Reinforcement Learning for Power-Flow Network Analysis

The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network topology, we are interested in finding network parameters with many equilibrium points. This corresponds to finding instances of the power flow equations with many real solutions. Current state-of-the art algorithms in computational algebra are not capable of answering this question for networks involving more than a small number of variables. To remedy this, we design a probabilistic reward function that gives a good approximation to this root count, and a state-space that mimics the space of power flow equations. We derive the average root count for a Gaussian model, and use this as a baseline for our RL agents. The agents discover instances of the power flow equations with many more solutions than the average baseline. This demonstrates the potential of RL for power-flow network design and analysis as well as the potential for RL to contribute meaningfully to problems that involve complex non-linear algebra or geometry. \footnote{Author order alphabetic, all authors contributed equally.