Forecasting Spot Electricity Market Prices Using Time Series Models

Transcription

1 C:\Documents and Settngs\Ethopa\Desktop\Forecastng Spot Electrcty Market Prces Usng Tme Seres Models.doc Forecastng Spot Electrcty Market Prces Usng Tme Seres Models by Dawt Halu Mazenga A thess Presented to Chalmers Unversty of Technology for the partal fulfllment of the degree of Master of Scence (MSc) n Electrc Power Engneerng Gothenburg, Sweden, June 008 Department of Energy & Envronment Dvson of Electrc Power Engneerng CHALMERS UNIVERSITY OF TECHNOLOGY

2 Forecastng Spot Electrcty Market Prces Usng Tme Seres Models Dawt Halu Mazenga Thess for the degree of Master of Scence n Electrc Power Engneerng Supervsor and Examner: Dr. Tuan A. Le Department of Energy and Envronment Dvson of Electrc Power Engneerng CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden, June 008

3 I know that thou canst do every thng, and that no thought can be wthholden from thee! Job 4: ሁሉን ታደርግ ዘንድ ቻይ Eንደሆንህ ሐሳብህም ይከለከል ዘንድ ከቶ Eንደማይቻል Aወቅሁ Iዮብ 4

4 Abstract The worldwde electrcty ndustry s n an era where an overwhelmng transton towards deregulaton s takng place. Snce ts start n the early 980s, the ndustry has been n a contnuous change to a dfferent atmosphere; the ultmate beneft beng provdng the enduse customer wth a relable but yet cheaper electrcty supply. In the old monopolstc system, utltes were the only authortatve body to set the tarff based on ther aggregate cost. In the contrary, as a newly emergng structure, deregulaton has come-up wth a new way of functonng; leadng generaton, transmsson and dstrbuton to be ndependent actvtes. Ths market s generally a customer drven market and snce the early days of deregulaton, prce forecastng has become an mportant task to all the market players engaged. Unless each body s farly aware of the market, t mght result n losses to a generatng company or nadequate supply to the system; resultng n a huge crss. Hence, understandng the market behavor s of vtal mportance for the well-functonng of the ndustry and the beneft of each party. Ths thess addresses the mportance of electrcty prce forecastng n the deregulated market. After a comprehensve revew of prevous works n the subject, t s concluded that forecast accuracy vares dependng on the forecast method used and the electrcty market under study. In ths thess multple lnear regresson approach are proposed to predct next day s electrcty prces. The developed models are tested n the Nord Pool and the Ontaro electrcty markets and satsfactory results are acheved. Comparng the forecast results from the two markets, results n the Nord Pool market are sgnfcantly more accurate than the Ontaro market. Ths arses from the fact that Ontaro market s very volatle and ts market prces are hardly predctable. The forecast results n ths thess work show that the proposed models perform very well wth the absence of volatlty. For nstance, the developed models for the frst week of December 007 generated results wth weekly Mean Absolute Percentage Error (MAPE) of about 5.04%. In early sprng even better results are acheved where the models generated results wth a daly MAPE of up to as low as.83% and weekly MAPE of about.96%. On the other hand, durng summer where prces vary consderably even between hours of the same day, the models generated a relatvely poor forecast. A day wth a prce of as low as.96 EURO/MWh to as hgh as 3.5 EURO/MWh s observed and ths prce fluctuaton contrbuted for poor forecast. For nstance, the models generated forecasts wth a weekly MAPE of about 3% for the perod from August 9 to Sept. 4, 007. For the Ontaro market, these models generated forecast results wth a weekly MAPE of about 7%. The ssue of strategc bddng s also dscussed n ths thess. Once the next day electrcty prce s forecasted, generatng companes schedule ther producton based on the forecasted electrcty prce and bd strategcally n order to maxmzng ther proft. An analyss on the correlaton between reservor level and market clearng prce s also carred out. Takng the Nord Pool market as a case study, t s found out that durng wnter there s a strong postve correlaton between the two; showng system prce ncreasng wth reservor level and vce versa. However, for other perods of the year a logcal negatve correlaton s observed; prce goes down wth an ncrease n reservor level and vce versa. v

5 Acknowledgments Durng the course of my studes, many colleagues and frends have contrbuted greatly and I would lke to take ths opportunty to thank them all. Frst and foremost, I would lke to express my deepest apprecaton and thank to my supervsor Dr. Tuan A. Le for hs nvaluable support and contnuous supervson n ths thess work. I also would lke to acknowledge the Swedsh Insttute and SIDA for the MKP scholarshp, whch I was recevng durng my study perod. My sncere thank also goes to the Nord Pool staff for allowng me to have access to ther data base. Fnally, I am grateful to my frend Mebtu for hs nvaluable help n ths work and also all my frends and personnel at Chalmers Unversty of Technology for the knowledge and prceless lessons that I have ganed durng those days. Ths thess s dedcated to Queen, wth Love; your support and courage have been wonderful n all those days! v

6 Table of Contents Abstract.v Acknowledgments....v Table of Contents...v Lst of Fgures..x Lst of Tables...x Acronyms......x Chapter. Introducton..... Research Motvaton... Objectves of the Work Outlne of the Thess 5. Strategc Bddng: A Bref Dscusson Introducton..6.. Prce Based Unt Commtment Strategc Bddng 0 3. Prce Forecastng n Deregulated Electrcty Market: A Comprehensve Revew Introducton Tme Seres Analyss and Its Applcatons Lnear Tme Seres Models and Forecastng Autoregressve Models Movng Average Models ARIMA Models Transfer Functon (TF) Regresson Analyss Smple Lnear Regresson Models Multple Lnear Regresson Models Dynamc Regresson Models Non-Lnear Tme Seres Models and Forecastng GARCH Models Artfcal Neural Network (ANN) Models..3 v

