A New Voltage Stability-Constrained Optimal Power-Flow Model: Sufficient Condition, SOCP Representation, and Relaxation

This paper proposes a novel voltage stability-constrained optimal power-flow (VSC-OPF) model utilizing a recently proposed sufficient condition on power-flow Jacobian nonsingularity. We show that this condition is second-order conic representable when load powers are fixed. Through the incorporation of the convex sufficient condition and thanks to the recent development of convex relaxation of OPF models, we cast a VSC-OPF formulation as a second-order cone program. An approximate model is introduced to improve the scalability of the formulation to larger systems. Extensive computation results on MATPOWER and NESTA instances confirm the effectiveness and efficiency of the formulation.