Proceedings of the 2011 International Conference on Power Engineering, Energy and Electrical Drives
Torremolinos (Málaga), Spain. May 2011
A SOM Neural Network Approach to Load Forecasting. Meteorological and Time Frame Influence. M. López(1), S. Valero IEEE Member(1), C. Senabre(1) and J. Aparicio(2) (1)
Universidad Miguel Hernández de Elche (UMH) Dpto. de Ingeniería de Sistemas Industriales. Área de Ing. Eléctrica Avd. de la Universidad s/n. Edif. Quórum-V. 03202. Elche. Spain (2) UMH- Center of Operations Research E-mails:
[email protected];
[email protected];
[email protected]
Abstract-An artificial neural network based on Kohonen selforganizing maps (SOM) and its application to short-term load forecasting (STLF) is presented. The proposed model is capable of forecasting up to 24 hour long profiles, up to 24 hours ahead of the beginning of the period. The input used by the model depends on the available information at the time of the forecast, and it may contain meteorological variables and previous hourly load values. Also, different time frames for the input training data are analyzed. The output of the model is a curve of the forecasted load for the specified period. The test of forecasting 2009 data from the Spanish power system resulted in a 2.67% MAPE (mean absolute percentage error).
I.
INTRODUCTION
Electric load forecasting has been a major area of research for the last decade and it is a key to success for many of the decision makers in the energy sector, from power generation to operation of the system [1]. Also, the recent liberalization being currently deployed in many electricity markets throughout the world makes load forecasting even more important to distributing and commercializing companies which now need, more than ever, to develop services to efficiently meet all of their customers’ needs. For commercializing agents and aggregators, an accurate load forecasting model is a compelling need at the time of estimating their purchase offers in an open electricity market [2, 3]. A. A Brief Background of Load Forecasting Many different approaches have been used in load forecasting. Neural networks and other artificial intelligence techniques have been extensively used in the last decade although more classical statistical methods have not entirely disappeared [4]. Among these classical methods, the most significant are regression-based models [5, 6] and time series models [7]. Time series models use the hypothesis that future loads can be predicted from past values, being therefore modeled as an autoregressive process. Multivariate regression technique considers the load profile as a linear combination of explanatory variables (including weather
978-1-4244-9843-7/11/$26.00 ©2011 IEEE
factors). Coefficients for this linear combination are estimated by least squares fittings or modern regression techniques. Neural networks are currently the most popular method to develop load forecasting tools. Multilayer perceptron (MLP) is the main structure used in these models [8, 9] but other techniques like self-organizing maps [10] or recurrent networks [11] are also good candidates for promising results. Fuzzy logic and other types of artificial intelligence are also present in recent literature especially as part of hybrid methods [12, 13]. B. Load Forecasting Using SOM networks Self-organizing maps are used to produce two dimensional representations of high-dimensional data. Fig. 1 shows an internal representation of a SOM network [14]. The input layer receives n-dimensional data and therefore the input layer has n neurons. The output layer is arranged in a bi-dimensional structure in which the number of output neurons m is defined by the size of the map. Each neuron on the input layer is connected to each neuron on the output layer by a weight factor wi,j. In this way, each cell on the map is associated with a weight vector of n dimensions, just like any data vector in the input space.
Fig.1. A three dimensional input space is projected on a 3x3 bidimensional output layer. Every cell on the map receives a weight component from each input neuron.
Type of Day Load Profiles 40.000
SUNDAY MONDAY*
35.000
FRIDAY SATURDAY
Load (MW)
A forecasting process based on SOM networks consists of a training phase and an association phase. During training, every time a data vector is presented to the map, the weights of the best matching neuron and its neighbors’ are updated to better match this training data. Once training is complete, the association phase can take place. In this phase, incomplete vectors are presented to the trained map in order to identify a best matching unit. The values missing from the vectors are the information that is not available yet and therefore, we need to forecast. The information stored in the best matching cell is used to complete the initial data and produce a forecast.
