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We argue that deterministic market clearing formulations introduce arbitrarydistortions between day-ahead and expected real-time prices that bias economicincentives and block diversification. We extend and analyze the stochasticclearing formulation proposed by Pritchard et al. (2010) in which the socialsurplus function induces penalties between day-ahead and real-time quantities.We prove that the formulation yields price distortions that are bounded by thebid prices, and we show that adding a similar penalty term to transmissionflows and phase angles ensures boundedness throughout the network. We provethat when the price distortions are zero, day-ahead quantities converge to thequantile of real-time counterparts. The undesired effects of price distortionssuggest that stochastic settings provide significant benefits overdeterministic ones that go beyond social surplus improvements. We proposeadditional metrics to evaluate these benefits.

A Stochastic Electricity Market Clearing Formulation with Consistent Pricing Properties