16639546

Global

model

for short-term load forecasting using

artificial neural networks

F.J. Marin, F. Garcia-Lagos, G. Joya and

F.

Sandoval

Abstract: A global model is presented for short-term electric load forecasting using artificial neural networks. The model predicts the complete curve of the 24 hourly values for the next day. The development of this model consists of three phases: a prior one, in which, starting from historical data, each day is classified according to its load profile by means of self-organising feature maps; the second consists of building and training the neural networks for each class; and the thrd is an on-line operation phase, in which the prediction is carried out by previously trained recurrent neural networks. The hstorical data correspond to the central Spanish area from 1989 to 1999. Extensive testing shows that this method has better forecasting accuracy and robustness than statistical techniques, and a greater ability to adapt to different meteorological and social environments than other neural methods. The results obtained in testing are found to be very accurate.

1 Introduction

Short-term prediction of load demand (1-7 days ahead) is very important for various operations in power systems, such as economic scheduling of generating capacity, fuel purchase scheduling, security analysis, and planning activities.

The aim of short-term load forecasting is to extrapolate past load behaviour while taking into account the effect of other influential factors, such as weather, season, day of the week etc. However, the relationships between hourly load and these factors are complex and nonlinear.

Conventional load forecasting techniques, based on statistical methods [l], present several limitations such as complexity of modelling, lack of flexibility and low accuracy of results.

Artificial neural networks (ANNs) are applied to forecasting problems since their distributed structure of weights and neurons permits complex relationships between variables to be considered without specifying them explicitly in advance [2]. However, load-forecasting models using a single neural network cannot offer good performance when dealing with the complete set of all the days in a year, which present dissimilar profiles due to seasonal, economic and cultural factors. To avoid these restrictions, we carry out a prior classification stage of days according to the similarity of their load profiles using a self-organised map.

Several authors have also implemented Kohonen neural networks to obtain typical load curves. These curves have been manipulated [3] with statistical techniques in the prediction phase and predicted values of the mean and

0 IEE, 2002

IEE Proceedings online no. 20020224

DOL IO. 1049/ip-gtd:20020224

Paper first received 30th May 2001 and in revised form 17th October 2001 F.J. Marin is with the Dpto. de Electrbnica, E.T.S.I. Infonnitica, Universidad de Mala@, 29071-MBlaga, Spain

F. Garcia-Lagos, G. Joya and F. Sandoval are with the Dpto. de Tecnologia Electrbnica, E.T.S.I. Telecomunicacibn, Universidad de Mil~iga, 29071- Milaga, Spain

variance of the day profiles are needed. Consequently, the problem of obtaining a direct load prediction is not completely solved, since the problem of the prediction of these parameters remains. Elsewhere [4, 51, the neural networks have non-homogenous input sets, mixing analo- gue and digital variables with very different ranges of values and meaning, malung difficult the weight adaptation over the training process. In addition, maximum and minimum temperatures are used as exogenous variables. We however, have verified the inability of a neural network to benefit from these variables in daily forecasting, hour by hour [6]. Still, the proposed system [5] is only applicable for regions

with fairly homogeneous meteorological seasons and the intervention of an expert is necessary.

We present a model that combines a self-organising feature map for pattern classification tasks and recurrent ANNs for daily forecasting (hour by hour). Recurrent ANNs, due to feed-back connections, have the ability to model time series in a very efficient way [7] and have shown more robustness with respect to variations in structure than feed-forward models, as we have demonstrated previously [6]. The most noteworthy characteristics of our model are that the prediction is based on recurrent ANNs; the input set is homogeneous, with only analogue load; its adapt- ability to different social and meteorological environments; and the classification stage significantly increases the similarity between the patterns of each class, which facilitates the prediction task of the A N N associated with this class.

2 Methodology

The prediction process consists of three phases. Fig. 1 shows these phases and their sequential activation. In the first phase, using historical data, a Kohonen’s self-organising map (SOM) classifies the days according to their load profile. T h s classification is performed only once over the life of the package, and it is conditioned by specific meteorological, social or economic factors for each regula- tion area. The second phase involves finding and training the network associated with each class, producing minimal

121 IEE Proc-Gener. Truiisni. Distrib, Vol. 149, No. 2, March 2002

Kohonen classifier

historical historical historical class 1 class 2 class N

I

daily and hourly

modules

I

recall

Elman's NN

training:

toc2$xtyd

off-line learning

daily

hourly recall phase

load forecasting

Fig. 1

forecasting with artificial neural networks

Functional components and operating mode of load

errors for training and generalisation. Elman recurrent networks have been selected for their recursive capacity and easy training algorithm. A cross-validation learning strategy has been used, thus avoiding overfitting problems.