7 3...3 SVM Models Forecastng the Market Prces Usng Tme Seres Models Introducton: Input Varable Selecton/Determnaton Seasonal Effects Hydro Reservor Level Temperature Reserve Margn Model Development and Forecastng Usng Multple Lnear Regresson Approach 3 5. Result and dscussons An Overvew of the Nord Pool Electrcty Market Model Descrptons Forecast Results, Analyss and Dscussons Prce Forecastng Usng ITMS Introducton to ITMS Results and Comparsons Forecastng the Ontaro Electrcty Market 6 6. Correlatons Between MCP and Hydro Reservor Level Introducton The Effect of Hydro Reservor Level on MCP Summary and Conclusons References Appendces..77 v

8 Lst of Fgures. Determnaton of MCP Short-term operatonal plannng actvtes of a GENCO partcpatng n electrcty market trades Multlayer perceptron Fundamental drvers of prce and how they feed nto model approach and results Prce pattern for some consecutve weeks of January Graph showng supply and demand curves representng all bds and offers System Prce determnaton n the Nord Pool Market Monthly Nord Pool electrcty prce (January 000- Aprl 008) Daly Nord Pool market prce for the year Forecasted and actual prces of the selected day of February st, 007 n the Nord Pool market Forecasted and actual prces of the selected day of March 9, 007 n the Nord Pool market Forecasted and actual prces of the selected day of March 30, 007 n the Nord Pool market Forecasted and actual prces of the selected day of March 3st, 007 n the Nord Pool market Forecasted and actual prces of the selected day of March 9-3st st, 007 for the Nord Pool market Forecasted and actual prces of the selected week (March 9-Aprl 4) of year 007 for the Nord Pool market Forecast Error for selected week (March 9-Aprl 4) of year 007 n the Nord Pool market Forecasted and actual prces of the selected day of May 6th of the year 007 for the Nord Pool market A one week forecast & actual prces for the last week of May 007 n the Nord Pool market Forecast Error for the last week of May 007 n the Nord Pool market...5 x

9 0. Forecasted and actual prces of the selected day (9th August 007) for the Nord Pool market Forecasted and actual prces of the selected day (30th August 007) for the Nord Pool market Forecasted and actual prces of the selected day (3st August 007) for the Nord Pool market Forecasted and actual prces for the days 9th-3st of August 007 n the Nord Pool market Forecasted and actual prces for selected week (August 9-Sept. 4, 007) n the Nord Pool market Forecast Error for the perod from Aug 9-Sept n the Nord Pool market Forecasted & actual prces for st week of December 007 for Nord Pool market Forecast Error for the st week December 007 n the Nord Pool market Forecasted prces usng ITSM and tme seres methods compared wth the actual prces for January 0, 007 n the Nord Pool market Forecasted prces usng ITSM and tme seres methods compared wth the actual prces for March, 007 n the Nord Pool market Forecasted prces usng ITSM and tme seres methods compared wth the actual prces for March, 007 n the Nord Pool market Forecasted prces usng ITSM and tme seres methods compared wth the actual prces for June 30, 007 n the Nord Pool market Ontaro prce forecast for week of the year Ontaro prce forecast for week 5 of the year Reservor Level Vs System Prce for the Nord Pool Market for the year Reservor level Vs system prce for weeks 9-34, 007 for the Nord Pool Market Reservor level Vs system prce for weeks 35-5, 007 for the Nord Pool Market Reservor level Vs system prce for weeks -8, 007 for the Nord Pool Market..69 x

10 Lst of Tables. Data for Multple Lnear Regresson Hourly Error for the selected day of May 6th Performance comparson between ITSM and the proposed lnear multple regresson methods Weekly MAPE (%) for dfferent models for the Ontaro market...63 x

11 Acronyms ANN AR ARIMA DAM DR GARCH HOEP ISO MA MAPE MCP MLP MLR PBUC SMP SVR TF UC Artfcal Neural Network Autoregressve Autoregressve Integrated Movng Average Day Ahead Market Dynamc Regresson General Auto Regressve Condtonal Heteroscedastc Hourly Ontaro Energy Prce Independent System Operator Movng Average Mean Absolute Percentage Error Market Clearng Prce Mult-Layer Perceptron Multple Lnear Regresson Prce-based Unt Commtment System Margnal Prce Support Vector Regresson Transfer Functon Unt Commtment x

12 Introducton Before deregulaton come to exstent a few decades back, the electrc power ndustres have been domnated by utltes that had full control over all actvtes n the area. However, after ts frst attempt n Latn Amerca, the ndustry has been n transton n most countres around the world. In a deregulated market, end-use customers have the choce to select ther electrcty suppler. Ths chapter presents the restructurng of the electrcty ndustry and ts beneft to the socety. Some of the mportant ssues n a deregulated market such as electrcty prce forecastng, prce volatlty and uncertanty are dscussed n detal. The ssue of strategc bddng of market partcpants s also dscussed n addton to how MCP s calculated n a deregulated market.. Research Motvaton Snce the early 980s, the worldwde electrcty ndustry has undergone numerous and fundamental changes. For many years, these electrc power ndustres have been domnated by large utltes that had an overall authorty over all actvtes. These utltes generally control every actvty n the sector such as generaton, transmsson and dstrbuton of power. These utltes were vertcally ntegrated utltes and n such a system consumers had only one electrcty provder and they were payng the tarff set by the utltes. Unlke the regulated market, however, deregulaton leads generaton, transmsson and dstrbuton to be splt and ndependent actvtes. The man drvng force behnd ths radcal change from the ntensvely monopoly to a deregulated electrcty market was the fact that competton could result n an effcent utlzaton of resources; that leads to supplyng the end customer wth a cheaper but yet more relable energy supply. Followng the early attempts of Latn Amerca, Brtan, Australa, Calforna, and the Scandnavan countres, most countres around the world have found themselves restructurng ther respectve electrcty markets [].

