  We argue that deterministic market clearing formulations introduce arbitrary
distortions between day-ahead and expected real-time 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 penalties between day-ahead and real-time 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 and phase angles ensures boundedness throughout the network. We prove
that when the price distortions are zero, day-ahead quantities converge to the
quantile of 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.
