A Nonlinear Negative-Imaginary Systems Framework with Actuator Saturation for Control of Electrical Power Systems

In the transition to net zero, it has been suggested that a massive expansion of the electric power grid will be required to support emerging renewable energy zones. In this paper, we propose the use of battery-based feedback control and nonlinear negative-imaginary (NNI) systems theory to reduce the need for such an expansion by enabling the more complete utilization of existing grid infrastructure. By constructing a novel Luré-Postnikov-like Lyapunov function, a stability result is developed for the feedback interconnection of a NNI system and a NNI controller. Additionally, a new class of NNI controllers is proposed to deal with actuator saturation. We show that in this control framework, the controller eventually leaves the saturation boundary, and the feedback system is locally stable in the sense of Lyapunov. This provides theoretical support for the application of battery-based control in electrical power systems. Validation through simulation results for single-machine-infinite-bus power systems supports our results. Our approach has the potential to enable a transmission line to operate at its maximum power capacity, as stability robustness is ensured by the use of a feedback controller.