Support Vector Machine Based Electricity Price Forecasting For Electricity Markets utilising Projected Assessment of System Adequacy Data.

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1 The Sixth International Power Engineering Conference (IPEC23, November 23, Singapore Support Vector Machine Baed Electricity Price Forecating For Electricity Maret utiliing Projected Aement of Sytem Adequacy Data. D. C. Sanom ( anom@itee.uq.edu.au, T. Down and T. K.Saha School of Information Technology and Electrical Engineering Univerity of Queenland Abtract In thi paper we preent an analyi of the reult of a tudy into wholeale (pot electricity price forecating with Support Vector Machine (SVM utiliing pat price and demand data and Projected Aement of Sytem Adequacy (PASA data. The forecating accuracy wa evaluated uing Autralian National Electricity Maret (NEM, New South Wale regional data over the year 22. The incluion of PASA data how little improvement in forecating accuracy. Keyword Price Forecating, Support Vector Machine, electricity maret. 1 INTRODUCTION Electrical Supply Indutrie (ESI worldwide have been retructured (deregulated with the intention of introducing level of competition into energy generation and retail energy ale. In any maret with level of competition information of future maret condition can contribute to giving maret participant a competitive advantage over their fellow maret participant. In an open auction tyle electricity maret uch a the Autralian National Electricity Maret (NEM [1] a large volume of information on hitorical and predicted maret condition i available to all maret participant. A the ESI i a large volume indutry all maret participant can gain advantage from even a mall increae in the accuracy of their electricity price forecat. A Electrical Power Engineer with experience in electrical load forecating [2] a logical tarting place for electricity price forecating wa to utilie the ame method a we ued for load forecating. Thi provided a fruitful tarting place a variation in electricity price depend on and o mirror the variation in electrical demand[3, 4]. However electricity price are far more volatile than electrical demand a price are alo a maret function of upply and demand. Electrical load vary in a table periodic way with eaonal and climate variation and weely and daily human activity pattern. Thu load could be forecated by utiliing a nowledge of thee periodic variation however the electrical load forecat can be improved by including prediction of future weather data. Load could be forecated by examining only pat demand data however the forecat can be improved by conidering a wider range of data. Electricity price are baed on the demand and o alo vary in imilar table periodic way a the demand however a the NEM regional electricity price i determined in an auction tyle maret baed on the economic principle of upply and demand. From economic principle we hypothei that electricity price would be influenced by the difference between available upply and the required demand at each intant in time. In previou tudie we have only utilied pat demand and price data [5, 6,14] in thi reearch we hope to improve our price forecat by utiliing a wider range of data. Some data that give an indication of future available upply or generation capacity and the projected required demand i found in the hort-term PASA file provided to maret participant by NEMMCO [13]. The reult of thee tet are being ued to invetigate the following hypothei, over the period teted the electricity price forecating accuracy for the NSW regional electricity price will be improved by the incluion of the PASA data variable into the input data et preented to the SVM forecating model. 2 SHORT-TERM PASA DATA The hort-term Projected Aement of Sytem Adequacy Data file are produced for the NEM by NEMMCO every two hour. The file contain projected half-hourly data for the next ix day tarting at 4:3

2 %! % (! %% #$#$ the day after the PASA file wa publihed. In thi reearch the data variable utilied from the PASA data are: 1 projected capacity required 2 projected reerve required 3 projected reerve urplu 4 projected regional demand 1% POE 5 projected regional demand 5% POE 6 projected regional demand 9% POE where POE i probability of being exceeded. Input y Training point claified low margin Boundary maximie margin. The projected capacity required i an approximation of the total regional generation capacity that i required for that half-hour. The capacity required i equal to the 1% POE regional demand forecat plu the et reerve required. The projected reerve required i the Minimum level of reerve required in the region a determined by the Reliability panel. Uually et at approximately 5 to 7% of the expected total regional demand. Through out the majority of the period in thi tudy the reerve required wa et at 66MW for the NSW region, which ha a total demand from 7 