Research Article Hybrid Wind Speed Forecasting Model Study...

Research ArticleHybrid Wind Speed Forecasting Model Study Based on SSAand Intelligent Optimized Algorithm

Wenyu Zhang Zhongyue Su Hongli Zhang Yanru Zhao and Zhiyuan Zhao

Key Laboratory for Semi-Arid Climate Change of the Ministry of Education College of Atmospheric Sciences Lanzhou UniversityKey Laboratory of Arid Climatic Change and Reducing Disaster of Gansu Province Lanzhou 730000 China

Correspondence should be addressed to Wenyu Zhang zhangwylzueducn

Received 9 January 2014 Accepted 13 February 2014 Published 3 April 2014

Academic Editor Suohai Fan

Copyright copy 2014 Wenyu Zhang et al This 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

Accurate wind speed forecasting is important for the reliable and efficient operation of the wind power system The present studyinvestigated singular spectrum analysis (SSA) with a reduced parameter algorithm in three time series models the autoregressiveintegrated moving average (ARIMA) model the support vector machine (SVM) model and the artificial neural network (ANN)model to forecast the wind speed in Shandong province China In the proposedmodel the weather research and forecastingmodel(WRF) is first employed as a physical background to provide the elements of weather data To reduce these noises SSA is usedto develop a self-adapting parameter selection algorithm that is fully data-driven After optimization the SSA-based forecastingmodels are applied to forecasting the immediate short-term wind speed and are adopted at ten wind farms in China Finallythe performance of the proposed approach is evaluated using observed data according to three error calculation methods Thesimulation results from ten cases show that the proposed method has better forecasting performance than the traditional methods

1 Introduction

Entering the 21st century countries worldwide face thedual pressures of environmental protection and economicgrowth To reduce energy-related toxic emissions in thecurrent energy infrastructure renewable energy shouldbe utilized with the goal of maintaining sustainabledevelopment and creating a better ecological environmentIn its ldquoSpecial Report on Renewable Energy Sourcesrdquothe IPCC 2011 states that renewable energies areaffordable and economically viable options for meetingthe electricity needs of people in developing countries[1] The extensive use of principal energy sources hasraised concerns about future security and the impactthey have had on climate To overcome the challengesof improving or maintaining energy security and mit-igating climate change low-carbon emission technologieshave attracted considerable interest worldwide resulting inincreased electricity generation from renewable sources Un-questionably renewable energies have huge potential buthow quickly their benefits can meet the growth of globalenergy demand hinges on government support to make

renewable energy cost-competitive in energy marketsAs fossil fuel prices increase and renewable technologiesmature renewable energies are becoming increasinglycompetitive a global effort will be required to constructa low-carbon society [2] For instance the InternationalEnergy Agency anticipates a rapid expansion of renewablessuch as hydroelectricity wind solar and geothermal energyproduction will rise from 840 million tons of oil equivalentin 2008 to nearly 3250 million tons of oil equivalent in2035 [3] The ldquoGlobal Wind Energy Outlook 2010rdquo projectsthat world wind energy production will increase more thantenfold by 2030 emphasizing the importance of wind as akey contributor to improving energy security and reducinggreenhouse gas emissions [4]

Among the various renewable energies wind energyis the most promising Wind energy has been the fastestgrowing renewable energy technology in the last ten yearsFurthermore it has been playing a crucial role in everydaylife for people in developing countries who account forone-third of the worldrsquos total population Wind energy alsosupports developed countries as one source of clean energyit helps them meet the 21st century energy demands [5]

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2014 Article ID 693205 14 pageshttpdxdoiorg1011552014693205

2 Abstract and Applied Analysis

Because of its economic and ecological advantages windpower has recently become one of the most popular alter-native energies accounting for approximately 10 of thenational power usage in European countries and this fig-ure exceeds 15 in Spain Germany and the USA [6]According to the GlobalWind Energy Council Report (2011)the worldrsquos wind power capacity grew by 225 in 2010adding 35802MW to bring total installations to 194390MWAlmost half of these additions were made in China whichexperienced an annual growth rate of approximately 65 [7]The worldrsquos total installed capacity of wind power reached254GW in June 2012 [8] However the main obstacle facingwind industry development is that wind is an intermittentenergy source which means that there is large variability inthe production of energy due to various factors such as windspeed air density and turbine characteristics Specificallyhorizontal air motion is defined as wind [9] and wind isdriven by uneven cooling and heating on the earthrsquos surfaceas well as the rotation of the earth Thus the occurrenceof wind has strong uncertainty in both space and timeThe nondeterminacy seriously limits wind power penetrationand threatens grid security Although wind power drives theturbines that generate electricity the complex fluctuations ofwind make it difficult to predict the power output The theo-retical amount of energy thatmight be generated fromwind isproportional to the cube of thewind speed and slight changesin the wind speed might cause significant changes in thetotal amount of electricity generated from the wind this alsocauses obstacles for power transportation [10] To guaranteethe security of the grid system the dispatching departmentmust balance the gridrsquos production and consumption withinvery small time intervals [11] Moreover due to the lack ofaccurate information about wind occurrence the efficiencyof wind turbines can also be limited [12] Several academicworks addressing wind energy attest to the increasing interestin this important theme

Generally there are two ways to solve this problemin wind power generation One is the large-scale transfor-mation of the existing electrical power system the mostpopular method is smart grid transformation which consistsof a digitally enabled power system [13] The core of asmart grid is the integration of secure and high-speed datacommunicationmdashbased on advanced computers electronicequipment intelligent components and moremdashto operatethe mixture system intelligently and effectively [14 15] Usingthe real-time information a smart grid can facilitate thedevelopment of wind power When wind-generated poweris insufficient other forms of energies can be used tosupplement power for a short time through a smart gridHowever currently there is no widely accepted standard-ized communicationnetwork infrastructure that could beapplied to power transformation through a smart grid [16]Another possible solution is to improve wind power tech-niques including wind-prediction techniques wind turbinetechniques wind energy storage techniques and combineddispatching Accurate wind information is important forestimating the wind power output Accurate estimations canbenefit not only increasing wind power penetration andmaintaining a stable grid system but also the combined

dispatching in a mixture power grid Under current electricalsystems developing wind-prediction techniques can be aneffective way to guarantee the security and stability of theelectrical system without increasing the running cost

In the past decades many approaches have been devel-oped for short-term load forecasting These methods can becategorized into different groups Some of these methodsassume a time series model structure and then try toidentify its parameters In actual power generation windpredictionsmdashespecially the short-term forecastsmdashare impor-tant for scheduling controlling and dispatching the energyconversion systems [17] The most important characteristicof windmdashspeedmdashcan be easily influenced by other meteoro-logical factors such as air temperature and air pressure aswell as obstacles and terrain [18]Thus wind speed predictionis not easy to address moreover wind speed modelinghas become one of the most difficult problems [19 20]The forecasting approach can be determined based on theavailable information and the time scale in question whichwill affect its application Short-term wind speed forecastingis a subclass of wind speed forecasting The time scales forshort-term forecasting range from a few seconds to minuteshours or several days [21]

Many methods of forecasting wind speed have been pro-posed In general they can be classified into two categoriesphysical methods and statistical methods

Physical methods are often referred to as meteorolog-ical predictions of wind speed they involve the numer-ical approximation of models that describe the state ofthe atmosphere [22] Numerical weather prediction (NWP)techniques one type of physical model-based approach relyon a class of physical models with numerical parameterscharacterizing local meteorological and geographical prop-erties such as temperature atmospheric pressure surfaceroughness and obstacles [23] NWP techniques include theweather research and forecasting (WRF) model and the fifthgeneration mesoscale model (MM5) These models alwaysuse physical data such as topography information pressureand temperature to forecast wind speed in the future [24 25]Typically prediction methods using NWP forecasts outper-form statistical approaches after a 3ndash6 h look-ahead timewhereas statistical approaches turn out to be quite reliable forvery short-term forecasts that is less than 6 h The optimalmodel most likely consists of a mixed approach which isvery often adopted by utilities to combine high accuracyfor very short horizons with longer forecasts of up to 48ndash72 h [26] Unlike physical models statistical methods makeforecasts by finding relationships using historical wind speeddata and sometimes other variables (eg wind direction ortemperature) The data used are recorded at the observationsite or at other nearby locations where data are available Inthe literature many statistical methods have been appliedto this topic such as the autoregressive integrated movingaverage (ARIMA) model Kalman filters and the general-ized autoregressive conditional heteroscedasticity (GARCH)model The statistical models can be used at any stage in themodeling process and they often combine various methodsinto one Physical and statistical models each have their ownadvantages for wind speed prediction but few forecasts use

Abstract and Applied Analysis 3

only one model Often the results of the physical predictionmerely represent the first step towards forecasting the windthus the physically predicted wind speed can be regarded asan auxiliary input to other statistical models [27] Currentlygrey models (GM) [28 29] and models based on artificialintelligence (AI) techniques have been developed for thisarea including the artificial neural networks (ANNs) ofmultilayer perceptrons (MLP) [30 31] radial basis function(RBF) [32] recurrent neural networks [33 34] and fuzzylogic [35 36] Neural networks can learn from past data andrecognize hidden patterns or relationships in historical obser-vations and use them to forecast future values The resultsindicate that prediction errors resulting from the Bayesiancombination approach always become smaller which is incontrast to artificial neural networks whose performance isnot consistent when the site or evaluation criterion changes[3] An annealing clustering ANN [37] a BP (back propaga-tion) neural network with rough set [38] a neural networkcombining wavelet transform and adaptive mutation particleswarm optimization [39] an ANN based on fuzzy logicmethods [40] and Bayesian neural networks integrating theMonte Carlo algorithm [41] have been proposed for short-term wind speed forecasting Combination models includethe adaptive particle swarm optimization-based combinedmethod [42] wavelet transform combination model basedon a neural network and an evolutionary algorithm [43]wavelet transforms and adaptivemodels [44] and an adaptivefuzzy combination model based on the self-organizing mapand support vector regression [45] In fact conventionallythe forecasting method is not classified as either physicalor statistical because most forecasting models include bothtechniques

