Expected-security-cost optimal power flow with small-signal stability constraints

The goal of the optimal power flow (OPF) problem is to find an electric power system operating point that optimizes some objective. This optimization problem is constrained, however, since the operating point is constrained by Kirchhoff's laws and key operating limits. In this paper, we include small-signal stability limits in the OPF, which ensure that when small disturbances occur within the system, oscillations that occur in state variables such as generator rotor speed will decay quickly, returning the system to a normal operating point. We also account for security by using an objective function that is the expected value of social welfare. This objective function includes security costs such as generator ramping and load interruption that may be necessary when a contingency occurs. Software was written in Matlab to solve this optimization problem with small-signal stability constraints, and the software was used to find the optimal pre-contingency and post-contingency operating points of a nine-bus system with three generators.