to 11MW. Projected reerve urplu i the urplu (poitive value or deficiency of available reerve (negative value compared to the capacity required. The 1% POE regional demand forecat i the regional demand forecat produced with a 1% probability of being exceeded (POE. Similarly the 5% POE forecat ha a 5% chance of being le than the actual demand at that half-hour. Training point claified high Input z Figure 1 Maximum Margin of Support Vector Machine To explain the principle of SVM we begin with an explanation of the application of a SVM to claify data point a high or low in a two dimenional input pace. The baic principal of SVM i to elect the upport vector (haded data point that decribe a threhold function (boundary for the data that maximie the claification margin (a in Figure 1 ubject to the contraint that at the upport vector the abolute value of the threhold function mut be greater than one a in Equation 1 (ee Figure 2. The non-upport vector data point (unhaded point do not effect the poition of the boundary. 3 SUPPORT VECTOR MACHINE THEORY With the goal of reducing the time and expertie required to contruct and train price forecating model we conidered the next generation of NN called upport vector machine (SVM. SVM have fewer obviou tuneable parameter than NN and the choice of parameter value may be le crucial for good forecating reult. The SVM i deigned to ytematically optimie it tructure (tune it parameter etting baed on the input training data. The Training of a SVM involve olving a quadratic optimiation, which ha one unique olution and doe not involve the random initialiation of weight a training NN doe. So any SVM with the ame parameter etting trained on identical data will give identical reult. Thi increae the repeatability of SVM forecat and o greatly reduce the number of training run required to find the optimum SVM parameter etting when compared to NN training. '' %%&& ## "!! "" +*, -. /112 3 / /,4, : Margin F(net<-1 F(net>+1 F(net = ;+< = C =D =E F8G1HI1G Figure 2 Threhold function for SVM net The following explanation of SVM i the combination of information from ource [7] [8], more information regarding SVM can be obtained from the ernel machine web ite[9]. Equation 1 optimiation to minimie margin

3 Y X minimie ubject for where to data y F ( W y ( W point 1 = 2 X i target ( W = 1,..., l + b 1 of W data T point To overcome the limitation that the SVM only applie to linearly eparable ytem the input (X are mapped "!$#%'& (*,+ #-'+./ dimenional pace where the ytem i linearly eparable. Thi can be undertood with the help of the very imple example in Figure 3 where the onedimenional ytem i not linearly eparable however if the ytem i mapped by a dot product into twodimenional pace the ytem become linearly eparable. high low low x Map to high dimenional pace uing tranform ] ^`_bä c d 1è fbg`h i 2(x Z [\ Not linearly eparable in one dimenional pace 2(x Figure 3 Example of mapping to higher dimenion to mae linearly eparable Thi method of mapping to higher dimenion to mae the ytem linearly eparable create two challenge; how to chooe a va : ;=< > 7:?A@AB> 5 C D E"FHG IJLK M GK it may be impractical to perform the dot product required for the margin optimiation in higher dimenional pace. To overcome thee two challenge a Kernel function i ued a hown in Equation 2. Thi Kernel function can implement the dot product between two mapping tranform without needing to now the mapping tranform function itelf. Equation 2 Kernel function to perform dot product of two mapping function K( X, X j = Φ( X Φ( X j Once the Kernel function ha been included the SVM training can be written a the quadratic optimiation problem in lagrangian multiplier form a: Equation 3 lagrangian formulation T ~ max W ( Λ = Λ Λ Where boundary Linearly eparable in two dimenional pace T [ DΛ] 1(x D = d y K( x, x, j j j and the vector of lagrangian multiplier i Λ = λ, λ,..., λ ( 1 2 l Solving thi quadratic optimiation give the vector of lagrangian multiplier (hadow price. Support vector are the only data point with non-zero lagrangian multiplier o only upport vector are required to produce a forecating model (i.e. decribe the boundary in Figure 1. upport vector S = X only if λ To produce forecat implement Equation 4 below a in Figure 4 Equation 4 output of SVM Input X x,1 X,2 X,3 X,4 X,l f ( X = ign( net( X net ( X = λ d K( S, X + b Figure 4 Structure of SVM To apply SVM to regreion forecat a NÖ PQ"R OS TOU NV W i applied for each data point, which allow for an error between the target price y and the output of the SVM. The optimiation then become: Equation 5 SVM training for regreion minimie ubject for to data y ( W X + b 1 + ξ where y i price of data point C i a parameter choen by the uer to aign penaltie to the error. A large C aign more penalty to the error o the SVM i trained to minimie error, can be conidered lower generaliation. A mall C aign le penalty to error o SVM i trained to minimie margin while allowing error, higher generaliation. From previou tudie a C between.1 and 1 wa found bet for electricity price forecating model. In thi paper all SVM model are trained with C et to.5. 1 T F ( W = ( W W + C ξ 2 point K(S 1,X K(S 2,X K(S 3,X K(S,X = 1,..., l Weight W λ 2 d 2 λ 3 d 3 λ d λ 1 d 1 Σ F(net

