LMP Based Zone Formation in Electricity Markets

Transcription

1 8th WSEAS Internatonal Conference on POWER SYSTEMS (PS 2008), Santander, Cantabra, Span, September 23-25, 2008 LMP Based Zone Formaton n Electrcty Markets SAURABH CHANANA, ASHWANI KUMAR, RAHUL SRIVASTAVA Electrcal Engneerng Department Natonal Insttute of Technology Kurukshetra Haryana INDIA Abstract: - Many deregulated markets n the world have adopted zonal approach to congeston management. Ths approach has an advantage of beng smple to understand as compared to the nodal approach. In ths work zone formaton based on Locatonal Margnal Prce (LMP) s nvestgated. LMPs can be calculated usng ether DC Optmal Power Flow (OPF) or full AC OPF. Frst the effect of usng these dfferent approaches on the zone formaton s studed by takng an IEEE 118 bus test system. Later on the mpact of mzng system loadng s observed on the zone formaton. Key-Words: - Locatonal margnal prce, Zonal congeston management, Maxmum loadng factor. 1 Nomenclature k l Pg Qg Pd Qd V S B(.) C(.) SW ρ ndex of generator buses ndex of demand buses ndex of buses ndex of lnes actve power generaton reactve power generaton actve power demand reactve power demand bus voltages lne flows demand beneft functon generator cost functon socal welfare system loadng factor 2 Introducton In recent tmes there has been ncreased publc pressure to deregulate electrcty sector. People are expectng better qualty of supply at most economcal prces. Ths could only be acheved by unbundlng the generaton, transmsson and dstrbuton busness and havng suffcent competton n the power generaton busness. Ths had led to emergence of compettve electrcty markets n varous parts of the world. Overall ths phenomenon s generally termed as deregulaton. When people started treatng electrcty as a commodty, they found t s very much unlke other commodtes. The property of electrcty that t can t be stored and t flows through the transmsson lnes as per laws of physcs, make t very pecular [1]. Hence, deregulated electrcty markets had to deal wth number of ssues such as congeston, losses, prcng, ancllary servces, market power etc. [2]. The most fundamental of these s the problem of congeston. Congeston arses n a system when the producers and consumers of electrc energy desre to produce and consume n amounts that would cause the transmsson system to operate at or beyond one or more transfer lmts [3]. The system operator (SO) n a compettve electrcty market s responsble for determnng the necessary actons to ensure that no volatons of grd constrants occur. The comprehensve set of actons of producers are referred as congeston management (CM), whch prncpally conssts of re-dspatch of generator and load levels so as to establsh a system state wthout volatons of system constrants. The cost of congeston management plays a maor role n attanng such a state [4]. In addton, SO may dvde a grd nto separate prcng zones to manage congeston. Two approaches, nodal congeston management and zonal congeston management have been adopted n deregulated electrcty markets around the world. Zonal approach has an advantage of beng smple to understand whereas nodal approach s more accurate [5]. Fundamental concept on whch these congeston management technques are based s the Locatonal Margnal Prce (LMP) also called the Spot Prce. Carams et. al. [6] had developed the basc theory of spot prcng of electrcty whch has ntroduced LMP as the bass of chargng for real power from the consumer and gvng payment to the generators. These LMPs are the Lagrange ISSN: ISBN:

2 8th WSEAS Internatonal Conference on POWER SYSTEMS (PS 2008), Santander, Cantabra, Span, September 23-25, 2008 Multplers of real power balance equaton n the Optmal Power Flow (OPF) formulaton. Accordng to [7] these LMPs would not only remunerate generaton and transmsson but also gve approprate sgnals for ther expanson. Varous authors [8, 9, 10] have nvestgated the composton of LMP and ts mpact on operaton of electrcty markets. In ths paper zone formaton based on Locatonal Margnal Prce (LMP) s nvestgated. LMPs can be calculates usng ether DC Optmal Power Flow (OPF) or full AC OPF. Frst the effect of usng these dfferent approaches on the zone formaton s studed by takng an IEEE 118 bus test system. In the second part the mpact of mzng system loadng s observed on the zone formaton. 3 Concept of LMP Wth the ntroducton of restructurng nto the electrc power ndustry, the prce of electrcty has become the focus of all actvtes n the power market. In general, the prce of commodty s determned by supply and demand. In the case of electrcty market, transmsson congeston also plays a crtcal role n determnng electrcty prces; market rules also have mpacts under certan crcumstances. The most basc prcng concept n electrcty market s Market Clearng Prce (MCP). Generally, when there s no transmsson congeston. MCP s the prce for the entre system. The process of determnng MCP s as follows. After recevng bds, SO aggregates the supply bds nto a supply curve and then aggregates demand bds nto a demand curve. The ntersecton of these two curves s the MCP. In some cases, the two curves may not ntersect at all. In other cases, there may be multple ntersectons. When there s congeston n system, the electrcty market cannot be cleared on the system level. Instead, the market has to be cleared on the bus level and the clearng prce at each bus s called locatonal margnal prce (LMP). Physcally, LMP s the cost of supplyng the next MW of load at a specfed locaton, after consderng the generaton margnal cost, cost of transmsson congeston, and losses. That s, LMP s the sum of generaton margnal cost, transmsson congeston cost and the cost of margnal losses. LMP=generaton margnal cost +congeston cost +cost of margnal losses Although the cost of losses s usually gnored. In general, LMP could be dfferent for dfferent buses, however when there s no congeston, LMP s same as that of MCP,when there s congeston, LMPs wll be determned based on the soluton of an optmal power flow (OPF) that consder transmsson lne constrants. LMP at any node n the system s the dual varable (sometmes called a shadow prce) for the equalty constrants at that node (sum of nectons of every sectons and wthdrawals s equal to zero). 4 Zone Formaton Based on LMP A transmsson congeston charge s ncurred when the system s constraned by physcal lmts. So a reasonable transmsson prcng method should provde some economc sgnal to reflect the charge due to the physcal constrants. One opton s based the charge on locatonal margnal prces. That s, the congeston charge for a specfed path s the product of the flow along the path and the prce dfferences between the two termnals of the flow along the path. Ths s called nodal congeston management. Ths approach s complex to apply practcally as number of nodes on whch LMPs are calculated wll be very large. In some markets a relatvely smple approach s used n whch the SO splts the system n dfferent prce zones at the predcted congeston bottlenecks. Spot market bdders must submt separate bds for each zone n whch they have generaton or load. Ths s called zonal congeston management. The number of prce zones n a market wll be far less makng ths approach smple to apply. Transmsson zones can be defned based on LMPs. In each zone, the LMP of energy s close to the margnal prce at all nodes nsde the zone. Dfferences n the margnal prce gve the constraned stuatons defnng zonal boundares, whch ndcate that the zonal defntons provde both economcal and physcal perspectves. Intally, zonal boundares may be defned based on hstorcal LMPs at dfferent nodes of the system, or equvalently, experence may be appled to dentfy lnes that are expected to be congested. Later, these ntally defned zones may be modfed (merged or subdvded) based on new LMPs. Because all nodes n a certan zone have smlar margnal prces, all nodes n a zone can be aggregated and though of as one node. We can represent the prce n a zone usng average locaton- ISSN: ISBN:

3 8th WSEAS Internatonal Conference on POWER SYSTEMS (PS 2008), Santander, Cantabra, Span, September 23-25, 2008 Prce($) Bus Number DC OPF Normal Loadng AC OPF Normal Loadng DC OPF Max Loadng AC OPF Max Loadng Fg.1 LMPs of IEEE 118 bus system for all cases. al margnal prce (ALMP). The ALMP n any zone s the average LMP of the nodes n that zone. 5 System Model For LMP Calculaton Mathematcally, LMP s dual varable of equalty constrant (sum of nectons and wthdrawals at a node s equal to zero) of an optmal power flow (OPF) problem whose obectve s to mze the socal welfare. Socal welfare s defned here as dfference between benefts to consumers and costs for generaton. 5.1 Formulaton of DC OPF The obectve functon n the problem tres to mze the socal welfare for the system: Max SW = B ( Pd) C( Pg) (1) Subect to followng equalty constrants Pgk Pdk = Pk (2) and followng nequalty constrants mn P P P (3) g g g l Sl (4) S To obtan LMPs at mum loadng followng obectve functon s used Max SW B (ρ * P ) C ( P ) (5) = d where ρ s the system loadng factor. g 5.1 Formulaton of AC OPF The obectve functon n the problem tres to mze the socal welfare for the system: Max SW = B ( Pd) C( Pg) (6) Subect to followng equalty constrants P P = P (7) gk dk k Qgk Qdk = Qk (8) and followng nequalty constrants mn Pg Pg Pg (9) mn Qg Qg Qg (10) mn V V V (11) k k k l Sl S (12) To obtan LMPs at mum loadng followng obectve functon s used Max SW = B (ρ * P ) C ( P ) (13) d where ρ s the system loadng factor. 6 Results A case study s done on IEEE 118 bus test system by usng both DC and AC OPF technques. System equatons descrbed n Sectons 5.1 and 5.2 are modeled n GAMS language. The soluton for nonlnear programmng problem s obtaned usng MINOS Solver. Frst the DC OPF was run for the base case data and results of the margnal prces at all the nodes were computed. After that, the DC OPF was g ISSN: ISBN:

4 8th WSEAS Internatonal Conference on POWER SYSTEMS (PS 2008), Santander, Cantabra, Span, September 23-25, 2008 run agan mzng the system loadng and margnal prces were calculated. Fg. 1 shows the nodal prces for the two cases aganst the respectve nodes to assst n the prelmnary formaton of groups. The unt of margnal prce used throughout the chapter s $/MWh From these fgures, one can roughly select groups of nodes whch have margnal prces n a close range and have smlar devaton n margnal prces, on change n the loadng. Table 1 Zone formaton wth DC OPF at Base Case A B C D 8 48 E Table 2 Zone formaton wth DC OPF at Maxmum Loadng A B 8 65 C D 5 64 E 7 67 F 7 74 G H I 5 72 J The outcome of zone formaton takng LMPs from DC OPF s gven n Table 1 and 2 for base case and mum loadng condton respectvely. It s observed that wth ncrease n system loadng not only the average LMP has ncreased but number of zones has also ncreased. Ths mples that congeston s appearng at more number of nterfaces as the system loadng s ncreased. The outcome of zone formaton takng LMPs from AC OPF s gven n Table 3 and 4 for base case and mum loadng condton respectvely. A pattern smlar to DC OPF cases s observed wth AC OPF cases too. Table 3 Zone formaton wth AC OPF at Base Case A B 6 39 C 5 40 D E 9 39 F Table 4 Zone formaton wth AC OPF at Maxmum Loadng Area No. of nodes Average LMP A B C 8 67 D E F 4 70 G 9 68 H Table 5 gves the comparson of executon tme and number of teratons for all cases. We know that by runnng AC OPF we get more accurate LMPs but the executon tme and number of teratons n case of AC OPF s much hgher than DC OPF. In actual markets the number of buses s very hgh hence AC OPF takes a long tme to converge to soluton. Gven the smlarty n zone formaton wth both methods, t can be concluded that t s better to adopt DC OPF for zone formaton. Table 5 Comparson of executon tme and numbers of teratons for DC and AC OPF DC OPF normal loadng DC OPF mum loadng AC OPF normal loadng AC OPF mum loadng ISSN: ISBN:

5 8th WSEAS Internatonal Conference on POWER SYSTEMS (PS 2008), Santander, Cantabra, Span, September 23-25, 2008 Executon tme Number of teratons s s s s Concluson Zone formaton for congeston management usng LMPs has been done n ths paper. The mportant conclusons of ths study are: 1. As the system loadng factor s ncreased the number of zones formed ncrease. At mum system loadng there are consderable numbers of zones due to ncrease n congested nterface. 2. Average LMPs of the zones also ncreases consderably wth ncrease n system loadng. 3. Zone formaton based on LMPs calculated from DC OPF s almost smlar to that of AC OPF. 4. Snce the executon tme and number of teraton s hgh n case of AC OPF and these parameters deterorated drastcally wth the ncrease n system sze, DC OPF s better suted for zone formaton. In future, the mpact of FACT devces lke UPFC on LMPs and zone formaton can be nvestgated usng ths model. Methods of optmal placement of ths devce resultng n desrable zone formatons can also be nvestgated. References: [1] S. Stoft, Power System Economcs Desgnng Markets for Electrcty, New York: IEEE/Wley, [2] M. Ilc, F. Galana, and L. Fnk, Power Systems Restructurng: Engneerng and Economcs. Norwell, MA: Kluwer, [3]R.D. Chrste, B.F. Wollenberg and I. Wangsten, Transmsson Management n the Deregulated Envronment, Proc. of the IEEE, Vol. 88, No.2, Feb. 2000, pp [4] H. Sngh, H. Shangyou and A. Papalexopoulos, Transmsson congeston management n compettve electrcty markets, IEEE Trans. Power Syst., Vol. 13, pp , May [5] W. W. Hogan, Contract networks for electrc power transmsson, J. Regulatory Econ., Vol. 4, pp , Sept [6] M.C. Carams, R. E. Bohn and F.C. Schweppe, Spot Prcng of Electrcty: Practce and Theory, IEEE Transactons on Power Apparatus and Systems, Vol. PAS-101, No. 9, pp , Sep [7] F.C. Schweppe, M.C. Carams, R.D. Tabors and R.E. Bohn, Spot prcng of Electrcty, Kluwer Academc Publshers, [8] L. Chen, H. Suzuk, T.Wach, and Y. Shmura, Components of nodal prces for electrc power systems, IEEE Trans. Power Syst., Vol. 17, No. 1, pp , Feb [9] K. Xe, Y. H. Song, J. Stonhan, E. Yu and G. Lu, Decomposton Model and Interor Pont Methods for Optmal Spot Prcng of Electrcty n Deregulated Envronments, IEEE Trans. Power Syst., Vol. 15, No. 1, pp , Feb [10]Zuy L and Hossen Danesh, Some Observatons on Market Clearng Prce and Locatonal Margnal Prce, IEEE PES General Meetng, ISSN: ISBN: