Very Short-Term Load Forecasting Using a Hybrid Neuro-Fuzzy Approach

Luciano Carli Moreira de Andrade Ivan Nunes da Silva Electrical Engineering Department

University of São Paulo São Carlos, Brazil

Electrical Engineering Department University of São Paulo

São Carlos, Brazil lucarli@sc.usp.br insilva@sc.usp.br

Abstract Abstract— The purpose of this work is to employ the Adaptive Neuro Fuzzy Inference System for performing very short-term load forecasting in power distribution substations, which can enable the development of more efficient automatic load control of electrical power load systems. The system inputs are two load demand time series, composed of data measured in five minutes intervals up to seven days from substations located in the cities of Cordeirópolis and Ubatuba – SP, Brazil. The Adaptive Neuro Fuzzy Inference System is a universal approximator that can be used in function approximation and forecasting. The results of the Adaptive Neuro Fuzzy Inference System in this paper are promising, where the average MAPE of Cordeirópolis was 0.7264% and of Ubatuba was 0.5163%.

Fuzzy neural networks; intelligent systems; load forecasting; power generation control; time series.

I. INTRODUCTION The introduction of deregulation in the electricity

industry made the accurate load demand forecasting become the most important object of the investments in the distribution system market, power planning and management strategies of national and international systems. Non accurate forecasting can increase the operational costs. The load demand overestimation results in an unnecessary spinning reserve. Moreover, the underestimation can cause supply disruption [1].

There are different approaches regarding a load demand forecasting. The forecasting horizons can cover some minutes to several years or decades. There are particular aims regarding each one of such horizons, which divided the load demand forecasting into long term forecasting, medium term forecasting, short term forecasting and very short term load forecasting.

The long term load forecasting has years or decades as horizons and it has the purpose to provide the demand evolution to producers and distributors, which allows the definition of strategies to increase the distribution lines capacity and to build new production plants.

The medium term forecasting has some weeks or months as horizon and its purpose is to allow the electrical grid maintenance planning, to schedule the purchase of fuel and serve as market research for the producers and resellers to negotiate contracts with other companies, decreasing the financial risks [2].

The short term forecasting is the most studied horizon regarding load demand forecasting and it has some hours as horizon. Many decisions can be taken based on accurate short term forecasting, like reliability analysis, safety evaluation, generators maintenance schedule, etc.

The last forecasting horizon and also focus of this work is the very short term horizon, i.e., some minutes ahead forecasting.

Power system generators attempt to regulate demand and supply of electricity to minimize fluctuations, adjusting the power generation to the frequent changes, i.e., it is imperative to make accurate forecasting minutes ahead in order to avoid undesirable disturbances involving power systems [3-4].

To meet this goal, it has to apply an efficient automatic control of power generation. It has to frequently update the energy generation based on samples obtained from the load and frequency power system itself. In typical systems, the control rate varies from one to ten minutes frequencies.

The load frequency control and economic dispatch functions also require forecasting from some to several minutes ahead. Very short term forecasting integrated with information about scheduled electrical power transactions, transmission availability, generation costs, the stock market prices and spinning reserve requirements are used to determine the best strategy of the utilities[5].

Very short term load demand forecasting requires an approach where the focus is the analyses of the measurements behavior recently observed to forecast the near future. Unlike the approaches applied in further horizons, where information of facts that affect the demand behavior, such as weather conditions, time etc. are ought to be extracted.

For such purpose, the studied time series are presented in Section II. Section III presents ANFIS tool aspects

2010 Eleventh Brazilian Symposium on Neural Networks

978-0-7695-4210-2/10 $26.00 © 2010 IEEE

DOI 10.1109/SBRN.2010.28

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applied in the load forecasting of this paper. In the section IV, the methodology to determine the best ANFIS architecture is described. In Section V the results are presented, and in Section VI the paper conclusion is presented.

II. TIME SERIES The load demand time series used in this paper were

measured during seven days, in five minutes intervals, from substations located in Cordeirópolis and Ubatuba, cities located at the countryside and seaside of São Paulo state, respectively. Figure 1 presents the time series graphics.

Figure 1. Time Series measured from substations located in Ubatuba and Cordeirópolis.

It can be concluded that the time series from Ubatuba

has evident seasonal behavior, i.e., the energy consumption is low around 1AM (the first hours of dawn), it increases during the morning until its first fall around 1PM (beginning of the evening). It increases again and reaches the maximum peak around 7PM (beginning of the night). After such peak, during the dusk, the consumption decreases until it reaches its minimum value around 1AM (during the dawn).

The Cordeirópolis time series presents seasonal behavior with low and high peaks, but with variations during the week days. The consumption is lower on Monday and Tuesday than on the other week days and in the weekend, its behavior presents the domestic energy consumption in that city.

III. ASPECTS OF ANFIS In this Section some aspects of ANFIS (Adaptive

Network based Fuzzy Inference System) are presented, a fuzzy inference system implemented with the adaptive networks framework. By using a hybrid learning procedure, ANFIS can build an input-output mapping based on human knowledge (as “if-then” rules) or in certain input-output pairs. ANFIS can be used, among other applications, in the modeling of nonlinear functions, in the identification of on-line components of a control system and time series forecasting, where the last one is the objective of this work.

Therefore, ANFIS is an architecture that will build a fuzzy set of rules “if-then” with appropriate membership functions to generate certain input-output pairs. Functionally, there are almost no restrictions regarding adaptive network functions, except that they are differentiable.

Regarding its structure, the only limitation in the network configuration is that it has to be the feedforward type. Due to these minimal restrictions, the adaptive networks are inserted in several areas.

ANFIS is a class of adaptive network that is functionally equivalent to a fuzzy inference system [6, 7].

A. ANFIS architecture For simplicity, the considered fuzzy inference system has

two inputs x and y and one output z. For a first order Sugeno model, a typical set of rules with two rules “if-then” can be presented as:

Rule 1: If x is A1 and y is B1 then 1111 ryqxpf ++=

Rule 2: If x is A2 and y is B2 then 2222 ryqxpf ++=

Figure 2 shows the mechanism of reasoning for this

Sugeno model [6, 7].

Figure 2. Reasoning mechanism for this Sugeno model [6, 7].

The related ANFIS architecture is depicted in Figure 3,

where the nodes in the same layer have the same functions (the output node i of the layer l is denoted as Ol,i)

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Figure 3. Equivalent ANFIS architecture [6, 7].

Layer 1: each node i of this layer is one adaptive node with the output defined by [6, 7]:

),(. xO Aiil μ= For i=1,2, ou (1)

),(2, yO Biil −= μ For i=3,4

where x (or y) is the node input and Ai (or Bi-2) is the associated fuzzy set of this node. In other words, this layer outputs are the values of the membership functions of the previous portion. For example, Ai can be expressed by the generalized bell membership function:

ib

i

i

Ai

acx

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −+

=2

1

1μ (2)

where ai is half the width of the membership function, bi controls the slope in the point where the membership function is equal to 0.5 and ci determines the center of the membership function. Layer 2: Each node of this layer is fixed and labeled by II, which multiplies the input signals and presents the result as output [6, 7]. For Example:

.2,1),()(,2 =×== iyxwO BiAiii μμ (3)

Each output node represents the firing strength of a rule (in fact, any other t-norm operator that performs generalized AND fuzzy can be used as node function in this layer).

Layer 3: Each node of this layer is labeled N. The i-th node calculates the ratio between the activation of the i-th rule for the activation of all rules [4, 5].

.2,1,21

,3 =+

== iww

wwO iii (4)

For convenience, the outputs of this layer will be called

normalized firing strengths. Layer 4: Each node i in this layer is a square node with a node function:

)(,4 iiiiiii ryqxpwfwO ++== (5)

where iw is the output of the layer 3 and { iii rqp ,, } is the parameter set. The parameters of this layer will be referred to as consequent parameters. Layer 5: The single node of this layer, labeled Σ, calculates the overall output as the sum of all input signals [4, 5].

∑∑

∑ ==

ii

iii

iiil w

fwfwO ,5 (6)

So, an adaptive network was built that has exactly the

same function of the Sugeno fuzzy model depicted by Figure 2 [6, 7].

IV. METHODOLOGY AND BEST ARCHITECTURE

A. Methodology The methodology used to determine the best ANFIS

architecture was the cross validation and, in this work, it occurred as described by the flowchart depicted in Figure 4 and by the following steps:

• Data normalization between -1 and 1. • Data splitting in sets of training, validation and test

according to the proportion of 5 days for training, 1 day for validation and 1 day for tests.

• Determination of the best input-output patterns. • Determination of the number of membership

functions. • Choice of the best input and output membership

functions. • Determination of the best optimization method. • Determination of the best number of epochs.

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Figure 4. Flowchart of the methodology used in this work.

The several architectures were evaluated by using MAPE

(Mean Average Percentage Error) calculated on the test set, i.e.:

%10011

×−

= ∑=

N

i i

ii

dod

NMAPE (7)

where di is the desired output, oi is the system output and N is the number of the test patterns.

B. The best architecture At the end of the cross validation process, the best

performance architecture (the lowest MAPE) was the following:

• Three inputs formed by two measures immediately

prior to the measure to be forecasted, plus one measure of the previous day at the same time of the forecasting measure.

• Three input generalized bell membership functions and one constant output membership function.

• Hybrid optimization method. • The number of training epochs necessary to adjust

ANFIS was 150 epochs.

V. RESULTS The purpose of this work is to present the use of ANFIS

in very short term load demand forecasting, to regulate the demand and supply of electrical energy in order to minimize the fluctuations and to avoid undesirable disturbances in power systems operations.

