# A Systematic Control Design Method with Active Damping Control in Voltage Source Converters
###### Abstract
The proportional-integral (PI) current control and active damping gains in Reference [12] are calculated by using the pole placement technique. Despite the simplicity in concept, selecting the desired closed-loop poles is a challenging task; it becomes more difficult or even impossible for a high-order MIMO system. A systematic design procedure based on the optimal control theorem is suggested in Reference [13] to avoid direct pole placement. However, weighting factors' selection is required [13; 14]. In References [15; 16; 17; 18; 19], a robust proportional-resonant (PR) current control design based on the H-infinity theorem and linear matrix inequalities (LMIs) is proposed to consider the impact of the grid SCR variations in the design procedure. However, the optimal robust H-infinity control leads to high control gains, making some difficulties for practical implementation [15; 16; 18]. Although the previous works provide valuable results, they did not consider the impact of PLL and outer control loops. Therefore, they suffer from some conservatism in their design. Moreover, active damping based on the feedforward PCC voltage or current feedback, which is widely suggested, is only efficient to damp oscillations in the LCL filter resonance range and not low-frequency oscillations due to the outer control loops interaction. In Reference [20], a state feedback-based active damping control to dampen low-frequency oscillations is proposed. However, a low-order and simplified model is considered for the fast dynamics parts (LCL filter, delay, and current controller) to simplify the control system design. Moreover, it suffers from shortcomings of the pole-placement techniques and recursive process. Finally, the possibility of implementing a high-performance PLL in weak grids was not discussed. Research work in Reference [21] introduced an improved current control design to reduce the negative impact of the PLL on the current controller in weak grids, which need extra capacitor current sensors. In Reference [22], an optimal control method is proposed to enhance the inner current control loop performance and reduce the negative impact of PLL in weak grids. However, many weighting factors are added to the design procedure, transparent relationships between tuning parameters and stability and performance indicators (e.g., damping factor and ratio) are not identified, and the outer control loops are not considered. The authors of Reference [23] presented a loop-at-a-time stability analysis (LAAT), and based on LAAT, a design algorithm for outer control loops (DVC and AVC) is also suggested. The proposed method is closely correlated to the characteristic loci in the generalized Nyquist criterion for MIMO systems and tries to overcome challenges regarding the MIMO control system design in the frequency domain. However, to reduce the complexity of the method, the inner current control loop and PLL are embedded inside the plant. In Reference [24], a fixed-structure H-infinity control design is presented to calculate the outer loops' control gains. However, the design procedure needs dynamic weighting function calculations for each input and output relation. In this regard, many parameters are required to be tuned, significantly affecting the system response and feasibility of the H-infinity optimization problem. Overall, the prior state-of-the-art methods mentioned above partially address grid uncertainties, low and high-frequency oscillations, control loops interaction, high-order MIMO structure, and recursive control system design. However, none of them succeeds in presenting a comprehensive and efficient solution, as summarized in Table 1. For example, all previous works consider only inner or outer control loops and ignore the other ones in the design step. When all control loops are considered simultaneously, the couplings of some inner and outer control parameters have appeared, leading to a nonlinear system and optimization problem.