4 4 PROCEDURE The SVM training and forecat were performed with the mysvm program developed by Stefan Rüping [1]. The program wa deigned to olve the dual of the optimiation in Equation 5 by dividing the training et into mall woring et or chun [11]. In thi tudy all forecat were even day into the future forecat utiliing real NEM data obtained from the NEMMCO web ite [13]. Note no data wa omitted not even very large price pie. The forecating tool were deigned to produce a practical forecat and o no data wa ued that would not be available to all maret participant at the time of producing the forecat. Timing terminology ued within thi paper: A tandard for the NEM the time t i defined a the trading half-hour. The half-hour i defined a the half-hour ending at that time. So the 48 th half-hour of the day i defined a the : half-hour which cover the trading period from 23:3 to :(midnight. So a day tart at the 1 t half-hour :3 covering the period from : to :3. NOW i at t=. The time at which the forecat i produced. Forecat time. The time in half-hour the forecat i for. A forecat time of 8/3/2 14:3 mean the forecat price i for the trading half-hour ending at 14:3 on 8/March/2. (note UK date format ued The delay. I the time t in half-hour before NOW. So a negative delay i in the future compared to NOW. Forecat ahead. I the time in half-hour for which the forecat i made into the future. Thu a one wee ahead forecat ha a forecat ahead of 336 halfhour. To allow the uer time to obtain and proce the hortterm PASA data file a minimum delay of one hour wa alway ued in proceing the data for producing thee forecat. In our early price forecating tudie it wa aumed that a very accurate forecat of future regional demand wa available and o the actual demand for the forecat time wa ued in producing the price forecat. In thi tudy no data after NOW i ued. The demand forecat ued are from the hort-term PASA file provided on the NEMMCO web ite. So the forecat produced in thi tudy are more practical reult than in our pat tudie. In previou tudie we found that uing a demand forecat intead of the actual demand reduced the accuracy of the price forecat by 1 to 4% (average of 2.3% depending of the accuracy of the demand forecat for that wee. All SVM price forecating model were trained with 28 day of data and teted by forecating the next even day of NSW regional electricity price. The reult were obtained by teting over 25 wee of data from the 12th of February to the 3 th of July 22. Thi data wa obtained from the NEMMCO web ite. The SVM forecating model utiliing PASA data were preented with all 15 variable in Table 1. The model not uing PASA data were preented with variable 1 to 4 and 11 to 15 only. Table 1 Input Variable Input to SVM Input Input Name Half-hour delay. Comment t= NOW Target pot price t=-336 Cent/MW 1 pot price t=3 1 hour 2 regional demand t=3 1 hour 3 daily half-hour t= weely half-hour t= capacity required N/a PASA File 6 reerve required N/a at delay t=2 7 reerve urplu N/a Data read at 8 PASA demand 1% N/a time delay 9 PASA demand 5% N/a t= PASA demand 9% N/a 11 pot price 48 1 day 12 pot price 96 2 day 13 pot price day 14 pot price wee 15 pot price wee 5 RESULTS 5.1 Value of PASA data The SVM price forecating model utiliing no PASA data gave forecating with a Mean Abolute Error (MAE of 28.6% and a Root Mean Squared (RMS error of 251. The addition of PASA data offered no ubtantial improvement in forecating accuracy to MAE 28.% and RMS 254. The plot of MAE and RMS are hown in Figure 8 and Figure 9. The plot for the model not uing PASA data were almot identical to thee plot. Both MAE and RMS error plot hown in thi paper are liding window average, with widow width of 48 and 336 half-hour. 5.2 Analyi of reult Before the winter load and pricing pattern began around the 2 th of May (uch a in Figure 5 the forecating reult were more acceptable with a MAE of 22.% and a RMS of After the 2 th of May the winter pattern began with the price piing mot weeday at 18: and/or 18:3 a hown in Figure 6. Thee large price increae were predictable a they occurred between 17: and 19:3, motly at 18: on weeday. In the NSW region over the winter period 18: to 18:3 i the pea load period of the day and o i expected to have the highet price of that day. However the magnitude