During the third phase or recall, the building ANNs provide two types of prediction: the load curve for the next day, hour by hour (daily module); and the load of the next hour (hourly module). These modules operate indepen- dently of each other and require different data for their operation.

To take into account the variations in power consump- tion over the years, an annual automatic re-training is performed, which is transparent to the user.

3 Kohonen classifier

The Kohonen algorithm [8] is a powerful self-organisation process, which generates, in a non-supervised way, a distribution of an input space V , in another space of smaller dimension V', preserving the topological relationships among the input vectors. The output space VM is represented by a two-dimensional array of neurons with a neighbour relation. Thus, a similar input vector will activate nearby neurons. During the learning process, each input vector

x

is compared with the weight vectors w i of each neuron in the network. The neuron whose weight vector is the nearest to the vector

x

is selected, modifying its weights and those of its neighbours according to eqn. 1:

W i ( t

+

1) = W i ( t )

+

&h;& - w;(t)) ₍₁₎ The neighbourhood function h,( ) determines the weight increment of each neuron as a function of proximity to the winner neuron. In our case, the neighbourhood area is determined by a square centred in the winner neuron, whose side diminishes until zero during the training. 1,. is the dynamic rate learning, which evolves during the learning, according to eqn. 2:

L O

q t ) = ~

( I

+%)

Ir0 is the initial rate learning (0.3); c is constant (0.2); t is the current iteration; and nn is the number of Deurons. The Kohonen algorithm is used with a 'toroidal' two-dimension network (10 x 10 size), where both top and bottom and left and right sides are attached. This structure permits an efficient utilisation of the neurons on the map limits. These neurons would produce a diffuse area in a 'flat' network.

122

Table 1: Day type identification with Kohonen's network

I

Class 1

Class 2

Class 3

Class 4

Class 5

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Class 13

Class 14

Class 15 (Special class)

Sunday from October t o March

Sundalrs from April, May and Septem- ber

Sundays in June, July and August

Saturdays from October t o March

Saturdays in April, May and September

Saturdays in June and July

Saturdisys in August

Mondays from October t o March

Mondays in April, May and September

Mondays in June, July and August

Tuesday t o Friday of August

Tuesday t o Friday from November t o March

Tuesday t o Friday of April, May, first two weeks of June, September and October

Tuesday t o Friday of third and fourth weeks of June and July

Easter period

Table 1 shows the final classification, where the daily load patterns (excluding 11 holidays and atypical days) were separated into 15 different classes. Classification results incorporate (as expected), the interactions between weather variables and calendar variables (day of the week and seasons). In this way, the c1a:ises respond to characteristics of the different days (Sundays, Mondays, Saturdays, weekdays) and to meteorological characteristics (seasonal- ity). Certain cultural components exist in the previous classification, shown by the special treatment of July and August, whch are not only summer months but also holiday months. The Easter period has been considered as a special class due to its particular characteristics, as shown later.

4 Off-line learning

For prediction, each class has a particular associated ANN. T h s specialisation improves the ANNs performance, obtaining more accurate predictions.

4. I

Starting from the historical data, a study is performed to determine the relationshp between the load and other variables, such as integral demand, maximum and mini- mum temperature, degree of cloudiness etc [6].

The hstorical data, including load consumption and weather type data from 1 January 1989 until 17 February 1999, have been supplied by Red Elkctrica de Espaiia (REE) and correspond to the central Spanish regulation area (Iberdrola2).

The variables included in 1rhe model were the daily load and the predicted integral demand. The most significant exogenous variable is the temperature. However, the measurements supplied to us, i.e. temperatures at 06:OO and 18:OO hours, have a very low correlation with the present load power [6], and consequently they were rejected. In any case, the influence of exogenous variables is indirectly incorporated in the classification phase and the predicted integral load.

Selection of input data

4.2 Choice of neural network paradigm

Several neural paradigms have been implemented such as multi-layer perceptron, radial basis function networks, Jordan recurrent network etc., but none have shown better forecasting accuracy than the Elman recurrent neural network [6], which was finally selected for our application. Elman networks are basically feed-forward nets, with their hidden layer recycled back as inputs, and a dynamic back- propagation training algorithm [7].

Recurrent ANNs are capacitated to internally encode temporal contexts from their feed-back connections. They evolve as a sequential system and, consequently, can describe a dynamical system evolution in a more efficient way than the feed-forward models. .

