Calculation of Voltage Stability Margins and Certification of Power Flow Insolvability Using Second-Order Cone Programming

Reliable power system operation requires maintaining sufficient voltage stability margins. Traditional techniques based on continuation and optimization calculate lower bounds for these margins and generally require appropriate initialization. Building on a previous semidefinite programming (SDP) formulation, this paper proposes a new second-order cone programming (SOCP) formulation which directly yields upper bounds for the voltage stability margin without needing to specify an initialization. Augmentation with integer-constrained variables enables consideration of reactive-power-limited generators. Further, leveraging the ability to globally solve these problems, this paper describes a sufficient condition for insolvability of the power flow equations. Trade-offs between tightness and computational speed of the SDP and SOCP relaxations are studied using large test cases representing portions of European power systems.