19 t ational Conference of te Hellenic Operational Researc ociety (HELOR 007), Arta, Greece, Jne 1-3 007. Modelin te Greek Electricity Market Panaiotis Andrianesis, Geore Liberopolos, Geore Kozanidis Department of Mecanical & Indstrial Enineerin, University of Tessaly, Volos, Greece pandrianesis@otmail.com, lib@mie.t.r, koz@mie.t.r Abstract Electricity market derelation as triered a nmber of sinificant canes in te Greek enery sector, mostly by allowin private-owned companies to become prodcers and sppliers of electricity. Tis paper examines te Day-Aead-cedlin (DA) proram wic was recently introdced by te new Grid Control and Power Excane Code for Electricity and forms te basis of te wolesale electricity market operation. DA aims at minimizin te total cost of servin enery load for te next day, nder conditions of ood and safe system operation, wile ensrin adeqate reserves. Te proram optimizes bot enery and reserve markets simltaneosly and incorporates a mecanism tat encoraes installation of new eneratin nits near consmption. Te oal is to maximize social benefit. Greece s special caracteristic is tat most of its power plants are located in te ort wile most of te enery consmption takes place in te ot. As a reslt, in case of excess load, a transmission constraint is activated, proibitin te transfer of te desired amont of enery from te ort to te ot. To deal wit tis particlarity of excess capacity in te ort, Greece is divided into two operational zones (ort ot) and prodcers are paid in different prices (Marinal Generatin Prices) wen te above transmission constraint is activated. In tis paper, we present a brief jstification of te two-zone model. We also make assmptions reardin te market rles and te nmeros tecnical constraints tat apply to te eneratin nits and to te transmission system in order to state a basic DA model. Te problem is formlated as a mixed inteer linear prorammin model and is solved sin te optimization software packae ILOG CPLEX 9.0. Finally, we propose a metodoloy in order to compte te ystem Marinal Price, wic is te price tat sppliers pay for enery. Reslts reveal an interaction between enery and reserve markets tat deserves frter investiation. Keywords: Electricity Market Derelation, Day Aead cedlin, ystem Marinal Price 1. Introdction Competition was introdced into te electricity sector in te 90 s, and liberalization proceeded wit different rates in varios parts of te world. In Greece, te electricity market derelation as triered a nmber of sinificant canes in te enery sector, mostly by allowin private-owned companies to become prodcers and sppliers of electricity.
6 Te recently establised Grid Control and Power Excane Code for Electricity [Relatory Atority for Enery (005)] introdced te Day-Aead-cedlin (DA) proram wic forms te basis of te wolesale electricity market operation. DA aims at minimizin te total cost of servin enery load for te next day, nder conditions of ood and safe system operation, wile ensrin adeqate reserves. Te proram optimizes bot enery and reserve markets simltaneosly and incorporates a mecanism tat encoraes installation of new eneratin nits near consmption. Te oal is to maximize social benefit. Greece as a special caracteristic concernin te location of eneration and consmption. Wile most of its power plants are located in te ort, te majority of te enery consmption takes place in te ot. As a reslt, a transmission constraint is activated in case of excess load, proibitin te transfer of te desired amont of enery from te ort to te ot. To deal wit tis particlarity of excess capacity in te ort, Greece is divided into two operational zones (ort ot) and prodcers are paid in different prices (Marinal Generatin Prices) wen te above transmission constraint is activated. ppliers, owever, face a niform price (ystem Marinal Price) reardless of teir exact location. In te next sections, we present a brief jstification of te two-zone model. We also make assmptions reardin te market rles and te nmeros tecnical constraints tat apply to te eneratin nits and to te transmission system, in order to state a basic DA model. Te problem is formlated as a mixed inteer linear prorammin model, and a metodoloy for te comptation of te ystem Marinal Price is proposed. A simple example is presented and solved sin te optimization software packae ILOG CPLEX 9.0. Reslts reveal an interaction between enery and reserve markets tat deserves more toro examination.. Operational Zones Te particlarity of excess capacity in te ort creates te need for a mecanism tat encoraes te installation of new eneratin nits near te ot, were te major demand is realized. Tis need becomes more intensive considerin te fact tat te lower cost power plants (linite) are also located in te ort, wic reslts in te sbstittion of low cost enery located in te ort by i cost enery prodced in te ot, drin te activation of te transmission constraint. Te establisment of two operational zones, in wic prodcers are paid in different prices (te Marinal Generatin Prices, MGP), provides te necessary motives for installin new capacity near consmption. ppliers, owever, contine to pay a niform price, te ystem Marinal Price (MP). We present te jstification for te establisment of te two operational zones, formlatin a simple bt rater indicative model.
