Optimal Control of Grid-Interfacing Inverters with Current Magnitude Limits

Grid-interfacing inverters act as the interface between renewable resources and the electric grid, and have the potential to offer fast and programmable responses compared to synchronous generators. With this flexibility there has been significant research efforts into determining the best way to control these inverters. An important nonlinear constraint in inverter control is a limit on the magnitude of the current, stemming from the need to protect semiconductor devices. Existing approaches either simply saturate a controller that is designed for unconstrained systems, or assume small perturbations and linearize a saturated system. These approaches can lead to stability issues or limit the control actions to be too conservative.In this paper, we directly focus on a nonlinear system that explicitly accounts for the saturation of the current magnitude. We use a Lyapunov stability approach to determine a stability condition for the system, guaranteeing that a class of controllers would be stabilizing if they satisfy a simple semidefinite programming condition. With this condition we fit a linear-feedback controller by sampling the output of (offline) model predictive control problems. This learned controller has improved performances with existing designs.