Several methods are being used to diagnose the dynam-ical characteristics of observational wind speed time seriesThe singular spectrum analysis (SSA) method which isa powerful technique for time series analysis has beenemployed elegantly and effectively in several areas suchas hydrology geophysics climatology and economics [46ndash49] Traditional approaches are based on statistical mod-els including linear regression methods [50] exponentialsmoothing [51] Box-Jenkins approaches [52] and Kalmanfilters [53] Essentially most of the traditional approaches arebased on linear analysis However the wind speed series areusually nonlinear As discussed earlier noise signals causedby unstable factors increase the difficulties associated withconvergence and forecasting accuracy Guo et al [54] andDong et al [55] considered the first IMF (intrinsic modefunction) obtained by EMD(empiricalmode decomposition)as noise and demonstrated that eliminating the first IMFimproved the forecasting accuracy in their experiments Inaddition the EMD-based signal filtering proposed in [56]indicates that noise potentially contains the first IMF or thefirst several IMFs Here SSA [57 58] has been employed tocharacterize the properties of wind speed and the hybridmodel with SSA is used for short-time forecasting The SSAtechnique incorporates the elements of classical time seriesanalysis multivariate geometry multivariate statistics signalprocessing and dynamical systems The aim of SSA is toobtain a decomposition of the original series into a set of

independent and interpretable components which include aslowly varying trend oscillatory components and randomnoise [57] One of the differences between traditional timeseries analysis methods and SSA is that SSA and SSA-relatedmethods could be applied to both classical time series analysisproblems and various other situations such as exploratoryanalysis for data-mining and parameter estimation in signalprocessing [59] The main reason for using nonparametricor data-driven techniques is that no previous assumptionsare required to analyze and perform forecasts such as thenormality of residuals the stationary of the time series or apredefined model structure Although SSA does not involveany forecasting algorithms the analysis reveals the naturalcharacteristics of time series One of the main advantages ofSSA compared to other nonparametric methods is that onlytwo parameters are used to simulate the time series in manyimplementations [60] and no model is assumed before theSSA method is adopted the subspace-based model is builtadaptively The other essential difference between SSA andthe majority of methods is that SSA does not require a priorimodel of a trend such as a priori knowledge of the numberof periodicities and period values to analyze time series witha trend or periodicity

Briefly the SSA method decomposes a time series intoa number of components with simpler structures such as aslowly varying trend oscillations and noise SSA belongs tothe general category of principal component analysis (PCA)methods which apply a linear transformation of the originaldata space into a feature space where the data set may berepresented by effective features while retaining most of theinformation content of the data [61] Wavelet analysis is apowerful tool for PCA and has been used for feature extrac-tion and denoising wind speed for a long time To optimallyfit the forecasting model the data must be stationary andhave a normal distribution In SSA these problems do notexist as the technique does not depend on any parameters asdoes the other model for the trend The SSA technique hasbeen used in a variety of fields such as signal processingnonlinear dynamics climate medicine and mathematicalstatistics [62] Additionally some denoising methods arebased on singular value decomposition (SVD) similar to theSSA method

The basic SSA method and forecasting models are pre-sented to address the short-term wind speed forecastingproblem The employed models meet two goals (1) using thereal data for SSA to eliminate cumulative error and (2) esti-mating the data trend using the history of the data to forecastshort-term data in wind speed Simulation results present theeffectiveness of the proposed method in characterizing andpredicting time series

In this paper a hybrid prediction algorithm is proposedfor short-term wind speed forecasting The proposed algo-rithm which integrates the advantages of the time seriesand SSA is adopted to develop a prediction model Therest of this paper is organized as follows In Section 2 thedata description and the research background are outlinedThe NWP model WRF is also introduced in Section 2 inSection 3 the SSA model for feature extraction is introducedand the main steps of the model are given which include


gt200Wm2 (high)lt50Wm2 (low)

In Shandong province Chinathe majority of wind farms are located in coastalareas with abundant wind resources gt 150wm2

Wm2150sim200Wm2

50sim100

Wm2100sim50

Figure 1 Chinese wind energy resource distribution and wind farms in Shandong province

decomposition and reconstructionThe methods contain thebasic processing of physical methods The performance ofwind speed data is described The main forecasting methodsand the results are presented and discussed in Section 5 withcomparisons to other methods A brief review of this paperand the future research are in Section 6

2 Background and Data Collection

Wind farms at 10 sites in Shandong China applied ourmethodologies The Shandong province located between114∘4751015840 E and 122∘4231015840 E and between 34∘2291015840N and38∘24011015840N in the eastern coastal area of China on the lowerreaches of the Yellow River covers an area of 157 times 105 km2which accounts for 16 of the total land area of China Asan economically powerful province with a large population(94 times 107 inhabitants in 2007) it has experienced rapidand sustained economic development with enormous energyconsumption With the rapid increase in wind energy inChina the total installed capacity of wind power in Shandongprovince reached 45623MW in 2012 Some of wind farms arenear the PacificOcean and their nominal power can reach upto 495MWThe prevailing wind speed in Shandong in Aprilaverages 1027ms No additional information is providedin the database about these wind farms (location nominalpower and so on) for confidentiality reasons This databasecontains information about 10 wind farms We denote theselected wind farms numbered 1 to 10 by wind farms Ato J respectively These wind farms have variable situationsand land surfaces which allowed the modelrsquos effectivenessto be sufficiently tested Thus our proposed model could bedemonstrated in very different settings

As shown in Figure 1 some wind farms in this study arelocated near the sea because of the different heat capacityvalues of the sea and the land there will be a sea breeze which

will blow in opposite directions during the day and night Inthis region frequent strong winds make it quite difficult toaccurately forecast synoptic processes

In all cases we collect observational speed data fromthe wind farm and meteorological weather forecasts from aNWP model In this database historical wind speed data areobtained every 15min and then averaged for each hour Wehave quarter data from 0000 April 1 2013 to 2345 April30 2013 which amounts to 2650 data points Meteorologicalwind simulation results include the temperature pressurehumidity wind speed and direction provided by the WRFmodel The forecasts of the models are hourly and are givenin terms of the coordinated universal time (UTC) and themaximum prediction horizon is 96 h Generally in thesemodels historical wind speed is used as an input at one of thepoints However in theNNmodel the temperature pressurehumidity and direction results from the WRF are also usedas input data In all of the wind farms analyzed data from thetwo groups (historical measurement and model forecasting)are divided in two sets the first portion of data is used to trainthemodels and the remaining data points are used to validatethe models

TheWRF mesoscale numerical model is now the currentgeneration ldquocommunityrdquo physics-based atmospheric modelserving the needs of both atmospheric research and oper-ational forecasting Recently the WRF model has becomeone of the most popular and widely used tools for numericweather prediction In this paper the WRF model is selectedas a representative of the physical models The main fore-casting data are used to provide forecasting factors to NNmodel

WRF is a fully compressible nonhydrostatic model witha large number of physics options regarding cumulus param-eterization cloud microphysics radiation PBL parameteri-zation and land-surface model In the WRF model a gridis defined as an integration of three-dimensional points


1125∘E 1150∘E 1175∘E 1200∘E 1225∘E

400∘N

375∘N

350∘N

325∘N

Shandong provinceWind farmSimulation domain

Figure 2 The simulation domains in WRF

Table 1 Model configuration of the WRF simulation

Physical optionsCumulus parameterization Grell 3D ensemble cumulus schemeShort-wave radiation RRTM schemeLong-wave radiation Dudhia schemeSurface layer physics Eta similarityLand-surface processes Fractional sea-icePlanetary boundary layer Mellor-Yamada-Janjic scheme

It contains a set of weather data (wind speed atmosphericpressure etc) For each grid there are a current time andan associated stop time The atmospheric status is simulatedby calculating a series of physical equations this is based notonly on the on-grid data but also on a specific physical modelThen the current time of the grid can be advanced by a time-step a unit of time [63] TheWRF simulation in this paper isperformed for the case of April 2013 in Shandong provinceChina The domains used in this simulation are shown inFigure 2

TheNational Centers for Environmental Prediction FinalAnalysis (1∘ times 1∘ 6-hourly) data (NCEP FNL) which include24 levels from surface to 10 hPa are used as the initial andlateral boundary conditions Details about theNCEP FNL areavailable at httprdaucaredudatasetsds0832The physicsoptions selected in this simulation are also shown in Table 1

3 SSA of Hourly Wind Speed of Wind Farmsin Shandong Province

31 SSA of a Time Series SSA is defined as amethod to obtaindetailed information from a noisy time series [64] Considerthe real-valued nonzero time series 119884

119879= (1199101 1199102 119910

119879) of

sufficient length 119879 The primary reconstruction process of

SSA is to decompose the original series into a set of subseries119883 = 119883

1+sdot sdot sdot+119883

119889and then reconstruct the original series [57

58]TheSSA technique consists of two complementary stagesdecomposition and reconstruction both stages include twoseparate steps

32 Decomposition This stage is subdivided into two stepsembedding and singular value decomposition (SVD)

321 Embedding Embedding can be regarded as a map-ping that converts a one-dimensional time series 119884

119879= (1199101

1199102 119910

119879) into the multidimensional series 119883

1 1198832

119883119870with vectors 119883

119894= (119910119894 119910119894+1 119910

119894+119871minus1)1015840

isin R119871 where119870 = 119879 minus 119871 + 1 Vectors 119883

119894are called 119871-lagged vectors where

119871 is an integer such that 2 le 119871 le 119879 The main result of thisstep is the definition of a trajectory matrix defined as

119883 = [1198831 1198832 119883

119870] = (

1199101

1199102

sdot sdot sdot 119910119870

1199102

1199103

sdot sdot sdot 119910119870+1

d

119910119871119910119871+1


) (1)

The trajectory matrix is a Hankel matrix where all of theelements along the diagonal 119894 + 119895 = const are equal [57]

322 Singular Value Decomposition (SVD) The SVD of1198831198831015840produces a set of 119871 eigenvalues 120582

1ge 1205822ge sdot sdot sdot ge 120582

119871ge 0 and

the corresponding eigenvectors1198801 1198802 119880

119871(often denoted

by empirical orthogonal functions (EOF)) Then the SVD ofthe trajectory matrix can be written as119883 = 119864

1+1198642+ sdot sdot sdot +119864

119889

where 119864119894= radic120582

119894119880119894119881119894

1015840 119889 is the rank of 1198831198831015840 (ie the numberof nonzero eigenvalues) and 119881

1 1198812 119881

119889are the principal

components (PC) defined as 119881119894= 1198831015840

119880119894radic120582119894 The collection

(radic120582119894 119880119894 119881119894) is referred to as the 119894th Eigen triple of the matrix

119883 If Γ = sum119889119894=1

120582119894 then 120582119894Γ is the proportion of variance of119883

explained by 119864119894 1198641which has the highest contribution [49]

while 119864119889has the lowest contribution SVD could be time-

consuming if the length of the time series is large (119879 gt 1000)

