A hybrid model of dynamic electricity price forecasting with emphasis on price volatility

Transcription

1 all times On a non-liquid market, te accuracy of a price A ybrid model of dynamic electricity price forecasting wit empasis on price volatility Marin Cerjan Abstract-- Accurate forecasting tools are essential in te operation of electric power systems, especially in regulated electricity market Electricity price forecasting is necessary for all market participants to optimize teir portfolios In tis paper we propose a ybrid metod approac for sort-term ourly electricity price forecasting e paper combines statistical tecniques for pre-processing of data and a multi-layer (MLP) neural network for forecasting electricity price and price spike detection Based on statistical analysis, days are arranged into several categories Similar days are examined by correlation significance of te istorical data Factors impacting te electricity price forecasting, including istorical price factors, load factors and wind production factors are discussed A price spike index (CWI) is defined for spike detection and forecasting Using proposed approac we created several forecasting models of diverse model complexity e metod is validated using te European Energy Excange (EEX) electricity price data records Finally, results are discussed wit respect to price volatility, wit empasis on te price forecasting accuracy Index erms data mining, neural network, price spikes, price volatility, sort term electricity price forecasting D I IRODUCIO uring te last twenty years, traditional vertically integrated electric utility structure as been deregulated and replaced by a competitive market e deregulated power market is an auction market wit market clearing prices Companies tat trade in te electricity market today, make extensive use of price prediction tecniques to stay competitive Along wit forecasting electricity prices, producers and traders can develop bidding strategies to maximize profits and minimize risks and allocate purcases between long term bilateral contracts and spot prices Electricity today is not storable in economically significant quantities and as a result electricity prices are volatile Except for volatility (elaborated in detail in Section IV), liquidity is anoter major market parameter Market liquidity is an asset's ability to be sold witout causing a significant cange in te price and wit minimum loss of value Error! Reference source not found e essential caracteristic of a liquid market is tat tere are available willing buyers and sellers at M Cerjan is wit HEP rade Ltd, Croatia, Ulica grada Vukovara 37, 0000 Zagreb (marincerjan@epr) forecasting procedure can significantly vary depending on te position of dominant player Witout knowing its position or te parameters affecting it, it is very callenging to forecast electricity prices in suc market [22] e European Energy Excange (EEX) is te most important energy excange in central Europe wic provides spot market for Germany, France, Austria and Switzerland for power derivatives and emission trading EEX is a igly liquid market affected by domestic and regional power system factors Due to importance and regional influence on te price of te EEX, it is important to find a suitable model for electricity spot market price forecasting [] Proposed metodology will be tested on te EEX price istory data Many attempts ave been made to predict electricity prices, ranging from traditional time series approaces to artificial intelligence, suc as fuzzy systems and artificial neural networks (A) [2] Auto regressive integrated moving average [3], dynamic regression and transfer function [4] and generalized auto regressive conditional eteroscedasticity [5] are te most widely used time series algoritms ime series tecniques exibit good performances, owever due to te use of linear modelling most of tem ave difficulties in predicting te ard nonlinear beaviours and rapid canges of te price signal [6] A as been extensively used by many researces on similar problems In problems wit adequate data for A training and straigt-forward selection of input-output samples, A are a powerful and flexible tool for forecasting and provide more accurate results tan time series models For example in [7] te A approac for weekly price forecasts as outperformed te time series ARIMA tecnique and te native procedure in all of te observed weeks Accuracy