Piecewise affine dispatch policies for economic dispatch under uncertainty

Stochastic optimization has become one of the fundamental mathematical frameworks for modeling power systems with important sources of uncertainty in the demand and supply sides. In this framework, a main challenge is to find optimal dispatch policies and settlement schemes that support a market equilibrium. In this paper, the economic dispatch under linear network constraints and resource uncertainty is revisited. Piece-wise affine continuous dispatch policies and locational prices that support a market equilibrium using a two-settlement scheme are derived. We find that the ex-post locational prices are piecewise affine continuous functions of the system uncertainties.