## 2 Circuit Structure and Operational Principle of Photovoltaic Grid-Connected Inverter  
A single-phase full-bridge photovoltaic (PV) grid-connected inverter is a typical circuit structure of photovoltaic grid-connected inverters. In single-phase PV grid-connected inverter, there are two typical structures, namely single-stage structure, and two-stage structure. The two-stage structure is to add a DC/DC converter in front of the DC/AC converter, which enables MPPT (Maximum Power Point Tracking) to be carried out in the DC/DC converter. For a single-stage structure, MPPT is placed in DC/AC. From the control point of view, the two-stage structure can be separated from the grid-connected control and MPPT control, which is more convenient for control, but low conversion efficiency. In the single-stage structure, the grid-connected control and MPPT control are integrated. Although the control is relatively complex, it can be easily realized at present. The single-stage structure is relatively simple, which helps improve efficiency. To express this more simply, in this paper, we use a single-stage structure for analysis. The circuit, as shown in Figure 1, consists of a power block, an isolation block, and a control block. In the power block, the PV array and the capacitor C\({}_{1}\) constitute the power input source; M\({}_{1}\)-M\({}_{4}\) constitute the full-bridge circuit; L\({}_{1}\), L\({}_{2}\), and C\({}_{2}\) constitute the LCL output filter; \(R_{\rm L}\) is the equivalent resistance of the circuit conductor wires; and \(u_{\rm g}\) is the signal of the public power grid. In Figure 1, \(i_{\rm PV}\) and \(u_{\rm PV}\) are the output current and output voltage of the PV array, respectively; \(u_{\rm C1}\) and \(i_{\rm C1}\) are the voltage and charging/discharging currents across the capacitor C\({}_{1}\), respectively; \(u_{\rm C1}=u_{\rm PV}\); \(i_{1}\) and \(i_{2}\) are the currents across the filter inductors L\({}_{1}\) and L\({}_{2}\), respectively; and \(u_{\rm C2}\) and \(i_{\rm C2}\) are the voltages across the capacitor C\({}_{2}\) and the charge/discharge currents, respectively. The voltage sensors 1 and 2 and current sensors 1 and 2 of the isolation block acquire the signals \(u_{\text{PV}}\) (i.e., \(u_{\text{C1}}\)), \(u_{\text{C2}}\), \(i_{\text{C1}}\), and \(i_{\text{C2}}\), respectively, and send them to the A/D samplings of the control block to obtain the corresponding digital signals \(u_{\text{PV}}(k)\), \(u_{\text{C2}}(k)\), \(i_{\text{C1}}(k)\), and \(i_{\text{C2}}(k)\). The PWM (Pulse Width Modulation) isolation driver is responsible for isolating the PWM generator of the control block and amplifying its signals for driving the power switches M\({}_{1}\)-M\({}_{4}\). In the control block, the predictive control algorithm \(\Gamma(\cdot)\) calculates the duty ratio \(D(k)\) of the PWM signal based on the digital signals \(u_{\text{PV}}(k)\), \(u_{\text{C2}}(k)\), \(i_{\text{C1}}(k)\), and \(i_{\text{C2}}(k)\). Whether unipolar polarity SPWM (Sinusoidal Pulse Width Modulation) or bipolar SPWM is used, the inverter can be effectively controlled. The principle of unipolar polarity SPWM and bipolar polarity SPWM are shown in Figure 2a,b, respectively. As shown in Figure 2, unipolar SPWM has more switch state combinations than bipolar SPWM. Both unipolar SPWM and bipolar SPWM can effectively control the inverter. To make the logic expression more concise, bipolar SPWM is used in the analysis of this paper. According to the bipolar SPWM principle, a Boolean logic variable \(S\) is defined as \(S\in\{0,1\}\), and then the switching logic of the power switches M\({}_{1}\)-M\({}_{4}\) is expressed as follows: M\({}_{1}=\) M\({}_{4}=\)\(S\), M\({}_{2}=\) M\({}_{3}=\)\(\overline{S}\), where  
\[S= \begin{cases}1&t\in[kT_{s},kT_{s}+D(k)T_{s}]\\ 0&t\in(kT_{s}+D(k)T_{s},(k+1)T_{s}]\end{cases}