Accurate modeling and QPSO-optimized fractional-order control of grid-connected solar PV systems using ORA and MSBL approximation

초록

This paper presents a comprehensive modeling, optimization, and real-time validation framework for fractional-order control of grid-connected solar PV systems. A high-fidelity 10th-order nonlinear state-space model is developed, in which the dynamics of fractional-order PI (FOPI) controllers are explicitly incorporated using the Oustaloup recursive approximation (ORA) and the modified stability boundary locus (MSBL) method while maintaining a low and fixed model order. The complete system is linearized for both approximation techniques to enable systematic small-signal stability analysis. A Quantum-behaved Particle Swarm Optimization (QPSO) approach is employed to optimally tune the fractional order design parameters for both approximation techniques. The MSBL outperforms ORA in terms of minimizing the spectral abscissa. Quantitatively, the optimized MSBL realization achieves a 10.5% reduction in spectral abscissa, increases the minimum damping ratio from 11.93% to 17.50% (46.7% improvement), and reduces DC-link and d-axis current overshoot by 57% and 38.6%, respectively, while preserving millisecond-level settling performance. The stability and robustness of the optimized MSBL-based controller are investigated through eigenvalue migration and modal analysis across a wide range of operating conditions. The proposed framework is further validated using OPAL-RT-based real-time simulation and controller-hardware-in-the-loop (C-HILS) experiments implemented on a Raspberry Pi platform under grid-disturbance scenarios, including low-voltage ride-through and voltage sag conditions. The results demonstrate that the optimized fractional-order control strategy achieves improved stability characteristics and robust performance under dynamic operating conditions.

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