# A Systematic Control Design Method with Active Damping Control in Voltage Source Converters
###### Abstract  
This paper proposes a systematic control design method for active damping control of grid-connected voltage source converters (VSCs). The proposed control method considers the conventional cascaded control loops and improves them by including additional states feedback-based active damping. In such a way, all control gains are lumped into one control gain matrix based on the proposed formulation. The lumping of all control gains into one matrix leads to a linear optimization problem, so different techniques can be used to calculate control gains. This work calculates them by using a simple but effective optimal control theorem as a noteworthy feature. The proposed control method can overcome the challenges of designing multiple control loops, evaluating wide time scale dynamics, and tuning required control parameters. Moreover, direct relationships between the proposed tuning parameters and system well-known stability and performance indicators such as maximum damping factor, minimum damping ratio, and the control efforts are identified, providing good physical insight. Finally, the proposed control structure and optimal gain calculations ensure power converter robustness against uncertainties in the grid's short-circuit ratio (SCR) and different operating-point conditions. When the grid's SCR changes from 10 (strong grid condition) to 1 (ultra-weak grid condition), the system under the proposed control method maintains good stability margins and simultaneously provides a fast dynamic response by facilitating the implementation of a high-bandwidth phase-locked loop (PLL). The performance of the proposed control strategy was investigated analytically and practically by conducting eigenvalue analysis, simulations, and experiments. voltage source converters (VSCs); grid-connected VSC; weak grids; robustness analysis; optimal-state feedback control Article  
A Systematic Control Design Method with Active Damping Control in Voltage Source Converters  
[PERSON], [PERSON]-  
connection point has a lower short circuit ratio (SCR) due to the high penetration level of power converters or long distance between distributed generators and the main grid. Many efforts have been made to present more efficient design strategies and enhance the control system's performance by including additional active damping terms to address the mentioned problems. Conventional design strategies such as the generalized Nyquist theorem or passivity theorem are based on the impedance model to investigate the system's stability and control-parameter selection [5; 6]. For instance, in Reference [7], a recursive adjustment procedure for the current controller's gains is suggested based on the frequency response. This work considers only the control delay effect. A comprehensive stability analysis and the current control design of a grid-connected LCL-filtered VSC are discussed in Reference [8]. To damp the LCL filter resonances and the negative impact of the control delay, a grid-side current control-based active damping and virtual flux-based active damping are proposed in References [9; 10], respectively. Moreover, to limit the negative impact of digital filters (commonly used in the CC and VFF) on the dissipativity of the output converter admittance, some design guidelines are proposed by Reference [11]. However, calculating the impedance model and performing a stability analysis are challenging and require high expertise and physical insight. Moreover, designing a control system and selecting the optimal values of the control parameters are not trivial tasks, especially for a high-order multi-input, multi-output (MIMO) system such as grid-connected VSCs. Therefore, the control gain selection is generally an iterative process. A full state-space feedback control method to improve the resonance damping of the LCL filter and increase the system robustness against the grid SCR variations is presented in References [12; 13].