\(G_{1}:\ t_{1}=(1-D)T_{s}\) (1)
\(G_{2}:\ T_{s}-t_{1}=DT_{s}\) (2)
\(G_{3}:\ t_{3}{-\ t}_{2}=(1-D)T_{s}\) (3)
\(G_{4}:\ T_{s}-(t_{3}{-\ t}_{1})=DT_{s}\) (4)
2.2. Operation Principles
In the proposed inverter, there are four different operation modes that
described in the following:
Mode 1\(,0\leq t\leq(1-D)T_{s}\): In this mode, the switches\(G_{1}\) and \(G_{4}\) are on, while \(G_{2}\) and\(G_{3}\) are off.
The following equations are resulted in this mode.
\(V_{L1}=V_{L4}=V_{\text{in}}\) (5)
\(V_{L3}=V_{\text{in}}-V_{c1}\) (6)
\(V_{L2}=V_{\text{in}}-V_{c2}\) (7)
Therefore inductors \(L_{1}\) and \(L_{4}\) are charged with the rate
of\(\frac{\ V_{\text{in}}}{L_{1}}\) and \(\frac{V_{\text{in}}}{L_{4}}\), respectively. Also the currents of inductors \(L_{2}\) and \(L_{3}\)are reduced with the rate of \(\frac{(V_{\text{in}}-V_{c2})}{L_{2}}\)and\(\ \frac{(V_{\text{in}}-V_{c1})}{L_{3}}\). This mode is shown in
Fig. 3.