Electrical Power and Energy Systems 28 (2006) 437–447 www.elsevier.com/locate/ijepes Intelligent short-term load forecasting in Turkey Ayca Kumluca Topalli b a,* , Ismet Erkmen b, Ihsan Topalli a a Beko Electronics Co., R&D, Sehit Fethibey Cad. 55/20, Pasaport, Izmir, Turkey Department of Electrical and Electronics Engineering, Middle East Technical University, Ankara, Turkey Received 9 July 2004; received in revised form 15 December 2005; accepted 24 February 2006 Abstract A method is proposed to forecast Turkey’s total electric load one day in advance by neural networks. A hybrid learning scheme that combines off-line learning with real-time forecasting is developed to use the available data for adapting the weights and to further adjust these connections according to changing conditions. Data are clustered due to the differences in their characteristics. Special days are extracted from the normal training sets and handled separately. In this way, a solution is provided for all load types, including working days, weekends and special holidays. A traditional ARMA model is constructed for the same data as a benchmark. Proposed method gives lower percent errors all the time, especially for holidays. The average error for year 2002 is obtained as 1.60%. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Artificial intelligence; Hybrid learning; Neural networks; STLF 1. Introduction Short-term load forecasting (STLF) can be defined as the forecasting of electric demand one-to-seven day(s) in advance. It plays an important role in operating the power systems both economically and securely. Basic functions such as unit commitment, hydro-thermal coordination, interchange evaluation, and security assessment require a reliable short-term load forecast [1]. STLF is not an easy task. Load series are generally complex and the load at a certain hour depends on the loads from undetermined number of past hours. Moreover, weather variables such as temperature, daylight time, winds, humidity, etc. affect the consumption considerably [2]. The traditional methods to STLF try to model the load as a time series, which causes inaccuracy of prediction and numerical instability [3]; or, a function of some exogenous factors, especially weather variables, which produces an * Corresponding author. Tel.: +90 232 4897110; fax: +90 232 4894695. E-mail addresses: aycat@beko.com.tr, atopalli@isnet.net.tr (A.K. Topalli), erkmen@metu.edu.tr (I. Erkmen), ihsant@beko.com.tr (I. Topalli). 0142-0615/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2006.02.004 averaged result due to assuming a stationary relationship between them [4]. Recently, intelligent methods, such as neural networks, fuzzy logic, expert systems, etc. have been started to be applied to STLF. Among the latest examples, [5–16] can be given. In order to propose a solution to the STLF problem, artificial intelligence approach is chosen in this work, as an alternative to traditional regression-based approaches. Elman network, which is a subclass of recurrent neural networks, is used as the structure. This kind of networks has not only feedforward but also feedback connections and this construction helps learning. A hybrid learning algorithm is proposed which combines off-line training with real-time learning to take the advantage of experience gained by past data and to make instantaneous forecasts. Knowing that one neural network will not be capable of handling all load types, several data clusters are formed. As a resemblance measure, correlation analysis is selected. Thinking that the past loads, temperature and time (hour, day, season, etc.) play the greatest roles in next day’s load; they are used as the input variables to the proposed model. 438 A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 Neural network forecasts are sufficiently good for weekdays and weekends; but, they have to be revised and modified for holidays. Therefore, a new approach that combines all similar forecasts for past years and gives a correction term is suggested for such cases. 