Trajectory Sensitivity Method for Transient Stability Constrained Optimal Power Flow Under Multi-contingency Condition

Transient stability constrained optimal power flow (TSC-OPF) problem was divided into three sub-problems: power flow, transient stability and trajectory sensitivity, and reduced-order quadratic programming OPF. According to power flow and transient stability computation, time varying trajectories of state and algebraic variables were calculated, from which transient stability was judged, and trajectory sensitivities of algebraic and state variables with respect to active power and reactive power of generators respectively at the moment of initial and instability time duration were obtained. Based on these trajectory sensitivities, TSC-OPF problem was converted into a reduced-order quadratic programming OPF model with incremental active and reactive power of generators as independent variables. Hence incremental active power and reactive power of generators were computed from this quadratic programming model. Through alternating solution of the above three sub-problems, the OPF solution which satisfies transient stability constraints can be achieved. Furthermore, a method to approach multiple contingencies was presented, which was not affected by disturbance type and mode. Results on New England 10-machine 39-bus and UK 20-machine 100-bus systems demonstrate that the proposed method has some advantages in terms of computational accuracy and speed.