Engineers often reduce proportional-resonant (PR) controllers to simpler proportional controllers, neglecting the phase lag at midfrequencies. This reduction can lead to the incorrect assumption that a single-loop-control inverter with grid-side current feedback destabilizes when the inductor- capacitor-inductor (LCL) resonant frequency (ωr) is below the critical frequency (ωcrit), i.e., when ωr ≤ ωcrit. In contrast, we found that the PR controllers can provide adequate phase lag at midfrequencies. Adjusting the controller parameters to increase this phase lag can stabilize the inverter under ωr ≤ ωcrit conditions without additional damping. Our research offers a robust stability design process that involves tuning PR controller parameters and optional phase margin (PM) compensation to ensure inverter stability and maintain good dynamic performance despite fluctuations in grid impedance. Initially, we establish a mathematical relationship between the controller parameters and the phase crossover frequency. This relationship is then used to set the phase crossover frequency to match the antiresonant frequency created by the inverter-side filter inductor and capacitor. Subsequently, we introduce an optional PM compensator to speed up the convergence of tracking error and reduce highfrequency oscillations. Finally, a case study highlights the control system’s robustness, transient performance, and flexibility of the design approach.

中文翻译：

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在比例谐振控制器中使用相位滞后的逆变器鲁棒稳定性设计


工程师经常将比例谐振 (PR) 控制器简化为更简单的比例控制器，忽略中频的相位滞后。这种减少可能导致错误的假设，即当电感器-电容器-电感器 (LCL) 谐振频率 (ωr) 低于临界频率 (ωcrit) 时，即当ωr ≤ ωcrit。相反，我们发现 PR 控制器可以在中频提供足够的相位滞后。调整控制器参数以增加相位滞后可以使逆变器稳定在 ωr ≤ ωcrit 条件下，而无需额外阻尼。我们的研究提供了强大的稳定性设计流程，其中包括调整 PR 控制器参数和可选的相位裕度 (PM) 补偿，以确保逆变器稳定性并在电网阻抗波动的情况下保持良好的动态性能。最初，我们在控制器参数和相位交叉频率之间建立数学关系。然后使用该关系来设置相位交叉频率，以匹配逆变器侧滤波电感器和电容器产生的反谐振频率。随后，我们引入了可选的 PM 补偿器来加速跟踪误差的收敛并减少高频振荡。最后，案例研究强调了控制系统的鲁棒性、瞬态性能和设计方法的灵活性。