# A Systematic Control Design Method with Active Damping Control in Voltage Source Converters
###### Abstract
In this respect, this paper tries to propose a new systematic design approach in order to simplify the control gains calculation by providing a linear optimization problem. Based on the new formulation, all control gains are lumped into one control gain matrix, and then different techniques can be used to calculate the system control gain matrix. Among others, this work employs the linear-quadratic regulator (LQR) design framework due to its efficiency and applicability. The main contributions of this paper are listed as follows:  
* Proposing a direct design approach with the minimum recursive process to calculate the control parameters,
* Providing a clear insight between tuning parameters and stability and performance indicators, \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**References**} & **Design** & **Inner** & **Outer** & **PLL** & **Weak Grid** & **Extra** & **Exprise** & **Optimizing** & **Applicability** \\  & **Technique** & **Control** & **Lops** & **Impact** & **Conditions** & **Current** & **Resensors** & **to Design** & **Efforts** & **to MIMO** \\ \hline
[7] & Nyquist & yes & no & no & no & no & medium & no & hard \\ \hline
[8] & Nyquist & yes & no & no & yes & no & medium & no & hard \\ \hline
[12] & Full state feedback & yes & no & no & yes & yes & low & no & medium \\ \hline
[13] & Optimal control & yes & no & no & no & yes & medium & yes & easy \\ \hline
[22] & Optimal control & yes & no & yes & yes & yes & medium & yes & easy \\ \hline
[15-17] & Robust H-infinity & yes & no & no & no & yes & high & yes & medium \\ \hline
[19] & Robust H-infinity & yes & no & no & yes & yes & high & yes & medium \\ \hline
[23] & loop-at-a-time & no & yes & no & yes & no & high & no & medium \\ \hline
[24] & Robust H-infinity & no & yes & yes & yes & yes & high & yes & medium \\ \hline Proposed & Optimal control & yes & yes & yes & yes & no & medium & yes & easy \\ \hline \hline \end{tabular}
\end{table} 
Table 1: State-of-the-art control-system design techniques. * Increasing system robustness against uncertainties in the grid impedance and operating point conditions,
* Improving system transient response and fault ride-through (FRT) capability by implementing a PLL with higher bandwidths. The remainder of this paper is organized as follows. Section 2 describes the under-studied system, a grid-connected LCL-filtered VSC with all control loops. The proposed nonlinear and linearized dynamics of a grid-connected VSC are also presented in this section. The proposed robust and optimal active damping control is introduced in Section 3. Furthermore, some guidelines for selecting the state and input weighting matrixes are provided. This section is completed with a comprehensive robustness analysis based on the eigenvalue analysis to consider the impact of different grid SCRs and operating point conditions. A comparison with the conventional one is also given. The analytical results were verified by several simulations and experimental tests under different operational conditions, as recounted in Section 4. Finally, Section 5 concludes this paper.