Optimal Distributed Nonlinear Battery Control

Energy storage plays a more important role than ever before, due to the transition to smart grid along with higher penetration of renewable resources. In this paper, we describe our optimal nonlinear battery control algorithm that can handle multiple batteries connected to the grid in a distributed and cost-optimal fashion, while maintaining low complexity of $O(N^{2})$ . In contrast to the state-of-the-art models, we use a high accuracy nonlinear battery model with 2% error. We present three distributed solutions: 1) a circular negotiation ring, providing convergence rates independent of the number of batteries; 2) a mean circular negotiation ring, converging very quickly for a low number of batteries; 3) a bisection method has a convergence rate independent of battery capacities. We compare our algorithm to the state-of-the-art algorithms and show that we can decrease the utility cost of an actual building by up to 50% compared with the batteryless case by 30% over the load-following heuristic and by 60% over a state-of-the-art optimal control algorithm designed using a linear battery model. For a constant load profile, optimal linear control incurs costs higher by 150% for model predictive control and 250% for single-trajectory solutions than for our algorithm.