Application of Linear Multi-step Methods to a Transient Stability Constrained Optimal Power Flow Model

This paper analyzes the application of three different multi-step numerical integration methods to a transient stability constrained optimal power flow (TSC-OPF) model. The methods are compared to the well-known trapezoidal rule in terms of accuracy, convergence, and computation time. Two of the methods are multiple-step integration algorithms from the Adams family that show good performance under certain conditions. The third method is a new technique obtained by reformulating the application of the trapezoidal rule to eliminate the rotor speed from the swing equations. This method is found to produce the same results as the ordinary trapezoidal rule with less computation time and can be a good alternative when it is not necessary to calculate the rotor speeds.