13 In the new deregulated market there are dfferent market players or partcpants ncludng generators, nvestors, traders, and load servng bodes that are engaged n the day to day actvtes of the market. Unlke the regulated market, n whch the utltes are the one who has the power to set the electrcty prce, the deregulated market s a customer drven market (prce s set by the supply-demand relatonshp) and customers have the rght to choose among dfferent electrcty supplers. Ths mples that knowng the supply-demand balance ahead of tme s extremely mportant for all market players and partcularly for generatng companes. Ths n turn mples the supply-demand balance, and hence the electrcty prce, must be pre-estmated before real tme operaton for maxmzng proft. And, snce the day the electrcty market has changed the way t functons, the need to precsely predct future electrcty prces has become a hot ssue n the area. Prce forecastng plays a key role n the new electrcty ndustry; n addton to helpng ndependent generators n settng up optmal bddng patterns and also desgnng physcal blateral contracts, market prces strongly affect the decson on nvestng a new generaton facltes n the long run. In general, dfferent market players need to know future electrcty prces as ther proftablty depends on them; whether t s the generatng companes or the ISO, large ndustral customers or nvestors, t s very crtcal to have ths forecast. One of the man reasons why electrcty prce forecastng s an mportant study s the very volatle nature of the market. Electrcty prces are hghly volatle by nature. Even though there always s a rsk of volatlty n almost every market, the degree of volatlty s hgher on electrcty markets than other markets. The man reason beng electrcal supply and demand need to be balanced n real tme; however, t s very costly to store electrcty. In general, there are a number of factors that affect the supply and demand balance and hence play a crtcal role on prce volatlty. Such factors nclude, among others, hydro generaton producton, avalablty of generatng unts, sudden changes n weather condtons, changes to prces of related commodtes such as fuel prce, and unexpected physcal problems n generaton and transmsson systems []. On the other hand, forecasts are uncertan because a number of prce determnants are not known n advance, such as weather, whch n turn affects the load or demand, and also future

14 ranfall, whch prncpally determnes the avalablty and amount of hydro generaton. Accordng to [3], there s more uncertanty n prce forecastng than n load forecastng and t's more complex because t needs forecastng of both supply and demand. As a result of ths very volatle and uncertan nature of electrcty market and the fact that electrcty s a commodty that consumers need n ther daly lfe to a great extent, a precse prce forecastng s of vtal mportance to all the players. Consequently, dfferent electrcty forecastng tools and models have been proposed by dfferent researchers across the globe. Equvalently to developng a forecastng model, the queston what s prce forecastng for each market player and how does each player use the forecast results n the process? s another pont of dscusson. Brefly speakng, prce forecastng for an ISO s determnng the Market Clearng Prce (MCP). However, t s not a true forecastng process for that t can smply calculate the MCP numercally after recevng bds from the dfferent partcpants [4]. In the contrary, for a generatng company forecastng s about predctng the MCP ahead of submttng ts bd wthout knowng the prces of other generatng companes (ts market opponents). Based on only a few avalable data, such as forecasted load, forecasted weather condtons and hstorcal data, generatng companes need to predct for future MCP. In a pool market, where electrc power sellers and buyers submt bds to a centralzed market place that clears the market for them, partcpants should submt a bd/offer that s as close to the MCP as possble. Otherwse, f the bd of a market partcpant s too hgh, t may end up wthout sellng any of ts energy. On the other hand, f the offer of a partcpant who competes for buyng power s too low, t may not be able to purchase [5]. In general, therefore, market predcton must generate a prce that s close to the MCP. MCP n power markets may be determned n the approach dscussed below. After all the partcpants submt ther respectve bds, all purchase and sell orders are aggregated nto two curves; one beng an aggregate demand curve and the other beng an aggregate supply curve. The system prce s then determned by the ntersecton of the aggregate supply and demand curves whch represent all bds and offers. In fgure, for nstance, the MCP s the ntersecton pont of the supply and demand curves. 3

15 Fgure : Determnaton of MCP Gven the above complex nature of the new electrcty ndustry, ths thess addresses the man ssues n the determnaton of the future electrcty market prce and also develops models for forecastng these energy prces. It also brefly presents the ssues of strategc bddng n the deregulated market where the objectve of generatng companes s maxmzng ther proft. Ths thess addresses the sad subject and dfferent prevously presented approaches are dscussed together wth the generaton schedulng problem. A seres of prevous prce data from the Nord Pool market s used to study the nature of the market and consequently develop forecast models.. Objectves of the Work Havng n mnd, n one hand, the sad very volatle, uncertan and hardly predctable nature of the electrcty market and knowng that electrcty s a commodty that every customer needs every day, on the other, the man objectves of ths thess work are presented below: - Make a thorough study of the electrcty market to fnd out whch of the determnng factors play the man role n settng the next days electrcty prce for a gven power market. - Revsng prevous researches n the area to evaluate the performance of the most effcent forecastng tools. 4

16 - Develop smple prce forecast models so that dfferent market players can use them to predct the next day electrcty prce of a respectve market. - Makng a forecast usng the developed models and compare the result wth the actual values to evaluate the performance of the models. - Dscuss how generatng companes use the forecast nformaton to formulate a successful bddng strategy and present a bref revew n the subject..3 Outlne of the Thess Chapter dscusses about strategc bddng n the deregulated electrcty market. Ths chapter brefly presents generaton schedulng problem and also revses prevous works n the subject. Strategc bddng s also presented and some conclusons are drawn. Chapter 3 presents a detaled revew of the electrcty market n the deregulated envronment. It also presents the dfferent approaches that can be used n forecastng dscplne. A detaled lterature revew of electrcty prce forecastng s presented dscussng prevously presented approaches ncludng ANN and ARIMA models. Fnally, a summary of these prevous works s presented and the usefulness of these works to the present thess s also dscussed. Chapter 4 presents a bref revew of the man factors that greatly affect the electrcty market prce n the deregulated market. It also dscusses the approaches and procedures that are followed to develop forecastng models where a multple lnear regresson approach s proposed. In Chapter 5 an overvew of the Nord Pool market s presented. Ths chapter also presents the developed models and the forecast results together wth ther comparson wth actual market values. In Chapter 6 the relatonshp between hydro reservor level and market clearng prce s dscussed n detal. Data from the Nord Pool market s used for the analyss. Accordngly, dfferent correlatons between the two varables are observed and the results are dscussed. Fnally, Chapter 7 presents the summary of the work and draws some conclusons based on the results found. At the end, t suggests drectons to future researchers n the feld. 5

17 _ Strategc Bddng: A Bref Dscusson In the deregulated ndustry the sole objectve of generatng companes s to maxmze ther beneft. To acheve ths objectve each generatng company formulates ts own strategc bddng. In ths secton a bref dscusson on ths subject s presented. Dfferent prevously presented approaches are dscussed and the generator schedulng problem together wth the PBUC s also addressed. PBUC s the schedulng of all avalable generatng unts n a way that cheep unts are scheduled to run frst and the expensve unts wll run only f the demand can not be meet wth the cheep avalable unts; the objectve beng maxmzng proft.. Introducton In the prevous chapter the overwhelmng transton of the electrcty ndustry towards deregulaton and the nature of the market are dscussed n detal. Added to that, the need to precsely forecast the market prce s also dscussed. Prce forecasts are mportant nputs for dfferent market players to make decson n ther day to day actvty n the market. For nstance, generatng companes, havng the objectve maxmzng ther proft, need to have a good forecast or estmate of next day s electrcty market prce so that they can organze ther generaton schedulng accordngly and also prepare ther bd strategcally. Ths chapter dscusses how generatng companes schedule ther producton based on forecasted electrcty prces and consequently presents a bref summary of prevously proposed strategc bddng methodologes. 6

18 _. Prce Based Unt Commtment In pool markets GENCOs are requred to compete for energy supply and assocated prce and may be they also provde start up prce offers, mn up and down tmes, ramp rates etc. to the market operator. Based on the nformaton receved, the market operator carres out a unt commtment to arrve at an optmal dspatch and settle the market and hence schedule the generaton. However, n blateral markets and also n some pool markets, the GENCOs are expected to carry out the unt commtment. The followng fgure shows the operatons plannng actvtes of a GENCO n blateral market wth the opton of partcpatng n the daly spot market. Ths s also applcable to GENCOs n pool markets where unt commtment decsons have to be nternalzed whle placng ther bds [6]. Fgure : Short-term operatonal plannng actvtes of a GENCO partcpatng n electrcty market trades [Source: 6] 7

19 In the old vertcally ntegrated monopolstc electrcty market, unt commtment s the schedulng of generatng unts so that avalable generatng unts run n such a way that total producton cost s kept to a mnmum whle all system and unt constrants are met. In the contrary, n the deregulated electrc power ndustry, however, unt commtment has a dfferent objectve. In the new envronment generatng companes compete to sell ther product (energy) havng the sole objectve of makng the maxmum possble proft. In the process they try to optmze ther generaton resources n order to maxmze ther proft. Ths optmzaton of all avalable resources to maxmze proft s referred to as unt commtment. It s nothng more than a wse schedulng of the avalable generatng unts so that cheep unts are scheduled to run frst whle expensve unts are kept uncommtted as long as the demand s met wth the cheep avalable unts; the objectve beng maxmzng proft. Ths schedulng usually spans from 4-hours to week ahead and plays a crucal role n developng successful bddng strateges. Once the hourly prce forecast for the next day s avalable, the GENCO can organze ts generaton schedule that maxmzes ts proft based on the forecasted prce and the avalable generaton unt and ther characterstcs [6]. As sad above, the objectve of the GENCO s maxmzng ts proft and the objectve functon s gven n [6] as: Proft = Revenue from Mathematcally t s gven as: - Payment for [ spot market sell + blateral power sell] spot market buy + unt operatng costs + start - up costs + shut - down costs () proft = ρ Mk PSell k + BC k CP k ρ NG k W, k CMn + PG, k GCst + UST, k ST + USD, k SD = Mk Buy k () Where: K s ndex of tme, ρ M s the spot market prce, PSell and PBuy are decson varables denotng the amount of power to be traded (sold and purchased, respectvely) from the spot market, BC s the blateral contracted power at a prce CP, CMn s the generaton cost at mnmum generaton lmt of the unt (P Mn ), GCst s the generaton cost beyond PMn, ST s the unt start-up cost and SD s the unt shut-down cost. W, UST, and USD are 8

