Applications of Complementarity Complementarity- -Based Models Based Models Applications of of Transmission- -Constrained Power Markets: Constrained Power Markets: of Transmission B- -NL Market Integration & NL Market Integration & B Power- -NOx NOx Market Interactions in PJM Market Interactions in PJM Power Yi-Hsu Chen The Johns Hopkins University, Baltimore, MD Fieke A.M. Rijkers Dienst Uitvoering en Toezicht Energie (Dte), Den Haag, NL Benjamin F. Hobbs The Johns Hopkins University, Baltimore, MD California ISO Market Surveillance Committee, Folsom, CA “Hartilijk danke” to NSF, ECN, & FERC for support; Todd Munson, Sven Leyffer, & Adrian Wals for their collaboration
Specific Questions: Specific Questions: • What are the benefits of Belgian-Dutch power market integration? – Methodology: COMPETES (a LCP Cournot model of transmission-constrained markets) – Effect of inefficient transmission & arbitrage • What strategies might generators use to exploit the interaction of electric power and NO x markets? – Methodology: MPEC Stackelberg model of NOx and power markets (transmission constrained) – Demonstrates ability to solve large scale (~20,000 variable) MPECs
Computational Approach: Computational Approach: Direct Solution of Equilibrium Conditions Direct Solution of Equilibrium Conditions Producer A Producer A Producer B Producer B Choose gen gen & & Choose Choose gen gen & & Choose sales to sales to sales to sales to maximize profit maximize profit maximize profit maximize profit s.t. capacity s.t. capacity s.t. capacity s.t. capacity st order ⇒ 1 ⇒ ⇒ 1 st order ⇒ 1 st order 1 st order conditions conditions conditions conditions ISO: Choose Transmission Flows to Max Value of Network ISO: Choose Transmission Flows to Max Value of Network st order conditions s.t. transmission constraints ⇒ ⇒ 1 1 st order conditions s.t. transmission constraints Consumers: Max Value - - Expenditures (Demand Curve) Expenditures (Demand Curve) Consumers: Max Value Market Clearing Conditions Market Clearing Conditions 1. Derive first-order conditions for each player 2. Impose market clearing conditions 3. Solve resulting system of conditions ( complementarity problem ) using PATH PATH
B- -NL Analysis NL Analysis B COMPETES Market Structure COMPETES Market Structure • Cournot generators compete in bilateral market • Competitive arbitragers in some markets • Two transmission pricing systems: – Physical network • Linearized DC load flow NL • Several nodes per country – Path-based representation B D • One node per country � one market price per country • Interfaces defined between countries F • Crediting for counterflows (netting vs. no-netting)
COMPETES COMPETES Inputs Inputs • Demand – 12 periods → 3 seasons, 4 load periods – Allocated to the nodes • Generation – 15 large power generating companies • 4 NL, 1 B, 2 F, 8 G – Plus competitive fringe – 5272 generating units – MC based on heat rate and fuel type
↔ NL Congestion management B ↔ NL Congestion management B Current Auction System Current Auction System • Yearly, monthly, daily • Available capacity for auction [www.tso- auction.nl] – B - NL: 1150 MW – Germany - NL: 2200 MW • Total import capacity to NL ≤ 400 MW per party • Price set by lowest accepted bid • Daily auction takes place before APX settles
↔ NL Congestion management B ↔ NL Congestion management B Proposal for market integration Proposal for market integration • Single market – One market price – TSO responsible for re-dispatch – Payments for constrained-off or -on • Market Coupling (Splitting) – Similar to the NordPool – If Congestion: two separate market prices
Effects of Market Coupling Effects of Market Coupling Differences relative to current situation Differences relative to current situation 1) Increased market access into Belgium – For (foreign) Generators and – For Traders → Introduce arbitrage 2) Netting of transmission capacity 3) Efficient co-ordination of ‘Auction’ and APX
Effects of Market Coupling Effects of Market Coupling Definition of scenarios Definition of scenarios Import cap on firms Import cap on arbitrageurs Netting B � NL NL � B NL � B B � NL NL � B G ↔ NL Electrabel Competitive No limit No limit No limit No limit No limit No limit Yes C Current 400 0 950 0 200 No No limit O situation U R B ↔ NL N Market splitting None* None* None* No limit No limit No limit O T