4.3 Choice

of

hidden neurons

The number of hidden layer neurons was selected by experimentation, varying between 30 (class 7) and 100 (class 12), depending on the size of training patterns. An optimal number of hidden neurons is very important because a high number of hidden neurons may produce over-parameter- isation effects, obtaining lower training errors but hgher generalisation errors [9]. In our experiments, Elman networks have shown to be less affected by this problem than multi-layer perceptrons [6].

4.4 Normalisation

Previous hourly loads and integral demand are scaled in the interval [- 1,

+

11 (Elman neuron activation interval), thus with a similar significance. The approach for scaling uses a linear transformation:

(3) IMAX - IMIN

YMAX - YMIN

YUIMIN - YMINIMAX

YS(h) = Y d h ) + y,, - yMN

Yu(lz) and Ys(h) are the unscaled and scaled values, respectively, at hour h, for both the load power and the integral demand;

Y M A x

and YMIN are the maximum and minimum values, respectively, of the training data; and IMAx and I,,, are the interval boundaries.

Table 2: Average forecasting error for daily module

4.5 Input and output patterns

The daily module provides the profile of the hourly load of day d. As input data, this module needs the forecasted integral demand for day d and the profile of actual hourly load for the previous day (d-I) of its class. Thus, the Elman network has 25 input neurons and 24 output neurons.

4.6

Re-training

Demand patterns are always changing due to seasonal and long-term trends, which require re-estimation of the model. Thus, when new data are available, ANNs must learn the new parameters from the extended sample period. This learning starts from the current parameter values, thus leading to minor changes in the estimated parameters. This is a substantial difference with the statistical model, where a full re-estimation of the model is necessary. In our model, the learning process is periodically performed automatically and is completely transparent to the users.

5 Results and discussion

ANNs training was performed using load data from 1

January 1989 to 31 December 1996. Testing was carried out with data from 1 January 1997 to 17 February 1999.

Standard deviation (SD) and mean absolute percentage errors (MAPE) were chosen as the forecasting accuracy measures. MAPE is the average amount by which the forecast deviates from the actual load and is given by

where PF(h) is the forecast load at hour h; P A @ ) is the actual load at hour h; and N is the total number of hours. Table 2 shows the MAPE and SD results for all classes in the training and testing periods for the daily module. The hourly module presents similar but somewhat better errors. The forecasting errors, averaged over the entire test for each day type, are found to be 1.45% for weekdays (classes

11, 12, 13 and 14); 1.46% for Saturdays (classes 5, 6 and 7);

i.

Training (1989-1996) Testing

1997 1998 17 February 1999

MAPE,% SD MAPE,% SD MAPE,% SD MAPE,% SD

Class 1 1.39

Class 2 1.65

Class 3 1.20

Class 4 1.37

Class 5 1.32

Class 6 1.24

Class 7 1.09

Class 8 1.71

Class 9 1.50

Class 10 1.30 Class 11 1.49

Class 12 1.29

Class 13 1.40

Class 14 1.03

Class 15 1.70 (Easter

period)

0.76

1.03

0.69

1.06

0.94

0.78

1.02

1.31

1.11

0.90

1.07

0.96

1.05

0.75

1.14

1.55

1.74

1.26

1.52

1.43

1.36

1.32

1.70

1.62

1.38

1.52

1.34

1.47

1.30

1.82

1.33

1.10

0.87

1.19

1.12

0.84

0.68

1.38 1.23

1.26

1.19

0.97

1.14

0.94

1.27

1.74

1.87

1.54

1.66

1.39

1.40

0.64

1.90

1.63

1.34

1.55

1.30

1.67

1.48

1.91

1.42 1.42 0.91

1.22

1.02

1.28 1.61 1.23

0.97

0.89

0.42

1.53 1.17 0.93

1.11

0.99

1.15

0.98 , 1.15 0.84 1.20

1.09

1.31

1.62% for Sundays (classes 1, 2, 3 and 4); 1.65% for Mondays (classes 8, 9 and 10); and 1.87% for Easter period (class 15). We highlight the following aspects.

Working days (classes 8 to 14) present very good results. Note that these classes have the highest number of days. On the other hand, the errors for these classes are affected by the presence of special days. In the Spanish system, these special days have a very changing distribution over the week and the year. Thus, a region with a high percentage of fixed special days will appreciably reduce the above errors.

