SPOT PRICE SIMULATION AND VOLATILITY ANALYSIS IN THE FUTURE IBERIAN ELECTRICITY MARKET

Transcription

1 SPOT PRICE SIMULATION AND VOLATILITY ANALYSIS IN THE FUTURE IBERIAN ELECTRICITY MARKET Jorge Sousa ISEL and FEUNL Lsbon, Portugal João Lagarto ISEL Lsbon, Portugal Ru Pestana REN, SA Lsbon, Portugal Abstract Prce volatlty s a maor ssue n lberalzed electrcty markets as far as rsk management s concerned. In ths paper we evaluate the mpact of the Portuguese and Spansh electrcty markets ntegraton on the day-ahead market prce volatlty. For that purpose we develop an adaptve conectural varatons model whch s mplemented n GAMS language. We estmate the degree of competton n the Spansh pool usng an teratve secant method appled to a conectural varatons olgopoly model. Usng the estmate obtaned, we smulate the Portuguese and Spansh markets n autarky and the ntegrated market, known as the Iberan Electrcty Market (IBELM). We present conclusons on the mpact of the IBELM on prces and volatltes from the Portuguese and Spansh markets pont of vew. Keywords: Prce volatlty, Rsk management, Conectural varatons, Iberan Electrcty Market, GAMS smulaton 1 INTRODUCTION In the past, power electrcty systems were run by vertcally ntegrated, typcally state owned, monopolstc companes, comprsng the generaton, transmsson, dstrbuton and supply actvtes. Maor uncertantes were passed through the fnal consumers by a tarff that ncluded all operatng and nvestment costs. Ths structure has been crtczed on dfferent grounds and reforms have taken place n many countres around the world. In lberalsed electrcty markets power producers and customers face a market rsk wth prces that can be very volatle, beng prce volatlty defned as a measure of the fluctuaton n prces observed over a perod of tme. Unlke other commodtes, electrcty lacks of relevant storage mechansms (wth the excepton of pumped storage hydro plants) whch mples the need for a contnuous balancng of demand and supply. On the other hand, n the short run, demand s very rgd n respect to prce. As a result, electrcty prces can change drastcally compared to the prces of other commodtes or equtes, leadng to an electrcty prce volatlty consstently and sgnfcantly hgher than other products. A large number of parameters determne prce volatlty such as fuel prces, foregn exchange rates, varaton n hydroelectrc producton, generaton avalablty, demand varablty and network congestons. Dfferent approaches for measurng wholesale electrcty market prce volatlty have been proposed by several authors. Alvarado and Raamaran [1] modelled electrcty prces assumng a random walk process wth a strong mean reverson, usng a frequency doman analyss to separate the cyclc component of prce. Benn et al. [] analysed the spot market prce volatlty n Span, Calforna, UK and PJM markets usng the concept of the expected prce. Ths tme doman approach was used to decompose the cyclc and random components of electrcty prces. Other studes were developed to ncorporate volatlty and estmate wholesale electrcty prces [3,4], as well as quantfyng rsk exposure of generaton companes (GENCOs) applyng fnancal methods lke Value-at-Rsk (VAR) [5]. For some authors electrcty spot market prce volatlty can be mtgated by usng dscrmnatory prce auctons (DPA) nstead of unform prce auctons (UPA) [6]. However, ths approach s crtczed on the grounds that DPA produce prces that converge to the level of the hghest prces observed wth the UPA [7]. The new world of uncertanty requres rsk management tools such as dervatve securtes (forwards, futures and optons) and blateral tradng [8]. In ths regard, t s of great nterest to evaluate the mpact of electrcty markets ntegraton, such as the upcomng Iberan Electrcty Market (IBELM), startng operaton foreseen untl June 5, whch ams the full lberalsaton and ntegraton of the Portuguese and Spansh electrcty markets. Bearng n mnd that the mpact of such an ntegraton s a maor concern for the Iberan power producers and consumers, we answer the followng queston: What s the mpact of the Portuguese and Spansh electrcty markets ntegraton on the day-ahead pool prces volatlty? For that purpose we carred out a study based on a 744 hourly demand data for the month of October. A pre-processng of the nput data was needed for the Spansh hydro generaton, snce t was avalable on a daly bass only. Therefore, a short-term hydrothermal model [9] was used to dvde the daly hydro energy reported by REE [1] nto equvalent hourly data. Portuguese power data was gven by the Portuguese system operator REN. A conectural varatons model was used to smulate the Portuguese and Spansh prce and volatlty n comparson to the smulated IBELM outcome. The 15th PSCC, Lege, -6 August 5 Sesson 15, Paper 5, Page 1

