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Equilibrium, uncertainty and risk in hydrothermal electricity systems
, 2014
"... The correspondence of competitive partial equilibrium with a social optimum is well documented in the welfare theorems of economics. These theorems can be applied to singleperiod electricity pool auctions in which pricetaking agents maximize profits at competitive prices, and extend naturally to ..."
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The correspondence of competitive partial equilibrium with a social optimum is well documented in the welfare theorems of economics. These theorems can be applied to singleperiod electricity pool auctions in which pricetaking agents maximize profits at competitive prices, and extend naturally to standard models with locational marginal prices. In hydrothermal markets where the auctions are repeated over many periods, agents seek to optimize their current and future profit accounting for future prices that depend on uncertain inflows. This makes the agent problems multistage stochastic optimization models, but perfectly competitive partial equilibrium still corresponds to a social optimum when all agents are risk neutral and share common knowledge of the probability distribution governing future inflows. The situation is complicated when agents are risk averse. In this setting we show under mild conditions that a social optimum corresponds to a competitive market equilibrium if agents have timeconsistent dynamic coherent risk measures and there are enough traded market instruments to hedge inflow uncertainty. We illustrate some of the consequences of risk aversion on market outcomes using a simple twostage competitive equilibrium model with three agents. 1
A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties
 SUBMITTED TO OPERATIONS RESEARCH
"... We argue that deterministic market clearing formulations introduce strong and arbitrary distortions between dayahead and expected realtime prices that bias economic incentives and block diversification. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) i ..."
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We argue that deterministic market clearing formulations introduce strong and arbitrary distortions between dayahead and expected realtime prices that bias economic incentives and block diversification. We extend and analyze the stochastic clearing formulation proposed by Pritchard et al. (2010) in which the social surplus function induces `1 penalties between dayahead and realtime quantities. We prove that the formulation yields price distortions that are bounded by the bid prices, and we show that adding a similar penalty term to transmission flows ensures boundedness throughout the network. We prove that when the price distortions are zero, dayahead quantities and flows converge to the medians of realtime counterparts. We demonstrate that convergence to expected value quantities can be induced by using a squared `2 penalty. The undesired effects of price distortions suggest that arguments based on social surplus alone are insufficient to fully appreciate the benefits of stochastic market settlements. We thus propose additional metrics to evaluate these benefits.
Equilibrium, uncertainty and risk in hydrothermal electricity systems
, 2013
"... The correspondence of competitive partial equilibrium with a social optimum is well documented in the welfare theorems of economics. These theorems can be applied to singleperiod electricity pool auctions in which pricetaking agents maximize pro ts at competitive prices, and extend naturally to s ..."
Abstract
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The correspondence of competitive partial equilibrium with a social optimum is well documented in the welfare theorems of economics. These theorems can be applied to singleperiod electricity pool auctions in which pricetaking agents maximize pro ts at competitive prices, and extend naturally to standard models with locational marginal prices. In hydrothermal markets where the auctions are repeated over many periods, agents seek to optimize their current and future pro
t accounting for future prices that depend on uncertain inows. In this setting perfectly competitive partial equilibrium corresponds to a social optimum when all agents share common knowledge of the probability distribution governing future inows. The situation is complicated when agents are risk averse. We illustrate some of the consequences of risk aversion on market outcomes using simple twostage competitive equilibrium models in which agents are endowed with coherent risk measures. In this setting we show that welfare is optimized in a competitive market if there are enough traded market instruments to hedge inow uncertainty but might not be if these are missing. 1