In order to do so, time series measured, in five minutes intervals, during seven days (beginning on Monday and finishing on Sunday), were studied. They were collected from substations located in Cordeirópolis and Ubatuba, cities located in the countryside and seaside of São Paulo state, respectively.

As soon as the best architecture was determined through cross validation (the lowest MAPE), the training curves were drawn, the MAPE of three distinct training was tabulated and their average calculated, also histograms with the distribution of relative errors for each one of the measures that are part of the test set were made. As presented in Section IV, the maximum number of epochs was 150, since a higher number of epochs didn’t present better performance of ANFIS.

A. Graphic and histogram of Cordeirópolis Figure 5 depicts the training and validation data curves

of Cordeirópolis city. As it can be seen, its learning curve presents a sharp drop in the error. Another interesting factor is that the training and validation errors converge to very similar values. Oscillations do not occur in the training and validation curves during the training process.

Figure 5. Training curve of Cordeirópolis.

Figure 6 presents the load curves in MW, measured load

curve (dashed blue) and forecasted load curve (solid red), of the data that are part of the test set (the last day). It can be seen that the behavior of the series are very similar and that, in just a small stretch, there is a slightly distinct behavior. With the aid of the histogram of Figure 7 the errors distribution and its value in the worst cases can be verified.

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The histogram of Figure 7, as previously mentioned,

presents the distribution of the relative errors for each one of the measures that form the test set. It can be seen that the errors are mostly lower than 1% and that, in the worst case, the obtained error was lower than 6%.

Figure 7. Histogram of the relative errors of Cordeirópolis.

Table 1 also indicates the good performance of ANFIS

to the load demand time series measured in the Cordeirópolis substation. It can be verified through the Table that the ANFIS was trained three times and it presents a MAPE about 0.72% and variance about 1.46x10-4 for the three cases, consequently, an average MAPE about the same value. It’s important to remembering that the forecasting is to one step forward.

B. Graphic and histogram of Ubatuba Figure 8 presents the training and validation curves for

the data of Ubatuba city. It can be seen that there was a small oscillation in the validation curve, which doesn’t

damage the convergence of the training process. In this case, unlike of the Cordeirópolis, the validation error is greater than the training error.

Figure 8. Training curve of Ubatuba.

Figure 9 presents the load curves in MW, the measured

in dashed blue and the forecasted in solid red, for the testing data of Ubatuba. Unlike Cordeirópolis’ case there is no stretch where the forecasted data has a distinct behavior of the measured data, i.e., in the case of Ubatuba, ANFIS presented an ability of generalization even higher than the case of Cordeirópolis.

Further information that leads to such conclusion can be

seen in Table 1, which presents the MAPE for three distinct trainings for one step forward forecasting for the data measured in the substation of Ubatuba.

The MAPE of each one of the trainings was about 0.51%. In consequence, the MAPE average for the training data of Ubatuba is about this value too.

Figure 6. Measured and forecasted curves of Cordeirópolis.

Figure 9. Measured and forecasted curves of Ubatuba.

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The histogram of Figure 10 presents the distribution of the relative data for each one of the measures that compose the testing set of the substation of Ubatuba. It can be seen that the majority of the errors are very close to zero and, in the worst case, the presented error is lower than 4%.

Figure 10 Histogram of the relative errors of Ubatuba.

C. Table of Cordeirópolis and Ubatuba

TABLE 1 . MAPE AND VARIANCE FOR THE SET OF TEST OF CORDEIRÓPOLIS AND UBATUBA IN THREE DISTINCT TRAINING EXECUTIONS.

Cordeirópolis Ubatuba

MAPE Variance MAPE Variance 0.7264 1.46E-04 0.5063 4.85E-050.7263 1.46E-04 0.5163 4.85E-050.7262 1.46E-04 0.5159 4.85E-05

VI. CONCLUSIONS The need of operation of power systems, close to its

limits, requires precise knowledge about the current and future state of it, where information about load and demand are an integral part of such knowledge.

In addition to the short term load demand forecasting, whose horizon ranges between a few hours to some weeks, the very short term forecasting, i.e., for the next minutes is also necessary to operate power systems in an economical and reliable way.

This paper describes a methodology, based on ANFIS, for forecasting one step forward in very short term. This methodology is applied in data measured in substations located in Cordeirópolis and Ubatuba, cities located in the countryside and seaside of São Paulo state, respectively.

The results were depicted in graphics of measured and forecasted demand for each one of the substations, allowing the comparative analysis between the curves. In the case of Cordeirópolis, a stretch can be identified, where the measured and forecasted series have a slightly distinct behavior but, through histograms of relative errors, it can be seen that the errors are lower than 6%.

In the case of Ubatuba, the measured and forecasted curves have similar behavior. The error in the worst case was lower than 4%.

The experimental results demonstrate that ANFIS is a good tool for forecasting one step forward for very short term load demand.

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