2. Theory 2.1. Recurrent neural networks Recurrent neural networks are neural networks with one or more feedback loops. In this work, Elman’s recurrent neural network is chosen as the model structure which has been shown to perform well in comparison to other recurrent architectures [4]. Elman’s network contains recurrent connections from the hidden neurons to a layer of context units consisting of unit delays. These context units store the outputs of the hidden neurons for one time step, and then feed them back to the input layer, as shown in Fig. 1. The variables in Fig. 1 can be expressed mathematically as: zj ðnÞ ¼  Taj ðnÞxðn w   xj ðnÞ ¼ W zj ðnÞ ;  Tb0 ðnÞxðnÞ sðnÞ ¼ w  1Þ þ  Tbj ðnÞ w uðnÞ target quantity, such as classification error with respect to a large set of input quantities. Recurrent learning extends backpropagation so that it applies to dynamic systems. This allows one to calculate the derivatives needed when optimizing an iterative analysis procedure, a neural network with memory, or a control system which maximizes performance over time [6]. Since there is no feedback at the output layer of Elman’s network, the weight update for this layer is done by standard error backpropagation D wb0 ðnÞ ¼ geðnÞsðnÞ½1  sðnÞxðnÞ where g is the step size parameter. For the hidden layer, Dwai;j ðnÞ ¼ geðnÞsðnÞ½1  sðnÞ ð2Þ ð3Þ yðnÞ ¼ WðsðnÞÞ ð4Þ q X k¼1 wb0 k ðnÞ oxk ðnÞ owai;j ðnÞ ð6Þ If Kkai;j ðnÞ is defined as the partial derivative of the state variable xk(n) with respect to the weight wai,j(n), then Dwai;j ðnÞ ¼ geðnÞsðnÞ½1  sðnÞ q X wb0 k ðnÞKkai;j ðnÞ ð7Þ k¼1 ð1Þ j ¼ 1; :::; q ð5Þ This partial derivative can be extended as follows: Kkai;j ðnÞ ¼ zk ðnÞ½1  zk ðnÞ " # q X l  wal;k ðnÞKai;j ðn  1Þ þ dkj xi ðn  1Þ ð8Þ l¼1 2.2. Learning algorithm for Elman’s neural network Standard backpropagation is simply an efficient and exact method for calculating all the derivatives of a single where dkj is the Kronecker delta,  1 k¼j dkj ¼ 0 elsewhere Fig. 1. Elman’s recurrent neural network. ð9Þ A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 Similarly, 439 3.1. Turkey’s electric load profile
wbi;j ðnÞ ¼ geðnÞsðnÞ½1  sðnÞ q X wb0 k ðnÞKkbi;j ðnÞ ð10Þ k¼1 Kkbi;j ðnÞ ¼ zk ðnÞ½1  zk ðnÞ " # q X l  wbl;k ðnÞKbi;j ðn  1Þ þ dkj ui ðnÞ ð11Þ l¼1 These recursive equations describe the nonlinear state dynamics of the learning process. Initial conditions are specified as Kkai;j ð0Þ ¼ Kkbi;j ð0Þ ¼ 0 8i; j; k ð12Þ which implies that initially the recurrent network resides in a constant state. 3. Data analysis and preprocessing The available data for this research are Turkey’s total hourly actual loads for the years 2001 and 2002, obtained through Turkish Electricity Authority; and, the hourly temperature measurements taken at Istanbul for the same years, obtained through Turkish General Directorate of Meteorology. In order to use these data in a meaningful and logical manner, first of all they should be closely analyzed and their dynamics should be clearly understood. Then they can be clustered into smaller sets according to some common characteristics and separate models can be built for each cluster. This is necessary because it has always been emphasized in the literature that it is impossible to reflect every different type of load behavior with a single model. The load profile is a dynamic process. Temporal variations, abrupt increases in demand, outages or other random disturbances all affect the load level. Fig. 2 shows hourly load averages for each day of the week from years 2001 to 2002. As shown in Fig. 2, apart from the absolute values, hourly averaged daily load shapes are almost identical for both years. Besides, this graph gives an idea about how the electric load varies from hour to hour and day to day. It is seen that four working days (Tuesday to Friday) have very similar patterns. Monday demand is lower from the beginning of the day till the morning; but it catches the working day trend for the rest of the day. Saturdays and Sundays are different than the other days. Fig. 3 represents the monthly averages of the load for the same years. Seasonal variations can be seen easily in Fig. 3. Winter demand is the greatest. Not as high as winter months, summer load is still large. Spring, especially May has the lowest demand. Autumn time is on average, neither too big, nor too small. 3.2. Correlation analysis If the training set of a neural network contains patterns that have characteristics close to each other and if the output carries the same kind of information as the inputs then this model gives successful results. In order to see the validity of this hypothesis, a measure of the resemblance between daily load sequences is thought to be established. In this respect, the correlation function is taken into consideration. Fig. 2. Hourly load averages for each day of the week in 2001 and 2002. 