Direct nonlinear interior point methods for optimal power flows

In this thesis, two new direct nonlinear programming approaches using the primal-dual interior point algorithm for optimal power flows (OPF) are derived: the pure direct nonlinear primal-dual interior point algorithm (PDIPA) and direct nonlinear predictor-corrector primal-dual interior point algorithm (PCPDIPA). They consist of three fundamental building blocks: Fiacco & McCormick's barrier method, Lagrange's method, and Newton's method. All inequalities in the OPF are dealt by Fiacco-McCormick's barrier method, and the objective function is augmented by barrier functions. In so doing, heuristic identification for binding constraints, which is the big challenging work in some alternative OPF algorithms, is not needed during the optimization process. The resulting barrier-problem consisting of equalities converges to the original OPF problem as the barrier parameter decreases towards zero, and it can be solved by Lagrange's method and Newton's method based on Karush-Kuhn-Tucker (KKT) first-order conditions. The major computational effort involved in PDIPA and PCPDIPA is in solving a sparse symmetrical system of equations. Since the sparsity structure of the system is fixed, ordering on the system variables to have minimum fill-ins in factorization only needs to be performed once by means of symbolic factorization. Several practical considerations and enhancement features are also addressed, such as the choice of a good starting point, sparse matrix techniques, real/reactive decoupling, hot start, relaxation of unnecessary constraints, etc.