一种基于降维观测的LCL并网逆变器阻尼控制方法

摘要

本发明公开了一种基于降维观测的LCL并网逆变器阻尼控制方法，该方法包括：建立并网LCL滤波器的单相系统微分方程；将系统方程分解为不需要重构的子系统与需要重构的子系统；求解重构子系统的特征多项式；设计重构子系统的降维观测器；求解降维观测器的特征方程。本发明控制方法省去了传统控制方法中电容电压或电容电流采样的传感器，通过前馈观测出电容电流进而抑制了系统谐振，提高了系统的可靠性。

主权项

一种基于降维观测的LCL并网逆变器阻尼控制方法，其特征在于，该方法包括：建立并网LCL滤波器的单相系统微分方程；将系统微分方程分解为非重构的子系统与需要重构的子系统；求解重构子系统的特征多项式；设计重构子系统的降维观测器；求解降维观测器的特征方程；建立并网LCL滤波器的单相系统微分方程：由该并网LCL滤波器系统状态空间描述可知，dq轴电容电压u_Cd与u_Cq、dq轴电网侧电流i_1d与i_1q以及dq轴变流器侧电流i_2d与i_2q为系统状态变量，而其中变流器侧电流i_2d与i_2q可由变流器侧电流传感器直接获得；为实现在dq轴上的状态观测器，分析单相系统的情况；并网LCL滤波器的单相系统微分方程式为：将系统微分方程分解为非重构的子系统与需要重构的子系统；并网LCL滤波器的输出方程式可整理为：i₂＝[1 0 0][i₂ i₁ u_c]^T；由于rank{[1 0 0]}＝1，故需要重构的状态变量为[i₁ u_c]^T，即将原系统分解为两个子系统，分别为非重构的子系统与需要重构的子系统，非重构子系统的表达式为：$\left[\stackrel{·}{i_2}\right]=\left[0\right]\left[i_2\right]+{\left[\begin{array}{cc}0& -1/L_2\end{array}\right]}^T\left[\begin{array}{c}{i}_1\\ u_c\end{array}\right]+\left[\begin{array}{cc}0& 1/L_2\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right];$其中，等号后第二项为重构子系统到非重构子系统的耦合矩阵，故定义该矩阵为重构子系统的输出，又由于其为1阶，故表示为η，如下所示：$\eta =\left[\begin{array}{cc}0& -1/L_2\end{array}\right]\left[\begin{array}{c}{i}_1\\ u_c\end{array}\right]=\left[\stackrel{·}{i_2}\right]-\left[0\right]\left[i_2\right]-\left[\begin{array}{cc}0& 1/L_2\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right];$则重构子系统的表达式为：$\left\{\begin{array}{c}\left[\begin{array}{c}\stackrel{·}{i_1}\\ \stackrel{·}{u_c}\end{array}\right]=\left[\begin{array}{cc}0& 1/L_1\\ -1/C& 0\end{array}\right]\left[\begin{array}{c}{i}_1\\ u_c\end{array}\right]+\left[\begin{array}{cc}-1/L_1& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right]+\left[\begin{array}{c}0\\ 1/C\end{array}\right]i_2\\ \eta =\left[\begin{array}{cc}0& -1/L_2\end{array}\right]\left[\begin{array}{c}{i}_1\\ u_c\end{array}\right]=\stackrel{·}{i_2}-1/L_2{u}_2\end{array}\right.;$求解重构子系统的特征多项式：$\det \left[\begin{array}{cc}s& -1/L_2\\ 1/C& 2\end{array}\right]=s^2+\frac{1}{L_{1}C};$其极点实部为0在虚轴上，故需要将观测器的期望极点设计在左半平面，即具有负实部；观测器的期望极点为p₁＝‑p_r+p_i·j、p₂＝‑p_r‑p_i·j，观测误差反馈矩阵为表示为：$\tilde{h}=\left[\begin{array}{c}{\tilde{h}}_1\\ {\tilde{h}}_2\end{array}\right];$设计重构子系统的降维观测器：为了估计[i₁ u_c]^T，需要对重构子系统设计基本观测器如下：$\left[\begin{array}{c}\stackrel{·}{\widehat{i_1}}\\ \stackrel{·}{\widehat{u_c}}\end{array}\right]=\left\{\left[\begin{array}{cc}0& 1/L_1\\ -1/C& 0\end{array}\right]-\left[\begin{array}{c}{\tilde{h}}_1\\ {\tilde{h}}_2\end{array}\right]\left[\begin{array}{cc}0& -\frac{1}{L_2}\end{array}\right]\right\}\left[\begin{array}{c}\widehat{i_1}\\ \widehat{u_c}\end{array}\right]+\left[\begin{array}{cc}-1/L_1& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right]+\left[\begin{array}{c}0\\ 1/C\end{array}\right]i_2+\left[\begin{array}{c}{\tilde{h}}_1\\ {\tilde{h}}_2\end{array}\right](\stackrel{·}{i_2}-\frac{1}{L_2}{u}_2);$将其i₂项移至等号左侧，并作变换写作：$\frac{d}{dt}\left[\begin{array}{c}\widehat{i_1}-{\tilde{h}}_1{i}_2\\ \widehat{u_c}-{\tilde{h}}_2{i}_2\end{array}\right]=\left[\begin{array}{cc}0& 1/L_1+{\tilde{h}}_1/L_2\\ -1/C& {\tilde{h}}_2/L_2\end{array}\right]\left[\begin{array}{c}(\widehat{i_1}-{\tilde{h}}_1{i}_2)+{\tilde{h}}_1{i}_2\\ ({\tilde{u}}_c-{\tilde{h}}_2{i}_2)+{\tilde{h}}_2{i}_2\end{array}\right]+\left[\begin{array}{cc}-1/L_1& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right]+\left[\begin{array}{c}0\\ 1/C\end{array}\right]i_2-\frac{1}{L_2}\left[\begin{array}{c}{\tilde{h}}_1\\ {\tilde{h}}_2\end{array}\right]u_2$至此，定义降维观测器的状态为：$\{\begin{array}{c}{O}_1=\widehat{i_1}-{\tilde{h}}_1{i}_2\\ O_2={\hat{u}}_c-{\tilde{h}}_2{i}_2\end{array};$得到降维观测器的状态空间方程：$\left[\begin{array}{c}{\stackrel{·}{O}}_1\\ {\stackrel{·}{O}}_2\end{array}\right]=\left[\begin{array}{cc}0& 1/L_1+\tilde{h}/L_2\\ -1/C& {\tilde{h}}_2/L_2\end{array}\right]\left[\begin{array}{c}{O}_1\\ O_2\end{array}\right]+\left[\begin{array}{c}{\tilde{h}}_2(1/L_1+{\tilde{h}}_1/L_2)\\ 1/C-\tilde{h}/C+{\tilde{h}}_2/L_2\end{array}\right]i_2+\left[\begin{array}{cc}-1/L_1& -\tilde{h}/L_2\\ 0& -{\tilde{h}}_2/L_2\end{array}\right]\left[\begin{array}{c}{u}_1\\ u_2\end{array}\right];$求解降维观测器的特征方程：观测的状态变量表达式为：$\left[\begin{array}{c}\widehat{i_1}\\ \widehat{u_c}\end{array}\right]=\left[\begin{array}{c}{O}_1\\ O_2\end{array}\right]+\left[\begin{array}{c}{\tilde{h}}_1\\ {\tilde{h}}_2\end{array}\right]i_2;$得到降维观测器的特征方程：$s^2+\frac{{\tilde{h}}_2}{L_2}s+\frac{1}{C}(\frac{1}{L_1}+\frac{{\tilde{h}}_1}{L_2})=0;$那么配置观测误差反馈矩阵与降维观测器极点实部与虚部的关系有：$\left\{\begin{array}{c}{\tilde{h}}_1=L_{2}C(p_r^2+p_i^2)-L_2/L_1\\ {\tilde{h}}_2=2L_2{p}_r\end{array}\right.;$在具体参数设计前应判断系统可观测性，由LCL滤波器系统状态空间描述分析可知，系统状态矩阵为：$A_0=\left[\begin{array}{cccccc}0& \omega & -1/C& 0& 1/C& 0\\ -\omega & 0& 0& -1/C& 0& 1/C\\ 1/L_1& 0& 0& \omega & 0& 0\\ 0& 1/L_1& -\omega & 0& 0& 0\\ -1/L_2& 0& 0& 0& 0& \omega \\ 0& -1/L_2& 0& 0& -\omega & 0\end{array}\right]---\left(18\right)$由于采用基于变流器侧电流闭环的矢量控制策略，故该系统输出向量为C_o＝[0 0 0 0 1 0]  (19)根据定常系统可观性的代数判据，并根据式(18)、式(19)可求出系统可观性矩阵为：$Q_o={\left[\begin{array}{cccc}{C}_O& C_O{A}_O& \mathrm{...}& C_O{A}_O^5\end{array}\right]}^T;$经过计算，系统可观性矩阵Q_O的秩为：rankQ_O＝6。