Improving Power System Voltage Stability by Using Demand Response to Maximize the Distance to the Closest Saddle-Node Bifurcation

Temporal load shifting via demand response can be used to improve power system frequency stability. Recent work has shown that spatio-temporal load shifting can also be used to improve power system static voltage stability. However, the best static voltage stability metric is an open question. In this paper, we propose a method to improve power system static voltage stability by maximizing the distance to the closest saddle-node bifurcation of the power flow. Specifically, we formulate a nonlinear nonconvex optimization problem in which we choose loading patterns that maximize this distance while also constraining the total system loading to remain constant so that the actions do not affect frequency stability. We derive the KKT conditions and solve the resulting nonlinear system of equations using the Newton-Raphson method and check if the solution is a local minimum. Using a 4-bus system and the IEEE 9-bus system as our test cases, we explore the performance of the algorithm and the accuracy of the obtained solutions. We compare the solution to those obtained using other voltage stability metrics including the smallest singular value of the power flow Jacobian and the loading margin, finding that all approaches produce different solutions. Using Kundur's two area system, we also explore some algorithm convergence issues.