Abstract:
Conventional grid-connected control for fractional-order virtual synchronous generators (FOVSG) can suffer from a trade-off in dynamic response performance between grid-connected active power and output frequency (referred to as “power-frequency”) under typical disturbances, such as step changes in active power reference and grid frequency. In this study, an improved grid-connected control strategy was proposed for FOVSG using active power differential feedback (APF), termed APF-FOVSG. A power dynamic compensation link, which extracted the derivative of the active power and passed it through a first-order filter, was incorporated into the existing FOVSG control structure, thereby forming the APF-FOVSG. This additional feedback path effectively introduced a structural damping term into the rotor motion equation, thus damping power oscillations with high-frequency response quality. The small-signal mathematical model of the APF-FOVSG grid-connected system was derived to explicitly account for the fractional-order dynamics of virtual inertia. The closed-loop transfer functions were obtained with active power and frequency responses to both internal (active power command) and external (grid frequency) disturbances. Furthermore, a parameter stability analysis was developed, including frequency-domain criteria (Bode plots and phase margin) and consistent time-domain validation. Oustaloup recursive filter was employed to approximate the fractional-order operator,
sμ, within the frequency range of interest (0.01 to 1000 rad/s) using a fifth-order rational transfer function. Excellent matching of magnitude and phase was obtained to facilitate practical implementation. The approximation accuracy was verified using Bode diagram comparison. The parameters were selected for the APF gain (
ka) and filter time constant (
τ). A systematic analysis was made to explore their impact on system stability and dynamic performance. Finally, a 100 kV·A FOVSG grid-connected system was implemented in MATLAB/Simulink simulation and a physical experimental platform. Comparative tests were conducted under two representative disturbance scenarios: a step increase in active power reference from 20 to 60 kW, and a step decrease in grid frequency from 50 to 49.95 Hz. The simulation and experimental results demonstrate that the APFFOVSG achieved simultaneous suppression of active power oscillations and frequency overshoot, compared with the conventional FOVSG, existing APF integer-order VSG (APFVSG), and the standard VSG. In the active power step test, the APF-FOVSG exhibited no dynamic oscillation in either active power or frequency, with a frequency overshoot amplitude of only 0.061 Hz (compared with 0.123 Hz for VSG, 0.151 Hz for FOVSG, and 0.064 Hz for APFVSG). In the grid frequency test, the APF-FOVSG again shared no oscillation, with an active power overshoot of 4.36% (versus 55.81% for VSG, 21.41% for FOVSG, and 16.32% for APFVSG). Conclusively, the superiority of the APF-FOVSG was validated for the power-frequency dynamic response, effectively resolving the trade-off inherent in existing FOVSG approaches. The findings can offer higher control flexibility, damping, and robust stability under various disturbances. A promising solution was provided for grid-connected inverters, particularly for inertia support and high-quality transient response.