Real-Time Voltage-Stability Enhancement via Demand Response

We propose a real-time algorithm that improves the voltage stability of a power network by rearranging the consumption level of loads participating in demand response (DR). Towards this end, we revisit an optimization problem that seeks to maximize the smallest singular value (SSV) of the power flow Jacobian subject to nonconvex power flows and limit constraints on voltages of PQ buses, real power generation of the slack generator, and reactive power generation of the slack and PV buses. Instead of linearizations or relaxations, we penalize the limit constraints and rely on network measurements to derive an online projected gradient update to determine DR decisions. The updated DR decisions are applied to the power network per iteration and latest measurements are fed back to the algorithm. Simulations on several standard transmission networks demonstrate that the proposed methodology improves the value of the SSV of the power flow Jacobian per time step while avoiding significant bound violations.