30.000
TUE+WED+THU
25.000
20.000
15.000
II. CASE STUDY Our electricity raw data are the hourly load profile for the whole country of Spain, from the year 2006 to 2009 [15]. In addition, up to 10 different meteorological variables are included as training data. Input space is formed by vectors of up to 60 components that contain meteorological and electrical load values as well as type of day and month information. The model projects this input space into a bidimensional map. When initialized, each weight vector has random values but, after a training data set is presented to the map, the weight vectors adapt to this training data set storing information from similar days in adjacent or, at least, near cells. After this training process, we can present new data vectors containing only the information that is available at the forecasting time. The network will then find the cell that best matches this incomplete data set. The information stored in this best matching unit and in its neighbor cells can be then used to fill in the data that were missing in the original vector. Data normalization, selection of the input space, time period used for training and other network architectural parameters will determine the performance of the model. III. DESIGN OF SOM MODELS In this section we present the different design decisions that characterize our model. We describe the type of original input data and the treatment these data require to be used. Then, we explain the different tests made regarding input selection and the definition of time frame used for training. Finally, a brief description of the map architecture is provided. A. Data Normalization and Preprocessing The influence of the type of day is taken into account by using five different SOM models for each type of day. In this way, only days of the same type are used to train the map used to forecast this given type of day. The first three types of day are Sundays, Saturdays and, Fridays. Mondays and days after a holiday form type day number 4, and Tuesdays, Wednesdays and Thursdays all together correspond to type day number 5. Typical load profile for each type of day is shown in fig. 2. In order to normalize data and eliminate trends due to economic growth (or recession), each hourly value is divided
Fig.2. Load profiles for the different types of day considered. Note that the first period is 6a.m.
by the average hourly load of the 365 previous days. Note that the notion of production day is used, meaning that each day begins and ends at 6a.m. Meteorological data include maximum, minimum and average day temperatures, wind speed, pressure, rain, visibility, cloudiness and humidity. The values are obtained and averaged from meteorological stations in all 52 provinces of Spain. Values are then normalized dividing each value over the maximum in its category. Each set of data which will be fed to the map in the training period is therefore formed by a vector containing meteorological information, the load profile of the previous day and the load profile of the forecast day. B. Input Selection The first objective of input selection tests is to determine which meteorological variables are the ones actually worth including in the model. To this end, the map is trained without any information from the previous day load. Forecasting is made by presenting new meteorological data to the map and obtaining the load profiles stored in the best matching cells of the map. In order to determine which group of meteorological variables obtained the best forecast, variables were included and excluded from a starting set by an optimizing algorithm. The algorithm would stop when no inclusion or exclusion of a variable would produce a set with a better forecasting result. Five different seeds were tested to ensure global optimum was found. The second objective of input selection is to determine how far back in the previous day we should go when including data in the model. Four models were designed to forecast a whole day, each in intervals of 2, 4, 6 and 8 hours. The result of making a forecast every 2 hours instead of every 8 hours is obviously more accurate. However, the aim of our test was to determine if more accurate forecasts were produced by using only recent information rather than using all the information available. The test consisted on training these maps first with all available information at the time of the forecast and then only with information from the 12 previous hours. Table I shows the extensive input space available to choose variables from.
TABLE I DEFINITION OF INPUT VARIABLES Inputs
25
Description Ld, h h={1,…,24} T={1,…,6}
26
Lmonth
1-24
27-50 Ld-1,h 51-60 Mn n={1,…10} d: forecasted day.
Comments
The size of the model is 10x10. This size is computationally time-efficient, while bigger sizes (20x20) did not produce any better results. IV. RESULTS
Hourly load in day d, hour h. Type of day Historical average hourly load for the forecasted day’s month Hourly load in day d-1, hour h. Meteorological variable n. h: production day hour.
C. Time Frame Used for Training The second most important design factor of the model is to determine the time frame of previous data to be used to train the map. In this study we have tested different training period structures in order to address this issue. Our first test consisted on simply using data first from the previous year and then from the two previous years. The training data remained the same when forecasting different days throughout the year. The second test includes the concept of windowed training [16]. For this test, a different set of training data is used for the forecast of each day. The training data set is formed by different combinations of 30, 60 or 90 previous days and an interval of 31 days centered on the forecasted day in the previous and / or two previous years. A graphical representation of this scheme is shown on fig. 3. D. Map Architecture The architectural definition of a SOM is based on its size and topology. For this model, a rectangular topology has been chosen due to its simplicity since cylindrical and toroidal models provided very similar results when tested.
