Virtual inertia and damping control (VIDC) improves the stability of DC microgrid (DC-MG). However, the potential positive feedback aggravates low-frequency oscillation induced by the interaction insides control loops, which is explained and solved in this paper. The multi-timescale impedance modelling framework is established to clarify stability mechanism of VIDC and the low-frequency oscillation of VIDC controlled DC-MG. Control loops of different timescales are visualized as independent loop virtual impedance (LVI) elements to form an impedance circuit considering the constant power load (CPL), rather than an all-in-one impedance as the external dynamic representation of power converters. Concrete impedance analysis is performed on LVI to reveal the impedance-shaping effect of control loops intuitively, the physical impedance nature of control parameters and the interaction among different timescale, which illustrates the stability mechanism of VIDC. The low-frequency oscillation (LC impedance interaction) in voltage- and inertia-loop is elaborated by RLC circuits of LVIs. The potential instability factors, resulting in poor damping against voltage oscillation, are also revealed. Thus, dynamic stability enhancement method is further proposed to compensate for the negative damping caused by positive feedbacks of VIDC and CPL, and super-capacitor is added to alleviate rapid voltage changes. Accordingly, the passivity property of system impedance is strengthened and the stability can be evaluated by Nyquist plot. Finally, the simulation and experiment results have validated the low-frequency oscillation analysis and stability enhancement method.

中文翻译：

---

基于多时间尺度阻抗模型的虚拟惯量控制直流微电网低频振荡分析

虚拟惯性和阻尼控制（VIDC）提高了直流微电网（DC-MG）的稳定性。然而，潜在的正反馈加剧了控制回路内部相互作用引起的低频振荡，本文对此进行了解释和解决。建立多时间尺度阻抗建模框架，阐明VIDC的稳定性机制和VIDC控制的DC-MG的低频振荡。不同时间尺度的控制回路可视化为独立回路虚拟阻抗(LVI) 元件，以形成阻抗电路考虑恒定功率负载 (CPL)，而不是一体式阻抗作为电源转换器的外部动态表示。对LVI进行了具体的阻抗分析，直观地揭示了控制回路的阻抗整形效果、控制参数的物理阻抗性质以及不同时间尺度之间的相互作用，说明了VIDC的稳定性机制。RLC详细阐述了电压和惯性回路中的低频振荡（LC阻抗相互作用）LVI 的电路。还揭示了潜在的不稳定因素，导致对电压振荡的阻尼较差。因此，进一步提出动态稳定性增强方法来补偿由VIDC和CPL的正反馈引起的负阻尼，并添加超级电容器以缓解电压的快速变化。因此，系统阻抗的无源特性得到加强，稳定性可以通过奈奎斯特图来评估。最后，仿真和实验结果验证了低频振荡分析和稳定性增强方法。