# Topology and Control Strategy of PV MVDC Grid-Connected Converter with LVRT Capability
## 2 Principle of the Converter
### Derivation of Voltage Gain  
In boost mode, the voltage gain can be obtained by volt-second balance of the leakage inductor \(L_{lk}\) and input inductor \(L_{in}\). It can be obtained by volt-second balance of the leakage inductor \(L_{lk}\) in buck mode. The voltage gain in boost and buck modes are shown in Table 1. The following is the derivation process of buck-DCM2 and boost-CCM2. In the buck-DCM2 mode, the volt-second balance of leakage inductor \(L_{lk}\) is given as:  
\[\bigg{(}V_{in}-\frac{V_{o}}{N}\bigg{)}D=\frac{V_{o}}{N}\bigg{(}\frac{1}{2}-D-D_ {Llk1}\bigg{)} \tag{1}\]  
\[D_{Llk1}=\frac{1}{2}-\frac{NV_{in}}{V_{o}}D \tag{2}\]  
\(D_{Llk1}\) is the current discontinuous time in buck mode as shown in Figure 3(b). \(N\) is the transformer turn ratio. The output current can be expressed as:  
\[I_{o}=\frac{V_{o}}{R}=\frac{NV_{in}-V_{o}}{N^{2}L_{lk}f_{s}}D\bigg{(}\frac{1} {2}-D_{Llk1}\bigg{)} \tag{3}\]  
\(f_{s}\) is the switching frequency. \(R\) is the load. The voltage gain in buck_DCM2 mode \(M_{buck\_DCM2}\) can be expressed as:  
\[M_{buck\_DCM2}=\frac{2 ND}{\sqrt{D^{2}+2K_{Llk}+D}} \tag{4}\]  
where \(K_{Llk}=2N^{2}L_{lk}f_{s}/R\). Figure 4: Switching sequence diagram in boost and buck modes. In boost-CCM2 mode, the volt-second balance of input inductor is given as:  
\[(V_{\text{C2}}-V_{in})(1-D)=V_{in}\left(D-\frac{1}{2}\right) \tag{5}\]  
The relationship between \(V_{in}\) and \(V_{\text{C2}}\) can be expressed as:  
\[\frac{V_{\text{C2}}}{V_{in}}=\frac{1}{2(1-D)} \tag{6}\]  
In the boost-CCM2 mode, the relationship between \(V_{o}\) and \(V_{\text{C2}}\) can be obtained by Equation (4):  
\[\frac{V_{o}}{V_{\text{C2}}}=\frac{2N(1-D)}{\sqrt{\left(1-D\right)^{2}+2K_{Llk} }+(1-D)} \tag{7}\]  
The voltage gain in boost-CCM1 mode \(M_{boost\_CCM1}\) can be expressed as:  
\[M_{boost\_CCM1}=\frac{V_{o}}{V_{in}}=\frac{V_{\text{C2}}}{V_{in}}\times\frac{ V_{o}}{V_{\text{C2}}} \tag{8}\]  
\[\bigg{(}V_{in}-\frac{V_{o}}{N}\bigg{)}D=\frac{V_{o}}{N}\bigg{(}\frac{1}{2}-D-D_ {Llk1}\bigg{)} \tag{1}\]0  
According to Table 1, the relationship between voltage gain and duty cycle can be obtained. Figure 5 shows the relationship between voltage gain and duty cycle. The voltage gain is related to \(K_{Llk}\). \(K_{Llk}\) is denoted as \(K_{Llk}=2N^{2}L_{lk}f_{S}/R\). As \(K_{Llk}\) increases, the voltage gain curve becomes flatter. Therefore, the voltage gain is able to increase by reducing the leakage inductor or increasing the load resistance. Table 2 lists the comparison of different isolated topologies related to circuit structure and performance. DAB has limitation of boosting capacity and the output voltage is lower than other topologies. Isolated boost has strong boosting capacity but cannot operate in low-voltage range. In the isolated buck-boost topologies [18; 20], buck and boost modes are achieved by coordinated control of active switches of the primary and secondary sides. The output voltage cannot reach MV level. Switch drivers and auxiliary power supply is  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Mode**} & **Voltage Gain** \\ \hline Boost-CCM1 & \(\frac{-\left(1-4D^{2}+4K_{Llk}\right)N}{8(1-D)^{2}}+\frac{N\sqrt{\left(1-4D^{ 2}+4K_{Llk}\right)^{2}+16(1-D)^{2}}}{8(1-D)^{2}}\) \\ \hline Boost-CCM2 & \(\frac{N}{\sqrt{\left(1-D\  
required on the high-voltage side. They must sustain high-voltage stress of common mode and differential mode. These will increase the complexity and reduce the reliability of the converter. In the proposed topology, there are no active switches but only diodes on the high-voltage side. By only controlling the low-voltage side active switches, the topology is able to switch between boost and buck mode. The output voltage of the proposed topology is easy to reach medium-voltage level. MVDC modules are able to be developed. That is important for the MVDC converter to reduce the module number and increase the power density. Meanwhile, only controller and switch drives are needed on the low-voltage side in the proposed topology.