Energy-Consistent Super-Twisting Sliding-Mode Control of a Grid-Forming LC Inverter: A Port-Hamiltonian Diagnostic Perspective

Abstract

This paper presents an energy-consistent super-twisting (ST) sliding-mode control design for a single-phase grid-forming inverter with an output LC filter, motivated by inverter-dominated low-inertia power-electronic applications. Throughout, energy-consistent refers to a sliding surface whose closed-loop motion is shaped to avoid large transient excursions of the filter Hamiltonian. The surface couples the voltage error, its integral, and the inductor current, and its design is informed by the port-Hamiltonian (PH) representation of the LC filter; the Hamiltonian is employed as a physically meaningful diagnostic rather than as a strict control structure. A super-twisting reaching law is used to provide continuous control action and finite-time convergence under bounded matched perturbations, with explicit gain conditions stated. An actuator saturation constraint is included in the model and its effect is reported. The proposed controller is benchmarked against a classical first-order SMC with boundary layer on the same sliding surface, isolating the contribution of the ST reaching law. Simulation studies on a grid-forming LC inverter subject to renewable-like disturbances and parameter uncertainties show that the ST controller reduces steady-state tracking error, control chatter, and Hamiltonian variation by a factor of two or more across the tested operating envelope, while the gain-sensitivity coefficient of variation of $\Delta {\mathcal{H}}$ stays below 3 over a [0.5,1.5]× nominal gain box.