

[40] M E Ropp M Begovic and A Rohatgi ldquoDetermination ofthe curvature derating factor for the georgia tech aquaticcenter photovoltaic arrayrdquo in Proceedings of the ConferenceRecord of the Twenty-Sixth IEEE Photovoltaic SpecialistsConference pp 1297ndash1300 Anaheim CA USA September1997

[41] O Ayvazogluyuksel and U B Filik ldquoEstimation methods ofglobal solar radiation cell temperature and solar powerforecasting A review and case study in Eskisehirrdquo Renewableand Sustainable Energy Reviews vol 91 pp 639ndash653 2018

[42] W Omran Performance Analysis of Grid-Connected Photo-voltaic System PhD dissertation Department of Electricaland Computer Engineering University of Waterloo OntarioCanada 2010

[43] C J Willmott and K Matsuura ldquoAdvantages of the meanabsolute error (MAE) over the root mean square error(RMSE) in assessing average model performancerdquo ClimateResearch vol 30 no 1 pp 79ndash82 2009

[44] T Chai and R R Draxler ldquoRoot mean square error (RMSE) ormean absolute error (MAE)mdasharguments against avoidingRMSE in the literaturerdquo Geoscientific Model Developmentvol 7 no 3 pp 1247ndash1250 2014

[45] J E Nash and J V Sutcliffe ldquoRiver flow forecasting throughconceptual models part I - A discussion of principlesrdquo Journalof Hydrology vol 10 no 3 pp 282ndash290 1970

[46] Y Chu H T C Pedro M Li and C F M Coimbra ldquoReal-time forecasting of solar irradiance ramps with smart imageprocessingrdquo Solar Energy vol 114 pp 91ndash104 2015

[47] C Cornaro M Pierro and F Bucci ldquoMaster optimizationprocess based on neural networks ensemble for 24-h solarirradiance forecastrdquo Solar Energy vol 111 pp 297ndash312 2015

[48] H Sun N Zhao X Zeng and D Yan ldquoStudy of solar ra-diation prediction and modeling of relationships betweensolar radiation and meteorological variablesrdquo Energy Con-version and Management vol 105 pp 880ndash890 2015

Advances in Civil Engineering 13