33 Reconstruction After decomposing the time series theresults include subseries 119883 = 119883

1+ sdot sdot sdot + 119883

119889 As in the de-

composition stage the reconstruction stage consists of twosteps grouping and averaging

331 Grouping In this step 119903 out of 119889 Eigen triples are se-lected by the user Let 119868 = 119894

1 1198942 119894

119903 be a group of 119903-

selected Eigen triples 119883119894= 1198831198941

+ 1198831198942

sdot sdot sdot + 119883119894119903

where 119883119894is

related to the ldquosignalrdquo of y while the rest of the (119889 minus 119903) Eigentriples denote the error term 120576

332 Averaging The group of 119903 components selected in theprevious stage is then used to reconstruct the deterministiccomponents of the time series The basic idea is to transformeach of the terms 119883

1198941

1198831198942

119883119894119903

into reconstructed timeseries 119910

1198941

1199101198942

119910119894119903

through the Hankelization process 119867()or diagonal averaging if 119911

119894119895 then 119894 + 119895 = 119896 + 1 Thus119867(119885) is

a time series of length 119879 reconstructed from the matrix 119885


05

1015

2025

30 0 10 20 3040 50 60 70 80 90

100

0

4

8

12

16

HoursDays

Win

d sp

eed

(ms

)

Figure 3 Wind speed diagram of wind farm A in April

At the end of the averaging step the reconstructed timeseries is an approximation of 119910

119910 = 119867(1198831198941

) + 119867(1198831198942

) + sdot sdot sdot + 119867 (119883119894119903

) + 119890 (2)

As noted by Alexdradov and Golyandina the reconstruc-tion of a single Eigen triple is based on the whole time seriesThis means that SSA is not a local method and hence isrobust to outliers

34Wind Speed and Its Properties The experimental data arethe wind speed time series of Shandong province in ms for30 days fromApril 1 to April 30 2013 For each series we take96 time series of different hourly wind speeds as a forecastingunit during forecasting processing An example of one suchwind farmrsquos wind speed is given in Figure 3

Within a month of each day the wind speed time serieshas an inconspicuous periodicity of 24 hours The generalrule is to select 119871 = 1198792 However in this case the timeseries of the forecasting period could define119871 and that will bemore appropriate In addition to the 119871 parameter for SSA thenumber of components 119903 defines how the components can beseparated To locate the parameter 119903 the detailed propertiesof the wind speed time series should be displayed A methodfor selecting 119903 out of 119889 components is requiring that thesum of their contributions be at least a predefined thresholdsuch as 90 Generally noise components will have a lowcontribution

To evaluate the contributions of the different compo-nents Figure 4 shows the principal components of windspeed in the SSA Each PCx represents the ordinal compo-nents separated from the original time series Note that PC1and PC2 are dominating in all components while PC3 andPC4 are subordinate Components PC5ndashPC7 and PC8ndashPC11could be classified as small parts which could be groupedHowever their contributions are still substantial The rest ofcomponents diminish very slowly but their contributions arelowThe construction of the time series will be based on theseEigen triples

35 Reconstruction and Preparation for Forecasting Ap-proaches As previously mentioned the window length 119871is decided using a characteristic forecasting time series inthe decomposition stage Therefore 119871 = 96 h is assumed

here which corresponds to a time series of 4 days of windspeed The reconstruction of a single Eigen triple is basedon the entire time series In this case a useful Eigen triple isdefined as one that improves the accuracy of the final forecastFigure 5 depicts the contributions of different Eigen triplesin forecasting The ldquopositiverdquo means that the contribution ofthese components is positive which reduces the MAPE andvice versa

The useful Eigen triples set is the group of 119903 componentsselected in the previous stage they are deterministic compo-nents of the time series Because the simulated data consist ofthe wind speed temperature humidity and pressure they arereconstructed in the same wayThe detailed process is shownin Figure 6 First the wind speed and the other weatherdata are rearranged as an 119871-length time series using the 119871determined in last section Second according to the calcu-lated accuracy for each component the principal componentsare divided into a positive components set and a negativecomponents set The positive component set includes thetrend and the harmonic components and the negative setmostly contains the noise Finally the reconstructed timeseries is provided as an 119903 times 4matrix

By selecting a set of useful components and consideringother negative components as noise some frequencies maybe filtered out completely In Figure 6 original predictionsrepresent the forecasting result without SSA which includesthe noise in simulation processing In other words this partcould be regarded as a forecast including all of the Eigentriples

4 Performance Metrics of Forecast Accuracy

To date a number of performance measures have been pro-posed and employed to evaluate the forecast accuracy but nosingle performance measure has been recognized as the uni-versal standard This actually complicates the performancecomparison of different forecasting models As a result weneed to assess the performance using multiple metrics andit is interesting to see if different metrics will give the sameperformance ranking for the tested models The metricsincluded in this study are mean absolute error (MAE) rootmean square error (RMSE) and mean absolute percentageerror (MAPE) [21]

MAE = 1

119879

119879

sum

119905=1

1003816100381610038161003816119910119905 minus 1198911199051003816100381610038161003816

RMSE = radic 1119879

119879

sum

119905=1

(119910119905minus 119891119905)2

MAPE = 1

119879

119879

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910119905minus 119891119905

119910119905

10038161003816100381610038161003816100381610038161003816

(3)

where 119910119905and 119891

119905denote the observations and the forecast

value frommodel 119905 respectively and 119879 is the number of dataused for performance evaluation and comparison

MAEmeasures the averagemagnitude of the errors of theforecasting setsMore specifically these involve the average of


0 50 1000

5

10

PC1

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

minus2

0

2

PC2

minus2

0

2

4

PC3

minus1

0

1

PC4

minus1

0

1

PC5

minus2

minus1

0

1

PC6

minus1

0

1

minus1

0

1

minus1

0

1

PC7

minus02

0

02

PC8

minus05

0

05

PC9

PC10

minus02

0

02

minus02

0

02

PC11

PC12

PC13

PC14

PC15

minus01

0

01

PC16

minus005

0

005

minus005

0

005

PC17

PC18

PC19

PC20

minus05

0

05

minus01

0

01

minus01

0

01

minus01

0

01

Figure 4 Principal components related to the 20 Eigen triples

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

minus05

0

05

minus1

0

1

2

minus05

0

05

MA

PE

Positive

Negative

MA

PEM

APE

Figure 5 The contributions of different Eigen triples to forecasting accuracy

the verification sample and the absolute values of the differ-ences between the forecasted results and the correspondingobservations MAE is a linear measure which means thatall of the individual differences are equally weighted in theaverage In contrast RMSE is a quadratic scoring rule thatmeasures the average magnitude of the error Because the

errors are squared before they are averaged the RMSE givesa relatively high weight to large errors This means thatthe RMSE is most useful when large errors are particularlyundesirable MAPE is a measure of accuracy in a fitted timeseries value in statistics specifically a trending value Thedifference between the actual value and the forecasted value


Wind speed Temperature PressureHumidity

Decomposition

Originalpredictions

W1

W2

Wn

T1

T2

Tn

H1

H2

Hn

P1

P2

Pn

Principalcomponents

Positivecomponents

Negativecomponents

NN

SVM

ARIMA

Reconstruction

Wi1

Wi2

Wir

Ti1

Ti2

Tir

Hi1

Hi2

Hir

Pi1

Pi2

Pir

Figure 6 Decomposition and reconstruction diagram of simulation data

is divided by the actual value The absolute value of thiscalculation is summed for every forecast point in time anddivided again by the total number of forecast points

5 Forecasting Models

The forecasting model is used to measure the performance ofthis hybrid algorithm It consists of the following algorithms

(1) Autoregressive Integrated Moving Average (ARIMA) Algo-rithm Introduced by Box and Jenkins [65] the ARIMAlinear models have dominated many areas as a populartime series forecasting approach As the application of thesemodels is very common a brief description is providedhere The linear function is based upon three parametric

linear components autoregression (AR) integration (I) andmoving average (MA)The autoregressive or ARIMA (119901 0 0)model is represented as follows

119910119905= 1205790+ 1205931119910119905minus1+ 1205932119910119905minus2+ sdot sdot sdot + 120593

119901119910119905minus119901+ 119890119905 (4)

where 119901 is the number of the autoregressive terms 119910119905is the

forecasted output 119910119905minus119901

is the observation at time 119905 minus 119901 and1205931 1205932 120593

119901are a finite set of parameters The 120593 terms are

determined by linear regression The 1205790term is the intercept

and 119890119905is the error associated with the regression This time

series depends only on the119901 past values of itself and a randomterm 119890

119905 The moving average or ARIMA (0 0 119902) method is

represented as

119910119905= 120583 minus 120579

1119890119905minus1minus 1205792119890119905minus2minus sdot sdot sdot minus 120579

119902119890119905minus119902+ 119890119905 (5)


where 119902 is the number of moving average terms 1205791 1205792 120579

119902

are the finite weights or parameters set and 120583 is the mean ofthe series This time series depends only on 119902 past randomterms and a present random term 119890

119905 As a particular case an

ARIMA(119901 0 119902) or ARMA(119901 119902) is a model for a time seriesthat depends on 119901 past values of itself and on 119902 past randomterms 119890

119905 The equation is shown as follows


119901119910119905minus119901+ 120583

minus 1205791119890119905minus1minus 1205792119890119905minus2minus sdot sdot sdot minus 120579

119902119890119905minus119902+ 119890119905

(6)

Finally an ARIMA(119901 119889 119902) is an ARIMA(119901 0 119902) modelfor a time series that has been different 119889 times The ARIMAmodels have the capability to include external independentor predictor variables

(2) Support Vector Machine (SVM) Algorithm The supportvector machine (SVM) was proposed by Vapnik [66] Basedon the structured risk minimization (SRM) principle theSVM minimizes an upper bound of the generalization errorinstead of the empirical error as in other neural networksAdditionally the SVM model generates the regression func-tion by applying a set of high-dimensional linear functionsThe SVM regression function is formulated as follows

119910 = 119908120593 (119909) + 119887 (7)

where 120593(119909) is called the feature which is nonlinearly mappedfrom the input space 119909The coefficients119908 and 119887 are estimatedby minimizing

119877 (119862) = 1198621

119873

119873

sum

119894=1

119871120576(119889119894 119910119894) +

1

21199082

[0 1]

119871120576(119889 119910) =

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 ge 120576

0 others

(8)

where both 119862 and 120576 are prescribed parameters The firstterm 119871

120576(119889 119910) is called the 120576-intensive loss function The 119889

119894

is the actual wind speed in the 119894th period This functionindicates that errors below 120576 are not penalized The term119862(1119873)sum

