Dynamics of Power* LCCC Lund University, Sweden Based on tutorial & panel lectures at Energy Systems Week , Cambridge UK Sean P. Meyn Joint work with: In-Koo Cho, Anupama Kowli, Matias Negrete-Pincetic, Ehsan Shafieeporfaard, Uday Shanbhag, and Gui Wang Coordinated Science Laboratory and the Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign, USA Thanks to NSF, AFOSR, and DOE / TCIPG *Dynamik i Makten (i grossistledet elmarknaderna) May 19, 2011
Outline 1 Can You Spot the Competitive Equilibrium? 2 Competitive Equilibria in Dynamic Markets 3 Coping with Uncertainty and Constraints 4 Conclusions 5 References 2 / 40
Can You Spot the Competitive Equilibrium? Nodal Power Prices $20,000 per MWh Otahuhu Stratford $10,000 $0 4am 9am 2pm 7pm 0 Spot the Competitive Equilibrium 3 / 40
Can You Spot the Competitive Equilibrium? Competitive Equilibrium Standard economic setting Perfect competition Long-run setting with uncertainty: �� � e − γt W D ( t ) dt K D ( G D ) = E �� � e − γt W S ( t ) , dt K S ( G S ) = E Consumers and suppliers each wish to maximize their individual welfare. Welfare functions defined with a price-process { P ( t ) : t ≥ 0 } 4 / 40
Can You Spot the Competitive Equilibrium? Competitive Equilibrium Standard economic setting Perfect competition Long-run setting with uncertainty: �� � e − γt W D ( t ) dt K D ( G D ) = E �� � e − γt W S ( t ) , dt K S ( G S ) = E Consumers and suppliers each wish to maximize their individual welfare. Welfare functions defined with a price-process { P ( t ) : t ≥ 0 } Price-taking assumption Key assumption of equilibrium theory: The price of power P ( t ) does not depend on the decisions of the market agents . 4 / 40
Can You Spot the Competitive Equilibrium? Competitive Equilibrium Efficiency Efficient Equilibrium Social Planner’s Problem: �� � e − γt � � max K ( G ) = E W S ( t ) + W D ( t ) dt 5 / 40
Can You Spot the Competitive Equilibrium? Competitive Equilibrium Efficiency Efficient Equilibrium Social Planner’s Problem: �� � e − γt � � max K ( G ) = E W S ( t ) + W D ( t ) dt Suppose that there exists a price process { P ∗ ( t ) } that forms an equlibrium : The consumers and suppliers agree, G S = G D = G . Suppose the agreed upon decisions G solve the SPP. Then, the market is called efficient . 5 / 40
Can You Spot the Competitive Equilibrium? Competitive Equilibrium Efficiency Efficient Equilibrium Social Planner’s Problem: �� � e − γt � � max K ( G ) = E W S ( t ) + W D ( t ) dt Suppose that there exists a price process { P ∗ ( t ) } that forms an equlibrium : The consumers and suppliers agree, G S = G D = G . Suppose the agreed upon decisions G solve the SPP. Then, the market is called efficient . Let’s look for examples of efficient equilibria! 5 / 40
Can You Spot the Competitive Equilibrium? Efficient Equilibrium? California, 2000 California, July 2000 Spinning reserve prices PX prices $/MWh 70 250 60 200 50 150 40 30 100 20 50 10 0 Weds Thurs Fri Sat Sun Mon Tues Weds 6 / 40
Can You Spot the Competitive Equilibrium? Efficient Equilibrium? 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