Assme a model wit two zones, namely ort () and ot (). Let q be te power prodced in te ort, and q te power prodced in te ot, wit q q, were is te total prodction. Also, let d be te demand for power (load) in te ort, and d te demand in te ot, wit d d D, were D is te total demand. Obviosly, tere mst be a balance between prodction and consmption, tat is, D. We assme linear price fnctions, wic represent te cost of prodcin enery in eac zone. Te correspondin prices will be P a q for te ort, and P a q, for te ot, wit a a. Te latter assmption is consistent wit te fact tat lower cost power plants are installed in te ort. In fire 1, te price fnctions for te ort and te ot are presented. Te orizontal axis represents te total prodction (down) tat eqals te total demand D (pper). antities for te ort are measred from te left, wile qantities for te ot are measred from te rit. Te vertical axis measres te price. d d 7 MGP ot MP ort MP MGP q q Fire 1. Two-zone model price fnctions In te two-zone model, and wen te transmission constraint is not active, te ystem Marinal Price MP will eqal te Marinal Generatin Price in te ort MGP as well as te Marinal Generatin Price in te ot MGP, tat is, MP MGP MGP a q a q. Wen te transmission constraint is activated, te prodction in te ort mst be redced by q, and te prodction in te ot mst be increased by te same amont q. Te modified qantities will be q q q and q q q, wit q
8 correspondin Marinal Generatin Prices MGP a q MGP and MGP a q MGP, Te new ystem Marinal Price MP will now be MGP q MGP q MP, wic, after some alebraic calclations, reslts in q q (a a ) q MP MP MP. Te loss for te prodcers in te ort is MGP q MGP q a q( q q ) 0, wile te profit for te prodcers in te ot is MGP q MGP q a q( q q ) 0. Prodcers as a wole ave a profit (a a ) q 0. Consmers, on te oter side, ave to pay a bier amont (MP MP ) (a a ) q 0, wic eqals te profit of te prodcers. We sall now refer to a sinle-zone model, in order to identify te different motives tat are provided. Wen te transmission constraint is not active, te resltin prices are te same wit te two-zone model, tat is, MP1 MGP1 a q a q MP. However, wen te constraint is activated, we ave MP 1 MGP 1 a q MP1. Comparin te two models, we observe tat te activation of te transmission constraint reslts in an increase of te prodction in te ot and a decrease of te prodction in te ort for bot models (sinle-zone and two-zone). As a reslt, te ystem Marinal Price increases, and tis increase is larer in te case of te sinlezone model. Moreover, in te sinle-zone model, prodcers in te ort are paid in a ier price wen te transmission constraint is activated. On te oter and, te activation of te transmission constraint in te two-zone model reslts in lower price for te prodcers in te ort and in ier price for te prodcers in te ot. It is terefore evident tat te two-zone model provides te rit incentives for te installation of new eneratin nits in te ot, tat is, near consmption. 3. Te DA Problem In order to model te DA problem, we ave to make a nmber of assmptions reardin te market rles and tecnical constraints of te system and of te eneratin nits. We first present a sinle-zone model witot transmission constraints and ten extend te formlation to describe a model wit two zones (ort and ot) and a transmission constraint between tem. Te DA problem is formlated as a mixed inteer linear prorammin model.