119873

119894=1

119871120576(119889119894 119910119894) is the empirical error The second

term (12)1199082 measures the flatness of the function 119862evaluates the model The positive slack variables 120577 and120577lowast represent the distance from the actual values to thecorresponding boundary values of the 120576-tube The equationis transformed into the following constrained formation

119877 (119908 120577 120577lowast

) =1

2119908119908119879

+ 119862lowast

(

119873

sum

119894=1

(120577119894+ 120577lowast

119894

)) (9)

subject to

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120577

lowast

119894

119889119894minus 119908120593 (119909

119894) minus 119887119894le 120576 + 120577

119894

120577119894 120577lowast

119894

ge 0 119894 = 1 2 119870119873

(10)

Finally they satisfy the equality

119891 (119909 120572 120572lowast

) =

119897

sum

119894=1

(120572119894minus 120572lowast

119894

)119870 (119909 119909119894) + 119887 (11)

Here 119870(119909 119909119894) is called the kernel function The value of the

kernel is equal to the inner product of two vectors 119909119894and 119909

119895

in the feature space 120593(119909119894) and 120593(119909

119895) such that 119870(119909

119894 119909119895) =

120593(119909119894) lowast 120593(119909

119895) Any function that satisfies Mercerrsquos condition

can be used as the kernel function [67] The Gaussian kernelfunction is used in this paper

(3) Artificial Neural Networks (ANN) Algorithm Artificialneural network (ANN) models are generally used for timeseries forecasting A neural network is a mathematical rep-resentation that is inspired by the way the brain processesinformation The model consists of an input layer an outputlayer and one or more intervening layers also referred to ashidden layers The hidden layers can capture the nonlinearrelationship between variables Each layer consists ofmultipleneurons that are connected to the neurons in adjacent layersBecause these networks contain many interacting nonlinearneurons inmultiple layers the networks can capture relativelycomplex performance ANN is already one of the modelsthat is able to approximate various nonlinearities in the dataseries Many types of ANN models have been suggestedin related research with the most popular one used forclassification being the multilayer perceptron (MLP) withback propagationThe output of the 119894th hidden neuron is thencomputed by processing the weighted inputs and its bias termℎ119894as follows

ℎ119894= 119891(119887

119894+

119899

sum

119895=1

119908119894119895119909119895) (12)

where 119908119894119895denotes the weight connecting input 119908

119894119895to hidden

unit ℎ119894

Similarly the output of the output layer is computed asfollows

119910 = 119891output

(119887 +

119899

sum

119895=1

119908119895119909119895) (13)

with 119899 presenting the number of hidden neurons and 119908119895

representing the weight connecting hidden unit 119895 to theoutput neuron A threshold function is then applied tomap the network output 119910 to a classification label Thetransfer functions 119891ℎ and 119891output allow the network to modelnonlinear relationships in the data

6 Forecast Results and Comparative Analysis

The last section consists of forecasting data calculation errorcomparison and results analysis The error calculation mod-ule provides different methods to compare the SSA techniquefor different forecasting methods in the 10 wind farms Thealgorithms are chosen based on the different theoreticalprinciples


Table 2 Comparison of RMSE for 10 wind farms

Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ

ARIMAOri-RMSE 138 354 752 327 300 598 381 134 161 975SSA-RMSE 134 349 133 304 228 559 481 157 143 896

SVMOri-RMSE 501 685 427 711 842 719 792 689 543 495SSA-RMSE 443 591 366 638 754 685 758 651 573 452

ANNOri-RMSE 145 434 188 617 122 363 310 253 164 898SSA-RMSE 131 398 137 292 064 676 514 163 097 936

Table 3 Comparison of MAE for 10 wind farms

Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ

ARIMAOri-MAE 101 325 713 299 263 584 353 098 111 967SSA-MAE 094 312 097 278 145 544 444 103 095 888

SVMOri-MAE 482 676 414 704 836 707 781 670 524 482SSA-MAE 431 589 359 629 749 676 745 641 561 439

ANNOri-MAE 098 414 176 586 105 341 277 237 137 890SSA-MAE 094 358 119 274 050 656 461 104 058 926

Table 4 Comparison of MAPE for 10 wind farms

Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ

ARIMAOri-MAPE 768 2433 5062 2038 1991 4081 2638 746 885 6829SSA-MAPE 728 2350 772 1897 1164 3790 3310 815 754 6255

SVMOri-MAPE 3376 4749 2885 4974 5913 4986 5517 4722 3638 3370SSA-MAPE 3016 4181 2523 4434 5298 4797 5247 4520 3922 3068

ANNOri-MAPE 777 3061 1244 4088 764 2366 2092 1632 1013 6277SSA-MAPE 726 2683 846 1885 390 4567 3456 830 463 6521

In the following the combined methodology is appliedto predict the future wind speed of the furthermost hours toeach forecasting period the results are shown in Tables 2 3and 4 Specifically the prediction performance is evaluatedusing the RMSE MAPE and MSE For these forecastingcases in different wind farms the only actual requirementfrom the wind farms is reducing the prediction error asmuch as possible In our recent research into wind speedforecasting the time series method relied on the historicaldata which are primarily used in immediate-short-termforecasting The forecast period is usually limited to 4 hoursdivided into quarter-hour periods To expand the forecast

period and observe the forecasting performance using theSSA technique the wind data in this paper are merged intoan hour as we mentioned earlier and the forecast period isextended from 4 hours to 7 hours The schematic diagram ofthe forecasting process is shown in Figure 7

As seen in Table 2 the forecasting performance valuesusing the SSA technique based on the ARIMA and the NNare much better than those of the SVM algorithm for mostof the wind farms For instance the values of RMSE for theARIMA and ANN at wind farm C are 133 and 137 less thanthe value of 366 obtained using SVM As we mentionedwhether the SSA technique reduces forecasting error is the


Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata

Initial data Initial data

Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space

Figure 7 Procedure chart of the forecasting process

WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)

Original prediction using ARIMASSA-ARIMA predictionOriginal prediction using SVMSSA-SVM predictionOriginal prediction using NNSSA-NN prediction

ARIMAoptimization

SVMoptimization

NNoptimization

This means that the error of theforecasting model is reduced

Figure 8 Final error reduction of wind farms in Shandong province

critical problem addressed in this paper So comparingthe Ori-group with the SSA-group it is apparent that theerror of the SSA-group is lower as measured by the RMSEFor example the value of SSA-RMSE in wind farm E usingANN decreases from 122 to 064 The value of SSA-RMSEin wind farm C using ARIMA decreases from 752 to 133However this is not the case across all 10 wind farms In casessuch as wind farm F in ANN wind farm G in ARIMA andwind farm I in SVM the RMSEs are relatively high Howeverthe number of these groups is small and there is no site wherethe RMSE of all three methods increases This conclusion

is presented in Table 2 and a detailed explanation will beprovided next

Similar to Tables 2 and 3 displays the values for MAEMAE is expressed as the absolute value of the error whichcan also be used to evaluate forecasting errors The MAEexhibits the same pattern as the RMSE The MAE of theOri-group is lower than the error of the SSA-group whichmeans that the SSA technique significantly improved theprediction accuracy As observed from the table the SSA-group is different from the Ori-group which has a substan-tially higher forecasting accuracy However the forecasting


errors associated with different methods make a substantialdifference

Details of the MAPE of forecasting results are given inTable 4 they are similar to the results from Tables 2 and 3The results reported in Table 4 are theMAPE results obtainedusing three different methods As we can see from the tablethe SSA-group has higher forecasting accuracy than the Ori-group The MAPE results in Table 4 show that the combinedmethod improves accuracy from 04 to 42 For examplethe ARIMA forecasting of wind farm C reduces the errorfrom 5062 to 772 whereas the ANN forecasting of windfarmD reduces the error from 4088 to 1885Most resultsindicate that the SSA technique significantly improves theprediction accuracy

TheRMSE iswidely used inwind farms and is the primaryerror measure used in this paper The RMSE results are dis-played in Figure 8 These results suggest that the SSA tech-nique is an excellent method for time series forecasting

7 Discussion and Conclusion

This paper provided a new wind speed forecasting methodby introducing an SSA algorithm In wind speed forecastingcases we proposed an effective method for defining theparameters of SSA and applied the new method to 10 windfarms in Shandong province Here SSA-based filtering con-sists of a data-separation technology with fewer parameterswhich is more efficient than the traditional noise reductionmethods used in recent research The proposed algorithmsignificantly outperforms the basic forecasting algorithm ina variety of different situations using ARIMA SVM andNN this conclusion is especially true for forecasting with atime series algorithm Secondly the method employs SSAto eliminate the noise series with an algorithm based onthe data itself which overcomes the limitations imposed bythe complexity of the algorithms Further the goal of theproposedmodel is not only to present an exact representationof the forecasting method itself but also to set up a series ofmethods for the process of decomposition and reconstructionthat will be generally capable of receiving new inputs

The interest in employing three different forecastingmethods based on different theoretical structures confirmedthat the accuracy and applicability of the forecast result areimproved however the forecasting capacities of the methodsthemselves were significantly different On the one handthe forecasting horizon was expanded from 4 hours to 7hours in these immediate-short-term winds speed forecastsThis method which consists of the decomposition andreconstruction of SSA will result in a better evaluation offorecasting method performance in a time series On theother hand there is not a universal method for wind speedforecasting different methods can be applied under differentconditions Although the behavior of SVM is unsatisfactorythe results of the other two forecasting methods are stillsuitable In fact this result is exactly what we expect inwind speed forecasting Because of the fluctuating natureof the wind series it is difficult to find an efficient andversatile optimization method Even to this day wind speed

forecasting remains a very laborious problem and theMAPEof such wind farms usually ranges from 25 to 40 [68]Although the versatility of this approach remains to be testedthis experiment which included 10wind farms demonstratesthat the method is useful for wind speed forecasting

Conflict of Interests

The authors declare that there is no conflict of interests re-garding the publication of this paper

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (41225018) and IAM (IAM201305)

References

[1] ldquoIPCC Special Report on Renewable Energy Sources andClimate Change Mitigationrdquo 2011 httpwwwipcc-wg3depublicationsspecial-reports

[2] K Y Oh J Y Kim J K Lee M S Ryu and J S LeeldquoAn assessment of wind energy potential at the demonstrationoffshore wind farm in Koreardquo Energy vol 46 pp 555ndash563 2012

[3] N Chaudhry and L Hughes ldquoForecasting the reliability ofwind-energy systems a new approach using the RL techniquerdquoApplied Energy vol 96 pp 422ndash430 2012