2 compettve paradgm among frms s modelled usng the proposed concept of adaptve conectural varaton. ADAPTIVE CONJECTURAL VARIATION Conectural varatons models became popular n electrcty markets smulatons because of ther ablty to forecast prces n lne to real data. In ths study we propose an orgnal contrbuton by adustng a conectural varatons model to observed data n order to access the degree of competton n each smulated perod. The model comprses supply, demand, market equlbrum and adaptve conectural varatons. From the supply sde, GENCOs bds are establshed by ther optmal strategy assumng a conectural varatons model. Demand s ftted to observed data from the Spansh pool - OMEL [11] usng a sgmod type functon. Market equlbrum s smulated usng a mxed complementary problem formulaton. The concept of adaptve conectural varaton s ntroduced to measure the degree of competton observed n each hour of OMEL. Ths level of competton s then assumed for the smulatons of the Portuguese, Spansh and IBELM markets for the same hours..1 Supply The supply of electrcty s done by GENCOs that hold dfferent generaton portfolo technologes. Each frm s cost s gven as a functon of ts output, accordng to equaton (1): C ( ) q a + b q + c q = (1) where q s the output of GENCO and a, b and c are non-negatve coeffcents. The margnal cost of generaton s gven by () as the dervatve of (1). () C ( q ) = b + c q In our model the coeffcents b and c are estmated usng a least squares mnmzaton (3). The parameters are computed so that the hghest valuaton pont and equlbrum pont are exactly matched, whch corresponds to ponts A: (, P max ) and B: (Q*, P*) n Fgure 1. P [c /kwh] A : (, Pmax) B : ( Q*, P*) Sgmod OMEL Demand OMEL Supply Q [MWh] Fgure 1: Sgmod fttng of the nverse demand. The demand that corresponds to (4) s gven by solvng the equaton n order to Q. k P Q( P) = k + ln (5) k1 P The demand of the Portuguese and Spansh systems n autarky, as well as ntegrated n the IBELM, s computed by extrapolaton of (5). Ths consderaton leads to the followng expresson for market m (Portugal, Span and IBELM): k P Qm(P) = βm Q(P) = βm k + ln (6) k1 P where β m s the scale factor gven by the relatonshp between the demand of market m and OMEL. The nverse demand functon of each market s then gven by: ( b, c ) m x = 1 x 1 [ b + c x y ] mn dx (3) Pm (Q) = k 1+ k1 e Q k βm (7) where x s the nstalled capacty by technology and y the correspondng varable costs.. Demand The nverse demand curve s ftted to the observed OMEL data usng a proposed sgmod type functon wth parameters k, k 1 and k, gven by expresson (4): k P( Q) = 1+ k eq k (4) 1.3 Market equlbrum The market equlbrum s reached by the soluton of the proft maxmzaton problem of the frms competng n an olgopoly market, wth cost functon defned by (1) and facng an exogenous nverse demand curve gven by (7). Ths problem s defned for frm n (8): max q s.t. π ( q ) = P( Q) q C ( q ) q K (8) 15th PSCC, Lege, -6 August 5 Sesson 15, Paper 5, Page

3 where q : power generaton of frm π : proft of frm Q : demand P(Q) : nverse demand functon C (q ) : generaton costs fo frm K : total nstalled capacty of frm The market clearng condton should also be met: q = Q (9) The soluton of (8) and (9) s reached usng game theory for the modellng of the strategc nteracton among all the frms. The necessary optmalty condtons (also suffcent for ths problem) of Karush-Kuhn-Tucker (KKT) for frm are gven by: KKT1: q K q : λ 1, λ (1) KKT: λ1 q = λ ( K q ) = (11) KKT3: dp P ( Q) + q C ( q ) + λ1 λ dq = (1) dp where represents the effect of the frm output dq on the market clearng prce (P). Ths effect can be decomposed nto drect and ndrect contrbutons, expressed by the chan rule of dervatve: dp dq P P = + q q q q P = ( 1 + θ) q where q q and θ =. q = (13) The parameter θ so defned represents the conecture that frm does about how ts rvals change ther quanttes s response to changes n ts own quantty. Therefore θ s called the conectural varatons parameter. The value of θ represents the degree of competton n the market. In fact, θ=-1 models the perfect competton paradgm whereas θ= represents the Cournot compettve outcome. Collusve arrangements among frms can be modelled by postve values of θ..4 Fndng the adaptve conectural varaton The conectural varatons model solves the market equlbrum for the supply and demand condtons wth the compettve paradgm assumed for the frms represented by parameter θ. Therefore, there exsts a dfferent market prce for each value of θ, assumng the same supply and demand condtons, whch represents the dfferent possble degrees of competton among frms, rangng from prefect competton (θ=-1) to colluson (θ postve). The relatonshp between prce and the conectural varaton parameter led to the concept of adaptve conectural varaton as the value of the degree of competton compatble wth a gven observed prce. Ths approach s mplemented by an teratve process based on the secant method. From ntal values for θ we smulate the correspondent prce. A new value for θ s then computed by the secant method. Ths process s repeated untl the devaton of the observed prce (P*) and the smulated prce s lower than an arbtrarly small constant (δ). The flow chart of Fgure shows the teratve process descrbed. Intalzaton θ -1 =, Solve P(θ -1 ) : Cournot θ = -1, Solve P(θ ) : Compettve n = P* < P (θ ) Fgure : Fndng the adaptve conectural varaton parameter usng the secant method. Is should be noted that a value of -1 s assgned to θ when P* s lower than the smulated compettve prce, meanng that the market prce corresponds to a possble short-run undercuttng bddng stuaton. no Secant method no yes P( θ ) * n P ( ) ( ) ( θ ) n n 1 θ P θ θn+ 1 = θn θ P n n 1 Solve P(θ n+1 ) P(θ n+1 ) P* < δ Update θ n-1 = θ n, θ n = θ n+1, n = n + 1 yes θ = -1 θ = θ n+1 15th PSCC, Lege, -6 August 5 Sesson 15, Paper 5, Page 3

