Accurate Analytical Modeling of Fractical-Order Grid-Following Inverters Using Oustaloup Approximation: Stability Region Characteristics and Simulation Validation

초록

？ Inverter-based resources, particularly grid-following (GFL) inverters, are essential in modern power systems with high renewable energy penetration. These inverters regulate their output in response to grid demands, but their stability heavily depends on control loop design. While traditional PI controllers offer simplicity, they may lack robustness under dynamic or uncertain grid conditions. Fractional-order PI (FOPI) controllers address these limitations by introducing non-integer order dynamics, enhancing control flexibility and robustness. However, incorporating fractional-order terms complicates state-space representation, which typically relies on first-order differential equations. This paper proposes a comprehensive modeling framework for GFL inverters using the Oustaloup recursive approximation to represent FOPI controllers. The approach yields a high-fidelity integer-order state-space model, enabling accurate analysis, control design, and stability assessment. The model is validated through both nonlinear and equivalent linearized system representations. Monte Carlo simulations are used to characterize robust stability regions across a wide range of fractional order values. The linearized model retains high accuracy while significantly reducing computational burden, making it suitable for large-scale and real-time studies. The proposed framework offers valuable insights into FOPI-controlled inverter dynamics and establishes a foundation for stability-constrained design, optimization, and hardware-in-the-loop validation in inverter-dominated grids.