Application of Learning Fuzzy Inference Systems in Electricity Load Forecast

Ahamd Lot?

School of Engineering Division of Mechanical and Manufacturing Engineering Nottingham Trent University Burton Street, Nottingham, NG1 4BU, United Kingdom ahmad.lotfi@ntu.ac.uk

Abstract. This paper highlights the results and applied techniques for the electricity load forecast competition organised by the European Network on Intelligent Technologies for Smart Adaptive Systems (www.eunite.org). The electricity load forecast problem is tackled in two di?erent stages by creating two di?erent models. The ?rst model will predict the temperature and the second model uses the predicted temperature to forecast the maximum electricity load. For both model, learning fuzzy inference systems are applied. Initial fuzzy rules are generated and then the numerical data provided by Eastern Slovakian Electricity Corporation are used to learn the parameters of the learning fuzzy inference systems. The learning technique is applied for both temperature and load forecast.

1

Introduction

This paper present the results and techniques applied for solving the electricity load forecast competition organised by the European Network on Intelligent Technologies for Smart Adaptive Systems (EUNITE). The electricity load forecast is a challenging problem introduced by the Eastern Slovakian Electricity Corporation, which can bring a very signi?cant ?nancial pro?t using more accurate prediction technology. The problem is to forecast maximum daily electricity load based on previous data available for electricity load and average daily temperature 1 . The average daily temperature and every half an hour load for the time period January 1997 until December 1998 are given. List of public holidays for the same period of time are also provided. The actual task is to supply the prediction of maximum daily values of electrical loads for January 1999. The electricity load consumption (Li , i = 1, 2, . . . , 365) is mainly in?uenced by the following factors: – – – –

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Average daily temperature (Ti ) Day of the week (Di ) Public holidays (Hi ) Time of the Day (ti )

http://neuron-ai.tuke.sk/competition

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Fig. 1. Maximum load (Li ) in 97 and 98 as a function of average daily temperature (Ti ) and day of the week (Di ). There are numerous things that can compose the electricity load which are very di?cult to be modelled. For instance during Christmas period shops are open very late which will increase the load regardless of the average temperature and in summer time more people intend to go on holiday and naturally the electricity consumption will be reduced. Even the consumer’s characteristics of electricity usage would not be similar in di?erent countries. As part of this competition we intend to create a simple model based on available measurement data. Figure (1) illustrates the maximum load in 97 and 98 as a function of average daily temperature and day of the week. The methodology used in this study is the learning fuzzy inference systems modelling for temperature and load forecast. Electricity load forecast is mainly tackled in two di?erent stages. The ?rst model will predict the temperature and the second model uses the predicted temperature to forecast the maximum electricity load. For both model, learning fuzzy inference systems are applied. More details on learning fuzzy inference systems and their training algorithm can be found in [1],[2],[3],[4].

2

Temperature Forecast

The average daily temperature in 95, 96, 87 and 98 are given and the average daily temperature in 99 must be predicted before we can forcast the load. The average temperature is represented by the variable Ti where i = 1, 2, . . . , 365. The only exception is for the year 1996 with 366 days (leap year). For ease of calculation and modelling it was decided to remove information about an extra day in 96. Comparing the correlation coe?cients of data for all years show that removing the data for February 29 would be the best with the maximum correlation coe?cients. The correlation coe?cients are given below.

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1.0000 ? 0.8351 ? ? ? 0.8180 0.8556

?

0.8351 1.0000 0.8309 0.8397

0.8180 0.8309 1.0000 0.8073

0.8556 0.8397 ? ? ? 0.8073 ? 1.0000

?

?i+365 from the current and past values of the A model was built that predict T average temperature, that is, Ti , and Ti?365 . A fuzzy rule of the following form will be used as the model for temperature forecast. If Ti (average temperature this year on Day i) is cold and Ti?365 (aver?i+365 age temperature last year on the same day) was very cold, . . . then T (average temperature next year on the same day) will be cold. Fuzzy if-then rules of the following con?guration can be employed for the modelling of linguistic information. ?j ... and Ti?p?365 is A ?p then T ?i+365 is Bk ?1 and ... Ti?j ?365 is A Rk : If Ti is A k k k ?i+365 where Rk is the label of k th rule, Ti?j ?365 : j = 0, 1, . . . , p is the j th input, T j ? is the output, Ak (k = 1, 2, . . . , n and j = 0, 1, . . . , p) is a fuzzy label, and Bk is either a real number or a linear combination of inputs Bk = q0i + q1k ? Ti + ?i+365 , for the ith day, as a function of inputs . . . + qpk ? Ti?p?365 . The decision, T Ti?j ?365 : j = 0, 1, . . . , p, is given in the following equation: ?i+365 = T

n i=1 wk Bk n i=1 wk

where Bk is the consequent parameters and wk is the rule ?ring strength given by:

p

wk =

j =0

?A ?j (Ti?j ?365 ) i = 1, 2, . . . , n

k

?j where ?A ?j is the membership function (MF) of the fuzzy value Ak . Some comk monly used MF shapes are Gaussian, triangular and trapezoidal. Regardless of the shape of MFs, they can be adjusted. Since the data provided is very limited and only four sets of training data is available, it is decided only the current year average temperature and a year earlier information to be used to forecast next year’s average temperature. ?i+365 = f (Ti , Ti?365 ) T

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?i in 99. Fig. 2. Predicted Temperature T A Fuzzy rule-based model with two inputs and one output was generated. For both inputs 4 membership functions in the universe of [?15? 30? ] are de?ned. The initial grade of membership functions are shown in Figure (3-a). The parameters of the membership functions were learned using the numerical data provided. The average daily temperature in [95, 96] and [96, 97] as the inputs and the average daily temperature in [97] and [98] as the output are applied for training of the learning fuzzy inference system. Figure (2) shows the predicated average temperature in 99 along with the minimum, maximum and average temperature for four years in 95,96,97 and 98.

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Maximum Electricity Load Forecast

To model the maximum energy consumption Li , i = 1, 2, . . . , 365, we consider that the maximum load is only function of the average temperature Ti , day of the week Di and wether that day is a public holiday or not represented by Hi . Di is a number between 1 to 7 representing Monday to Sunday respectively. Hi is 1 if the ith day of the year is a public holiday. The above expression can be formulated as follows: Li = g (Ti , Di , Hi ) i = 1, 2, . . . , 365

Since the average temperature information is not available and it should be predicted, the actual modelling of the load forecast can be formulated as follows: ? i = g (T ?i , Di , Hi ) L i = 1, 2, . . . , 365

A learning fuzzy inference system was again employed to predict the load. A fuzzy rule of the following form will be used to model the electricity load.

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Fig. 3. Membership Functions of Temperature Ti , Day of the week Di , and Public holiday Hi . If Ti (average temperature this year on Day i) is cold and Di (Day of the ?i week) is Thursday and Hi (that day is a public holiday) is true, then L (Maximum load on the same day) will be Low. A fuzzy inference system with 3 inputs and 1 output is built. The fuzzy values for all three inputs of the fuzzy inference system are given below.

?1 A 1: ?1 A 2: ?1 A 3: ?1 A 4: Very Cold Cold Mild Warm ?2 A 1: ?2 A 1: ?2 A 1: ?2 A 1: ?2 A 1: ?2 A 1: ?2 A 1: Monday (1) Tuesday (2) Wednesday (3) Thursday (4) Friday (5) Saturday (6) Sunday (7) ?3 A 1 : No Holiday (0) ?3 A 2 : Public holiday (1)

The membership functions of the above fuzzy values are illustrated in Figure (3).

4

results

To give an indication of the success of the proposed method to forecast the maximum electrical load, this section presents brief results. The average temperature in 95, 96, 97 and 98 are used for training the ?rst model. The learning method was used for 500 epochs. Using the learned model and average temperature in 97 and 98 as the inputs, the forecast for average temperature in 99 calculated. Figure (2) shows the predicated average temperature in 99.

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? i in 99. Fig. 4. Predicted Maximum Electricity Load L The second model to forecast the maximum load was created by the information provided. For this model the fuzzy inference system with 4 ? 7 ? 2 = 56 rules were used. The information in 97 was used for training and then the data in 98 was employed for testing the algorithm. Employing the achieved results for the temperature in 99, the second model is used to forecast the maximum electricity load in 99. The training algorithm was sloped after 200 epochs. Figure (4) shows the maximum predicted load in January 99 along with the minimum and maximum load for the same period in 97 and 98.

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Conclusions

The temperature forecast is relatively more di?cult than load forecast. For temperature forecast a long history of data would make the forecast more accurate. If there are some errors in load prediction, it could be caused mainly from the temperature forecast.

References

1. J.-S. R. Jang, C.-T. Sun, and E. Mizutani. Neuro-Fuzzy and Soft Computing; A Computational Approach to Learning and Machine Intelligence. Prentice Hall, NJ, 1997. 2. A. Lot?. Learning Fuzzy Rule-Based Systems, chapter in Fuzzy Learning and Applications. CRC Press, USA, 2001. 3. A. Lot?, H. C. Andersen, and A. C. Tsoi. Interpretation preservation of adaptive fuzzy inference systems. International Journal of Approximate Reasoning, 15(4):379–394, 1996. 4. A. Lot? and A. C. Tsoi. Learning fuzzy inference systems using an adaptive membership function scheme. IEEE Trans. on Systems, Man, and Cybernetics, 26(2):326–331, 1996.