# Coordinated Mitigation Control for Wideband Harmonic of the Photovoltaic Grid-Connected Inverter
## 4 Dead Zone Compensation Method of PV Inverter
### Dead Zone Compensation Method  
In the fluctuation range of grid-connected current from Figure 11, the duration of the current tailing effect is almost zero, so the compensated voltage can be approximately calculated by Equation (8). \[U_{\mathrm{d}}=T_{\mathrm{d}}U_{\mathrm{dc}} \tag{8}\]  
Due to the fact that the nonideal switching state is unavoidable in practical applications, a narrow pulse compensation strategy is adopted to achieve an accurate compensation result. The voltage which needs to be compensated is distributed evenly into the modulated signal of IGBT by area equivalence method. Therefore, the actual modulated voltage is added on a narrow pulse component equal to the error voltage. Figure 13 shows the schematic of modulation voltage compensation. Figure 12: The influence of current trailing. Since directly deleting the dead zone is impossible, the modulation voltage is slightly over-modulated before generating the PWM signal, which can offset the low-order harmonics caused by the error voltage to a certain extent. Therefore, the proportion of nonideal effects in the actual inverter output voltage can be reduced. Equation (9) shows the superimposed narrow pulse single in the proposed theory. \[U_{\text{add}}=\text{sign}(I_{\text{a}})\frac{T_{\text{d}}}{T_{\text{s}}}U_{ \text{dc}} \tag{9}\]  
The PWM signal is generated after the modulated session, so the over-modulated part of the voltage extends the turn-on time \(T_{\text{on}}\) of IGBT. Meanwhile, the extra turn-on time offsets the unideal delay. The performance of the proposed adaptive low-order harmonic mitigation strategy in the PWM signal is shown in Figure 14.  
In this figure, \(U_{\text{com}}\) represents the extra turn-on time caused by the proposed narrow pulse signal. When \(I_{\text{a}}>0\), \(Q_{1}\) remains on, and the narrow pulse compensates for the error voltage generated by the upper bridge. After \(Q_{1}\) cuts off, the narrow pulse compensates for the error voltage caused by the lower bridge. Similarly, when \(I_{\text{a}}<0\), it complements the process of \(I_{\text{a}}>0\). However, the PV's output current is low in cloudy weather, low temperature, or other severe conditions. In the above cases, the quality of the power generated by the PVs becomes worse, and the effect of the current trailing can no longer be ignored. The compensation for minor current working conditions is consistent with the above method. Figure 14: Compensation voltage in PWM signal. Figure 13: Schematic of modulation voltage compensation. However, unlike the preceding, the modulation voltage error can no longer be expressed in Equation (8) but should be expressed in Equation (7). Accordingly, the narrow pulse modulated voltage should also be represented in Equation (10). \[U_{\text{add}}=\frac{U_{\text{dead}}}{T_{\text{s}}}=\text{sign}(I_{\text{a}}) \frac{U_{\text{dc}}}{T_{\text{s}}}(T_{\text{d}}-\frac{KI_{\text{a}}}{2}) \tag{10}\]  
Since the slope coefficient \(K\) in the Equation (7) is unknown, many experiments with different \(K\) values must be performed to update the proper initial value. The slope coefficient accuracy can be guaranteed based on the THD results of these experiments. The harmonic current caused by the dead zone voltage is mainly 6 \(k\pm 1\) order, (k = 1, 2, 3,... ). The high-order component can be ignored due to the existence of an LCL filter. Therefore, only the fifth and seventh harmonic currents under ideal power supply conditions should be analyzed. The required flow diagram of parameter correction is shown in Figure 15.  
The value of \(K\) depends mainly on the type of IGBT, so different PV inverters all need the search process of \(K\) shown in the above figure. From the flowchart, the relationship between \(K\) and \(I_{\text{a}}\) can be established. Once the value of \(K\) is determined, there is no need to configure any extra hardware or software, such as the observers or filters.