of a certain metod can be evaluated by mean absolute percentage error (MAPE) Altoug te concept of MAPE sounds very simple and convincing, it as two major drawbacks in practical applications If tere are zero values (wic can appen as EEX allows prices in te range from to 3500 ), a division by zero will occur On a perfect fit, owever, MAPE will be zero Wit regard to its upper level, MAPE as no restriction Wen calculating an average MAPE for multiple time series, a few numbers in te series tat ave a very ig MAPE migt distort a comparison between average MAPEs of time series fitted wit different metods Error! Reference source not found Our goal is to reuse existing metods for price forecasting to create a ybrid price forecasting model wic combines

2 2 advantages of existing tecniques to cover specificity of electricity price movements Initially data is processed and filtered using statistical metods resulting wit a data model of similar days is model is ten improved by using a multilayer (MLP) neural network or price spike detection and forecasting We validated our approac using te EEX electricity price istory data, and evaluated our results by applying several measures of accuracy (MAPE, MAE and RMSE) In addition we empasized te problem of price volatility by sowing ow price volatility affects te accuracy of eac forecasting metod e rest of te paper is organized as follows Section II describes price forecasting framework Section III is devoted to te proposed forecasting metodology wile section IV describes price volatility Section V provides our simulation results Finally, Section VI concludes te paper consumption and wind production from Point Carbon web service [24] were used Day-aead forecasted consumption and wind production data were taken as additional input for increased performance II PRICE FORECASIG FRAMEWORK Most of te existing studies of electricity price forecasting use only istorical price and consumption data to forecast electricity prices over various time spans [-7] We found it important to include wind power production istory data as it is te resource wit most volatile production ratio During te last decade, wind power generation as experienced a powerful breaktroug due to incentives, preferential price, Kyoto Protocol commitments and tecnical acievement, as well as oter renewable energy resources In Europe, ordic consumers benefit financially from te presence of Danis wind on te power market [8] In recent years, Germany also as a ig penetration of wind power (Fig ) However, ig volatility of te wind power can cause price drops on te power excange to below zero values, furter increasing price volatility For example, te minimum price of as occurred on [9-20] Fig 2 Flow cart of te ybrid electricity price forecasting model Daily price istory data is processed wit data mining tecnique wic defines: I Similar day types II Relevant istory orizon for similar days H() III Hourly correlation time orizon H() Fig Wind power capacity and generation in Germany Day type can be divided in tree categories: working days (Monday-Friday), Saturdays and Sundays/Holidays Days before or after olidays also reveal distinct beaviour, but due to te negligible influence on forecasting performance, tese cases are ignored and not analysed e proposed ybrid price forecasting model as bot linear (similar day) and nonlinear (A) forecasting capabilities ime orizon is day-aead and te price is forecasted for every our e price forecasting framework and metodology are presented in Fig 2 As model input, istorical data for prices,

3 3 Fig 3 Daily price correlation for D nearest neigbours o define te relevant istory orizon for similar days H() we performed a istorical price data analysis on an annual base, and ave selected a significant ourly price correlation coefficient of 085 Our analysis sowed tat tis correlation coefficient corresponds to a time period D = 28 days, in average (Fig 3) H ( ), D () Prior to performing te forecast, ourly orizon is defined by applying (I) and (II) Hourly orizon k + and k - ( significant neigbours sown in green in Fig4) are different for every forecasted price p() but generally two nearest neigbours always ave te igest correlation In some cases te maximum correlation coefficient between neigbouring ours is 080 erefore we decided to use tis value as minimum correlation coefficient for defining te ourly orizon Detailed preview of te ourly