20 bnary varables denotng unt status (=ON, 0=OFF), unt start-up status (=Start-up, 0=NO) and unt shut-down status (=Shut-down, 0=No) respectvely. Whle schedulng ts generatng unts and optmzng ts generaton so as to meet the blateral contracts and trade durng the next day, the GENCO should take a number of complex ssues nto account. These complex ssues may arse from the fact that electrcty market prces are very uncertan n the deregulated ndustry. Added to that, there are dfferent techncal constrants related to unt operatons such as mnmum up and down tmes, mnmum and maxmum generaton lmts and others [6]. These constrants are presented mathematcally below:. Unt Generaton Lmts: P Mn P, k W, k P Max (3). Unt Mnmum ON/OFF Duratons: MUT V th n= MDT U th m=, k n+ ; k MUT, k m+ ; k MDT (4) (5) 3. Unt Rampng Constrants: P RUP P as unt ramps up (6), k, k P RDN P as unt ramps down (7), k, k 4. Must-run: W = ; MR; k (8), k In [7] dfferent methods that have been used to solve the UC schedulng problems are presented. The method used for the UC schedulng may vary dependng on the type of forecasts (load, nflow or prces), dfferent tme nterval, system combnatons and system constrants. Some of these methods nclude prorty lst, expert system, lnear and non lnear programmng, dynamc programmng and smulated annealng. However, lke the one used n the tradtonal electrcty markets, all the methods proposed above are based on cost 9

21 mnmzaton objectve. In the sad paper a genetc algorthm for the PBUC problem whch consders softer demand constrants and allocates fxed and transtonal costs to scheduled hours s dscussed va a cross-reference. A 0/ mxed nteger lnear programmng to maxmze the unt proft from sellng both energy and spnnng reserve n spot market s also dscussed. Each method may have ts own advantage and dsadvantage as a result of the forecast, the system constrants or other factors. However, the objectve n all cases s maxmzng proft. Therefore, dependng on an approprate method, optmal power schedulng can be planned and hence successful bddng strateges. Once the next day s UC and tradng decsons for buy/sell are obtaned usng an approprate method, the next stage s to determne the bddng strateges [6]..3 Strategc Bddng Due to the nature of the electrcty ndustry, the present power market s more or less an mperfect compettve market. The man reasons, among others, are frst customers have dffcultes n choosng ther preferred suppler due to network transmsson constrants. Added to that, snce the ndustry needs a large nvestment, there are only a lmted number of supplers. Ths mperfect nature of the ndustry gves generatng companes to bd at hgher prces than ther margnal producton costs and ncrease ther profts. When a generator bds for a prce that s dfferent from the margnal cost wth the ntenton of ncreasng ts proft, t s called strategc bddng; and the establshng an optmal bddng strategy to maxmze ther proft s an mportant task for the generatng company [8]. There are a number of parameters that affect the bddng strategy of a GENCO. Whle the techncal constrants on unt operaton, load and weather forecast and hydro energy avalablty are dscussed to be some of the man factors [6] has underlned the mportance of market clearng prces of the prevous day and also MCP spannng up to the past years. Ths nformaton together wth a good forecast of the next day s prce s sad to be a very mportant nput n formulatng bddng strateges. It s also underlned that t s very crucal to be aware of the unt generatng costs and the system margnal cost characterstc as generaton s ncreased. In general, a successful bddng strategy could be generated from understandng the complex nteracton between the dfferent techncal aspects of unt 0

22 operatons, economc nterests of the GENCO as well as the uncertantes assocated wth market tradng. In recent years a number of strategc bddng models have been proposed by dfferent researchers. These dfferent approaches can generally be grouped nto three man categores. The frst category refers to the approach that s based on estmatng the market clearng prce; consequently, bd prce s then determned to be slghtly lower than the estmated MCP. The second one s based on games theory and the thrd category s based on estmatng the bddng behavor of compettors based on ther prevous bddng data. Furthermore, market smulaton and emprcal analyss methods have also been used to nvestgate strategc bddng behavor, but reported for not leadng to systematc approaches for buldng bddng strateges [9]. In the frst approach, once the MCP forecast s found, determnng the bddng strategy s straghtforward; bd prce can be determned to be slghtly lower than the forecasted MCP. However, as t s dscussed prevously electrcty prce forecastng s a complcated task. Ths method has seldom been appled n developng bddng strateges n electrcty markets. Game theory s another approach and a number of publcatons have been carred out to address the bddng strategy problem usng ths approach and t has been used as a means of developng a successful bddng strategy n the newly deregulated electrcty market. Ths approach takes the fact that market partcpants react to compettor strateges n order to maxmze ther pay-off nto account [0]. In [] game theory was used to develop a strategc bddng where a competton among partcpants of a pool market was modeled as a non-cooperatve game. In the paper t was assumed that each partcpant has ncomplete nformaton of the game; partcpants know only ther own operaton costs. And a game of complete but mperfect nformaton s formulated where techncal constrants are not consdered and the game was solved usng Nash Equlbrum soluton. The thrd approach s based on the bddng behavor of the market opponents and accordng to [9] most of the methods publshed so far are based on estmatons of bddng behavor of

23 compettors n whch dfferent technques, such as probablty analyss and fuzzy sets are utlzed for estmaton. Whch ever method s mplemented to strategc bddng, the objectve s maxmzng the GENCO s proft n the market. Hence, once the prce forecast s made for the next day and the generaton schedulng s made accordngly, the GENCO can formulate ts bddng strateges usng the above nputs such as the prce forecast nformaton and the approprate generaton schedule and consequently submt ts bd.

