Optimal Power Flow with Complementarity Constraints

This paper proposes a mathematical program with complementarity constraints to better model the relationship between the base, or current, operating point and the maximum loading point in a power system when solving maximum loading problems. Complementarity problems can model a large variety of practical situations. In general, these problems are based on the idea that the complementarity condition can be used to model a change in system behaviour. Complementarity problems have a disjunctive character; a system will behave according to different rules under different circumstances. This paper proposes an optimization based stability problem that incorporates the change of behaviour of generator buses when one of their reactive output limits is attained. The proposed optimal power flow with complementarity constraints is applied to three sets of problems: 1) maximum stability problem, 2) multistage maximum stability margin problem based on an economic optimal power flow first stage, 3) voltage security constrained optimal power flow (VSC-OPF). Numerical results for two IEEE benchmark test systems are presented and discussed based on the three different problem formulations