Optimal operation of distribution networks with synchronous generators via transient stability constrained optimal power flow

A common approach to deal with transient stability constraints in optimization problems is the combination of a numerical discretization method with interior point methods (IPMs) for solving large-scale nonlinear programming (NLP). The numerical discretization is adopted to convert the differential equations that describe the electromechanical transients in power systems in a set of algebraic equations to be included into a conventional optimal power flow (OPF) problem. The resulting transient stability constrained optimal power flow (TSC-OPF) problem, however, suffers with the curse of dimensionality, high computational time and memory consumption to solve it, even for small systems. To relieve this computational burden, this paper proposes an algorithm that aims at solving a TSC-OPF problem via primal-dual IPM with only a few time steps of numerical discretization in post-fault period, which is enough to ensure the rotor angle first swing stability. Once the TSC-OPF problem is solved, a numerical discretization method is applied to calculate the system trajectory from the first rotor angle peak in post-fault period. An important contribution of the proposed algorithm is to provide a proper accuracy on the computation of constant admittance loads. Numerical results are obtained for a 9-bus distribution network with the purpose of providing a proper sizing of DG units based on synchronous generators and an optimal operation to the network.