A. Meteorological and Previous Loads Influence Tests on the influence of meteorological variables on load forecasting accuracy show that average temperature is the most significant one along with pressure. The algorithm was initialized with five different seeds each test converging (see fig. 4) to the same two variables as the optimal combination with a 4.99% error. Another test was carried out in order to assess the importance of meteorological data when the load from the previous hours is available. In this test, different forecasts were done, each one including 0, 6, 12, 18 and 24 hourly loads of the previous day in the input vector. In each case, the forecast was made both with and without meteorological input. The result of this test shows that when information of previous hours load is available, meteorological information is almost of no value at all, and when more than 12 hours of the previous day have elapsed they even have a negative effect (see fig. 5). This result is coherent with the one obtained by M. Sforna y F. Proverbio in [9] and shows the little influence that meteorological variables have when considering electric load from large regions. Also, when considering different types of day, we see a larger influence of meteorological variables on Sundays than on any other type of day, probably because industrial load is less significant on this type of day. When we consider the effect of including previous load in the model, what we are actually doing is measuring how the forecast improves when made closer to the beginning of the forecasted period. To this regard, when the forecast is made 24 hours before the beginning of the forecasted period an error of 4,99% is obtained; nevertheless, if the forecast is made 24 hours later (at the beginning of the forecasted
90d
MAPE with different meteorological inputs
5,60%
60d
Seed 1 Seed 2 Seed 3 Seed 4 Seed 5
5,50%
30d 5,40%
Forecas ting day
MAPE
2009
5,30%
5,20%
31 days 5,10%
2008
5,00%
31 days 4,90%
2007 Fig. 3. Graphical representation of time frame selection for training data. 3x3 different time frame structures can be determined from combining the 3 periods from the current year with the number of previous years used (0,1 or 3).
1
2
3
4
5
6
7
8
# Iteration
Fig. 4. Evolution of MAPE when applying optimization algorithm to 5 random groups of meteorological variables as model input. All five seeds converge to average temperature and pressure as most significant variables.
Meteorological influence on load forecasting 5,50%
With met. input 5,00%
Without met. input
either 1 or 2 years before the forecasting day does not show significant differences, although the training with data from 2 years and 60 previous days is the most accurate (2.67%). A third test was designed to determine if different training period windows should be used throughout the year. However, no significant improvement was obtained from it.
MAPE
4,50%
4,00%
3,50%
3,00% 0
6
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Number of hourly loads from the previous day available
Fig. 5. Decrease of meteorological influence when electrical load data from previous day becomes available.
period) and the load profile from these 24 hours is inserted in the model, the error reaches 3.40%. When the forecasting moment moves forward into the forecasted day (more forecasts are made as new data become available), the error becomes smaller. The most remarkable result is that when forecast is made more frequently than 4 times a day, a better result is reached when limiting the previous load used to 12 hours prior to forecasting time than when using all information available. This means that when forecasting brief periods of time recent information is more significant than the information of the previous day in the same period.
C. Reducing Lead-Time In some cases, load forecasting is not made just once at one particular moment but it is continuously updated with a given frequency. In these cases, it is expected that more frequently updated models will obtain better results. We have included a test in our study to prove this assumption. Forecasts are made every 8, 6, 4 and 2 hours, and a 12 hour window is used when updating every 4 and 2 hours. The result can be seen in fig. 7 and it shows an improvement from 2.52% (every 8 hours) to 2.23% (every 2 hours). D. Error Throughout the Year In terms of MAPE, the results are not consistent throughout the year. Specifically, months that contain short periods of holidays (March, April, January and December) have the highest errors (see fig. 8). In further research, a possible approach to this issue would be to create a new type Effect of Reducing Lead‐Time 2,70%
12 hour window
B. Effect of Different Training Periods The first approach of simply considering the same training period for each day proved to be inefficient, obtaining a 3.4% error when using training data only from the previous year. The second test in which we tried out specific training data sets for each day produced much better results. The most significant improvement comes when data from previous years (1 or 2) is used along with data from the current year. The results shown in fig. 6 prove that using either 30, 60 or 90 days previous to the forecasting day along with data from Effect of Training Data Time Frame Selection
Error (MAPE)
2,55%
Fixed window
2,40%
2,25%
2,10%
1,95% 8
6
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Time in between forecasts (hours)
Fig. 7. Result when forecast frequency is increased. Note that when period between forecasts is shortened, the result from limiting previous load input to 12 hours is significantly better.
0,034
Forecast Error Along the Year
0,0325 0,031 0,0295
4,50%
0,028
Error (MAPE)
Error (MAPE)
5,50%
0,0265 0,025
3,50%
2,50%
Training Data Time Frame Structure 1,50%
Fig. 6. Result of modifying the time frame used to train the maps. Use data from previous years rather than only using current year produces a breakthrough in MAPE.
