Critical cases in the optimal power flow

This paper presents a systematic analysis of the main reasons for the failure of solution algorithms in the general power system nonlinear optimal power flow (OPF) problem. It defines the concept of critical and noncritical OPF problems and identifies and categorizes the main types of such cases. In essence, a noncritical case is one where a small variation in a parameter leads to a small change in the optimum solution. Alternatively, critical cases are such that a small variation in a problem parameter leads to either the loss of local optimality or feasibility. Both of these can result in a sharp discontinuity in the solution. Numerical and theoretical examples illustrate each of these cases