This work investigates the problem of controller design for the inverters in an islanded microgrid. Robust $\mu$ -synthesis controllers and local droop controllers are designed to regulate the output voltages of inverters and share power among them, respectively. The designed controllers alleviate the need for additional sensors to measure the states of the system by relying only on output feedback. It is shown that the designed $\mu$ -synthesis controller properly damps resonant oscillations, and its performance is robust to the control-loop time delay and parameter uncertainties. The stability of a droop-controlled islanded microgrid including multiple distributed generation (DG) units is analyzed by linearizing the nonlinear power flow model around the nominal operating point and applying theorems from linear algebra. It is indicated that the droop controller stabilizes the microgrid system with dominantly inductive tie-line impedances for all values of resistive-inductive loads, while for the case of resistive-capacitive loads the stability is conditioned on an upper bound on the load susceptances. The robust performance of the designed $\mu$ -synthesis controller is studied analytically, compared with the similar analysis in an $H_{\infty}$ control (benchmark) framework, and verified by simulations for a four DG benchmark microgrid. Furthermore, the robustness of the droop controllers is analyzed by Monte Carlo simulations in the presence of local voltage fluctuations and phase differences among neighboring DGs.

中文翻译：

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逆变器主导下垂控制孤岛微电网中的鲁棒控制器综合与分析


这项工作研究了孤岛微电网中逆变器的控制器设计问题。鲁棒的$\mu$合成控制器和局部下垂控制器分别设计用于调节逆变器的输出电压并在它们之间共享功率。所设计的控制器仅依靠输出反馈来减少对额外传感器来测量系统状态的需求。结果表明，设计的 $\mu$ 合成控制器能够适当地抑制谐振振荡，并且其性能对于控制环时间延迟和参数不确定性具有鲁棒性。通过对标称工作点附近的非线性潮流模型进行线性化并应用线性代数定理，分析了包括多个分布式发电（DG）单元的下垂控制孤岛微电网的稳定性。结果表明，对于所有阻感负载值，下垂控制器都能以感性联络线阻抗为主的微电网系统保持稳定，而对于阻性负载的情况，稳定性取决于负载电纳的上限。对所设计的 $\mu$ 综合控制器的鲁棒性能进行了分析研究，与 $H_{\infty}$ 控制（基准）框架中的类似分析进行了比较，并通过四 DG 基准微电网的模拟进行了验证。此外，在存在局部电压波动和相邻 DG 之间相位差的情况下，通过蒙特卡罗模拟分析了下垂控制器的鲁棒性。