Invesigaion of Convex Hull Pricing a Midwes ISO Paul Gribik Prepared for HEPG Cambridge, MA Ocober 1, 2009 Opinions expressed are hose of he auhor and may no represen hose of Midwes ISO
MISO s Curren Pricing Mehod Midwes ISO marke srucure: Bid-based day-ahead marke using securiy consrained uni commimen and economic dispach (SCUC and SCED); Bid-based reliabiliy commimen process using SCUC o ensure ha sufficien capaciy will be on-line o mee forecas real-ime requiremens; Bid-based real-ime securiy consrained economic dispach. Locaional prices for day-ahead and real-ime selemens deermined d in SCED wih fixed commimen as se in SCUC. The price a a locaion is he marginal cos of meeing he energy requiremen (or ancillary service requiremen) in he SCED. Prices are produced by solving he dual of he SCED problem. 2
Basis for Curren Locaional Prices Assume fixed commimen. Microeconomics: The prices are marke clearing prices. Each generaor (load) would wan o produce (consume) as scheduled o maximize is profis. The prices are efficien prices. All generaors and loads would wan o follow he schedule, which maximizes socieal surplus. Game heory (marke games): Using he prices o allocae he socieal surplus o generaors, loads, and ransmission righs holders eliminaes incenives o leave he pool dispach. No subse of generaors and loads could improve is overall posiion by scheduling ouside he marke. The allocaion of socieal surplus using he prices is in he core of he marke game. 3
Effecs of Adding Commimen o he Mix Make commimen decisions par of he problem. Microeconomics: There usually are no marke clearing prices. Canno se prices which would incenivize profi maximizing generaors (loads) o produce (consume) a scheduled levels. Under MISO s curren pricing mehod, sar-up coss and no- load coss do no affec he marke prices.» MISO pays uplifs o ensure ha generaors are no paid less han heir bid coss for producion.» This is RSG in MISO. Game heory (marke games): There may no be prices ha can be used o allocae socieal surplus ha compleely eliminae any incenive for paries o self schedule. MISO worked wih LECG o develop a pricing approach o address hese and oher shorcomings. 4
Convex Hull Pricing Convex hull prices (CHPs) are calculaed by solving he dual of he SCUC problem raher han he SCED problem. Convex hull prices: Minimize he addiional paymens (uplifs) needed o incenivize profi maximizing generaors (loads) o produce (consume) a scheduled levels. Incorporae sar-up coss and no-load coss in he prices. Minimize incenives for paries o leave he pool commimen and dispach o self schedule when convex hull prices are used o allocae socieal surplus. Any addiional profi ha a coaliion could achieve by self-scheduling ouside he marke is bounded by he uplifs described above. Since finding rading parners wih whom o self-schedule is no wihou coss, his ends o reduce any incenive o schedule ouside he marke. 5
SCUC We can wrie a sylized version of SCUC: GenCos g LoadVal d min i i j j g, d i j subjec o e T g e Flow T T k T d LossSen d g OffSe max g d F k, Consrains on individual generaors i Consrains on individual demands k j 6
Dual for SCUC (CHP Problem) We can form a dual for he SCUC: OffSe F max k k k GenCosi gi LoadVal j d j i j min T T T T g, max d k Flowk, e g e d LossSen d g g d k subjec o Consrains on individual generaors i j Consrains on individual demands subjec o k 0 The convex hull prices are e LossSen k k Flow k 7
Solving for Convex Hull Prices The SCUC dual is a difficul problem: Is objecive funcion is non-differeniable; I is very large scale for he MISO s sysem: Around 5000 ransmission consrains; Around 1000 generaors; 24 coupled hours in day-ahead. MISO worked wih consulans o es several classes of soluion echniques: Subgradien descen mehods; Cuing plane mehods. Analyic Cener Cuing Plane appears o be mos promising. 8
Handling Transmission Consrains MISO s sysem has around 5000 ransmission consrains, however very few are binding in SCUC/SCED in any hour. Usually less han 10 ransmission consrains are binding in a given hour. To reduce he number of ransmission consrains in he CHP problem, we seleced binding and near binding ransmission i consrains in he SCUC/SCED soluion. 9
Example Problem Example problem from November 2007. Day-Ahead marke (energy only). Number of generaors: 1009 Number of ransmission consrains modeled: 18 Sudy period: 24 hours. Compuer used: 64 bi desk op, 2.33GHz, 4GB of RAM running Windows XP 64 bi. Performance summary: Number of ieraions: 191 Soluion ime: 223 seconds The sofware was for proof of concep. I was no opimized for speed. LPs solved using MATLAB. No performance enhancemen mehods such as ho-saring he LPs using soluion from previous ieraion were used. All indicaions are ha problem can be solved in pracice. 10
Dual Objecive Funcion Value by Ieraion 18,000,000 17,000,000 16,000,000 15,000,000 14,000,000 13,000,000 12,000,000 11,000,000 10,000,000 9,000,000 8,000,000 7,000,000 6,000,000 5,000,000 4,000,000 3,000,000 2,000,000 1,000,000 0 0-1,000,000 20 40 60 80 100 120 140 160 180 200 11
1.00E+00 Convergence of Dual Price Vecor 1.00E-01 01 pimal Prices) / Norm m(opimal Prices) Norm(Prices - O 1.00E-02 02 1.00E-03 1.00E-04 1.00E-05 0 20 40 60 80 100 120 140 160 180 200 12
Comparison of Convex Hull Prices and Curren Prices Convex hull prices a reference node compared o curren prices a reference node: The average convex hull price a he reference node is $24.0/MWh compared o he average reference node price of $21.8/MWh using curren pricing srucure. The increase of $2.2/MWh reflecs he effecs of including sar-up and no-load coss in seing prices. 13
Why Include Near-Binding Consrains MISO may have o commi a generaor o manage a ransmission consrain. If he generaor is no commied, he flow may exceed he ransmission limi. Wih he generaor commied, he flow may be under he limi. Curren pricing mehod would se a shadow price of zero on he consrain since i is no binding in SCED. No price difference exiss beween nodes on eiher side of he consrain even hough h coss are incurred o manage he consrain. Convex hull pricing ses a non-zero shadow price on he consrain based on he need o commi a uni o manage he consrain. The consrain is financially binding and price differences exis beween nodes on differen sides of he consrain. This has been observed in example problems. 14
Curren Work MISO is working wih LECG o address inegraing g Day-Ahead and Real-Time markes. Handling of uplifs arising in he wo markes o ensure ha a paricipan is no paid wice for he same acion. Deermining which resources and coss o include when calculaing Real-Time CHPs. MISO is also working wih sofware vendors. Complee he incorporaion of ancillary services in he CHP sofware. Improve soluion algorihms. 15
Paul Gribik Conac Informaion Sr. Direcor, Marke Developmen and Analysis pgribik@midwesiso.org 317-249-5146 16