[4] GWEC ldquoGlobalWindEnergyCouncilrdquo 2010 http wwwgwecnetfileadmindocumentsPublicationsGWEO20201020finalpdf

[5] W Zhang J Wu J Wang W Zhao and L Shen ldquoPerformanceanalysis of four modified approaches for wind speed forecast-ingrdquo Applied Energy vol 99 pp 324ndash333 2012

[6] M Carolin Mabel and E Fernandez ldquoAnalysis of wind powergeneration and prediction using ANN a case studyrdquo RenewableEnergy vol 33 no 5 pp 986ndash992 2008

[7] S Rehman A M Mahbub Alam J P Meyer and L M Al-Hadhrami ldquoWind speed characteristics and resource assess-ment using weibull parametersrdquo International Journal of GreenEnergy vol 9 no 8 pp 800ndash814 2012

[8] P Kou F Gao and X Guan ldquoSparse online warped Gaussianprocess for wind power probabilistic forecastingrdquo AppliedEnergy vol 108 pp 410ndash428 2013

[9] A Oztopal ldquoArtificial neural network approach to spatialestimation of wind velocity datardquo Energy Conversion andManagement vol 47 no 4 pp 395ndash406 2006

[10] X Li K Hubacek and Y L Siu ldquoWind power in Chinamdashdreamor realityrdquo Energy vol 37 no 1 pp 51ndash60 2012

[11] L Lazic G Pejanovic and M Zivkovic ldquoWind forecasts forwind power generation using the EtamodelrdquoRenewable Energyvol 35 no 6 pp 1236ndash1243 2010

[12] MMonfared H Rastegar and HM Kojabadi ldquoA new strategyfor wind speed forecasting using artificial intelligent methodsrdquoRenewable Energy vol 34 no 3 pp 845ndash848 2009

[13] Smart grid ldquoWikipediardquo 2012 httpenwikipediaorgwikiSmart grid

[14] W Wang Y Xu and M Khanna ldquoA survey on the communi-cation architectures in smart gridrdquo Computer Networks vol 55no 15 pp 3604ndash3629 2011


[15] Y NWu J Chen and L R Liu ldquoConstruction of Chinarsquos smartgrid information system analysisrdquo Renewable amp SustainableEnergy Reviews vol 15 pp 4236ndash4241 2011

[16] J Gao Y Xiao J Liu W Liang and C L P Chen ldquoA survey ofcommunicationnetworking in SmartGridsrdquo FutureGenerationComputer Systems vol 28 no 2 pp 391ndash404 2012

[17] M G de Giorgi A Ficarella and M Tarantino ldquoAssessmentof the benefits of numerical weather predictions in wind powerforecasting based on statistical methodsrdquo Energy vol 36 no 7pp 3968ndash3978 2011

[18] Z Guo J Zhao W Zhang and J Wang ldquoA corrected hybridapproach for wind speed prediction inHexi Corridor of ChinardquoEnergy vol 36 no 3 pp 1668ndash1679 2011

[19] I J Ramırez-Rosado and L A Fernandez-Jimenez ldquoAnadvancedmodel for short-term forecasting of mean wind speedandwind electric powerrdquoControl and Intelligent Systems vol 32no 1 pp 21ndash26 2004

[20] A Sfetsos ldquoA novel approach for the forecasting of mean hourlywind speed time seriesrdquo Renewable Energy vol 27 no 2 pp163ndash174 2002

[21] G Li and J Shi ldquoOn comparing three artificial neural networksfor wind speed forecastingrdquo Applied Energy vol 87 no 7 pp2313ndash2320 2010

[22] H Liu J Shi and E Erdem ldquoPrediction of wind speed timeseries using modified Taylor Kriging methodrdquo Energy vol 35no 12 pp 4870ndash4879 2010

[23] K Chen and J Yu ldquoShort-term wind speed prediction usingan unscented Kalman filter based state-space support vectorregression approachrdquo Applied Energy vol 113 pp 690ndash7052014

[24] L Landberg ldquoShort-term prediction of the power productionfrom wind farmsrdquo Journal of Wind Engineering and IndustrialAerodynamics vol 80 no 1-2 pp 207ndash220 1999

[25] M Negnevitsky and C W Potter ldquoInnovative short-term windgeneration prediction techniquesrdquo in Proceedings of the IEEEPES Power Systems Conference and Exposition (PSCE rsquo06) pp60ndash65 November 2006

[26] F Cassola andM Burlando ldquoWind speed andwind energy fore-cast through Kalman filtering of NumericalWeather Predictionmodel outputrdquo Applied Energy vol 99 pp 154ndash166 2012

[27] M Lei L Shiyan J Chuanwen L Hongling and Z Yan ldquoAreview on the forecasting of wind speed and generated powerrdquoRenewable and Sustainable Energy Reviews vol 13 no 4 pp915ndash920 2009

[28] S J Wu and S L Lin ldquoIntelligent web-based fuzzy and greymodels for hourly wind speed forecastrdquo International Journalof Computers vol 4 pp 235ndash242 2010

[29] J-F Li B-H Zhang G-L Xie Y Li and C-X Mao ldquoGreypredictor models for wind speed-wind power predictionrdquoPower System Protection and Control vol 38 no 19 pp 151ndash1592010

[30] L Lin J T Eriksson H Vihriala and L Soderlund ldquoPredictingwind behavior with neural networksrdquo in Proceedings the Euro-pean Wind Energy Conference pp 655ndash658

[31] M C Alexiadis P S Dokopoulos H S Sahsamanoglou andI M Manousaridis ldquoShort-term forecasting of wind speed andrelated electrical powerrdquo Solar Energy vol 63 no 1 pp 61ndash681998

[32] H G Beyer T Degner J Haussmann M Hoffman and PRujan ldquoShort term forecast of wind speed and power output ofa wind turbine with neural networksrdquo in Proceedings of the 2ndEuropeanCongress on Intelligent Techniques and SoftComputingpp 349ndash352 1994

[33] G N Kariniotakis G S Stavrakakis and E F Nogaret ldquoWindpower forecasting using advanced neural networks modelsrdquoIEEE Transactions on Energy Conversion vol 11 no 4 pp 762ndash767 1996

[34] A More and M C Deo ldquoForecasting wind with neuralnetworksrdquoMarine Structures vol 16 no 1 pp 35ndash49 2003

[35] G Kariniotakis G S Stavrakakis and E F Nogaret ldquoAfuzzy logic and neural network based wind power modelrdquo inProceedings of the European Wind Energy Conference pp 596ndash599 1996

[36] X Wang G Sideratos N Hatziargyriou and L H TsoukalasldquoWind speed forecasting for power system operational plan-ningrdquo in Proceedings of the International Conference on Proba-bilistic Methods Applied to Power Systems pp 470ndash474 Septem-ber 2004

[37] HMori andA Yuihara ldquoDeterministic annealing clustering forANN-based short-term load forecastingrdquo IEEE Transactions onPower Systems vol 16 no 3 pp 545ndash551 2001

[38] Z Xiao S-J Ye B Zhong and C-X Sun ldquoBP neural networkwith rough set for short term load forecastingrdquo Expert Systemswith Applications vol 36 no 1 pp 273ndash279 2009

[39] X Zhang W Yan and Z Bao ldquoShort-term load forecastingof power systems by combination of wavelet transform andAMPSO based neural networkrdquo Energy Procedia vol 13 pp6006ndash6016 2011

[40] A Badri Z Ameli and A Birjandi ldquoApplication of artificialneural networks and fuzzy logic methods for short termloadforecastingrdquo Energy Procedia vol 14 pp 1883ndash1888 2012

[41] D-X Niu H-F Shi andDDWu ldquoShort-term load forecastingusing bayesian neural networks learned byHybridMonte Carloalgorithmrdquo Applied Soft Computing Journal vol 12 no 6 pp1822ndash1827 2012

[42] H Y Yamin Q El-Dwairi and S M Shahidehpour ldquoAnew approach for GenCos profit based unit commitment inday-ahead competitive electricity markets considering reserveuncertaintyrdquo International Journal of Electrical Power amp EnergySystems vol 29 no 8 pp 609ndash616 2007

[43] G Mokryani and P Siano ldquoEvaluating the integration ofwind power into distribution networks by using monte carlosimulationrdquo International Journal of Electrical Power amp EnergySystems vol 53 pp 244ndash255 2013

[44] G Mokryani and P Siano ldquoCombined monte carlo simulationand OPF for wind turbines integration into distribution net-worksrdquoElectric Power SystemsResearch vol 103 pp 37ndash48 2013

[45] G Mokryani and P Siano ldquoOptimal wind turbines placementwithin a distribution market environmentrdquo Applied Soft Com-puting vol 13 no 10 pp 4038ndash4046 2013

[46] R Vautard and M Ghil ldquoSingular spectrum analysis in non-linear dynamics with applications to paleoclimatic time seriesrdquoPhysica D Nonlinear Phenomena vol 35 no 3 pp 395ndash4241989

[47] R Vautard P Yiou and M Ghil ldquoSingular-spectrum analysisa toolkit for short noisy chaotic signalsrdquo Physica D NonlinearPhenomena vol 58 no 1ndash4 pp 95ndash126 1992

[48] M de Carvalho P C Rodrigues and A Rua ldquoTracking theUS business cycle with a singular spectrum analysisrdquo EconomicsLetters vol 114 no 1 pp 32ndash35 2012


[49] H Hassani S Heravi and A Zhigljavsky ldquoForecasting Euro-pean industrial production with singular spectrum analysisrdquoInternational Journal of Forecasting vol 25 no 1 pp 103ndash1182009

[50] A D Papalexopoulos and T C Hesterberg ldquoA regression-based approach to short-term system load forecastingrdquo IEEETransactions on Power Systems vol 5 no 4 pp 1535ndash1547 1990

[51] W R Christiaanse ldquoShort term load forecasting using generalexponential smoothingrdquo IEEETransactions on Power ApparatusSystems vol 90 no 2 pp 900ndash911 1971

[52] S-J Huang and K-R Shih ldquoShort-term load forecasting viaARMA model identification including non-Gaussian processconsiderationsrdquo IEEETransactions on Power Systems vol 18 no2 pp 673ndash679 2003

[53] H M Al-Hamadi and S A Soliman ldquoShort-term electric loadforecasting based on Kalman filtering algorithm with movingwindow weather and load modelrdquo Electric Power SystemsResearch vol 68 no 1 pp 47ndash59 2004

[54] Z Guo W Zhao H Lu and J Wang ldquoMulti-step forecastingfor wind speed using a modified EMD-based artificial neuralnetwork modelrdquo Renewable Energy vol 37 no 1 pp 241ndash2492012

[55] Y Dong J Wang H Jiang and J Wu ldquoShort-term electricityprice forecast based on the improved hybrid modelrdquo EnergyConversion and Management vol 52 no 8-9 pp 2987ndash29952011

[56] A-O Boudraa and J-C Cexus ldquoEMD-based signal filteringrdquoIEEE Transactions on Instrumentation and Measurement vol56 no 6 pp 2196ndash2202 2007

[57] H Hassani ldquoSingular spectrum analysis methodology andcomparisonrdquo Journal of Data Science vol 5 pp 239ndash257 2007

[58] N Golyandina V Nekrutkin and A Zhigljavsky Analysis ofTime Series Structure SSA and Related Techniques Chapman ampHallCRC 2001

[59] N Golyandina and A Korobeynikov ldquoBasic singular spectrumanalysis and forecasting with Rrdquo Computational Statistics ampData Analysis vol 71 pp 934ndash954 2014

[60] M Claudio and S Rocco ldquoSingular spectrum analysis andforecasting of failure time seriesrdquo Reliability Engineering ampSystem Safety vol 114 pp 126ndash136 2013

[61] G Tzagkarakis M Papadopouli and P Tsakalides ldquoTrend fore-casting based on Singular SpectrumAnalysis of trafficworkloadin a large-scale wireless LANrdquo Performance Evaluation vol 66no 3-5 pp 173ndash190 2009

[62] C A F Marques J A Ferreira A Rocha et al ldquoSingularspectrum analysis and forecasting of hydrological time seriesrdquoPhysics and Chemistry of the Earth vol 31 no 18 pp 1172ndash11792006

[63] S M Sadjadi Weather Research and Forecasting Model 2 2Documentation A Step-by-step guide of a Model Run 2007

[64] K Afshar and N Bigdeli ldquoData analysis and short term loadforecasting in Iran electricity market using singular spectralanalysis (SSA)rdquo Energy vol 36 no 5 pp 2620ndash2627 2011

[65] G E P Box andG JenkinsTime Series Analysis Forecasting andControl Holden-Day San Francisco Calif USA 1970

[66] V Vapnik The Nature of Statistic Learning Theory SpringerNew York NY USA 1995

[67] P-F Pai and C-S Lin ldquoA hybrid ARIMA and support vectormachines model in stock price forecastingrdquo Omega vol 33 no6 pp 497ndash505 2005

[68] Z-H Guo J Wu H-Y Lu and J-Z Wang ldquoA case studyon a hybrid wind speed forecasting method using BP neuralnetworkrdquo Knowledge-Based Systems vol 24 no 7 pp 1048ndash1056 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Because of its economic and ecological advantages windpower has recently become one of the most popular alter-native energies accounting for approximately 10 of thenational power usage in European countries and this fig-ure exceeds 15 in Spain Germany and the USA [6]According to the GlobalWind Energy Council Report (2011)the worldrsquos wind power capacity grew by 225 in 2010adding 35802MW to bring total installations to 194390MWAlmost half of these additions were made in China whichexperienced an annual growth rate of approximately 65 [7]The worldrsquos total installed capacity of wind power reached254GW in June 2012 [8] However the main obstacle facingwind industry development is that wind is an intermittentenergy source which means that there is large variability inthe production of energy due to various factors such as windspeed air density and turbine characteristics Specificallyhorizontal air motion is defined as wind [9] and wind isdriven by uneven cooling and heating on the earthrsquos surfaceas well as the rotation of the earth Thus the occurrenceof wind has strong uncertainty in both space and timeThe nondeterminacy seriously limits wind power penetrationand threatens grid security Although wind power drives theturbines that generate electricity the complex fluctuations ofwind make it difficult to predict the power output The theo-retical amount of energy thatmight be generated fromwind isproportional to the cube of thewind speed and slight changesin the wind speed might cause significant changes in thetotal amount of electricity generated from the wind this alsocauses obstacles for power transportation [10] To guaranteethe security of the grid system the dispatching departmentmust balance the gridrsquos production and consumption withinvery small time intervals [11] Moreover due to the lack ofaccurate information about wind occurrence the efficiencyof wind turbines can also be limited [12] Several academicworks addressing wind energy attest to the increasing interestin this important theme

Generally there are two ways to solve this problemin wind power generation One is the large-scale transfor-mation of the existing electrical power system the mostpopular method is smart grid transformation which consistsof a digitally enabled power system [13] The core of asmart grid is the integration of secure and high-speed datacommunicationmdashbased on advanced computers electronicequipment intelligent components and moremdashto operatethe mixture system intelligently and effectively [14 15] Usingthe real-time information a smart grid can facilitate thedevelopment of wind power When wind-generated poweris insufficient other forms of energies can be used tosupplement power for a short time through a smart gridHowever currently there is no widely accepted standard-ized communicationnetwork infrastructure that could beapplied to power transformation through a smart grid [16]Another possible solution is to improve wind power tech-niques including wind-prediction techniques wind turbinetechniques wind energy storage techniques and combineddispatching Accurate wind information is important forestimating the wind power output Accurate estimations canbenefit not only increasing wind power penetration andmaintaining a stable grid system but also the combined

dispatching in a mixture power grid Under current electricalsystems developing wind-prediction techniques can be aneffective way to guarantee the security and stability of theelectrical system without increasing the running cost

In the past decades many approaches have been devel-oped for short-term load forecasting These methods can becategorized into different groups Some of these methodsassume a time series model structure and then try toidentify its parameters In actual power generation windpredictionsmdashespecially the short-term forecastsmdashare impor-tant for scheduling controlling and dispatching the energyconversion systems [17] The most important characteristicof windmdashspeedmdashcan be easily influenced by other meteoro-logical factors such as air temperature and air pressure aswell as obstacles and terrain [18]Thus wind speed predictionis not easy to address moreover wind speed modelinghas become one of the most difficult problems [19 20]The forecasting approach can be determined based on theavailable information and the time scale in question whichwill affect its application Short-term wind speed forecastingis a subclass of wind speed forecasting The time scales forshort-term forecasting range from a few seconds to minuteshours or several days [21]

Many methods of forecasting wind speed have been pro-posed In general they can be classified into two categoriesphysical methods and statistical methods

Physical methods are often referred to as meteorolog-ical predictions of wind speed they involve the numer-ical approximation of models that describe the state ofthe atmosphere [22] Numerical weather prediction (NWP)techniques one type of physical model-based approach relyon a class of physical models with numerical parameterscharacterizing local meteorological and geographical prop-erties such as temperature atmospheric pressure surfaceroughness and obstacles [23] NWP techniques include theweather research and forecasting (WRF) model and the fifthgeneration mesoscale model (MM5) These models alwaysuse physical data such as topography information pressureand temperature to forecast wind speed in the future [24 25]Typically prediction methods using NWP forecasts outper-form statistical approaches after a 3ndash6 h look-ahead timewhereas statistical approaches turn out to be quite reliable forvery short-term forecasts that is less than 6 h The optimalmodel most likely consists of a mixed approach which isvery often adopted by utilities to combine high accuracyfor very short horizons with longer forecasts of up to 48ndash72 h [26] Unlike physical models statistical methods makeforecasts by finding relationships using historical wind speeddata and sometimes other variables (eg wind direction ortemperature) The data used are recorded at the observationsite or at other nearby locations where data are available Inthe literature many statistical methods have been appliedto this topic such as the autoregressive integrated movingaverage (ARIMA) model Kalman filters and the general-ized autoregressive conditional heteroscedasticity (GARCH)model The statistical models can be used at any stage in themodeling process and they often combine various methodsinto one Physical and statistical models each have their ownadvantages for wind speed prediction but few forecasts use











Wm2150sim200Wm2

50sim100

Wm2100sim50











1125∘E 1150∘E 1175∘E 1200∘E 1225∘E

400∘N

375∘N

350∘N

325∘N









119879= (1199101 1199102 119910

119879) of








119879= (1199101

1199102 119910


1 1198832

119883119870with vectors 119883

119894= (119910119894 119910119894+1 119910

119894+119871minus1)1015840




119883 = [1198831 1198832 119883

119870] = (

1199101

1199102


1199102

1199103


d

119910119871119910119871+1


) (1)




119871ge 0 and




1+1198642+ sdot sdot sdot +119864

119889

where 119864119894= radic120582

119894119880119894119881119894


1 1198812 119881





119883 If Γ = sum119889119894=1










1 1198942 119894

119903 be a group of 119903-


+ 1198831198942

sdot sdot sdot + 119883119894119903

where 119883119894is



1198941

1198831198942

119883119894119903


1198941

1199101198942

119910119894119903


119894119895 then 119894 + 119895 = 119896 + 1 Thus119867(119885) is



05

1015

2025

30 0 10 20 3040 50 60 70 80 90

100

0

4

8

12

16

HoursDays

Win

d sp

eed

(ms

)



119910 = 119867(1198831198941

) + 119867(1198831198942

) + sdot sdot sdot + 119867 (119883119894119903

) + 119890 (2)











MAE = 1

119879

119879

sum

119905=1

1003816100381610038161003816119910119905 minus 1198911199051003816100381610038161003816


119879

sum

119905=1

(119910119905minus 119891119905)2

MAPE = 1

119879

119879

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910119905minus 119891119905

119910119905

10038161003816100381610038161003816100381610038161003816

(3)

where 119910119905and 119891





0 50 1000

5

10

PC1

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

minus2

0

2

PC2

minus2

0

2

4

PC3

minus1

0

1

PC4

minus1

0

1

PC5

minus2

minus1

0

1

PC6

minus1

0

1

minus1

0

1

minus1

0

1

PC7

minus02

0

02

PC8

minus05

0

05

PC9

PC10

minus02

0

02

minus02

0

02

PC11

PC12

PC13

PC14

PC15

minus01

0

01

PC16

minus005

0

005

minus005

0

005

PC17

PC18

PC19

PC20

minus05

0

05

minus01

0

01

minus01

0

01

minus01

0

01


0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

minus05

0

05

minus1

0

1

2

minus05

0

05

MA

PE

Positive

Negative

MA

PEM

APE






Decomposition

Originalpredictions

W1

W2

Wn

T1

T2

Tn

H1

H2

Hn

P1

P2

Pn

Principalcomponents

Positivecomponents

Negativecomponents

NN

SVM

ARIMA

Reconstruction

Wi1

Wi2

Wir

Ti1

Ti2

Tir

Hi1

Hi2

Hir

Pi1

Pi2

Pir








119901119910119905minus119901+ 119890119905 (4)









represented as

119910119905= 120583 minus 120579


119902119890119905minus119902+ 119890119905 (5)



