Economic dispatch of power systems with LMP-dependent demands: A non-iterative MILP model

Highlights: • We analyze the market instability caused by the discontinuity of LMP. • We demonstrate that the possibility of market instability is non-negligible. • We suggest a relaxed LMP scheme which guarantees the existence of equilibrium. • We propose a non-iterative model to calculate the equilibrium solution. The proliferation of demand response programs in the smart grid provides the system operator unique opportunities to reduce the load peak and alleviate network congestions. This paper considers the economic dispatch problem with elastic demands which flexibly respond to the locational marginal prices (LMPs). However, LMP is the dual variable of optimal power flow (OPF) problem and thus is unknown before the OPF problem is solved. Without LMP, the elastic demand is unclear, and the OPF problem cannot be set up. Given this interactive nature, it is difficult to acquire the dispatch strategy as well as the LMP according to the traditional OPF method. This paper thoroughly addresses this problem. Specifically, the limitation of the traditional LMP scheme in the described situation is analyzed. An equilibrium solution may not exist because the demand function and the discontinuous LMP may not have an intersection. To overcome this difficulty, LMP at the discontinuity point is redefined, so that the dispatch problem always has an equilibrium solution. A mixed-integer linear programming model for the economic dispatch problem with LMP-dependent load is proposed, and the equilibrium solution simultaneously offers the dispatch strategy and LMPs. Case studies demonstrate the difficulties of traditional approaches and the effectiveness of the proposed method.