Stuart-Landau Oscillator-Based Grid-Forming Control with Gray-Box High-Gain Observer for Filter Parameter Variation

This paper investigates the application of Stuart-Landau nonlinear oscillators in grid-forming inverters to enhance grid reliability, disturbance rejection, and dynamic performance under non-ideal loading conditions. A cascaded control architecture is proposed, incorporating a nonlinear inner-loop controller grounded in passivity-based principles to ensure global asymptotic stability and superior dynamic behavior. To address magnetic saturation effects, a gray-box modeling framework is introduced, which combines first-principles physical equations with empirical data via a high-gain observer for real-time estimation of nonlinear inductance. This enables adaptive tuning of control parameters to maintain performance across varying operating conditions. The control strategy is evaluated through extensive simulations in MATLAB/Simulink and PLECS, show-casing its robustness against load disturbances and parameter uncertainties. The results demonstrate significant improvements in voltage regulation, transient response, and overall inverter resilience in weak or unbalanced grid scenarios.