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基于有功微分反馈的分数阶虚拟同步机并网控制方法

Grid-connected control method of fractional-order virtual synchronous generator based on active power differential feedback

  • 摘要: 针对已有分数阶虚拟同步机(fractional-order virtual synchronous generator,FOVSG)并网控制方法在有功指令阶跃、电网频率阶跃等扰动下存在的并网有功与输出频率(简称“功频”)动态响应性能难以兼顾的问题,提出一种基于有功微分反馈(active power differential feedback,APF)的FOVSG(APF-FOVSG)并网控制方法,将基于有功微分反馈的功率动态补偿环节引入至FOVSG控制结构中以构成APF-FOVSG,建立APF-FOVSG并网系统的小信号数学模型,并给出相应的参数稳定性分析方法。最后,建立100 kV·A FOVSG并网系统的MATLAB软件仿真和物理实验平台进行验证。APF-FOVSG在有功指令从20 kW阶跃至60 kW时,无功频动态振荡,输出频率过冲幅值仅为0.061 Hz(VSG为0.123 Hz,FOVSG为0.151 Hz);在电网频率从50 Hz阶跃至49.95 Hz时,有功超调量仅为4.36%(VSG为55.81%,FOVSG为21.41%)。所提方法能够同时抑制有功振荡与频率过冲,有效解决了已有FOVSG功频响应性能难以兼顾的问题,具有更高的控制灵活性与阻尼特性,为构网型逆变器兼顾惯性支撑与暂态响应提供了新的解决方案。

     

    Abstract: The conventional grid-connected control method for fractional-order virtual synchronous generators (FOVSG) suffers from a critical trade-off in dynamic response performance between grid-connected active power and output frequency (hereinafter referred to as “power-frequency”) under typical disturbances, such as step changes in active power reference and grid frequency. To overcome this inherent limitation, this paper explicitly proposes an improved grid-connected control strategy for FOVSG based on active power differential feedback (APF), designated as APF-FOVSG. A power dynamic compensation link, which extracts the derivative of the active power and passes it through a first-order filter, is incorporated into the existing FOVSG control structure, thereby forming the APF-FOVSG. This additional feedback path effectively introduces a structural damping term into the rotor motion equation, enhancing the system’s ability to dampen power oscillations without sacrificing frequency response quality. The small-signal mathematical model of the APF-FOVSG grid-connected system is rigorously derived, explicitly accounting for the fractional-order dynamics of the virtual inertia. Based on this model, the closed-loop transfer functions relating active power and frequency responses to both internal (active power command) and external (grid frequency) disturbances are obtained. Furthermore, a comprehensive parameter stability analysis method is developed, which includes frequency-domain criteria (Bode plots, phase margin) and consistent time-domain validation. To facilitate practical implementation, the Oustaloup recursive filter is 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, and the approximation accuracy is verified through Bode diagram comparison, showing excellent matching in both magnitude and phase. The parameter selection guidelines for the APF gain ka and filter time constant τ are discussed, and their impact on system stability and dynamic performance is analyzed. Finally, a 100 kV·A FOVSG grid-connected system is implemented both in MATLAB/Simulink simulation and on a physical experimental platform. Extensive comparative tests are conducted under two representative disturbance scenarios: a step increase in active power reference from 20 kW to 60 kW, and a step decrease in grid frequency from 50 Hz to 49.95 Hz. The simulation and experimental results consistently demonstrate that, unlike the conventional FOVSG, the existing APF-based integer-order VSG (APF-VSG), and the standard VSG, the proposed APF-FOVSG method achieves simultaneous suppression of active power oscillations and frequency overshoot. In the active power step test, the APF-FOVSG exhibits no dynamic oscillation in either active power or frequency, with a frequency overshoot amplitude of only 0.061 Hz (compared to 0.123 Hz for VSG, 0.151 Hz for FOVSG, and 0.064 Hz for APF-VSG). In the grid frequency step test, the APF-FOVSG again shows no oscillation, with an active power overshoot of merely 4.36% (versus 55.81% for VSG, 21.41% for FOVSG, and 16.32% for APF-VSG). These results conclusively validate the superiority of the proposed APF-FOVSG method in enhancing power-frequency dynamic response performance, effectively resolving the trade-off inherent in existing FOVSG approaches. The proposed method offers higher control flexibility, improved damping characteristics, and robust stability under various disturbances, making it a promising solution for grid-connected inverters requiring both inertia support and high-quality transient response.

     

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