Safe Model-Free Optimal Voltage Control via Continuous-Time Zeroth-Order Methods

To maintain voltage security with limited system model information, we develop a model-free optimal voltage control algorithm based on projected primal-dual gradient dynamics and continuous-time zeroth-order method (extremum seeking control). This proposed algorithm i) operates purely based on voltage measurements and does not require any other model information (model-free), ii) drives the voltage magnitudes back to the acceptable range while satisfying the power capacity constraints all the time (safety), and iii) minimizes the total operating cost (optimality). Moreover, this algorithm is implemented in a decentralized fashion where the privacy of controllable devices is preserved and plug-and-play operation is enabled. We prove that the proposed algorithm is semi-globally practically asymptotically stable and is structurally robust to small measurement noises. Lastly, the performance of this algorithm is further demonstrated via numerical simulations.