119902






119901119910119905minus119901+ 120583


119902119890119905minus119902+ 119890119905

(6)



119910 = 119908120593 (119909) + 119887 (7)


119877 (119862) = 1198621

119873

119873

sum

119894=1

119871120576(119889119894 119910119894) +

1

21199082

[0 1]

119871120576(119889 119910) =

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 ge 120576

0 others

(8)



119894


119873

119894=1



119877 (119908 120577 120577lowast

) =1

2119908119908119879

+ 119862lowast

(

119873

sum

119894=1

(120577119894+ 120577lowast

119894

)) (9)

subject to

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120577

lowast

119894

119889119894minus 119908120593 (119909

119894) minus 119887119894le 120576 + 120577

119894

120577119894 120577lowast

119894

ge 0 119894 = 1 2 119870119873

(10)


119891 (119909 120572 120572lowast

) =

119897

sum

119894=1

(120572119894minus 120572lowast

119894

)119870 (119909 119909119894) + 119887 (11)



119895


119895) such that 119870(119909

119894 119909119895) =

120593(119909119894) lowast 120593(119909




ℎ119894= 119891(119887

119894+

119899

sum

119895=1

119908119894119895119909119895) (12)


119894119895to hidden

unit ℎ119894


119910 = 119891output

(119887 +

119899

sum

119895=1

119908119895119909119895) (13)







Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ








Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata


Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space


WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)


ARIMAoptimization

SVMoptimization

NNoptimization
















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Wm2150sim200Wm2

50sim100

Wm2100sim50











1125∘E 1150∘E 1175∘E 1200∘E 1225∘E

400∘N

375∘N

350∘N

325∘N









119879= (1199101 1199102 119910

119879) of








119879= (1199101

1199102 119910


1 1198832

119883119870with vectors 119883

119894= (119910119894 119910119894+1 119910

119894+119871minus1)1015840




119883 = [1198831 1198832 119883

119870] = (

1199101

1199102


1199102

1199103


d

119910119871119910119871+1


) (1)




119871ge 0 and




1+1198642+ sdot sdot sdot +119864

119889

where 119864119894= radic120582

119894119880119894119881119894


1 1198812 119881





119883 If Γ = sum119889119894=1










1 1198942 119894

119903 be a group of 119903-


+ 1198831198942

sdot sdot sdot + 119883119894119903

where 119883119894is



1198941

1198831198942

119883119894119903


1198941

1199101198942

119910119894119903


119894119895 then 119894 + 119895 = 119896 + 1 Thus119867(119885) is



05

1015

2025

30 0 10 20 3040 50 60 70 80 90

100

0

4

8

12

16

HoursDays

Win

d sp

eed

(ms

)



119910 = 119867(1198831198941

) + 119867(1198831198942

) + sdot sdot sdot + 119867 (119883119894119903

) + 119890 (2)











MAE = 1

119879

119879

sum

119905=1

1003816100381610038161003816119910119905 minus 1198911199051003816100381610038161003816


119879

sum

119905=1

(119910119905minus 119891119905)2

MAPE = 1

119879

119879

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910119905minus 119891119905

119910119905

10038161003816100381610038161003816100381610038161003816

(3)

where 119910119905and 119891





0 50 1000

5

10

PC1

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

minus2

0

2

PC2

minus2

0

2

4

PC3

minus1

0

1

PC4

minus1

0

1

PC5

minus2

minus1

0

1

PC6

minus1

0

1

minus1

0

1

minus1

0

1

PC7

minus02

0

02

PC8

minus05

0

05

PC9

PC10

minus02

0

02

minus02

0

02

PC11

PC12

PC13

PC14

PC15

minus01

0

01

PC16

minus005

0

005

minus005

0

005

PC17

PC18

PC19

PC20

minus05

0

05

minus01

0

01

minus01

0

01

minus01

0

01


0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

minus05

0

05

minus1

0

1

2

minus05

0

05

MA

PE

Positive

Negative

MA

PEM

APE






Decomposition

Originalpredictions

W1

W2

Wn

T1

T2

Tn

H1

H2

Hn

P1

P2

Pn

Principalcomponents

Positivecomponents

Negativecomponents

NN

SVM

ARIMA

Reconstruction

Wi1

Wi2

Wir

Ti1

Ti2

Tir

Hi1

Hi2

Hir

Pi1

Pi2

Pir








119901119910119905minus119901+ 119890119905 (4)









represented as

119910119905= 120583 minus 120579


119902119890119905minus119902+ 119890119905 (5)



119902






119901119910119905minus119901+ 120583


119902119890119905minus119902+ 119890119905

(6)



119910 = 119908120593 (119909) + 119887 (7)


119877 (119862) = 1198621

119873

119873

sum

119894=1

119871120576(119889119894 119910119894) +

1

21199082

[0 1]

119871120576(119889 119910) =

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 ge 120576

0 others

(8)



119894


119873

119894=1



119877 (119908 120577 120577lowast

) =1

2119908119908119879

+ 119862lowast

(

119873

sum

119894=1

(120577119894+ 120577lowast

119894

)) (9)

subject to

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120577

lowast

119894

119889119894minus 119908120593 (119909

119894) minus 119887119894le 120576 + 120577

119894

120577119894 120577lowast

119894

ge 0 119894 = 1 2 119870119873

(10)


119891 (119909 120572 120572lowast

) =

119897

sum

119894=1

(120572119894minus 120572lowast

119894

)119870 (119909 119909119894) + 119887 (11)



119895


119895) such that 119870(119909

119894 119909119895) =

120593(119909119894) lowast 120593(119909




ℎ119894= 119891(119887

119894+

119899

sum

119895=1

119908119894119895119909119895) (12)


119894119895to hidden

unit ℎ119894


119910 = 119891output

(119887 +

119899

sum

119895=1

119908119895119909119895) (13)







Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ








Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata


Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space


WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)


ARIMAoptimization

SVMoptimization

NNoptimization
















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1125∘E 1150∘E 1175∘E 1200∘E 1225∘E

400∘N

375∘N

350∘N

325∘N









119879= (1199101 1199102 119910

119879) of








119879= (1199101

1199102 119910


1 1198832

119883119870with vectors 119883

119894= (119910119894 119910119894+1 119910

119894+119871minus1)1015840




119883 = [1198831 1198832 119883

119870] = (

1199101

1199102


1199102

1199103


d

119910119871119910119871+1


) (1)




119871ge 0 and




1+1198642+ sdot sdot sdot +119864

119889

where 119864119894= radic120582

119894119880119894119881119894


1 1198812 119881





119883 If Γ = sum119889119894=1










1 1198942 119894

119903 be a group of 119903-


+ 1198831198942

sdot sdot sdot + 119883119894119903

where 119883119894is



1198941

1198831198942

119883119894119903


1198941

1199101198942

119910119894119903


119894119895 then 119894 + 119895 = 119896 + 1 Thus119867(119885) is



05

1015

2025

30 0 10 20 3040 50 60 70 80 90

100

0

4

8

12

16

HoursDays

Win

d sp

eed

(ms

)



119910 = 119867(1198831198941

) + 119867(1198831198942

) + sdot sdot sdot + 119867 (119883119894119903

) + 119890 (2)











MAE = 1

119879

119879

sum

119905=1

1003816100381610038161003816119910119905 minus 1198911199051003816100381610038161003816


119879

sum

119905=1

(119910119905minus 119891119905)2

MAPE = 1

119879

119879

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910119905minus 119891119905

119910119905

10038161003816100381610038161003816100381610038161003816

(3)

where 119910119905and 119891





0 50 1000

5

10

PC1

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

minus2

0

2

PC2

minus2

0

2

4

PC3

minus1

0

1

PC4

minus1

0

1

PC5

minus2

minus1

0

1

PC6

minus1

0

1

minus1

0

1

minus1

0

1

PC7

minus02

0

02

PC8

minus05

0

05

PC9

PC10

minus02

0

02

minus02

0

02

PC11

PC12

PC13

PC14

PC15

minus01

0

01

PC16

minus005

0

005

minus005

0

005

PC17

PC18

PC19

PC20

minus05

0

05

minus01

0

01

minus01

0

01

minus01

0

01


0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

minus05

0

05

minus1

0

1

2

minus05

0

05

MA

PE

Positive

Negative

MA

PEM

APE






Decomposition

Originalpredictions

W1

W2

Wn

T1

T2

Tn

H1

H2

Hn

P1

P2

Pn

Principalcomponents

Positivecomponents

Negativecomponents

NN

SVM

ARIMA

Reconstruction

Wi1

Wi2

Wir

Ti1

Ti2

Tir

Hi1

Hi2

Hir

Pi1

Pi2

Pir








119901119910119905minus119901+ 119890119905 (4)









represented as

119910119905= 120583 minus 120579


119902119890119905minus119902+ 119890119905 (5)



119902






119901119910119905minus119901+ 120583


119902119890119905minus119902+ 119890119905

(6)



119910 = 119908120593 (119909) + 119887 (7)


119877 (119862) = 1198621

119873

119873

sum

119894=1

119871120576(119889119894 119910119894) +

1

21199082

[0 1]

119871120576(119889 119910) =

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 ge 120576

0 others

(8)



119894


119873

119894=1



119877 (119908 120577 120577lowast

) =1

2119908119908119879

+ 119862lowast

(

119873

sum

119894=1

(120577119894+ 120577lowast

119894

)) (9)

subject to

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120577

lowast

119894

119889119894minus 119908120593 (119909

119894) minus 119887119894le 120576 + 120577

119894

120577119894 120577lowast

119894

ge 0 119894 = 1 2 119870119873

(10)


119891 (119909 120572 120572lowast

) =

119897

sum

119894=1

(120572119894minus 120572lowast

119894

)119870 (119909 119909119894) + 119887 (11)



119895


119895) such that 119870(119909

119894 119909119895) =

120593(119909119894) lowast 120593(119909




ℎ119894= 119891(119887

119894+

119899

sum

119895=1

119908119894119895119909119895) (12)


119894119895to hidden

unit ℎ119894


119910 = 119891output

(119887 +

119899

sum

119895=1

119908119895119909119895) (13)







Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ








Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata


Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space


WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)


ARIMAoptimization

SVMoptimization

NNoptimization
















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










05

1015

2025

30 0 10 20 3040 50 60 70 80 90

100

0

4

8

12

16

HoursDays

Win

d sp

eed

(ms

)



119910 = 119867(1198831198941

) + 119867(1198831198942

) + sdot sdot sdot + 119867 (119883119894119903

) + 119890 (2)