price correlations is sown in Fig 4, were correlations iger tan 080 are marked in green H ( ) p( ), p( ) (2) t k t k + Fig 4 Correlation matrix of EEX ourly data averages for te period from to III PRICE FORECASIG MEHODOLOGY Our approac of using ybrid forecasting model, based on similar-day analysis, improved by neural network and price spikes detection and forecasting is sown in Fig 2 Data set is filtered using a data mining tecnique described in Section II Eac our is observed separately and ten forecasted as price spike or normal price using a neural network We defined te ourly price p() for day as a cumulative value of linear and non-linear (neural network and price spike) components: p( ) = L + + S (3) were L -linear ourly component -neural network ourly component S -ourly price spike component e ybrid forecasting model consists of: A Similar Days Metodology Electricity price forecasting metods based on similar days metodology were presented by Paras Mandal et al in numerous works, suc as [][4] Similar price days are selected based on a Euclidian norm Euclidian norm wit weigted factors was used in order to evaluate te similarity between forecasted days and similar days [] Due to a ig correlation between consumption and price for observed market, tese two parameters are cosen for day-aead price forecasting [] D = DL + DP + + DL + DP (4) D = ω L i Li ( ) 2 Lt (5) L = Li Li p (6) L i D = ω P i Pi ( ) 2 Pt Pi = Pi Pi p (8) were L t - load for forecasted day P t - price for forecasted day L p t load on similar day in past P p t - price on similar day in past ΔL t - te load deviation between forecasted day and similar days ΔP t - te price deviation at time t ω weigted factor is determined using last square metod based on regression model constructed by using istorical load and price data Input data for te proposed metod incudes consumption and wind forecast data taken from te Point Carbon web service [24] (underlying tecniques used for consumption and wind forecasts are out of te scope of tis paper) Similar days wit realised prices are examined by consumption and wind production data mining metod e result of tis process is te linear price component from equation (2) defined as: (7)

4 4 L = p( ) + δ t (9) i i p( ) p = ( ) δ (0) i = were - number of similar days δ - average ourly difference between forecasted ours e linear price component can be observed as independent because it represents a starting point for te forecasting model wic can be improved by neural network and price spikes component eural etwork Arcitecture eural networks are applied widely for solving different problems wic in general are difficult to solve by umans or conventional computational algoritms In power systems te As ave been used to solve problems suc as load forecasting, unit commitment, power system topology recognition, safety analysis, price forecasting etc For ourly neural network component used in our approac, a multi-layer feed-forward neural network is proposed as sown in Fig 5 e neural network is composed of one input layer, one idden and one output layer We ave defined input variables for te A to be load forecast, wind forecast and ourly price, wind and load deviation from average values on similar days ereby, tis A is used to forecast ourly deviation from te similar days function wit regards to a forecasted day reductions appen rarely and cannot be predicted wit confidence In te proposed forecasting model we categorize prices as eiter regular (normal) or price spikes Price spikes are determined using an approac similar to [23] In () price spike criteria defines were α represents average value on similar days for observed our and σ is a standard deviation p ( ) < α ± 2σ () After extracting price spikes data it is important to find ow consumption and wind production affect te price spikes An index was created wic unifies consumption and wind production canges to create a signal wic detects possibility of price spikes Consumption and wind index (CWI) proposed in our approac consists of two components were CC refers to te relative degree of forecasted consumption wit te initial consumption on similar days and CW refers to forecasted wind production wit te initial wind production on similar days CWI = CC * CW (2) C( ) CC = (3) C sd Ci i C sd = = (4) L W -k- i +k+ - +k+ Hidden Layer Output Layer Hourly neural network component W ( ) CW = (5) W sd W i i W sd = = were: C -consumption in our C sd -average consumption on similar days W -wind production in our W sd -average wind production on similar days -number of similar days (6) Fig 5 Proposed A model for ourly neural network component forecasting Price spikes detection and forecast Due to te fact tat tere is no efficient way for storing electric energy, all electricity produced as to be consumed fortwit Imbalances between consumption and production lead to electricity price jumps (ie price spikes) wic can be several times iger or lower tan te regular price One possible cause of imbalance are weater conditions wic ave an effect on consumption, production from renewable energy sources, unexpected outages and reductions of cross-border capacities Some of tese events like outages or capacity Applying te CWI to te wole data set indicates tat ig price deviations appen for lower value of te coefficient (Fig 6) If te error of forecasted wind production and consumption is lower tan 0, a price spike may appen in te observed our After calculating te CWI index of a possible price spike, te ourly price spike component S (3) can be calculated Since price spikes appen rarely, we experienced a lack of data to be used for te neural network calculation erefore S was calculated using a linear approximation wit two variables; wind and consumption

5 For tis study volatility is calculated as a standard deviation of aritmetic return over a time window because EEX prices can be negative Wen te prices are negative, te logaritmic return cannot be calculated as in (20) 5 Fig 6 Correlation of CWI and standard deviation for observed ours IV PRICE VOLAILIY Volatility refers to unpredictable fluctuations of a process observed over time In finance, volatility is a measure for variation of a price of a financial instrument over time [8] Past volatility is derived from a time series of te past market prices It is a criterion to study te risk associated wit olding assets wen tere is an uncertainty in te future value of te assets In [9] past volatility is calculated as standard deviation of aritmetic and logaritmic return over a time window If p t is a spot price for a commodity at te time t, aritmetic return over time period is defined as pt pt Rt, = (7) p t te logaritmic return over time is defined as pt rt, = ln = ln( pt) ln( pt ) (8) pt Wen returns are small, te aritmetic and logaritmic returns are approximately equal pt rt, = ln = ln( + Rt, ) Rt, (9) pt Given te return values, te estimated value of past volatility can be calculated as 0 ( rt, r, ) i= σ, = (20) were σ, - te estimated value of past volatility, o - te number of r t, observations r - te average over te time window 0 Fig 7 Volatility fluctuations and traded volume sow tat volatility jumps were more severe on lower levels of EEX spot market liquidity It is interesting to observe te volatility fluctuation on EEX over te last five years in dependence wit traded volume Fig 7 sows muc iger volatility values occurring between 2005 and 200 is period coincides wit te growt of wind power production (Fig ) so it can be concluded tat for some time market prices were under influence of renewable energy production It can also be concluded tat price volatility depends on traded energy volume, as from 200, wit an increase in trade volume te price, te volatility is lower tan in previous years V CASE SUDY We tested our approac for electricity price forecasting on te EEX price istory data from a time period Data was processed in Microsoft Excel wit Palisade Decision ool and Visual Basic ree cases were observed: I Forecasting wit similar days (SD) II Forecasting wit similar days and neural network (SD+) III Forecasting wit similar days, neural network and price spikes detection (SD++PS) Our results are presented in able below Model performance was evaluated wit MAPE were y t is a realized value at time t and f t is forecasted value at time t in te time period 00 yt ft MAPE = (2) t= yt Price spikes brougt outliers in results and tat was te reason for including two additional error measures: MAE and RMSE For example, in December price distribution was scattered and a large number of price spikes wic increased MAPE MAE = f t y t (22) t=

