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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 <sc>Matpower</sc> and NESTA instances confirm the effectiveness and efficiency of the formulation.

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