Original Contributions to Fractional-Order Control Theory for Power Electronic Converters in Renewable Energy Systems: Applications to Nigerian Grid Integration

This research develops original theoretical contributions to fractional-order control theory for power electronic converters in grid-connected renewable energy systems, with specific application to the Nigerian grid integration context where non-ideal grid conditions including voltage harmonics, frequency deviations, and phase imbalances challenge conventional integer-order controller performance. Fractional-order control, which generalises classical PID control to non-integer derivative and integral orders, offers theoretically superior robustness and disturbance rejection properties under uncertain plant dynamics, but its application to grid-tied inverters in weak and distorted grid environments representative of Nigeria remains largely unexplored in the literature. The theoretical contribution consists of three components: the derivation of stability conditions for fractional-order controlled grid-tied inverters connected to grids with non-ideal characteristics quantified from Nigerian grid measurement data; the development of a systematic parameter optimisation methodology for fractional-order controllers using a multi-objective formulation that simultaneously minimises harmonic injection, grid synchronisation error, and transient overshoot; and a novel digital implementation scheme for fractional-order operators that maintains computational efficiency on standard DSP platforms. The theoretical framework is validated through hardware experimentation using a 10kW prototype grid-tied inverter operating on a grid emulator programmed with recorded Nigerian grid disturbance profiles from TCN SCADA data. Experimental results confirm 23 percent improvement in total harmonic distortion of injected current and 41 percent reduction in synchronisation time during grid voltage dip events compared to optimised PI control. Keywords: fractional-order control, power electronic converter, grid integration, renewable energy, Nigeria.