A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties

We argue that deterministic market clearing formulations introduce arbitrary distortions between day-ahead and expected real-time prices that bias economic incentives. We extend and analyze a previously proposed stochastic clearing formulation in which the social surplus function induces penalties between day-ahead and real-time quantities. We prove that the formulation yields price bounded price distortions, and we show that adding a similar penalty term to transmission flows and phase angles ensures boundedness throughout the network. We prove that when the price distortions are zero, day-ahead quantities equal a quantile of their real-time counterparts. The undesired effects of price distortions suggest that stochastic settings provide significant benefits over deterministic ones that go beyond social surplus improvements. We propose additional metrics to evaluate these benefits.