Second order sensitivities for constrained reactive optimal power flow

Usually, the main purpose of optimal reactive power flow (ORPF) programs is to minimize the total power losses of a network, maintaining the voltage profile within an acceptable range. This model was adopted by almost all the vertically integrated utilities. Nowadays, in the liberalized environment, a new ORPF formulation, aimed at an explicit maximization of the system security, is more suitable. In this sense, N-1 constraints should be included in Security-constrained ORPF (SCORPF). It is well known that in Security-constrained optimization problems, N-1 constraints are introduced in terms of changes in the branch currents. These changes can be calculated quite reliably, under some assumptions, by the Inverse Matrix Modification Lemma (IMML). However, when facing the reactive sub-problem, the post contingency changes of voltage magnitudes can be computed by the IMML, but the same accuracy as in the real subproblem cannot be ensured. In this paper, second-order sensitivities of bus voltages are computed in order to provide a means to determine voltage variations after contingencies; they can be suitably adopted in SCORPF.