# Coordinated Mitigation Control for Wideband Harmonic of the Photovoltaic Grid-Connected Inverter
## 1 Introduction
The literature [24] proposed a compensation method with a square wave for steady-state application, and low-order harmonics can be reduced under most operating conditions. However, the error voltage variation under low-current operating conditions is not considered, which may cause overcompensation. In [25], the trapezoidal method is introduced to improve the adaptability of the compensation voltage model based on phase currents. The amplitude of compensation voltage becomes smaller and more effective in near zero current due to the slope change in the trapezoid waveform. The accuracy of the compensated voltage model determines the validity of such methods. Otherwise, the power quality will deteriorate due to the overcompensation voltage. Many scholars have adopted the second method of current injection to obtain the nonideal voltage error under various operating conditions. This method achieves better suppression of current harmonics by improving the compensation voltage accuracy. In [26], a look-up table (LUT) method is proposed to enhance compensation accuracy, but this method has specific requirements for controller storage space. In [27] introduces a plan of fitting functions is introduced to construct compensating voltage commands, but universality is hard to guarantee. In addition, some trapping algorithms, observers, and controller parameter optimization can also suppress the corresponding harmonic components [28; 29; 30; 31; 32]. In [33], the state space matrix explains the participation degree of the control loops, and a controller design method is proposed considering the current harmonic distortion rate. Virtual impedance is another effective filtering method, and the virtual impedance constructed in [34] effectively reduces the fifth and seventh harmonics, but such methods have high requirements for frequency component extraction. In summary, scholars have produced extensive achievements in resonance and harmonic analysis and suppression, separately. However, the resonance point is still difficult to capture, and the dead zone or other nonideal switching states are complex and variable. Thus the suppression of high-order or low-order harmonics alone will be difficult to adapt to the wideband properties. It also makes research which combines the two aspects remaining as a gap in large-scale promotion in engineering. Therefore, this paper proposes a resonance and dead zone compensation cooperative control strategy for LCL inverters, and its contributions are as follows:  
1. Firstly, this paper derives the control transfer function of the closed-loop system and analyzes the key reason for the resonance of LCL inverters by plotting a Bode diagram. In addition, the paper explains the mechanism by which the dead zone generates low-order harmonic current by analyzing the switching state of modulation voltage. 2. Then, a high-frequency resonance mitigation strategy is proposed to improve the power quality of the PVs. Feeding the extracted capacitor current into the modulated voltage output can solve the problem of the PV resonance effectively. 3. Finally, considering the influence of parasitic capacitor charging and discharging on the dead zone voltage error under different operating conditions, an adaptive compensation strategy is proposed to suit multiple working conditions from the measured data. The layout of this paper is organized as follows. Section 2 introduces the topology and control structure of the PV grid-connected inverter, including the analysis of resonance and harmonic generation mechanisms. Section 3 shows the active damping control strategy. Section 4 presents the measured PV data and proposes an adaptive dead zone voltage compensation method. Section 5 contains a study of comparative simulation experiments. Section 6 is the summary of the conclusions.