Model results Model results Competitive scenario Competitive scenario €/MWh MWh €/ 28.0 28.0 0 1.1 0 9.1 29.1 29.1 0 18.9 18.9 10.2 4.6 14.3 14.3
Model results Model results Current Situation vs. Competitive €/MWh MWh Current Situation vs. Competitive €/ - No netting No netting - 33.5 (+5.5) (+5.5) 33.5 0 ↔ G Arbitrage NL ↔ - Arbitrage NL G - 0 - Belgium Belgium ‘ ‘closed closed’ ’ - 0 - Imports NL 400 MW Imports NL 400 MW - per party per party 10.9 45.9 (+16.9) (+16.9) 45.9 0 22.5 22.5 22.3 (+3.6) (+3.6) 7.9 14.0 ( 14.0 (- -.3) .3)
Model results Model results Market Splitting vs. Current Situation €/MWh MWh Market Splitting vs. Current Situation €/ ↔ B Netting NL ↔ - Netting NL B - 37.9 (+4.4) (+4.4) 37.9 1.0 ↔ G Arbitrage NL ↔ - Arbitrage NL G - 0 - Belgium open: Belgium open: - 0 ↔ B Arbitrage NL ↔ B Arbitrage NL 16.1 37.4 ( (- -8.5) 8.5) 37.4 0.4 22.2 22.2 14.7 (- -.4) .4) ( 7.5 14.1 (+.1) 14.1 (+.1)
Welfare Compared to Perfect Competition Welfare Compared to Perfect Competition 2500 1500 Difference with competitive Million €/yr 500 -500 -1500 -2500 -3500 Current Situation Market Splitting Consumer Surplus Generators profit Transmission revenue Welfare
Effects of Market Coupling Effects of Market Coupling • Market Coupling affects prices, increases welfare (+ 182 M€/yr more than current) – Induced by lower prices in Belgium – Increased welfare is mainly in Belgium • What is “in it” for the Netherlands? – Profits Dutch generators increase – But consumer surplus decreases more
PJM Power Market PJM Power Market & USEPA NO NO x Program Analysis & USEPA x Program Analysis Can the NOx market be PJM Transmission Zones profitably manipulated by a PN PN large generator who is long on allowances? PL PL PS PJM Market PS – Peak Load 50,000 MW JC JC ME PE ME PE – Average Load-weighted Price - AE AE BC BC 30.7 $/MWh Source: www.pjm.com USEPA NO x Program PEP PEP DPL DPL – Cap-and-Trade – 9 states participated in 2000 – Total Allowances: 195,401 tons
Model Assumptions Model Assumptions • Market structure – Generators compete to sign bilateral contracts – ISO provides transmission services between nodes • Network – 500 kV network: 14 nodes, 18 arcs, no transmission losses – Linearized “DC” load flow approximation: Power Transfer Distribution Factors (PTDFs) • Producers – 791 generation units – 6 largest producers (capacity share: 4% to 18%) • Largest is Stackelberg leader • Others: – Cournot strategy in electricity market – Price taking in NO x market – Remaining producers are price takers (3 producers) • Consumers – Linear demand at each node – 5 demand periods in ozone season • ISO allocates transmission capacity to highest value
Stackelberg Stackelberg Analysis Analysis Stackelberg Leader L p NOx (X L ) L’s decisions X L : p i (X L ) {Allowance bought q NOx,L W i (X L ) Energy decisions g i,A , s i,L } NO x Market B A Power Market 2 1 P 1 P 2 d 1 d 2
Stackelberg Leader’s Problem Leader’s Problem Stackelberg • The firm with a longest position in NOx market and greatest power sales is designated as the leader: w q = Stackelberg’s NO x withholding variable [tons] NO = Firm’s available NO x allowances [tons] x q f ∑ ∑ + − − − MAX {[ p s ( s ) W ] s [ C ( g ) W g ] W i if ≠ ig i if if if i if s , g , q i g f if i f NO − − − NO NO w x p E q q [ ( )] } x x f f ≤ ∀ g CAP i s.t.: , if if ∑ ∑ = s g if if i i ≥ ∀ s g i 0, if , if NO ≤ ≤ W x q q 0 f ∑ NO ≤ ⊥ − + ≤ NO NO w x p E q q 0 ( ) 0 x x f f f • Other Producer Complementarity Equilibrium Conditions • Market Clearing Conditions
ISO Optimization Problem ISO Optimization Problem Quadratic Loss Functions Quadratic Loss Functions • ISO’s decision variables: y = transmission service from hub to i i Losses q = generation purchases from node i (to make up losses) i t = positive flow from i to j ij • ISO’s maximizes the “value of services” : ∑ π = − Losses Losses MAX t y q W y p q ( , , ) ( ) ISO ij i i i i i i i ∑ − + − − ≤ ∀ Losses Kirchhoff’s Current Law s t . .: y q ( t (1 L t ) t ) 0, i i i ∈ ij ji ji ji j J i ( ) ∑ − = ∀ ∈ Kirchhoff’s Voltage Law R t t k i j v k ( ) 0, ,( , ) ( ) ∈ ij ij ji ( , ) i j v k ( ) ∑ = Services Balance y 0 i i ≤ ≤ ∀ T ij = capacity of line (i,j) t T i j 0 , , ij ij ≥ ∀ Losses q 0, i i – Solution allocates transmission capacity to most valuable transactions • Define the model’s KKTs (complementarity conditions), one per variable x ISO
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