Figs. 2 4 show the errors corresponding to working days. Fig. 2 shows the forecasting errors for February 1998 (Tuesday-Friday, class 12). The error is even less than 1.6%. For tlus class and period the MAPE is 0.80% with a SD of 0.62. Fig. 3 shows the forecasting errors for the third and fourth weeks of October 1998 (Tuesday-Friday, class 13). For t h s class and period the MAPE is 1.20% with a SD of 0.86. Fig. 4 shows the training and testing average errors, hour by hour, for all patterns of class 14 (Tuesday- Friday of the second and third weeks of June and all of July).

1.6

1 4

1 2

1 0

0 8

0 6

0 4

0 2

0 8

a I

0 5 10 15 20 25

time, h

Fig. 2 M A P E for Tuesday-Friday of February 1998 (class 12)

3.0

2.5

2.0

8

a 1.5

I

1 .o

0.5

0

0 5 10 15 20 25

time, h

Fig. 3

(class 13)

M A P E for the third and fourth weeks of October 1998

The summer period (classes 3, 6, 7, 10 and 14) presents very good results for worlung days and weekends. Fig. 5

shows the comparison between forecasting and actual load curves for the working days of the third week of July 1997

1 24

2.0

1 .8

1.6

$ 1.4

W- n

2

1.2

1 .o

0.8

0.6

0 5 10 15 20 25

time, h

Fig. 4 M A P E for all patterns of class I4

5000

4500

z

4000

d

'

3500

3000

2500' ' ' ' ' ' ' ' '

0 10 20 30 40 50 60 70 80 90 100 Tuesday 15 July 1997 time, h Friday 18 July 1997 Fig. 5 Forecasting results for third week of July 1997

(Tuesday-Friday), whch presents a MAPE of 0.61%. As

summer is a special period, both for meteorologcal and holiday criteria, these results, illustrate one of the main characteristics of our predict or: its correct behaviour in different social, cultural and meteorological environments (adaptability).

Classes with higher errors (classes 1, 2, 4, 5, 8 and 9) correspond to periods that include very special days, such as

C h s t m a s and Easter. Class 1 presents bigger errors for December and for months of transition between seasons, e.g. October and March (Fig. 6). With respect to classes 2, 5, and 9, May and September have average errors of 1.42% and 1.58% (for 1997), respectively, but April has an average error of 2.19% because it usually contains the Easter period. This period is of particular interest due to the incidence of public holidays and the large number of people who enjoy vacations during the whole week, and its high incidence on days before and after the Easter period. Therefore, a specific class (class 15) of the days associated with Easter (12 days) has been included. For this class, the results for 1998 are shown in Fig. 7. Table 2 shows the MAPE and SD results for this period (class 15).

Christmas, however, has not been included as a specfic class because it produces different social behaviour depending on when the feast days fall during the week.

2.5

2.0

g 1.5

w

a

a

=

1.0

0.5

0

Oct Nov Dec Jan Feb Mar

Fig. 6

class I

Comparisons of load forecasting errors for m o n t h of

6 Conclusions

We have described the methodology, implementation and results of a load forecasting package composed of two modules: the daily module, whch forecasts the load demand profile of a entire day; and the hourly module, which forecasts the load demand of the next hour. This update process is very useful to correct the accuracy of the load prediction on days with extreme weather conditions and on special days, including days before and after public holidays.

In our methodology, each day is classified according to its load profile by means of Kohonen maps. For each class, the prediction is then carried out with ANNs. Elman networks have been selected since they show a greater generalisation ability than other studied paradigms. Results show the utility of our system to classify the daily load as a function of meteorological, social and economic factors. Regular periods such as working and summer days present very low errors. The greatest errors arose in special periods such as Christmas and Easter.

With a new class for Easter, a great reduction in the error has been obtained. The errors in the Christmas period and special days are greater than those for the normal days because of the changing position of the feast days during the corresponding periods.

The robustness and adaptability of our system to other regulation areas is based on the capability of Kohonen maps to extract non-evident environmental, cultural and economic factors, and the special ability of recurrent ANNs to model time series. The performance of our proposed model was extensively assessed through experimentation, and compared with other statistical and neural paradigms.

6500

6000

5500

5000

z

4500

m

-

4000

3500

3000

2500 I I I , 1

0 50 100 150 200 250 300

Friday 3 April 1998 time, h Tuesday 14 April 1998 Fig. 7 Forecast and actual load curves f o r Euster period 1998

7 Acknowledgments

This work has been partially supported by Eliop S.A., contract 8.06/58.8 18, and the Spanish Comision Intermi- nisterial de Ciencia y Tecnologia (CICYT), Project TIC98- 0562. The authors would like to thank Red Electrica de Espaiia (REE), for supplying data and comments, and the referees for their useful suggestions.

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3

4

5

6

7

8

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