## 2 DAB DC/DC Resonant Converter TPS Close Loop Control Scheme
### DAB LCC Resonant Converter TPS Control Performance Design Anallysis  
Table 3 shows the wireless charging transformer configuration and parameters. The transformer turns ratio is 1:1. The transmitter and receiver coil parameters are identical. Table 4 shows the design requirement specification. The nominal AC load is calculated from the nominal DC load resistance for the diode rectifier operation. Table 5 shows the LCC circuit parameters from the design calculation using the method given in [12]. The LCC resonant circuit design analysis assumes that the rectifier is operating at \(\beta\)s(deg) = 180\({}^{\circ}\) with unity AC power factor with battery equivalent resistance change. The method presented in [12] is applied for the LCC resonant circuit performance calculation. The switching loss and conduction loss of power electronic switches are ignored in the calculation. Figure 6 shows the frequency sensitivity analysis of DC transconductance gain for the DAB DC/DC converter vs. the power factor angle of the DAB inverter bridge. The transconductance gain is defined as the ratio of the DC/DC converter DC output current vs. DC input voltage. It decides the DAB converter DC current output capability in CC mode charging. The benefit of the fixed AC load resistance from rectifier phase shift control is that DC/DC converter DC current output capability will not be affected by the mutual coupling factor variation in CC mode charging operation. \begin{table}
\begin{tabular}{l l c} \hline \hline \multicolumn{1}{c}{**Symbol**} & **Parameter** & **Value** \\ \hline V\({}_{\text{dc}}\) & DC input voltage & 30 V \\ \hline V\({}_{\text{o}}\) & DC output voltage & 24–48 V \\ \hline P\({}_{\text{o}}\) & Maximum DC output power & 50 W \\ \hline \(f_{\text{sw}}\) & Resonant frequency & 30 kHz \\ \hline R\({}_{\text{dc}}\) (norm) & Nominal DC load resistance & 47 \(\Omega\) \\ \hline R\({}_{\text{ac}}\) (norm) & Nominal AC load resistance & 38 \(\Omega\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Design requirement for LCC resonant converter. Figure 7 shows the frequency sensitivity analysis of DC voltage gain for the DAB DC/DC converter vs. the inverter power factor angle. The voltage gain is defined as the ratio of the DC output voltage vs. DC input voltage, and it decides the DC/DC converter DC voltage output capability. The DC voltage gain variation is significant due to the AC load resistance change and relatively minor due to the mutual inductance change. The benefit of the fixed AC load resistance from rectifier phase shift control is that the DC voltage gain variation will be significantly reduced in battery CV mode charging application. Figure 8 shows DC input/output voltage/current calculated at different inverter phase shift angle \(\beta\)p (deg) settings vs. AC load resistance change. This result shows that DC output voltage and current magnitude at the same AC load resistance value change significantly with inverter phase shift angle \(\beta\)p (deg). The inverter phase shift angle can be  
Figure 6: DC transconductance gain and inverter power factor angle with respect to DAB switching frequency change. Figure 7: DC voltage gain vs. inverter power factor angle with respect to DAB switching frequency change. applied to regulate the charging voltage and current in CC or CV mode charging operation. If the AC load resistance can be fixed to \(\text{R}_{\text{ac}}\) (norm) = 38 \(\Omega\) using rectifier phase shift \(\beta\)s regulation, the maximum output voltage and maximum input and output currents are limited to smaller value ranges. Figure 9 shows DC input and DC output power and power transfer efficiency calculated at different \(\beta\)p (deg) under AC load resistance change conditions. This result shows that DC input and output power change with inverter phase shift angle \(\beta\)p (deg). However, the efficiency does not change with the inverter phase shift angle \(\beta\)p (deg).