3.1 inle-zone Model Te model describes a sinle zone, wit no transmission constraints and no losses. Te prodcers sbmit offers for providin enery for eac or of te followin day, as a stepwise fnction of price-qantity pairs, wit sccessive prices strictly nondecreasin. Prodcers also sbmit offers for reserves. We assme tat tere is only one type of reserve, considerin te ability to increase otpt and provide more enery to te system (witin a specific period of time). Offers for reserve are sbmitted as a pair of price-qantity tat stands for all te ors of te followin day. Te demand and te reserve reqirements for eac or of te followin day are exoenosly determined. Lastly, we consider te constraints of tecnical minimm, tecnical maximm and maximm reserve for eac eneratin nit. Te followin notation is sed: ets: U et of eneratin nits Parameters: Generatin nit Dispatcin period (or) b Block of enery offer antity of enery offer for nit, and block b bid,b P,b, Price of enery offer for nit, block b, and or UC tart-p cost for nit max Tecnical maximm for nit min Tecnical minimm for nit R antity of reserve offer for nit, and or bid r P Price of reserve offer for nit D Demand (load) for or R Reserve reqirements for or T Initial tats for nit req 0 Decision variables: antity of te enery offer inclded in te DA for nit, block b and,b, or R antity of te reserve offer inclded in te DA for nit, and or, T tats for nit, and or. Binary variable wit 1: OΝ, and 0: OFF, 9
10 Y tart-p for nit, and or. Dependent binary variable wit 1: tart-p, Ten, te DA problem is formlated as follows: sbject to: min { P P R Y UC },b,,r,,t,,y, (1) r,b,,b,,,,b,,,,b, D 0,b bid,b,,,b () T,b, (3) max,b, R, T,, b min,b, T,, b bid,, (4) (5) R T R, (6) req R, R (7) Y, T, T, 1, (8) T T 1.1(1 Y ) 0.1, (9),, 1, T T (10) 0,0 Te model minimizes te cost fnction (1), wic incldes te total prodction cost for enery and reserve as well as te start-p costs. Constraint () refers to te enery balance. Constraints (3)-(5) are related wit te tecnical caracteristics of te eneratin nits. More specifically, constraint (3) states tat te qantity of enery for eac block tat is inclded in te DA can not exceed te maximm qantity of te specific block, as tis as been declared in te enery offer. Constraint (4) ensres tat te enery and reserve inclded in te DA does not exceed te tecnical maximm. Constraint (5) ensres tat te qantity of enery inclded in te DA can not be less tan te nit s tecnical minimm. Constraints (6) και (7) refer to reserves. Constraint (6) declares tat te reserve inclded in te DA can not exceed te maximm reserve availability of te nit, and constraint (7) ensres adeqate reserves for te system. Constraints (8) and (9) are sed to overcome a non-linearity tat is associated wit te start-p binary variable Y,. Tis rop of ineqalities as replaced te eqation Y, T, (1 T, 1 ), wic defines te start-p. Lastly, eqation (10) provides te initial state of te nits.
ote tat neiter te ystem Marinal Price nor te price for reserve ave been inclded in te formlation. In a linear prorammin problem, and nder marinal cost teory, [cweppe Et. Al. (1988)] eqilibrim prices appear as te sadow prices of te enery balance constraint. Terefore, one possible way to calclate te MP in te mixed inteer linear prorammin wold be to fix te inteer variables to teir optimm vales, and ten calclate te sadow prices for te linear prorammin problem. However, te coplin effect of enery and reserve markets tat is observed in bot te objective fnction (cost for enery pls cost for reserve), and te tecnical maximm constraint (enery pls reserve can not exceed maximm otpt), as a direct impact on te vale of te MP. 3. Two-Zone Model Te model describes a system wit two zones and a transmission constraint between tem. Tere is no need to restate te complete formlation for te two-zone model, as te formlation stated above for te sinle-zone can be extended addin te necessary sets, parameters, decision variables and constraints. Te objective fnction remains te same. Te additional elements are presented below. ets: U et of eneratin nits in te ort (sbset of U ) U et of eneratin nits in te ot (sbset of U ) Parameters: D Demand in te ort for or D Demand in te ot for or F Transmission constraint max Decision variables: F Constraints: Enery flow from te ort to te ot for or U,b, D F 0 U,b U,b, D F 0 U,b 11 (11) (1) Fmax F Fmax (13)
