Robust Online Voltage Control with an Unknown Grid Topology

Voltage control generally requires accurate information about the grid's topology in order to guarantee network stability. However, accurate topology identification is a challenging problem for existing methods, especially as the grid is subject to increasingly frequent reconfiguration due to the adoption of renewable energy. Further, running existing control mechanisms with incorrect network information may lead to unstable control. In this work, we combine a nested convex body chasing algorithm with a robust predictive controller to achieve provably finite-time convergence to safe voltage limits in the online setting where the network topology is initially unknown. Specifically, the online controller does not know the true network topology and line parameters, but instead must learn them over time by narrowing down the set of network topologies and line parameters that are consistent with its observations and adjusting reactive power generation accordingly to keep voltages within desired safety limits. We demonstrate the effectiveness of the approach using a case study, which shows that in practical settings the controller is indeed able to narrow the set of consistent topologies quickly enough to make control decisions that ensure stability.