# Analysis and Design of A PMQR-Type Repetitive Control Scheme for Grid-Connected H6 Inverters
## 1 Introduction  
Distributed power generation systems (DPGSs) based on renewable energy sources have been increasingly implemented world-wide, such as wind and solar energy [1]. The inverter configurations and corresponding current control strategies play an important roles in a grid-connected DPGS. Being a key interface equipment between a power generation source and the utility grid, the grid-tied inverter needs to ensure a high power conversion efficiency and guarantee the high-quality current injection into the grid. Typically, the output current total harmonic distortion (THD), which is a crucial index for assessing the power quality, must be less than 5% for both wind turbines and photovoltaic arrays connected to the grid [2]. In order to obtain a high-quality grid current and maintain a low output current THD value, researchers have proposed various current control strategies, such as PI control [3], proportional-repetitive (PR) control [4] and repetitive control [5]. Due to the absence of the transformer between the power generation source and utility grid to achieve galvanic isolation, there are potential power quality and safety issues in grid-connected inverters [6]. To tackle these issues, various inverter topologies have been designed [7; 8]. For instance, full-bridge inverters are the most commonly used, which have a nice compromise among efficiency, complexity, and cost. However, this will generate relatively large common-mode leakage current, which increases the current harmonic content injected into grid and system loss. Half-bridge inverters with only two active switches are immune to leakage currents. However, this requires twice the inputvoltage of a full-bridge inverter. Practice has shown that adding more active switches to the full-bridge topology with a suitable PWM modulation strategy can achieve both high efficiency and low leakage current. The transformer-less H6 inverter, which features a simple structure, high efficiency, small ground leakage current, and low output current distortion, can be extensively used in the renewable energy power generation industry [9; 10]. Various grid-tied current control techniques have been proposed to achieve the steady-state harmonics suppression. Among these control methods, the proportional-integral (PI) and proportional-repetitive (PR) control are popular methods [11; 12; 13; 14]. The PI control scheme is commonly used in the stationary reference frame (SRF) for its simple control structure, ease of implementation, and good transient response [14]. However, a PI controller is unable to track a sinusoidal reference with zero steady-state error because of the limited control-loop gain [15]. It also lacks sufficient suppression ability for low frequency harmonics. On the other hand, the PR control technique, using the stationary reference frame, can efficiently overcome the aforementioned disadvantages of the PI control scheme. Thus, it possesses a high reputation in grid-connected control. The PR controller is composed of a proportional component like PI control and a resonant controller that acts as a sinusoidal integrator [12]. Theoretically, an ideal PR compensator introduces an infinite gain at resonant frequency, which is equal to grid frequency, to achieve a good sinusoidal reference current tracking effect. However, a PR controller will cause periodic disturbances at frequencies distinct from its resonant frequency and is unable to turn its control gain independently. The proportional multiple resonant control scheme together with its improved design can address the issue of multi-frequency harmonics compensation efficiently [16; 17; 18; 19]. However, there is no doubt that multiple resonant (or quasi-resonant) controllers will lead to computational cost and significantly increase implementation complexity [20]. The repetitive controller (RC) has been presented with a simplified control structure, tracking many harmonics simultaneously. For the design of repetitive control, the control plant can be simplified as a single-input-single-output system.