6 6 RMSE = ( f y ) t= t t 2 ABLE I PERFORMACES OF HE PROPOSED HYBRID MODEL FOR HOURLY ELECRICIY PRICE FORECASIG Mont Dec-0 Jan- Feb- Mar- Apr- May- Jun- Forecasting Model MAPE MAE RMSE volatility SD 2,8% 7,48 9,38 SD+ 8,50% 7,32 0,43 SD++PS 6,79% 6,45 0,42 SD,36% 6,00 7,44 SD+ 2,20% 7,33 9,53 SD++PS 0,39% 6,89 9,08 SD 9,2% 9,38 8,9 SD+ 7,84% 5,48 7,24 SD++PS 5,87% 4,59 6,55 SD 4,88% 4,84 6,05 SD+ 3,73% 4,0 5,3 SD++PS 3,62% 3,89 4,5 SD 0,86% 5,69 6,98 SD+ 7,52% 5,29 6,9 SD++PS 5,03% 4,58 6,3 SD 7,5% 5,85 6,55 SD+ 6,96% 5,45 6,0 SD++PS 6,% 5,2 5,95 SD 3,05% 5,49 6,4 SD+ 2,90% 5,55 6,8 SD++PS 5,55% 4,30 5,50 SD 0,63% 5,90 7,4 Average SD+ 8,49% 5,75 7,08 SD++PS 6,20% 5,26 6,92 umber of price spikes 8, , ,22 0 9,67 59,73 9 2,0 4 3, ,05 68 (23) Simulation results sow tat similar days metod wit neural network and price spikes detection gives te best results Price volatility is a dominant factor affecting te forecast model accuracy In case of low price volatility, suc as Marc 20, simple models suc as similar days gave adequate results wit forecasting error similar to advanced models wit neural network and price spikes detection In case of ig volatility, suc as December 200, advanced models gave better results erefore it is very important not only to evaluate te forecasting model against te forecast error but also to analyse te complexity of te result distribution, in tis case defined by price volatility VI COCLUSIO e main difference between te proposed model and oter existing metods for sort-term electricity price forecasting is in its data utilization approac In te proposed approac, te data is pre-processed by statistical metods prior to eac analysis Forecasting results obtained by a combination of metods: similar days metod (SD), neural network forecasting () and price spikes (PS) in te following combinations; SD, SD+, SD++PS were presented; eac, respectably, proving to be more accurate Price volatility as significant influence on te forecasting results Simple forecasting models produced satisfactory results in cases of low price volatility Our metod proved robust enoug even in cases of ig price volatility VII REFERECES [] European Energy Excange, October 20, [Online], Available: wwweexcom [2] AAbraam, Baikunt, and PLMaanti, Hybrid Intellingent systems for stock [3] J Contreras, R Espínola, F J ogales, and A J Conejo, ARIMA models to predict next-day electricity prices, IEEE rans Power Syst, vol 8, no 3, pp , Aug 2003 [4] F J ogales, J Contreras, A J Conejo, and R Espínola, Forecasting next-day electricity prices by time series models, IEEE rans Power Syst, vol 7, no 2, pp , May 2002 [5] R C Garcia, J Contreras, M van Akkeren, and J B C Garcia, A GARCH forecasting model to predict day-aead electricity prices, IEEE rans Power Syst, vol 20, no 2, pp , May 2005 [6] M Pindoriya, S Sing, and S K Sing An Adaptive Wavelet eural etwork-based Energy, IEEE ransaction on power system, Vol 23, o 3, August, 2008 [7] JPS Catal ao, SJPS Mariano, VMF Mendes, LAFM Ferreira: Sort-term electricity prices forecasting in a competitive market: A neural network approac, Electric Power Systems Researc , 2007 [8] M Saidepour; 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7 7 [9] H Zareipour, K Battacerya, C A Canizared: Electricity market price volatility: e case of Ontario, Energy Policy 35, , 2007 [20] C Urllic: Realized Volatility and Price Spikes in Electricity Markets:e Influence of Observation Frequency,,June 2009 [2] Effect of Wind Energy on Electricity Market Prices, October 20, [Online], Available: ttp://wwweweaorg/indexpp?id=640 [22] M Andor, K Flinkerbusc, M Janssen, B Liebau, M Wobben: egative Strompreise und der Varrang Erneurbarer Energien, Z Energiewirtsc 34, 9-99, 200 [23] Data of istorical electricity prices from European Energy Excange, July 20, [Online], Available: ttp://wwweexcom/en/download [24] Data of istorical and forecasted consumption and wind production, July 20, [Online], Available: ttp://wwwpointcarboncom/ trading/pmteex/resources/downloads/latest/ [25] Mileta, D, Simic, Z Skok, M: Forecasting prices of electricity on HUPX, Energy Market (EEM), 20 8t International Conference on te European, 20 VIII BIOGRAPHIES and trading strategies Marin Cerjan was born on August 8 t 984 in Virovitica, Croatia He received MEng degree in Power Systems at Faculty of Electrical Engineering and Computing, Zagreb in 2008 He is a PD candidate at tat Faculty conducting researc in power markets wit special empasis on long-term system optimization He is employee of HEP rade, energy trading department His areas of interest are forecasting, optimization problems, energy market