This article provides as contribution a systematic design procedure for robust current control of grid-tied inverters with LCL filters affected by inductor magnetic soft-saturation and also by uncertain grid impedances. The proposed design is based on the following: first, a polytopic time-varying model to describe the effect of the inductances variations; second, a set of linear matrix inequalities to design fixed (robust) state feedback gains, ensuring bounded settling times for the closed-loop transient responses. A less conservative set of linear matrix inequalities is used to certify the procedure. Experimental results from real-time simulations and from a real prototype with commercial powder core inductors show that the proposed procedure can provide superior results than conventional controllers designed not taking into account the soft-saturation. The results with the proposed controller comply with the IEEE 1547 Standard, leading to grid currents with low harmonic content, respecting limits prescribed by this standard even under distorted grid voltages.

中文翻译：

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受LCL滤波器软饱和影响的并网逆变器的鲁棒电流控制

本文提供了一种系统设计程序，用于对受电感软饱和和不确定电网阻抗影响的带有 LCL 滤波器的并网逆变器进行稳健的电流控制。所提出的设计基于以下内容：首先，一个多面体时变模型来描述电感变化的影响；其次，一组线性矩阵不等式设计固定（稳健）状态反馈增益，确保闭环瞬态响应的有界稳定时间。一组不太保守的线性矩阵不等式用于证明该过程。来自实时模拟和具有商用粉芯电感器的真实原型的实验结果表明，与未考虑软饱和设计的传统控制器相比，所提出的程序可以提供更好的结果。建议控制器的结果符合 IEEE 1547 标准，导致电网电流具有低谐波含量，即使在电网电压失真的情况下也符合该标准规定的限制。