Controlling nonlinear batteries for power systems: Trading off performance and battery life

Batteries can be used to provide ancillary services to electric power systems; however, a battery's energy storage capacity degrades as it consumes and produces power. To improve the economics of batteries, we wish to control them in ways that minimize degradation. This is a challenging task because i) battery dynamics are nonlinear, ii) battery power dynamics are on a completely different timescale than battery degradation dynamics, and iii) batteries only have one control input (current) and if we wish to achieve two objectives (signal tracking accuracy and degradation minimization) we must trade-off between them. We extend an existing nonlinear battery model, pose the battery control/management problem as a tracking control problem, and develop three controllers based upon PID control, feedback linearization, and sliding mode control. In simulation, we show how the controllers enable us to easily tradeoff tracking accuracy and battery life, and how explicitly considering nonlinear battery dynamics in the controllers improves performance. We also show how state estimation error and model mismatch impact the performance of the feedback linearization controller, and how the sliding model control is more more robust to these errors.