# A Systematic Control Design Method with Active Damping Control in Voltage Source Converters
## 5 Conclusions  
This paper proposes a new design approach for robust and optimal active damping control of voltage source converters (VSCs) for grid applications. Based on the proposed formulation, all control gains are considered in one control gain matrix, leading to a linear optimization problem. Then different state-of-the-art techniques can be employed to calculate control gains in such a way the control system meets the desired stability and performance criteria. Among others, this paper used the linear-quadratic regulator (LQR) to calculate all control gains optimally and straightforwardly. In this respect, almost direct relationships between the tuning parameters and stability and performance indices such as maximum damping factor, minimum damping ratio and control gain matrix are identified, which considerably reduces the iterative process in the conventional control system design.  
Thanks to the proposed control structure and optimal control gains calculation, the proposed method provides a fast dynamic response and significantly increases the system robustness and disturbance rejection capability under ultra-weak grid conditions. For example, the possibility of implementing a PLL bandwidth of more than 50 Hz under a grid SCR lower than two is obtained, which effectively suppresses disturbances on the control system and conducts fault ride-through of grid-connected VSCs.  
The performance of the proposed control method under different operating conditions is comprehensively investigated by simulations and experiments and compared with the conventional one. The obtained results demonstrate the performance of the proposed control method under various operating conditions.  
For future works, an extension of the proposed methodology to other VSC-based power system applications, such as active power filters and uninterruptable power supplies, is recommended. For these applications, extra resonators at desired harmonics are required to compensate for nonlinear loads, making the control system design difficult.  
Conceptualization, H.G.-K., P.D., C.W. and F.B.; methodology, H.G.-K.; software, H.G.-K.; validation, H.G.-K.; formal analysis, H.G.-K. and P.D.; investigation, H.G.-K., P.D., C.W. and F.B.; resources, P.D. and F.B.; data curation, H.G.-K.; writing--original draft preparation, H.G.-K.; writing--review and editing, H.G.-K., P.D., C.W. and F.B.; visualization, H.G.-K.; supervision, F.B., P.D. and C.W.; project administration, H.G.-K.; funding acquisition, F.B. and P.D. All authors have read and agreed to the published version of the manuscript.  
This work is supported by the Reliable Power Electronic-Based Power System project at AAU Energy, Aalborg University, Aalborg, Denmark, as a part of the Villum Investigator Program funded by the Villum Foundation.  
Not applicable.  
Figure 18: Experimental results showing the system response under 20% voltage sag at the grid voltage (SCR = 1.21, \(L_{g}\) = 15.5 mH, and \(P\) = 5 kW): (**a**) the conventional control method (\(f_{PLL}\) = 10 Hz) and (**b**) the proposed control method (\(f_{PLL}\) = 50 Hz).