Fractional-Order Reactive Power Control for Electro-Thermal-Constrained Fault Ride-Through of Grid-Forming Converters

Grid-forming converters are essential for low-inertia power systems. However, their semiconductor current and junction-temperature limits make them vulnerable to protection-triggered blocking and thermal overstress during severe voltage sags. Existing control methods still struggle to suppress fault-instant current surges and the associated transient thermal stress induced by rapid overcurrent, which restricts the continuous operation of grid-forming converters during fault ride-through. This paper proposes a two-stage coordinated electro-thermal control strategy centered on fractional-order reactive power regulation. First, a fractional-order operator is embedded into the reactive-power loop of the virtual synchronous generator to smooth the transient response of the internal electromotive force and directly suppress the amplitude of fault-induced inrush current. By introducing a continuously tunable order, the proposed controller enhances transient damping, mitigates the waterbed effect trade-off associated with integer-order control, and reduces the initial junction-temperature shock at the fault instant. A constraint-based feasible-region identification procedure is then developed, in which a full-range parameter sweep is performed to screen fractional orders under stability, current, and thermal constraints. Second, generalized discontinuous pulse-width modulation and switching-frequency reduction are jointly applied to mitigate post-transient thermal accumulation. Electro-thermal co-simulation results indicate that, under the specified voltage-sag condition, the proposed strategy reduces transient overcurrent and thermal stress and improves the simulated fault-ride-through performance of grid-forming converters without additional hardware thermal margins.