440 A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 Fig. 3. Monthly averages of the load in 2001 and 2002. Cross correlation coefficients are computed for each data pair as follows: S xy C xy ¼ pffiffiffiffiffiffiffiffiffiffiffiffi S xx S yy ð13Þ with S xy ¼ n X 3.3. Data clustering jxi  xjjy i  y j; S xx ¼ n X 2 ðxi  xÞ ; i¼1 i¼1 S yy ¼ As seen from Table 1, weekdays are highly correlated with each other; but, Saturday and Sunday have lower correlations with each other and with weekdays. Monday is the day which has the lowest correlations with the other weekdays. n X 2 ðy i  y Þ ð14Þ i¼1 where x and y represent the data pairs, x and y are the mean values calculated over the samples and n is the number of samples. Table 1 summarizes the correlations of the daily electric load consumptions in year 2002. Column (D + i) represents the ith day after the day D, given row-wise. Table 1 Daily load correlations in year 2002 D D+1 D+2 D+3 D+4 D+5 D+6 Monday Tuesday Wednesday Thursday Friday Saturday Sunday 0.988 0.989 0.991 0.991 0.979 0.878 0.767 0.977 0.985 0.985 0.972 0.829 0.941 0.802 0.975 0.979 0.966 0.825 0.969 0.956 0.818 0.969 0.956 0.818 0.975 0.979 0.966 0.825 0.941 0.802 0.977 0.985 0.985 0.972 0.829 0.767 0.988 0.989 0.991 0.991 0.979 0.878 Under the light of Turkey’s electric load profile given above and correlation analysis performed on the available data, an efficient clustering can be done. First of all, religious and national holidays should be excluded from the regular day data and handled separately since their characteristics are completely different. Then, four weekdays (Tuesday–Friday) can be examined in the same cluster. It does not seem necessary to create a distinct cluster for each of these weekdays as they are highly correlated. Moreover, a cluster should be formed for the first hours of Monday (00:00–08:00), because they come just after the weekend and do not resemble the other weekdays. The remaining hours of Monday can be evaluated in the working days cluster. For weekends, two clusters should be formed as Saturdays and Sundays since they have unique characteristics. One exception can be done here, the single day national holidays that come across to Sundays are not too much different than the regular Sundays, so they can be put together in the same cluster. 4. Proposed model and obtained results for regular days A model is proposed here to forecast Turkey’s total electric load one day in advance, providing a hybrid learning, 441 A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 which combines both off-line and real-time trainings. The aim is to prepare the model for real-time forecasts by training it with the available past data. Therefore, the hourly load data of the first year (2001) are used in off-line learning to adjust randomly initialized synaptic weights, and then the model undergoes real-time learning with the data of the next year (2002). The next year’s data are used as if they were real-time data by feeding them to the network in time order and only once. Errors are calculated as the actual data become available and weights are further updated in this phase. Joining these two types of learning has an advantage of starting real-time application with the weights that are already brought near to optimal values. In order to prevent model from over-fitting and memorizing the data in the off-line learning, the data are divided into training and validation sets. After randomizing the weights, input/output pairs from the training set are randomly presented for a predetermined number of cycles, which is taken as 1,000,000 here. Error is backpropagated and weights are adjusted in each cycle. At the end of each 100,000 cycle, weights are stored and the model is tested with the validation set, formed by 10% of the off-line data, chosen randomly and never given to the neural network during the off-line training. In this way, there are 10 validation errors and corresponding ten weight sets when the offline learning is finished. Weights giving the minimum validation error are considered as the final off-line weights. Real-time training begins with these final off-line weights and the same network structure. But the weights are further updated by the backpropagation algorithm with the application of ordered real-time data. This phase can be considered as a fine tuning for the system trained by last year’s data and on-line adaptation to the current year. Separate neural networks are formed for each cluster and different input variables are used. However, an Elman network with one hidden layer having ten neurons, and sigmoid nonlinearity is the fixed model structure. Loads that are used as inputs to the neural networks are normalized according to the yearly minimum and maximum values. There is no problem for off-line data since they are available for the whole year. However, real-time data for a complete year will not be at hand at the time of forecast, and thus the lowest and the greatest loads cannot be determined. So, real-time data should be normalized using the off-line data range. Knowing that the electric consumption is increasing every year, minimum value