Equilibrium, uncertainty and risk in hydro-thermal electricity systems

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 single-period electricity pool auctions in which price-taking agents maximize profits at competitive prices, and extend naturally to standard models with locational marginal prices. In hydro-thermal 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. In this setting perfectly competitive partial equilibrium corresponds to a social optimum when all agents share common knowledge of the probability distribution governing future inflows. The situation is complicated when agents are risk averse. We illustrate some of the consequences of risk aversion on market outcomes using simple two-stage 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 inflow uncertainty but might not be if these are missing.