4 3 SPOT PRICE SIMULATION The model of adaptve conectural varatons was mplemented n GAMS language for the smulaton of the 744 hours of October. The observed and smulated prces of the Spansh pool are shown n Fgure 3 where the adaptve conectural varaton θ s also dsplayed. Compettve behavour close to perfect competton s observed n off-peak hours whereas the use of market power s evdent n peak hours. Usng the estmate hourly value of θ we smulate the market prce for Portugal, Span and IBELM, whch s shown f Fgure 4. From ths fgure t can be observed that Portuguese prces are always sgnfcantly hgher than the IBELM prces, specally n peak hours. On the other hand, Spansh prces are always close to the IBELM prces, beng lower n off-peak hours and hgher n peak hours. Ths fact can be explaned by the dfferences n compettve behavour among perods. In off-peak hours the nstalled capacty n sgnfcantly hgher than the demand and no frm has enough market power. Therefore, the perfect competton paradgm apples, and prces n the ntegrated market (IBELM) are n between the prces of the two separate markets (hgher n Portugal and lower n Span) as shown n [1]. On peak hours, when some frms produce at maxmum capacty, there s ncreased market power of the other frms on the resdual demand. In ths case, ntegraton has a mtgaton mpact on market power, leadng to a prce n the ntegrated market lower than the prce that would occur n each of the two separated markets, as descrbed n [13]. P [c /kwh] 7 θ \ Prc_OMEL P_Sp θteta Fgure 3: Observed OMEL prces (Prc_OMEL) vs smulated Spansh (P_Sp) prces and estmate conectural varaton (θ). P [c /kwh] 14 1 Portugal Span IBELM P_Pt P_Sp P_IBELM Fgure 4: Smulated prces for Portugal (P_Pt), Span (P_Sp) and IBELM (P_IBELM). 15th PSCC, Lege, -6 August 5 Sesson 15, Paper 5, Page 4

5 4 VOLATILITY ANALYSIS Prce volatlty s a measure of the varablty of prce n a gven perod of tme. In order to evaluate the prce volatlty we compute hourly prce changes (u t ), gven by (14). volatlty s lower than the volatlty of each market operatng separately. In order to calculate the prce volatlty trend over the month we defne a 4 hour rollng wndow n whch we apply the volatlty expresson (15), defnng ths way the one-day prce volatlty, gven by expresson (16). u P P P (14) t = t = t t 1 Prce volatlty s then gven by the estmate of the standard devaton of u. The volatlty s computed as n (15). s1day = 3 + t= ( u u ) t 3 (16) s = N ( ut u ) (15) t= 1 N 1 Usng the smulated prces for Portugal, Span and IBELM, dsplayed n Fgure 4, we compute the prce volatlty for each market accordng to expresson (15). Portugal Span IBELM Table 1: Prce volatlty for Portugal, Span and IBELM based on smulated October prces [c /kwh]. The results of prce volatlty shown n Table 1 present evdence that the ntegraton of the Portuguese and the Spansh electrcty markets nto the IBELM wll have a stablzaton effect on prces, snce IBELM prce The one-day prce volatlty for Portugal, Span and IBELM s shown n Fgure 5. The results dsplayed n Fgure 5 show that the IBELM one-day prce volatlty s always lower than the prce volatlty of the Portuguese and Spansh markets operatng separately. It can also be noted that weekdays have hgher volatlty than weekends. The results can best be understood f we look nto the prce smulatons presented n the prevous secton, as shown n Fgure 4. From the analyss of Fgure 4 t seems qute obvous that prce volatlty of the Portuguese market s much hgher that the prce volatlty of the Spansh and IBELM markets. For the Spansh market t s observed that prces change n a wder range than the prces n IBELM, beng lower n off-peak hours and hgher n peak hours. As a result, Spansh volatlty s consstently hgher than IBELM volatlty, as dsplayed n Table 1 and n Fgure 5. [c /kwh], 1,8 1,6 1,4 1, Portugal 1,,8,6,4,, Span IBELM s_1day_pt s_1day_sp s_1day_ibelm Fgure 5: One day rollng volatlty (s_1day) for Portugal, Span and IBELM. 15th PSCC, Lege, -6 August 5 Sesson 15, Paper 5, Page 5

