Distributed learning for optimal allocation in radial power systems

We revisit the classical log-linear learning algorithm for optimal allocation of DC/AC converters and synchronous machines in radial (no loops) power systems. The objective is to assign to each generator node a type; either a synchronous machine or a DC/AC converter in closed-loop with droop control, while minimizing the steady state angle deviation relative to an optimum associated with unknown optimal configuration of synchronous machines and DC/AC converters. Additionally, we study the robustness of the learning algorithm against uniform drop in the line susceptances and with respect to well-defined feasibility region describing admissible power deviations. We show guaranteed probabilistic convergence to maximizers of the perturbed potential function with feasible power flows and demonstrate our theoretical findings via simulative example of power network with six generation units.