is taken as the minimum of the off-line data and maximum value is taken as 10% more of the off-line maximum. Consequently, both off-line and real-time data sets are normalized with these new minimum and maximum values in order to synchronize them. If a data happens to be outside the normalized data range, then the node outputs at the neural network will be saturated for this data. Days which are national or religious holidays are not considered in the regular clusters, instead they are handled separately. There are two input parameters that are common to all neural networks: hour and season. To present the cyclic continuity, hour is given as a half sinusoid hC ¼ sinðph=24Þ ð15Þ where hC is the cyclical hour and h is the actual hour. Season input is determined by looking at the monthly averaged loads. To reflect these variations, season input is given as in Table 2. Correlation analysis shows that, weekdays are highly correlated to each other; so for a weekday output, again weekday inputs should be used. Therefore, for the Early Monday model, load and temperature values from past three weekdays for the same hour to be forecast are given as inputs. For the Weekday model, day of the week is the additional input variable. For weekends, only the same type of data should be used. However in that case, data are separated in one week time. Taking the previous data may not be enough since this interval is rather long. For example, temperature might change considerably in a week and this affects the load consumption. Therefore, for the Saturday model, together with the past two week’s data, the difference of the two previous Friday loads (Saturday loads for the Sunday model) is used to express weekly variations, i.e., to indicate the load tendency of the current week with respect to the last week. Experiments have been done with a PC having a 1.7 GHz Intel Pentium 4 processor and 256 MB of RAM. Each training takes approximately 3–4 h. Table 3 summarizes the mean absolute percent errors (MAPEs) according to the clusters. As can be noticed, year 2001 errors are quite high as compared to year 2002 in Table 3. This is because there is no 2000 data to train the network off-line as the hybrid method proposes. Hence, off-line training could not be performed and weights could not be brought to meaningful values prior to the real-time Table 2 Neural network input representing the season Months Season input April, May June, September, October March, July, August, November January, February, December 0.1 0.3 0.6 0.9 Table 3 Summary of the forecast errors by the proposed model Cluster Error in years (%) 2001 2002 Early Monday Weekday Saturday Sunday Weighted average 61.25 9.28 19.75 12.86 13.96 1.97 1.39 1.47 1.99 1.51 442 A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 Fig. 4. The actual loads and neural network outputs for the best daily forecast. Fig. 5. Percent errors between the actual loads and neural network outputs for the best daily forecast. Fig. 6. The actual loads and neural network outputs for the worst daily forecast. Fig. 7. Percent errors between the actual loads and neural network outputs for the worst daily forecast. A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 training. Real-time forecasts should start with random weights and due to the fact that in real-time, there is no time for off-line training and inputs cannot be applied more than once, this fine tuning phase is not adequate itself and therefore, it gives unsuccessful results. For this reason, this is a good example to show that the hybrid learning is worthwhile. For 2002, it gives reasonable forecasts, with weekday cluster being the most successful one. It is generally difficult to have a good estimate for Sunday data; indeed, the error figures here are higher than the other clusters, but still in the acceptable ranges. Similarly, Monday morning shows unique characteristics, hard to capture. But the model performs well also for it. To show the best and the worst daily performances in year 2002, Figs. 4–7 are given. 22 August 2002, Thursday has the lowest forecast error with 0.48%, whereas 26 January 2002, Saturday has the greatest error with 2.18%. 