# Improved PR Control Strategy for an LCL Three-Phase Grid-Connected Inverter Based on Active Damping
## 1 Introduction  
High power factor and low grid-connected current total harmonic distortion are common requirements for grid-connected inverters [1; 2; 3]. Pulse-width modulation (PWM) technology has a wide range of applications in the field of inverters, but a grid-connected inverter using PWM control technology will produce many switching frequency sub-harmonics, which seriously threaten the power quality and safe operation of the power grid [4; 5; 6]. In order to reduce the harmonic content of the grid-connected current, an appropriate grid-connected current filter must be adopted [7; 8; 9]. At present, L-type and LCL-type filters are widely used in harmonic suppression of grid-connected inverter output current. Under the same capacity, an LCL filter has strong attenuation ability to high frequency interference and has a good prospect for engineering application. However, the inherent disadvantage of the low damping resonance of an LCL filter in inverter control technology is still under discussion [10; 11]. Compared with the passive damping control method, active damping can provide an appropriate damping coefficient without increasing the extra loss of the system, thus achieving the purpose of weakening the resonant peak [12; 13; 14]. Common active damping control techniques include capacitor current feedback [15; 16], capacitor voltage primary differential feedback [17], grid-connected current secondary differential feedback [18; 19], and multi-state variable combined control [20; 21], etc. Amongthem, the capacitance current proportional feedback damping effect is good, easy to realize, and the application is also the most common. For the control method of a three-phase grid-connected inverter, the current common method is to convert it from a three-phase stationary coordinate system to a two-phase stationary coordinate system (\(\alpha\)-\(\beta\)) or two-phase synchronous rotating coordinate system (\(d\)-\(q\)) [22; 23; 24]. In the \(d\)-\(q\) coordinate system, all control variables are DC flow, the classical PI controller can be used to realize the non-static error control of grid-connected current, and the implementation method is flexible and simple, so it has been widely used. However, there is coupling in the \(d\)-\(q\) coordinate system of the three-phase grid-connected inverter. If the active power and reactive power can be controlled independently, decoupling must be carried out. For L-type grid-connected inverters, there is only one group of coupling terms between the \(d\) axis and \(q\) axis, and the decoupling process is relatively simple. However, for LCL-type three-phase grid-connected inverters, there are three groups of coupling terms between the \(d\) axis and \(q\) axis, and the decoupling process is very complicated [25]. In practical application, due to factors such as system parameter error and interference, it is almost impossible for the inverter to achieve complete power decoupling. In the \(\alpha\)-\(\beta\) coordinate system, there is no coupling term between the \(\alpha\) axis and \(\beta\) axis, which creates favorable conditions for independent control of active power and reactive power. However, in the \(\alpha\)-\(\beta\) coordinate system, all control quantities are AC quantities. In order to realize static error-free control, unless the gain of the controller is infinite, it is particularly important to find a controller with high gain [26; 27; 28]. As for the control technology of grid current in a three-phase grid-connected inverter, the commonly used control methods include proportional-integral (PI) control, proportional-resonant (PR) control, and quasi-proportional-resonant (QPR) control. The PI control structure is simple and easy to implement and is suitable for DC flow control, but the AC PI controller cannot realize non-static error control [29]. Increasing the feedforward link of the grid voltage ratio can reduce the steady-state error of grid-connected current, but cannot effectively suppress the harmonics [30].