6 5 CONCLUSIONS Ths paper shows the mpact on prce volatlty of the Portuguese and Spansh forthcomng market ntegraton foreseen for June 5. Usng hstorc data from OMEL, we access ths mpact usng a proposed model of adaptve conectural varatons to estmate the degree of competton presented n the Spansh pool. The results acheved for ths estmate show that the Spansh market s qute compettve n off-peak hours, wth prces very close to short-run margnal costs, characterzed by values of the conectural varaton parameter close to the perfect competton paradgm. In peak hours, our smulatons show evdence of ncreased market power due to the lack of nstalled capacty of some compettors. The degree of competton estmate for the Spansh market was used to smulate the autarky market prces of Portugal and Span, and the ntegrated IBELM market. As a result we conclude that autarky Portuguese prces are always hgher than the autarky Spansh prces and the ntegrated IBELM prces. Ths s due to the hgh market concentraton n Portugal and generaton technology portfolo of Portuguese GENCOs. Therefore, the ntegraton wth the Spansh market promotes prce reductons for Portugal snce t mtgates market power and nduces the use of more effcent technologes. Moreover, Portuguese prce volatlty s also lowered wth the IBELM creaton, once prce would vary n a much narrow range. On the other hand, autarky prces for Span change n a wder range n comparson to IBELM, beng lower n off-peak hours and hgher n peak hours. Ths s because off-peak hours are close to compettve and the ntegrated prce would be n between the two separate markets. In peak hours the effect of market power reducton s enhanced and IBELM prces are lower. Therefore the market ntegraton would promote a reducton on the Spansh prce volatlty. In concluson, we found strong evdence that IBELM wll promote prce stablty both from the Portuguese and Spansh markets pont of vew, leadng to a less rsky market for Iberan power producers and consumers. REFERENCES [1] F. Alvarado and R. Raaraman, Understandng Prce Volatlty n Electrcty Markets, Proceedngs of the 33 rd Hawa Internatonal Conference on System Scences, January [] M. Benn, M. Marracc, P. Pelach and A. Venturn, Day-ahead Market Prce Volatlty Analyss n Deregulated Electrcty Markets, IEEE Power Engneerng Socety Summer Meetng, Vol. 3, pp , July [3] R. Deb, R. Albert, L.-L. Hsue and N. Brown, How to Incorporate Volatlty and Rsk n Electrcty Prce Forecastng, The Electrcty Journal, Vol. 13, No. 4, pp 65-75, May [4] V. Nemeyer, Forecastng Long-term Electrc Prce Volatlty for Valuaton of Real Power Optons, Proceedngs of the 33 rd Hawa Internatonal Conference on System Scences, January [5] R. W. Dahlgren, C.-C. Lu and J. Lawarree, Volatlty n the Calforna Power Market: Source, Methodology and Recommendatons, IEE Proceedngs on Generaton, Transmsson and Dstrbuton, Vol. 148, No., pp , March 1 [6] T. Mount, Market Power and Prce Volatlty n Restructured Markets for Electrcty, Proceedngs of the 3 nd Annual Hawa Internatonal Conference on System Scences, Vol. 3, January 1999 [7] S. Rassent, V. Smth and B. Wlson, Dscrmnatory Prce Auctons n Electrcty Markets: Low Volatlty at the Expense of Hgh Prce Levels, Journal of Regulatory Economcs, 3: pp 19-13, 3 [8] J. Hull, Introducton to Futures and Optons Markets, Prentce-Hall, 1995 [9] A.J. Wood and B.F. Wollenberg, Power Generaton, Operaton & Control, John Wley & Sons, 1984 [1] REE - Red Eléctrca de España webste: [11] OMEL Compaña Operadora del Mercado Español de Electrcdad webste: [1] J. Sousa, and V. Mendes, The Iberan Electrcty Market - Impacts on power producer profts, consumer surplus and socal welfare n the wholesale market, Proc. ENERGEX 4, May 4 [13] J. Sousa and V. Mendes, Integraton of Electrcty Markets: Impacts on Power Producer Profts, Consumer Surplus and Socal Welfare, Proc. 8 th Portuguese-Spansh Congress n Electrcal Engneerng, July 3 15th PSCC, Lege, -6 August 5 Sesson 15, Paper 5, Page 6