5. Handling the special days In Turkey, there are two kinds of holidays, national and religious. National holidays are fixed in time, but religious holidays are moving each year. Table 4 is given to show the distribution of the existing data. Due to breakdowns in the system, measurements for certain days could not be taken. Although the percentages of the special days are small as compared to the regular days, it is important to forecast Table 4 Number of regular vs. special days in the available data 2001 Regular weekday Special weekday Regular weekend Special weekend Total 2002 n % n % 237 11 91 7 346 68.50 3.18 26.30 2.02 100.00 244 11 97 5 357 68.35 3.08 27.17 1.40 100.00 443 the loads of such days as well, in order to have a complete model. It is a known fact that electric consumption decreases on holidays, as shown in Figs. 8 and 9. If the neural networks, designed for regular load forecasting, are directly used for special day load forecasting, large errors are observed because of this fact [1]. Therefore, they should be analyzed separately. One exception can be done to single day holidays that coincide to Sundays. They are not so much different than the regular Sunday data, as given in Fig. 10; therefore, there is no need to form a cluster for this kind of data; instead, they can be put into the Sunday training set. The regular neural networks can be employed to forecast holiday loads if their outputs are adjusted to remove the gap between holiday and regular data. To remove this gap, holiday data from previous years are observed and a correction term is calculated. This correction term is then used to subtract an amount from the neural network output, found as if it were a normal day load. It can be shown mathematically as: LSpecial ðd; hÞ ¼ y NN ðd; hÞ  Cðd; hÞy NN ðd; hÞ ¼ ð1  Cðd; hÞÞy NN ðd; hÞ ð16Þ where LSpecial(d, h) is the special day load to be forecast for day d and hour h; yNN(d, h) is the neural network output which is the regular day forecast for the same day and hour; and C(d, h) is the correction term in percentage, changing according to day and hour, introduced for holiday adjustment. The regular forecast component yNN(d, h) is obtained via the neural network which is trained for the same day type with the special day under consideration, but without including the special days in training. Therefore, it is expertized in forecasting the normal loads and output becomes larger than the load of the holiday. That is why a correction term is needed. The correction term in the equation above is the average of the percent deviations of the regular neural network Fig. 8. Load differences between 23 April 2002 Tuesday and neighboring days. 444 A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 Fig. 9. Load differences between 23 February 2002 Saturday and neighboring Saturdays. Fig. 10. Load differences between 19 May 2002 Sunday and neighboring Sundays. forecasts from the actual loads of the special days in previous years. This can be expressed as: n 1X y NN ði; hÞ  Lði; hÞ ð17Þ Cðd; hÞ ¼ n i¼1 y NN ði; hÞ where yNN(i, h) is the regular neural network output for the ith special day from the previous years; L(i, h) is the actual load, and n is the number of the special days. A similar approach was given in the work of Bakirtzis et al. [1], but they have chosen to use an absolute value in MWs as the correction term, not the percent of the forecast value. They have obtained that correction term from the absolute differences of the previous years’ predictions. This approach is not followed here but modified as taking the percent variations; thinking that percentage is more informative than absolute values since yearly load consumptions do not remain the same. Table 5 lists the special days of year 2002, and gives the base forecast and corrected errors. As seen from Table 5, forecasts would not be successful if they were predicted only by a neural network and no cor- Table 5 Regular and corrected errors for the special days of 2002 Special day Regular NN error (%) Corrected error (%) 22 February 02 Friday 23 February 02 Saturday 23 April 02 Tuesday 19 May 02 Sunday 30 August 02 Friday 28 October 02 Monday 29 October 02 Tuesday 04 December 02 Wednesday 05 December 02 Thursday 06 December 02 Friday 07 December 02 Saturday 08 December 02 Sunday 09 December 02 Monday Average 44.76 19.35 7.17 1.53 7.86 5.96 10.34 15.38 44.32 47.65 33.47 12.60 7.81 19.86 5.73 5.47 1.32 1.53 1.13 4.81 4.08 2.05 3.80 5.85 5.68 5.15 6.66 4.10 rective action was taken. On the average, correction term makes the percent error reduce from 19.86% to 4.10%, which proves its validity and necessity. A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 In Figs. 11–14 given below, the best and the worst results for the above special days are presented. The effect of correction term is clearly seen in these figures. 445 As an overall error figure, it can be given that the average of real-time forecast errors in year 2002, including working days, weekends and special holidays is 1.60%, Fig. 11. Actual, forecast and corrected values for the best special day, 30 August 2002, Friday. Fig. 12. Percent forecast and corrected errors for the best special day. Fig. 13. Actual, forecast and corrected values for the worst special day, 9 December 2002, Mon. 446 A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 Fig. 14. Percent forecast and corrected errors for the worst special day. which is quite below 2.00%, the accepted success limit in the literature. 