Online Battery Storage Management via Lyapunov Optimization in Active Distribution Grids

We consider low run-time complexity power management in distribution grids with renewable energy sources (RESs) and batteries, where forecasts are unavailable. We propose iterative Lyapunov Real-time Control (iLypRC), a fast online algorithm, which does not need forecasts, for the real-time battery control. iLypRC is designed via Lyapunov optimization and applies either to follow a previously computed dispatch plan or to optimize the monetary cost, while it satisfies look-ahead state-of-energy constraints. iLypRC requires only bounds on the uncertain quantities for each real-time interval. iLypRC efficiently accounts for grid losses, battery efficiency, and grid constraints via iterative linearizations of the power flow equations. We compute a theoretical upper bound on the difference between the cost of iLypRC and the cost of an oracle. Finally, numerical evaluations (using real data) on a 4-bus distribution grid and a 34-bus real Swiss grid show that iLypRC achieves a cost very close to that of a model predictive control (MPC) with a good forecast, but iLypRC needs no forecast and has much lower run-time complexity. Also, when the MPC forecast is inaccurate, iLypRC outperforms MPC.