Wide-Frequency Power Decoupling and Accurate Reactive Power Control for Andronov-Hopf Virtual Oscillator-Based Grid-Forming Inverters

The Andronov-Hopf virtual oscillator control is a grid-forming control strategy based on instantaneous current feedback, which provides voltage and frequency support in weak grids. However, the unavoidable power coupling and inherent inaccuracies in power tracking control lead to steady-state errors and dynamic oscillations, which severely restrict the power delivery and the grid support capability. Therefore, this paper proposes an optimized loop-shaping-based power control (OLPC) strategy to ensure system stability. First, to address the inability of the relative gain array to evaluate feedback dynamics, a closed-loop transfer function array is developed. It explicitly reveals two limitations: failure to achieve power decoupling and amplification of reactive power tracking errors. Subsequently, the objectives of OLPC are formulated in the frequency domain using bandwidth design specifications. Then, the optimal parameters are obtained by reformulating the parameter design problem as a convex optimization problem. Compared to the virtual inductor methods, the OLPC exhibits superior wide-frequency power decoupling, more accurate reactive power tracking, and faster power response. Finally, the theoretical analysis and proposed method are validated through experiments.