5 of thee daily price pie did not have any obviou pattern and o will be a focu of our next tudy. 9 Compare demand forecat error againt price 25 RMS Error for price forecat with PASA RMS meaure of Error total hal-hour Demand forecat error [MW] total hal-hour actual price predicted price day RMS average wee RMS average Figure 5 Good accuracy wee 3 rd to 9 th of March 2 One poible olution i to ue two eparate forecating model one for the very important pea demand and therefore price period and another model to forecat the price for the remainder of the time. When the half-hour 18: and 18:3 were removed from model the error of the reult improved (marginally to 27.1% MAE and (ignificantly to 86 RMS a the RMS meaure emphaie larger error RMS Error for price forecat with PASA total hal-hour actual price predicted price(all le than 5 day RMS average wee RMS average Figure 6 Poor accuracy wee 26/6/2 to 1/7/2 5.3 Importance of generation Capacity Our hypothei in performing thi reearch wa that the price baed on a upply and demand maret would depend on the difference between generation capacity and required demand and therefore the difference between NEMMCO demand forecat of required generation and the actual required demand at the time of upply. Figure 7 how reult for the error in demand forecating and the price for wee 19 of the forecating period. Thi wa typical for the period under tudy with only a wea correlation found between the error in demand forecating and the change in electricity price. Thu baed on our reult our hypothei would eem to be le important than other factor uch a abolute demand magnitude and generator bidding trategie. Price pie not caued by ytem failure appeared to occur at 18:3 on winter weeday night. The timing of thee pie wa independent of whether the required demand wa in exce or le than the expected demand obtained from load forecat. Were thee price pie a reult of the demand or of generator bidding behaviour? RMS meaure of Error actual price [$/MW] demand error [MW] Figure 7 Demand error and price 26/6 to 2/7/2 6 CONCLUSIONS The PASA data provided only a mall improvement in the accuracy of the SVM price forecating model. Baed on thee reult the cot and time in collecting and proceing the PASA data i not jutified by the improvement in forecat accuracy. The accuracy of the demand forecat or nowing the difference between expected generation capacity and the required demand wa not a crucial in price forecating a nowing the time of day and magnitude of the pea demand. However the magnitude of pea demand did not correlate with the magnitude of the price pie. Our future reearch need to explore and verify our growing belief that undertanding generator bidding trategie and regulation and regulatory change would be more beneficial to electricity price forecating than hitorical tatitical baed method. The quetion for the ESI i, ha electricity pricing evolved into a dynamic maret where the action and trategie of participant are of equal or more importance than the determinitic idea and method of power ytem analyi and load forecating? 7 REFERENCES [1] Publihed by NEMMCO," An Introduction to Autralia' National Electricity Maret: NEMMCO", Available at [13]. [2] H. S. Hippert, "Neural networ for hort-term load forecating: a review and evaluation," IEEE Tranaction on Power Sytem, vol. 16, pp , 21. [3] Sapelu A, "Pool price forecating: a neural networ application," UPEC 94 Conference paper, vol. 2, pp. 84, [4] Ramay B, "A neural networ for predicting ytem marginal price in the UK power pool," Univerity of Dundee UK, [5] Sanom-D and Saha-TK, "Neural Networ for Forecating Electricity Pool Price in a Deregulated Electricity Supply Indutry," AUPEC'99 Darwin Autralia Proceeding, pp. 214, 1999.

6 [6] Sanom-D, Down-T and Saha-TK, "Evaluation of upport vector machine baed forecating tool in electricity price forecating for Autralian National electricity maret," AUPEC22 proceeding, 22. [7] C. Corte, "Support-vector networ," Machine Learning, vol. 2, pp , [8] Platt-JC, "Sequential Minimal Optimization: A Fat Algorithm for Training Support Vector Machine," Microoft reearch report, [9] [1] S. Rüping, "mysvm oftware," under oftware -> mysvm. [11] E. Ouna, R. Freund, and F. Giroi, Support vector machine: training and application: Maachuett Intitute of Technology, [13] NEMMCO web ite acceed Dec [14] Z. Xu and Z. Y. Dong, "Development of a Wavelet and SVM Model for Electricity Price Forecating", Submitted to IEEE Tran on Power Sytem,22. MAE error for price Forecat with PASA data MAE( = 1*(forecat( - actual( / actual( % day MAE average = {um over n=-48 to of [MAE(n]} /48 wee MAE average = {um over n=- 336 to of [MAE(n]} /336 2% 18% 16% 14% 12% 1% 8% 6% 4% error MAE 1 2% total half-hour % actual price (appear vertical only day MAE average wee MAE average Figure 8 MAE error for Price Forecat with PASA data RMS Error for price forecat with PASA quared error( = (forecat( - actual(^2 day RMS average = qrt{{um over n=- 48 to of [error(n]} /48} wee RMS average = qrt{{um over n=-336 to of [error(n]} /336} Error RMS meaure total half-hour actual price (appear vertical only day RMS average wee RMS average Figure 9 RMS Error for price forecat with PASA data