## 2 DAB DC/DC Resonant Converter TPS Close Loop Control Scheme  
### DAB DC/DC Resonant Converter TPS PWM Modulation  
DAB DC/DC resonant converter has a symmetrical circuit structure. It is suitable for the bi-directional operation of a wireless charging system at a single resonant frequency with high-power density and high efficiency. Figure 1 shows the wireless charging DAB LCC resonant DC/DC converter circuit with transmitter side H-bridge DC/AC inverter and receiver side H-bridge AC/DC active rectifier. The function description of the symbols denoted in Figure 1 is given in Table 1. In this paper, \(\text{R}_{\text{ac\_out}}\) is the study focus for rectifier side control and is denoted as \"\(\text{R}_{\text{ac}}\)\". Figure 2 illustrates the triangle PWM carrier signals, the PWM gating signals of the top switches of the inverter and rectifier Legs, and the resulting AC voltage waveforms of \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt}} \hline \hline \multicolumn{1}{c}{**Symbol**} & \multicolumn{1}{c}{**Function Description**} \\ \hline \(\text{C}_{\text{1p}}\) and \(\text{C}_{\text{1s}}\) & LCC primary and secondary side series compensation capacitances \\ \hline \(\text{C}_{\text{2p}}\) and \(\text{C}_{\text{2s}}\) & LCC primary and secondary side parallel compensation capacitances \\ \hline \(\text{L}_{\text{1p}}\) and \(\text{L}_{\text{1s}}\) & LCC primary and secondary side compensation inductance \\ \hline \(\text{V}_{\text{dc\_inv}}=\text{V}_{\text{dc}}\) & inverter DC input voltage \\ \hline \(\text{I}_{\text{dc\_inv}}\) & inverter DC input current \\ \hline \(\text{V}_{\text{dc\_rec}}=\text{Vo}\) & rectifier DC output voltage \\ \hline \(\text{I}_{\text{dc\_rec}}=\text{Io}\) & rectifier DC output current \\ \hline \(\text{R}_{\text{dc}}\) & rectifier DC output side equivalent battery DC resistance \\ \hline \(\text{R}_{\text{ac}}=\text{R}_{\text{ac\_out}}\) & rectifier AC side equivalent resistance \\  & = LCC resonant circuit load resistance \\ \hline \(\text{R}_{\text{ac\_in}}=\text{R}_{\text{ac\_inv}}\) & Inverter AC side equivalent resistance \\  & = Inverter AC load resistance \\ \hline \hline \end{tabular}
\end{table} 
Table 1: DAB LCC resonant converter circuit notation definition. Figure 1: Wireless charging DAB LCC Resonant DC/DC resonant converter. the inverter and rectifier for DAB TPS PWM modulation. The same color is used for signal notation and the signal itself. The PWM carrier signals generate the PWM gating signals. The gating signal for the bottom switch has the opposite polarity as the top switch of the same Leg. A turn-on delay is applied for all gating signals to generate a dead time to prevent short-through fault of the inverter and rectifier Leg. The inverter and rectifier AC voltage waveforms are generated by the inverter and rectifier PWM gating signals. Table 2 listed out phase shift angles with their PWM carrier signal sources and the results shown in inverter/rectifier AC voltage waveforms. The phase shift time between two Legs is defined as the period between positive zero-crossings of the PWM carrier signals for the two Legs. The phase shift time is converted to phase shift angle in degree, with the ratio of one PWM cycle 360\({}^{\circ}\). The magnitude of the inverter/rectifier AC voltage pulse is the same as its corresponding DC voltage. The polarity of phase shift angle \(\delta\) determines the power flow direction of the bidirectional DAB converter. For DAB LCC resonant converter, the optimized inverter-to-rectifier phase shift angle \(\delta=90^{\circ}\) with inverter AC voltage leads the rectifier AC voltage to achieve unity power factor operation of the DAB converter for battery charging. The detailed derivation process will be given in Section 2.2.2.