# Research on Composite Control Strategy of Quasi-Z-Source DC-DC Converter for Fuel Cell Vehicles
## 2 Topology Operation Principle Analysis and Dynamic Modeling  
The DC-DC converter topology based on the quasi-Z-source network is shown in Figure 1. \(u_{\text{in}}\) is the output voltage of the fuel cell. \(D_{1}\) is the reversed blocking diode, which prevents the current from flowing back to the fuel cell. The quasi-Z-source network is composed of \(L_{1}\), \(D_{2}\), \(L_{2}\), \(C_{1}\), \(C_{2}\). The switch-capacitor network is composed of \(D_{3}\), \(D_{4}\), \(D_{5}\), \(C_{3}\), \(C_{4}\) and \(C_{5}\). \(R\) is the load resistance and \(u_{\text{o}}\) is the output voltage of the converter. There is only one power switch \(Q\) in the topology.  
Figure 1: The DC–DC converter topology based on the quasi-Z-source network.  
where \(u_{L1\text{off}}\) and \(u_{L2\text{off}}\) are, respectively, the inductor voltages across \(L_{1}\) and \(L_{2}\) when the power switch \(Q\) is turned off.  
\[\left\{\begin{array}{l}I_{\text{C1 off}}=I_{\text{C2 off}}+I_{L1}-I_{L2}\\ I_{\text{C3 off}}=-I_{\text{C4 off}}-I_{\text{O}}\\ I_{\text{C5 off}}=I_{L1}-I_{\text{O}}-I_{\text{C1 off}}\end{array}\right. \tag{4}\]  
where \(I_{\text{C1 off}}\), \(I_{\text{C2 off}}\), \(I_{\text{C3 off}}\), \(I_{\text{C4 off}}\) and \(I_{\text{C5 off}}\) are, respectively, the average capacitor currents of \(C_{1}\), \(C_{2}\), \(C_{3}\), \(C_{4}\) and \(C_{5}\) when the power switch \(Q\) is turned off.  
Equation (5) is obtained by applying the voltage-second balance principle to inductors \(L_{1}\) and \(L_{2}\) and Equation (6) is obtained by applying the ampere-second balance principle to capacitors \(C_{1}\), \(C_{2}\), \(C_{3}\), \(C_{4}\) and \(C_{5}\).  
\[\left\{\begin{array}{l}u_{L1\text{on}}\times dT+u_{L1\text{off}}\times(1-d)T =0\\ u_{L2\text{on}}\times dT+u_{L2\text{off}}\times(1-d)T=0\\ \end{array}\right. \tag{5}\]  
\[\left\{\begin{array}{l}I_{\text{C1 on}}\times dT+I_{\text{C1 off}}\times(1-d) T=0\\ I_{\text{C2 on}}\times dT+I_{\text{C2 off}}\times(1-d)T=0\\ I_{\text{C3 on}}\times dT+I_{\text{C3 off}}\times(1-d)T=0\\ I_{\text{C4 on}}\times dT+I_{\text{C4 off}}\times(1-d)T=0\\ I_{\text{C5 on}}\times dT+I_{\text{C5 off}}\times(1-d)T=0\end{array}\right. \tag{6}\]  
where \(d\) is the duty cycle. \(T\) is the switch period of power switch \(Q\).  
According to Equations (1), (3) and (5), the voltage gain \(M\) is obtained as shown in Equation (7).  
\[M=\frac{u_{\text{O}}}{u_{\text{in}}}=\frac{2}{1-2d} \tag{7}\]  
where \(0<d<0.5\).  
Assuming that the input power is equal to the output power, Equation (8) can be obtained.  
\[u_{\text{in}}\times I_{\text{in}}=u_{\text{O}}\times I_{\text{O}} \tag{8}\]  
where \(I_{\text{in}}\) is the input average current of the converter.  
According to Equations (2), (4), (6) and (8), the current relationship can be obtained as shown in Equation (9).  
\[I_{L1}=I_{L2}=I_{\text{in}}=\frac{2}{1-2d}I_{\text{O}} \tag{9}\]  
Figure 3: The circuit operation state when power switch \(Q\) is turned off.  
According to Figures 2 and 3 and Equations (1), (3) and (5), the voltage stresses across diodes, the power switch and capacitors are obtained as shown in Equation (10). The voltage stress across diode \(D_{1}\) is not considered, and is always turned on.  
\[\left\{\begin{array}{l}u_{D2}=u_{C1}+u_{C2}=u_{O}/2\\ u_{D3}=u_{C5}=u_{O}/2\\ u_{D4}=u_{C3}=u_{O}/2\\ u_{D5}=u_{C4}=u_{O}/2\\ u_{Q}=u_{C5}=u_{O}/2\\ \end{array}\right. \tag{10}\]  
According to Equation (7), the converter has high gain and wide voltage input range. The duty cycle is always less than 0.5. From Equation (10), the voltage stresses across components are low, which is suitable for the DC-DC converter for fuel cell vehicle.