24 _ 3 Prce Forecastng n Deregulated Electrcty Market: A Comprehensve Revew Followng the poneerng restructurng of the electrcty ndustry n the early 980s, dfferent market players are engaged n the new deregulated market today. Ths new market s customer drven and prce forecastng plays a crucal role to every market player. Followng ths fact, a number of prce forecastng approaches have been developed. Tme seres models are among the proposed approaches wth reasonably good results. ARIMA models, for nstance, are reported to predct market prces wth a reported MWE forecast error of up to only 5% n Calfornan market whle TF and DF models gve a result wth an average weekly error of only 3% for the same market. On the other hand, a MAPE of about 9% s reported usng ANN for the England-Wales market. In ths secton prce forecastng n the deregulated electrcty market s studed and detal lterature revew on dfferent prevously reported forecast models s also presented. 3. Introducton In Chapter, the transton of the electrcty ndustry from the vertcally ntegrated monopolstc market to the one domnated by compettve market has been presented n detal. Followng ths reform, a new wndow has been opened to researchers, economsts, software developers, and dfferent professonals across the globe. Economsts work hard to assess the mpact of the new ndustry on a respectve naton; researchers work day-n-dayout to address the dfferent ssues n the area, for nstance, market behavor and system stabltes; software engneers contrbute ther best to fnd some means for mmckng a 3

25 system and consequently solve system problems, securty ssues, make predctons and a lot more. In ths newly deregulated ndustry prce forecastng has become ncreasngly mportant to every market player engaged n the sector. However, ths was not the case under the regulated market where prce forecastng was all about estmatng the overhead cost of the utlty, or forecastng the components that make up the prce [3]. The utltes set the tarff based on ther total cost of generaton, transmsson and dstrbuton and customers had no opton but to pay the tarff set by these utltes. The electrcty prce n the deregulated market s characterzed by ts very volatle and uncertan nature. The nature of a market may vary from one naton to another based on dfferent factors such as geographcal locaton and type of the electrc power plant. However, due to the fact that a number of factors determne the prce, the market n general s very complex and dffcult to deal wth. Unless we have ample nformaton on these factors and the extent of ther nfluence on the market, t would be hard to accurately predct the market regardless of the market under study or the forecast model used. As sad earler, every market player needs to know the electrcty prce ahead of real-tme operaton for one or other reason. It s very mportant for load servng bodes to know the amount of power that ther customers are lkely to use and also how best to secure ther needs through a mx of long term and short-term contracts. On the other hand, knowng how prce varatons among dfferent regons may affect dspatchng of generators and demand on the transmsson networks s a determnant factor for transmsson organzatons. Smlarly, large ndustral customers need to assess ther exposure to market prce volatlty and hedge ther rsks through long-term, fxed prce contracts, partcpaton n demand response programs, tme of use rates, nterruptble load programs and so on [3]. Recallng the fact sad above, electrcty prce forecastng has drawn the attenton of dfferent scholars and researchers across the globe n the past few decades. Beng a new area of nterest, a number of prce forecastng methods for the electrcty market have been proposed recently. In general, these prce forecast tools fall n to two man categores (approaches). 4

26 The frst approach s the detaled market smulaton approach n whch a lot of market nformaton s needed. Power utltes and market operators manly use these smulatonbased methods. In these methods the actual market dspatch s mtated by consderng ntal supply offers, demand bds, and system operatng constrants. However, as these methods requre full nsght nto the system operaton, they are not practcal for market partcpants. The second category refers to those that are based on mathematcal or analyss-based approaches. These approaches forecast future prces usng hstorcal operaton data [, ]. In ths thess work analyss-based method has been used for electrcty market prce forecastng n the deregulated market. In ths part of the thess the study of electrcty prce forecastng, the dfferent approaches to the problem and a revson of prevous studes n the area are presented n detal. 3. Tme Seres Analyss and Its Applcatons A tme seres s a set or sequence of observed data arranged n chronologcal order and n an equally spaced tme ntervals such as daly or hourly ar temperature. Tme seres occurs n many felds and the analyss of tme seres has got a wde applcaton n areas lke process control, economc forecastng, marketng, populaton studes, bomedcal scence and many more areas. Tme seres analyss uses systematc approaches to extract nformaton and understand the characterstcs of a physcal system that creates the tme seres. There are a number of dfferent approaches to deal wth tme seres analyss ncludng dynamc model buldng and performng correlatons. Analyzng a tme seres may arse from dfferent objectves of the analyst. One may be nterested n process or qualty control; for ths scenaro a tme seres whch measures the qualty of a manufacturng process can be generated. It can also be used to obtan descrptve or statstcal measures of a tme seres. In another scenaro, f n case observatons are taken on two or more varables, t may be possble to use the varaton n one varable to explan the varaton on the other; ths can help to understand the nature of the relatonshp between the two. Fnally, one may be nterested to predct future values based on an observed tme seres. Ths s very mportant n sales engneerng and the analyss of economc and ndustral tme seres [3]. 5

27 Buldng mathematcal models for an observed tme seres and consequently usng these models to make tme seres forecastng s one of the most mportant applcatons of tme seres analyss. Tme seres forecastng s the predcton of future events based on already known past events usng an approprate model. Accordngly, there are dfferent models that can be used for tme seres forecastng. 3.. Lnear Tme Seres Models and Forecastng 3... Autoregressve Models In the feld of statstcal modelng of tme seres, Autoregressve (AR) processes and Movng Average (MA) processes are may be the most mportant approaches. Autoregressve (AR) models of a tme seres can be used to forecast the value z t of a tme seres based on a seres of prevous values z t, z t,...z t p. An AR model can smple be defned as: Z t = C + φ Z t + φz t φpz t P + ε t (9) Where: φ, φ, φ 3,... φ p are coeffcents; ε t s a forecast error and C s a constant Ths AR model s called AR model wth an order of p and the current value Z depends on or related to prevous values. The above equaton can also be wrtten equvalently as: Z t p = C + φ Z t + ε t = (0) 3... Movng Average Models Movng Average (MA) s also one of the technques used n the analyss of tme seres. It s found by takng the average of sub sequences. As the process n a tme seres goes on, each new observaton s added to the average and the oldest observaton may be dropped and hence the average moves; consequently, the name movng average. A MA model s mathematcally defned as: Z t = ε + t q j= θ ε j t j () Where θ j are model parameters and ε t s error 6

