Transient stability constrained optimal power flow applied to distribution systems with synchronous generators

This paper proposes a Transient Stability Constrained Optimal Power Flow (TSC-OPF) formulation in order to calculate the optimum operating point of synchronous generators in distribution networks, in terms of dispatch of their active and reactive powers. However, the problem is complex due to the high number of constraints and variables, as well as, the presence of nonlinear constraints. To circumvent these adversities, an optimization problem is proposed in this paper with the application of a set of mathematical approximations in the constraints of the active and reactive power balance equations. In addition, an approximation is explored in the swing equation of synchronous generators belonging to a group of coherent machines, particularly regarding the active power injection from the generators. The proposed TSC-OPF is tested in a 31-bus radial distribution system with two and four generators. The results show that the running time to solve the proposed optimization problem with approximations becomes smaller when compared to the time to solve it without approximations.