Impacts of transmission line limits on electricity market equilibrium

Abstract

This paper presents a systematic analysis about the impacts of transmission line limits (network constraints) on the market equilibrium. The bidding in power market is modeled as a two-level optimization problem, where in top level the ISO solves an optimal power flow (OPF) for maximizing the social welfare, and in the second level individual supplier (generator) seeks the maximum profits by the bidding of linear supply function to ISO. The existence of transmission line limit will divide suppliers' decision space into different regions, where within either region the constraint may be strictly binding or strictly relaxant. The fact that constraints have different status in different regions causes the different optimal strategy for generator. The possible market equilibrium is searched through the intersection of optimal response curves in different regions. At first, this paper investigates a simple three-node system, it is found that, after the inclusion of one transmission line limit, there may be a continuum of equilibrium, or there is no pure strategy equilibrium; if the equilibrium exists, there will be no nodal price difference or no congestion charge. Then the analytical conclusions are generalized to a complicated system. Numerical results support the analytical conclusions very well.