A Decentralized Polytopic Control Design for a Nonlinear Grid-Forming Inverter Model

Autonomous inverter-based microgrids present new operational challenges, as the stabilizing inertia of synchronous generators is absent. The design of efficient control policies for grid-forming inverters is, however, a nontrivial problem where multiple control objectives need to be satisfied. We consider the problem of designing a controller that achieves desirable objectives. We propose in this paper a decentralized polytopic control design that yields a state feedback voltage controller that stabilizes the inverters in the presence of droop-like controllers aiming to achieve power sharing. The voltage controller is synthesized via a convex optimization problem that uses a detailed nonlinear inverter model, where the nonlinearities are taken into account via a quasi-Linear Parameter Varying formulation. Our control design guarantees stability and plug-and-play capability via a decentralized condition with passivity properties, and appropriate performance specifications are satisfied, including voltage tracking capability, restricted control input, and robustness to state deviations. Our approach allows using a user-defined operating point, and through the polytopic control design it allows us to take into account the bounds on the inverter state deviations. The performance of the controller is illustrated via simulations with detailed nonlinear models in a realistic setting.