JAN
FEB MAR APR MAY JUN
JUL AGO SEP
Fig. 8. Distribution of error throughout the year.
OCT NOV DEC
of day for specific holidays and their eves. Similar results have been obtained when forecasting load from other Southern European countries (Italy, Greece) [8, 9]. V. CONCLUSIONS SOM networks have been proven to be a successful tool for load forecasting. The results obtained with this model are comparable to those obtained with more popular techniques like MLP or support vector regression. In addition, the methodology presented in this paper provides a comprehensive way to analyze new set of data helping to identify meteorological dependencies and self-correlation of load profiles. The model has proven to be very flexible in terms of input variables, forecasting frequency and forecasted period length. This particular feature makes the model easily applicable to many different usages. ACKNOWLEDGMENTS This research was financed by the Research Project with reference GV/2010/080-Valencian Government, Department of Education, and directed by Prof. Dr. Sergio Valero Verdú. REFERENCES [1] Weron, Rafal, “Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach”. 2007. John Wiley & Sons, Ltd. [2] Valero, S.; Ortiz, M.; Senabre, C.; Alvarez, C.; Franco, F.J.G.; Gabaldon, A.; “Methods for customer and demand response policies selection in new electricity markets.” Generation, Transmission & Distribution, IET. Volume: 1 , Issue: 1 . Publication Year: 2007 , Page(s): 104 – 110. [3] Verdu, S.V.; Garcia, M.O.; Senabre, C.; Marin, A.G.; Franco, F.J.G. “Classification, Filtering, and Identification of Electrical Customer Load Patterns Through the Use of Self-Organizing Maps.” Power Systems, IEEE Transactions on. Volume: 21 , Issue: 4. Publication Year: 2006 , Page(s): 1672 – 1682. [4] H. S. Hippert; C. E. Pedreira; R. C. Souza; “Neural networks for shortterm load forecasting: a review and evaluation“ IEEE Transactions on Power Systems In Power Systems, IEEE Transactions on, Vol. 16, No. 1. (2001), pp. 44-55. [5] Papalexopoulos, A. D., T. C. Hesterberg, 1990, "A regression-based approach to short-term system load forecasting", IEEE Transactions on Power Systems, Vol. 5, No. 4, November 1990, pp. 1535-1547. [6] T. Haida; S. Muto. “Regression based peak load forecasting using a Transformation technique,” IEEE Trans. Power Systems, vol. 9, no. 4, pp. 1788–1794, 1994. [7] Hagan, M. T. and S. M. Behr, 1987, "The time series approach to short term load forecasting", IEEE Transaction on Power Systems, Vol. PWRS-2, No. 3, August 1987, pp, 785-791. [8] S. J. Kiartzis, A. G. Bakirtzis, V. Petridis, 1995, “Short-term load forecasting using neural networks” Electric Power Systems Research Volume 33, Issue 1, April 1995, Pages 1-6. [9] M. Sforna, F. Proverbio, 1995, “A neural network operator oriented short-term and online load forecasting environment”, Electric Power Systems Research Volume 33, Issue 2, May 1995, Pages 139-149. [10] M. Cottrell, B. Girard, and P. Rousset, “Forecasting of curves using a Kohonen classification,” J. Forecast., vol. 17, pp. 429–439, 1998. [11] J. Vermaak and E. C. Botha, “Recurrent neural networks for short-term load forecasting,” IEEE Trans. Power Systems, vol. 13, no. 1, pp. 126– 132, 1998. [12] D. Srinivasan, A. C. Liew, and C. S. Chang, “Forecasting daily load curves using a hybrid fuzzy-neural approach,” IEE Proc.—Gener. Transm. Distrib., vol. 141, no. 6, pp. 561–567, 1994.
[13] H. R. Kassaei, A. Keyhani, T.Woung, and M. Rahman, “A hybrid fuzzy, neural network bus load modeling and predication,” IEEE Trans. Power Systems, vol. 14, no. 2, pp. 718–724, 1999. [14] T. Kohonen, Self-Organisation and Associative Memory (3rd edn.), Springer-Verlag, Berlin, 1989 [15] REE, Red Eléctrica de España, www.ree.es [16] M. Djukanovic; S. Ruzic; B. Babic; D. J. Sobajic; Y-H. Pao. “A neuralnet based short term load forecasting using moving window procedure”. 1994. International Journal of Electrical Power & Energy Systems Volume 17, Issue 6, December 1995, Pages 391-397.