28 _ ARIMA Models Autoregressve Movng Average (ARMA) models are among the very useful models n statstcs that can be used to understand a tme seres data or for future predcton. These models are formed by combnng AR and MA models. Gven an equally sequenced values of a statonary stochastc process Z by Z t, Z t,..., an ARMA (p, q) can be expressed as [4]: Z t p φz t + ε t + = = C + θ ε q j= j t j () Where c, φ and θ j are the model parameters to be estmated and ε t s an error Most tme seres n practce are non-statonary. In order to ft a statonary model, such as the one dscussed above, t s necessary to remove non-statonary sources of varaton. If the tme seres that we are nterested about s found to be non-statonary n the mean, then the seres can be dfferenced. By ntegratng ARMA (p, q) process to the d th order, a model that s capable of descrbng certan types of non-statonary seres can be found. Ths model s called Autoregressve Integrated Movng Average or ARIMA (p, d, q), where d s a postve nteger [4]. ARIMA models have been used n dfferent areas where there s a need for tme seres and, n the past have been manly used for load forecastng due to ther satsfactory accuracy and mathematcal soundness. In recent years ARIMA models have been proposed as electrcty prce forecastng tools. Contreras et al. [5] have proposed ARIMA models to predct next-day electrcty market prces for the Spansh and Calfornan markets. Whle a separate modelng for the two markets s proposed n the paper, the proposed general ARIMA formulaton has the followng form: φ ( B) p t = θ ( B) ε (3) t Where P t s prce at tme t, φ(b) and θ (B) are functons of the backshft operator B: B l p t = P t- andε t s the error term; ths term s assumed to be a randomly drawn seres from a normal dstrbuton wth zero mean and constant varance δ. Functons φ(b) and θ (B) have specal forms and they can contan factors of polynomal functons of the form B l Φ φ( ) = φ B l and/or B l Θ θ ( ) = θ B l. = = l l 7

29 Accordngly, the authors have developed the fnal models for both markets. The proposed model for the Spansh electrcty markets s presented below: ( φ B φ 0 B ( θ 0 68 φ B φ B φ B B θ B 3 φ B ) ( φ θ B B 5 φ B ) ( φ B φ ) ε t 336 B φ B φ B )log p φ B t φ B 48 = c + ( θ B 48 φ B φ B θ B )( θ B Accordng to the paper, these models were tested for ther accuracy on both the Spansh and the Calfornan markets and Average Mean Weekly Errors (MWE) of around 0% n the Spansh market and around 5% n the stable perod of the Calfornan market (or around % consderng the three weeks, and wthout explanatory varables) are reported ) (4) Smlarly, a day-ahead electrcty prce forecastng tool usng the wavelet transform and ARIMA models s proposed by [6]. The paper dscussed use of the wavelet transform to decompose the hstorcal and usually ll-behaved prce seres nto set of better-behaved consttutve seres. It s dscussed that the use of the wavelet transform as a preprocessor of forecastng data mproves the predctng behavor of any technque such as ARIMA, transfer functon, neural network and others; t convert a prce seres n a set of consttutve seres. These seres present a better behavor (more stable varance and no outlers) than the orgnal prce seres, and therefore, they can be predcted more accurately. It s reported that test results on the electrcty market of manland Span for the year 00 have shown good forecast accuracy; a weekly error of about 4.78% for wnter season and about.7% for the fall season beng the mnmum and maxmum forecast errors respectvely. The paper has compared the results found usng the proposed Wavelet-ARIMA model wth the standard ARIMA models and the later model gves a less accurate result. For the same study perod, ARIMA gves a weekly error of 6.3% for wnter and 3.78% for the fall season. Other ARIMA models that have been reported so far nclude [, 7, 8]. In [9], smple tme seres models wth and wthout exogenous varables, ARMAX and ARMA process, s studed where the system load has been taken as the only exogenous varable. In ths paper, as each hour dsplays a dstnct prce profle reflectng the daly varaton of demand, costs, and operatonal constrants, separately modelng for each hour of 8

30 the day (leadng to 68 models for a week) was dscussed and concluded for beng tme consumng and unsatsfactory and rather a sngle model for the whole week s proposed. The proposed models are tested usng the Calforna power market prces and loads from the perod proceedng and ncludng the market crash. Accordngly, mean weekly error (MWE) of up to about 3.04% and as hgh as 3.9% are reported. The forecast results are compared wth the results found usng dfferent methods ncludng DR, TF and ARIMA models. Whereas, the results found usng the proposed model are relatvely less accurate than DR and TF models, they are sad to have better accuracy than ARIMA models. In the present thess work a separate model for each hour of the day s used and dscussed n detal n the next chapters Transfer Functon (TF) Transfer Functon (TF) models are proposed to forecast electrcty market prces based on past electrcty prces and demand [8]. Ths approach deals wth seral correlaton and has been tested on the PJM electrcty market. Gven the electrcty prce at hour t denoted by p t and the correspondng electrcty demand d t and consderng the fact that these seres are not statonary, the followng expressons denote the transformatons to obtan statonary seres of demand and prce respectvely as [8]: x = f ( d ) and y = f ( p ) (5) t t Consequently, the transfer functon model that represents the relatonshp between the above two seres s gven as: Where B s the backshft operator: Bz modeled as: y = c + v( B) t x t t t + η t t k t, B zt = zt B zt = = z,..., z t k (6) and the functon v s v( B) = v c + v B + v B (7) and s denomnated the transfer functon and the coeffcents v n ths functon descrbe the dynamc relatonshp between the demand and prce seres. The predcton model that s developed by [8] based on the above transfer methodology s gven below: 9