MAE = 1

119879

119879

sum

119905=1

1003816100381610038161003816119910119905 minus 1198911199051003816100381610038161003816


119879

sum

119905=1

(119910119905minus 119891119905)2

MAPE = 1

119879

119879

sum

119905=1

10038161003816100381610038161003816100381610038161003816

119910119905minus 119891119905

119910119905

10038161003816100381610038161003816100381610038161003816

(3)

where 119910119905and 119891





0 50 1000

5

10

PC1

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

minus2

0

2

PC2

minus2

0

2

4

PC3

minus1

0

1

PC4

minus1

0

1

PC5

minus2

minus1

0

1

PC6

minus1

0

1

minus1

0

1

minus1

0

1

PC7

minus02

0

02

PC8

minus05

0

05

PC9

PC10

minus02

0

02

minus02

0

02

PC11

PC12

PC13

PC14

PC15

minus01

0

01

PC16

minus005

0

005

minus005

0

005

PC17

PC18

PC19

PC20

minus05

0

05

minus01

0

01

minus01

0

01

minus01

0

01


0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

minus05

0

05

minus1

0

1

2

minus05

0

05

MA

PE

Positive

Negative

MA

PEM

APE






Decomposition

Originalpredictions

W1

W2

Wn

T1

T2

Tn

H1

H2

Hn

P1

P2

Pn

Principalcomponents

Positivecomponents

Negativecomponents

NN

SVM

ARIMA

Reconstruction

Wi1

Wi2

Wir

Ti1

Ti2

Tir

Hi1

Hi2

Hir

Pi1

Pi2

Pir








119901119910119905minus119901+ 119890119905 (4)









represented as

119910119905= 120583 minus 120579


119902119890119905minus119902+ 119890119905 (5)



119902






119901119910119905minus119901+ 120583


119902119890119905minus119902+ 119890119905

(6)



119910 = 119908120593 (119909) + 119887 (7)


119877 (119862) = 1198621

119873

119873

sum

119894=1

119871120576(119889119894 119910119894) +

1

21199082

[0 1]

119871120576(119889 119910) =

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 ge 120576

0 others

(8)



119894


119873

119894=1



119877 (119908 120577 120577lowast

) =1

2119908119908119879

+ 119862lowast

(

119873

sum

119894=1

(120577119894+ 120577lowast

119894

)) (9)

subject to

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120577

lowast

119894

119889119894minus 119908120593 (119909

119894) minus 119887119894le 120576 + 120577

119894

120577119894 120577lowast

119894

ge 0 119894 = 1 2 119870119873

(10)


119891 (119909 120572 120572lowast

) =

119897

sum

119894=1

(120572119894minus 120572lowast

119894

)119870 (119909 119909119894) + 119887 (11)



119895


119895) such that 119870(119909

119894 119909119895) =

120593(119909119894) lowast 120593(119909




ℎ119894= 119891(119887

119894+

119899

sum

119895=1

119908119894119895119909119895) (12)


119894119895to hidden

unit ℎ119894


119910 = 119891output

(119887 +

119899

sum

119895=1

119908119895119909119895) (13)







Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ








Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata


Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space


WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)


ARIMAoptimization

SVMoptimization

NNoptimization
















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 50 1000

5

10

PC1

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours0 50 100

Hours

minus2

0

2

PC2

minus2

0

2

4

PC3

minus1

0

1

PC4

minus1

0

1

PC5

minus2

minus1

0

1

PC6

minus1

0

1

minus1

0

1

minus1

0

1

PC7

minus02

0

02

PC8

minus05

0

05

PC9

PC10

minus02

0

02

minus02

0

02

PC11

PC12

PC13

PC14

PC15

minus01

0

01

PC16

minus005

0

005

minus005

0

005

PC17

PC18

PC19

PC20

minus05

0

05

minus01

0

01

minus01

0

01

minus01

0

01


0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

0 2 4 6 8 10 12 14 16 18 20

minus05

0

05

minus1

0

1

2

minus05

0

05

MA

PE

Positive

Negative

MA

PEM

APE






Decomposition

Originalpredictions

W1

W2

Wn

T1

T2

Tn

H1

H2

Hn

P1

P2

Pn

Principalcomponents

Positivecomponents

Negativecomponents

NN

SVM

ARIMA

Reconstruction

Wi1

Wi2

Wir

Ti1

Ti2

Tir

Hi1

Hi2

Hir

Pi1

Pi2

Pir








119901119910119905minus119901+ 119890119905 (4)









represented as

119910119905= 120583 minus 120579


119902119890119905minus119902+ 119890119905 (5)



119902






119901119910119905minus119901+ 120583


119902119890119905minus119902+ 119890119905

(6)



119910 = 119908120593 (119909) + 119887 (7)


119877 (119862) = 1198621

119873

119873

sum

119894=1

119871120576(119889119894 119910119894) +

1

21199082

[0 1]

119871120576(119889 119910) =

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 ge 120576

0 others

(8)



119894


119873

119894=1



119877 (119908 120577 120577lowast

) =1

2119908119908119879

+ 119862lowast

(

119873

sum

119894=1

(120577119894+ 120577lowast

119894

)) (9)

subject to

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120577

lowast

119894

119889119894minus 119908120593 (119909

119894) minus 119887119894le 120576 + 120577

119894

120577119894 120577lowast

119894

ge 0 119894 = 1 2 119870119873

(10)


119891 (119909 120572 120572lowast

) =

119897

sum

119894=1

(120572119894minus 120572lowast

119894

)119870 (119909 119909119894) + 119887 (11)



119895


119895) such that 119870(119909

119894 119909119895) =

120593(119909119894) lowast 120593(119909




ℎ119894= 119891(119887

119894+

119899

sum

119895=1

119908119894119895119909119895) (12)


119894119895to hidden

unit ℎ119894


119910 = 119891output

(119887 +

119899

sum

119895=1

119908119895119909119895) (13)







Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ








Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata


Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space


WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)


ARIMAoptimization

SVMoptimization

NNoptimization
















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Decomposition

Originalpredictions

W1

W2

Wn

T1

T2

Tn

H1

H2

Hn

P1

P2

Pn

Principalcomponents

Positivecomponents

Negativecomponents

NN

SVM

ARIMA

Reconstruction

Wi1

Wi2

Wir

Ti1

Ti2

Tir

Hi1

Hi2

Hir

Pi1

Pi2

Pir








119901119910119905minus119901+ 119890119905 (4)









represented as

119910119905= 120583 minus 120579


119902119890119905minus119902+ 119890119905 (5)



119902






119901119910119905minus119901+ 120583


119902119890119905minus119902+ 119890119905

(6)



119910 = 119908120593 (119909) + 119887 (7)


119877 (119862) = 1198621

119873

119873

sum

119894=1

119871120576(119889119894 119910119894) +

1

21199082

[0 1]

119871120576(119889 119910) =

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 ge 120576

0 others

(8)



119894


119873

119894=1



119877 (119908 120577 120577lowast

) =1

2119908119908119879

+ 119862lowast

(

119873

sum

119894=1

(120577119894+ 120577lowast

119894

)) (9)

subject to

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120577

lowast

119894

119889119894minus 119908120593 (119909

119894) minus 119887119894le 120576 + 120577

119894

120577119894 120577lowast

119894

ge 0 119894 = 1 2 119870119873

(10)


119891 (119909 120572 120572lowast

) =

119897

sum

119894=1

(120572119894minus 120572lowast

119894

)119870 (119909 119909119894) + 119887 (11)



119895


119895) such that 119870(119909

119894 119909119895) =

120593(119909119894) lowast 120593(119909




ℎ119894= 119891(119887

119894+

119899

sum

119895=1

119908119894119895119909119895) (12)


119894119895to hidden

unit ℎ119894


119910 = 119891output

(119887 +

119899

sum

119895=1

119908119895119909119895) (13)







Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ








Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata


Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space


WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)


ARIMAoptimization

SVMoptimization

NNoptimization
















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119902






119901119910119905minus119901+ 120583


119902119890119905minus119902+ 119890119905

(6)



119910 = 119908120593 (119909) + 119887 (7)


119877 (119862) = 1198621

119873

119873

sum

119894=1

119871120576(119889119894 119910119894) +

1

21199082

[0 1]

119871120576(119889 119910) =

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 minus 120576

1003816100381610038161003816119889 minus 1199101003816100381610038161003816 ge 120576

0 others

(8)



119894


119873

119894=1



119877 (119908 120577 120577lowast

) =1

2119908119908119879

+ 119862lowast

(

119873

sum

119894=1

(120577119894+ 120577lowast

119894

)) (9)

subject to

119908120593 (119909119894) + 119887119894minus 119889119894le 120576 + 120577

lowast

119894

119889119894minus 119908120593 (119909

119894) minus 119887119894le 120576 + 120577

119894

120577119894 120577lowast

119894

ge 0 119894 = 1 2 119870119873

(10)


119891 (119909 120572 120572lowast

) =

119897

sum

119894=1

(120572119894minus 120572lowast

119894

)119870 (119909 119909119894) + 119887 (11)



119895


119895) such that 119870(119909

119894 119909119895) =

120593(119909119894) lowast 120593(119909




ℎ119894= 119891(119887

119894+

119899

sum

119895=1

119908119894119895119909119895) (12)


119894119895to hidden

unit ℎ119894


119910 = 119891output

(119887 +

119899

sum

119895=1

119908119895119909119895) (13)







Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ








Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata


Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space


WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)


ARIMAoptimization

SVMoptimization

NNoptimization
















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ





Wind farmA

Wind farmB

Wind farmC

Wind farmD

Wind farmE

Wind farmF

Wind farmG

Wind farmH

Wind farmI

Wind farmJ








Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata


Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space


WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)


ARIMAoptimization

SVMoptimization

NNoptimization
















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Wind speed

Temperature

Pressure

Humidity

WRF

Initial data

NN

Forecastingdata


Forecastingdata

Forecastingdata

SVM

Inputspace

Feature

y

O x

y

O x

ARIMA

Stationary

Diff

ACF and PACF

Estimated parameter

Examine

Observed data

Windfarm

space


WF-

A

WF-

B

WF-

C

WF-

D

WF-

E

WF-

F

WF-

G

WF-

H

WF-

I

WF-

J

0

5

10

15

Wind farms

Root

mea

n sq

uare

erro

r (RM

SE)


ARIMAoptimization

SVMoptimization

NNoptimization
















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















Acknowledgments


References














































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra








































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Hybrid Wind Speed Forecasting Model Study...

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Transcript of Research Article Hybrid Wind Speed Forecasting Model Study...