A general parametric optimal power flow

This paper is a generalization and extension of earlier research in parametric optimal power flow (OPF). Its principal features are: (i) the use of a full nonlinear OPF model, (ii) a more general parameterization of equalities, inequalities and objective function, and (iii) an algorithm that exactly tracks the OPF behaviour in terms of the continuation parameter. The parameterization allows one to distinguish between two phases. One serves to find the OPF solution to a static problem for a fixed load and network starting from an arbitrary initial condition. The second, finds the trajectories corresponding to varying loads. The optimal trajectories, in both phases, offer an excellent visualization of the complex nature of the OPF solutions, that is, the highly nonlinear behaviour and the sensitivity of the solutions to parameter variations