31 Wth: Where a t s the whte nose 4 68 w0 + w B + wb + w4b + w68b v B) = (8) 4 ( δ B )( δ B ) ( ( φ B)( φ B ( θ B θ 68 4 B 68 4 )( φ )( θ B 4 68 B 4 68 ) η = t 8 θ B )( θ B 68 ) a t (9) As can be seen above, the paper relates the prce at hour t to the values of demands at hours t, t-, t-, t-4 and t-68. It s reported that testng the performance of the developed models usng the PJM electrcty market resulted n a prce forecast wth a MAPE error of about 9.50% Regresson Analyss Many problems n engneerng and scence nvolve explorng the relatonshps between two or more varables. Regresson analyss s a statstcal technque that s very useful for these types of problems. Regresson has got wde applcatons ncludng predcton and process control. In regresson analyss, the am s to model the dependent varable n the regresson equaton as a functon of the ndependent varables, constants and an error term. The performance of the model depends on the estmate of the constants and coeffcents [0]. In the followng sectons dfferent types of regresson models are presented Smple Lnear Regresson Models A smple lnear regresson consders a sngle regressor or predctor x and a dependent or response varable Y. Assumng the relatonshp between Y and x s a straght lne and that the observaton Y at each level of x s a random varable, the expected value of Y for each value of x s: y = β 0 + βx + ε =,, 3,...,n (0) Where the ntercept β0 and the slope β are unknown regresson coeffcents and ε t s a random error. Ths reference has been extensvely used for the dscussons under sectons and 4. 0

32 _ Multple Lnear Regresson Models As sad above, f a dependent varable s affected by only one ndependent varable, then the tme seres s a smple lnear regresson. However, f there are more than one ndependent regressor varables n a tme seres, then the regresson model s sad to be multple regresson model. In general, the dependent varable or response Y may be related to k ndependent or regressor varables. The general form of multple regresson model s: Y = β 0 + βx + β x β k xk + e () As t s presented mathematcally, ths approach models the relatonshp between two or more explanatory varables and a dependent varable by fttng a lnear equaton to the observed data. To estmate the parameters or regresson coeffcents the method of least square can be used. Once the coeffcents are estmated, the new value of the dependent varable can then be easly found. The above approach s dscussed n detal n [0]. In the present thess work multple lnear regresson method s used to predct electrcty prces n the deregulated electrcty market Dynamc Regresson Models Lnear and multple regressons dscussed above are n general called tradtonal regressons. If the data under study have rregular and cyclcal component that mght not ft well wth the above tradtonal regresson models, dynamc regresson (DR) models are good optons []. Dynamc regresson models are dscussed n detal n []. The relatonshp between a dependent varable y and a set of explanatory varables x, =,,3,,n, at tme t s expressed usng a constant c, a transfer functon f, and a dsturbance term N t as follows: t ( x, t,..., xn, t N t () y = c + f ) + The dynamc regresson model s derved n the sad work and s presented as: y t n r j yt + φ yt φ p yt p ) + ω, j B x, t = j= 0 = c + ( φ + ε t (3)

33 ω, j corresponds to the coeffcents for x at lag j to be estmated, φ are model parameters to be estmated, B s a backshft operator and up to p past values of the dependent varable are ncluded as explanatory varables. The DR models were used n [] to forecast the Ontaro electrcty prce where a weekly MAPE error of about 5% s reported. Ths seems a poor forecast result; however, consderng the very volatle nature of the Ontaro market, t s concluded that ths error seems acceptable. Nogales et al. [] have also proposed a multvarate TF and DR models to forecast next-day electrcty prces n Spansh and Calfornan electrcty markets. Ths paper used demand as the only explanatory varable and the forecast results reported usng these TF and DR models have gven better accuracy than the standard ARIMA models; gvng an average weekly error of 5% for the Spansh and 3% for the Calfornan markets. 3.. Non-Lnear Tme Seres Models and Forecastng 3... GARCH Models General Auto Regressve Condtonal Heteroscedastc (GARCH) s among the well know tme seres analyss models used n the feld of statstcs and engneerng. The GARCH approach addresses the problem of homoskedastcty that other lnear tmes seres model, such as ARMA, do not deal wth. ARMA models generally assume a constant varance and covarance functon. Electrcty spot prces, however, present varous forms of non lnear dynamcs; the man one beng the strong dependence of the varablty of the seres on ts own past [3]. GARCH, a non-lnear tme seres model, was proposed by [4] to predct day-ahead electrcty prces where emprcal results from the deregulated manland Span and Calforna electrcty-markets are dscussed. Unlke ARIMA models, GARCH consder the moments of a tme seres as varant; the error term does not have zero mean and constant varance. In ths approach, the error term s assumed to be serally correlated and can be modeled by an Auto Regressve (AR) process. As a result, a GARCH process can measure the mpled volatlty of a tme seres due to prce spkes. The GARCH model presented by [4] provdes 4-hour