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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 for fractional-order virtual synchronous generator based on active power differential feedback

  • 摘要: 为解决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软件仿真和物理试验平台进行验证。APF-FOVSG在有功指令从20 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 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: 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.

     

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