1 Constraints (11) and (1) declare te enery balance in eac zone (ort and ot). Te zonal enery balance mst now inclde te net transfer between te two zones wic is defined by te decision variable F. Constraint (13) describes te transmission constraint (limit) between te two zones. 4. merical Reslts Te followin example incldes 8 eneratin nits. For simplicity, we examine te sinle-zone model and assme tat te enery and reserve offers ave one block wit te same price for all te ors. Data for te eneratin nits and te level of demand for eac or are provided in Tables 1 and. Unit bid,1 P,1, UC Table 1. Units Data max min bid R 1 3000 30 4500000 3000 1000 00 0 1 1500 35 50000 1500 500 100 0 1 3 1500 50 187500 1500 400 450 5 0 4 1500 55 187500 1500 400 450 5 0 5 1000 70 45000 1000 50 150 5 0 6 1000 75 45000 1000 50 150 5 0 7 50 90 0 50 0 50 15 0 8 50 95 0 50 0 50 15 0 Table. Demand Levels r P 0 T 1 3 4 5 6 7 8 9 10 11 1 6000 5500 550 5000 5000 5000 550 5750 6500 6500 7000 6750 13 14 15 16 17 18 19 0 1 3 4 6700 6700 6700 6600 6500 6400 6500 6600 6600 6600 6500 6000 req Lastly, we assme a fixed level of reserve, R 1400,. Te example as been solved sin te matematical prorammin lanae AMPL [Forer Et. Al. (1993)] and te optimization software packae ILOG CPLEX 9.0. Te reslts are presented in Table 3.
13 Unit T, 1 Y, 1 Table 3. Reslts R,1,, 1 1-4 - 1-4:3000-1-4-1-:1500, 3:1450, 4-6:100, 7:1450, 8-4:1500 3 1-4 1 1:1050, :600, 3-7:400, 8:850, 9-10:1050, 11:100, 1-4:1050 4 1-4 1 1:450, -8:400, 9-10:950, 11:1050, 1:950, 13-15:900, 16:1050, 17:950, 18:850, 19:950, 0-:1050, 3:950, 4:450-1-10:450, 11:300, 1-4:450 1-4:450 5 11-15 11 11-15:50 11-15:150 6 - - - - 7 1-4 1-1-4:50 8 1-4 1-1-11:50, 1-15:100, 16-4:50 Te most interestin otcome is te resltin dispatc drin or 11. Unit 5 starts prodcin in or 11, and provides 150 nits of reserve at price 5, wile nit s 3 reserve wit te same price (5) is redced by 150 nits. Unit s 8 reserve remains 50 despite its i price (15). Tis does not appen drin ors 1-15. Unit s 8 (expensive) reserve is ten redced by 150, and nit s 3 (ceap) reserve is increased by 150. Te explanation for tis strane reslt is related wit te level of demand drin or 11 (7000), wic is 500 nits more tan or 10. To cover tis demand wit te least cost, wile ensrin sfficient reserve, nit s 3 prodction is increased by 150, and becase of te tecnical maximm constraint (as tis constraint was already bindin drin or 10), its reserve as to be decreased by 150. Unit s 4 prodction is also increased by 100, reacin wit te reserve its tecnical maximm, and nit 5 is introdced to cover te rest 50 nits of demand and 150 nits of reserve. Tis coplin effect and sbstittability of enery and reserve raise a nmber of qestions abot te comptation of te MP tat ave to be frter examined. 5. Conclsions mmarizin or findins, we can conclde tat te establisment of two operational zones (ort and ot) provides te necessary motives for te installation of new eneratin nits near consmption (in te ot). Te DA proram was formlated
14 as a mixed inteer linear prorammin problem for bot sinle and two-zone models, and a possible way to compte te MP was proposed. Finally, an example wit 8 nits was solved and reslts tat reveal interaction between enery and reserve were presented. As for te ftre, tere is no dobt tat nderstandin te way in wic enery and reserve interact will elp s define te market prices in a way tat stimlates competition. References Forer R., Gay D.M. and Kernian B.W. (1993). AMPL: A Modelin Lanae for Matematical Prorammin. Boyd & Fraser, Massacsetts. Relatory Atority for Enery. (005). Grid Control and Power Excane Code for Electricity. Atens. cweppe F.C., Caramanis M.C., Tabors R.D., Bon R.E. (1988). pot Pricin of Electricity. Klwer Academic Pblisers, Boston/Dordrect/London.