6. Comparison with ARMA method Traditional STLF models, such as regression or stochastic time series are widely used in electric generation units as they have proven their validity especially for weekday forecasts. Any new method having a different approach than these conventional ones should give better results in order to be accepted. Therefore, the model proposed in this work should also be compared with a classical model that does the same task. Stochastic time series method appears to be the most popular approach that has been used and is still being applied to STLF in the electric power industry [17]. There are many names encountered in the literature for this approach, for example autoregressive-moving average (ARMA) models, integrated autoregressive-moving average (ARIMA) models, Box-Jenkins method, linear time series models, etc. In the autoregressive moving-average process, the current value of the load series y(t) is expressed linearly in terms of its values at previous periods and in terms of current and previous values of a white noise, a(t). For an autoregressive moving-average process of order p and q, i.e., ARMA(p, q), the model is written as Cluster ARMA error (%) RNN error (%) Early Monday Remaining weekdays Saturday Sunday Special days Weighted average 3.50 1.53 2.72 3.45 10.34 2.33 1.97 1.39 1.47 1.99 4.10 1.60 Regular data are again clustered into four sets as before and tests are repeated for each of them. Special days are grouped among themselves. Results are shown in Table 6, together with the errors obtained by the proposed recurrent neural network model. It is obvious and easy to comment about Table 6. ARMA model gives best forecasts for weekdays but not as successful as the recurrent neural network model. For weekends and Monday morning, it is quite worse and for special days, it is almost useless. These results show that, this traditional method – depending only on a time series and not making use of other parameters, such as temperature, hour of the day or day of the week, etc. – is weaker than the proposed adaptive, intelligent neural network based method. 7. Conclusions yðtÞ ¼ /1 yðt  1Þ þ    þ /p yðt  pÞ þ aðtÞ  h1 aðt  1Þ      hq aðt  qÞ Table 6 ARMA and recurrent neural network results for STLF in year 2002 ð18Þ A stochastic time series model is constructed for STLF in order to be compared with the intelligent model, based on recurrent neural networks whose experimental results were presented previously. For estimating the parameters, MATLAB built-in function ‘‘armarts’’ is used. Here, data of years 2001 and 2002 undergo the tests. Parameters, p and q that cause the lowest error in year 2001 are found and corresponding / and h values are applied to year 2002 for estimating the 24-h ahead load. The highlights of this research are the hybrid learning for recurrent neural networks, which combines off-line and real-time trainings; data clustering considering the Turkey’s load consumption profile; and the proposed solutions for all day types, including special days. Proposed hybrid learning prepares the model for realtime load forecasting by training it first with the available off-line data and getting the weights ready. During the real-time application, weights are undergone to a fine tuning operation in order to track the changing conditions. By merging these two phases, the neural network model gains A.K. Topalli et al. / Electrical Power and Energy Systems 28 (2006) 437–447 experience from the past data; therefore, results become better than the standard learning methods. Clustering is performed after a detailed data analysis, based on correlation measures, daily and seasonal variations, holiday behaviors, etc. Then separate neural network models are constructed for each cluster. Special day forecast, which is the most difficult part of the STLF, is achieved by again the neural network method; but, the output is adjusted by a correction term, found through the difference between past years’ forecasts and actual special day loads. With this correction approach, errors reduce considerably. The overall result, as in the form of percent forecast error averaged through a year, is 1.60% for all clusters of year 2002 including the special days and it verifies that the building blocks of this work contribute positively to the solution of the STLF problem. 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