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, s^μ, 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 (k_a) 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 APF-FOVSG 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.

Grid-forming virtual synchronous generator (GFVSG) can improve the voltage regulation ability and frequency stability of power grid, but it has the problem of grid connected active power dynamic oscillation similar to that of traditional synchronous generator under the conditions of internal disturbance of active power command and external disturbance of power network frequency. To solve this problem, the grid connected active power closed loop equivalent control model of the grid connected system for grid-forming virtual synchronous generator is established, and the reasons for the dynamic oscillation of the grid connected active power of grid-forming virtual synchronous generator under the disturbance of internal active power command and external power network frequency are analyzed in this study. An improved grid-forming virtual synchronous generator control method based on loop reconstruction mechanism (LRM-GFVSG) is proposed, and the corresponding parameter design method is given in detail. Finally, the MATLAB simulation platform as well as experimental platform of 100 kV·A GFVSG grid connected system are established, then the feasibility and superiority of the improved LRM-GFVSG control method in suppressing the dynamic oscillation of the grid connected active power of grid-forming virtual synchronous generator are verified by the simulation and experimental comparison results. Simulation and experimental comparison results show that the grid connected active power closed loop control system of GFVSG is upgraded to a second order oscillation control system due to the introduction of virtual inertia control. Therefore, the grid connected active power and output frequency of the grid connected system of grid-forming virtual synchronous generator are prone to dynamic oscillation and overshoot under the disturbance of internal active power command and external power network frequency. Although increasing the value of the virtual damping parameter of grid-forming virtual synchronous generator can improve the ability to suppress the dynamic oscillation and overshoot of the grid connected active power as well as its output frequency, the steady-state deviation of the grid connected active power is introduced. Compared with grid-forming virtual synchronous generator, the existing grid-forming virtual synchronous generator control method based on feedforward compensation (FFC-GFVSG) as well as the existing grid-forming virtual synchronous generator control method based on feedback compensation (FBC-GFVSG), on the one hand, under the simulation and experimental test conditions where the active power instruction jumps from 20 kW to 60 kW, the improved control method of LRM-GFVSG can improve the transient damping characteristics of the grid tied system, and realize the effective suppression of the dynamic oscillation and overshooting of the grid connected active power as well as its output frequency, and the grid connected active power has a faster dynamic response speed. On the other hand, under the simulation and experimental test conditions where the frequency of the power grid jumps from 50 Hz to 49.95 Hz, the improved control method of LRM-GFVSG can improve the transient damping characteristics of the grid tied system, effectively suppress the dynamic oscillation and overshoot in the grid connected active power as well as its output frequency, and eliminate the steady state deviation of the grid connected active power when the power network frequency deviates from the rated frequency.