## 5 Conclusions and Discussions  
This paper proposes TPS closed-loop control method to realize the unity power factor operation of wireless charging DAB LCC resonant converter at optimized resonant circuit AC load resistance. The efficacy improvement for the proposed TPS control comes mainly from unity power factor operation of the DAB inverter and rectifier. ZVS in CC mode operation helps to improve the efficiency as well. The R\({}_{\text{ac}}\) feedback control improves the efficiency in CV mode charging operation only. One inverter/rectifier Leg may lose ZVS switching in CV mode charging control, which may lower the efficiency at CV mode than CC mode charging. The analytical calculation of the LCC resonant converter performance using its resonant equivalent circuit model shows that the converter output DC voltage/current and input/output power changes with inverter phase shift angle for the same resonant circuit AC load resistance level. The mathematical analysis provides the theoretical foundation to implement the battery charging current and voltage feedback control with inverter phase shift regulation. The analytical calculation result shows that the AC load resistance of the LCC resonant circuit is another crucial factor which significantly affects the voltage, current, power, and power efficiency of the resonant converter. There is an optimized AC load resistance value for maximum efficiency operation. For a unidirectional LCC resonant circuit with a diode rectifier, the significant variation of equivalent battery load resistance maps into the considerable variation of AC load resistance with a gain factor of \(8/\pi^{2}\). The power efficiency will be degraded when the equivalent battery resistance is significantly increased in CV mode charging. The variation of AC load resistance also causes considerable DC voltage gain variation and inverter load impedance frequency curve shape changes. In DAB TPS control, the low-efficiency issue in CV mode charging can be resolved with AC load resistance feedback control around at optimal target by regulating the rectifier phase shift angle. The ratio of rectifier AC resistance and equivalent battery DC resistance is derived as a non-linear function for rectifier phase shift angle. The AC load resistance is estimated from measured DC load resistance and rectifier phase shift angle to construct the feedback control signal. Lastly, the inverter-to-rectifier phase shift angle for unity power factor operation of the DAB LCC resonant converter is mathematically proven to be \(\delta=90^{\circ}\). This setting ensures minimizing the reactive power flow in LCC resonant circuit. Therefore, it maximizes the LCC resonant circuit efficiency. Figure 31: DAB smooth startup transition stage (2): rectifier \(\delta\) (deg) auto-adjustment to achieve unity power factor control of rectifier DAB bridge. The simulation analysis and experimental test are conducted to validate the performance of the proposed DAB resonant converter high-efficiency control solution. The simulation and experimental results verified that the proposed DAB control system works as designed. DC output voltage and current can be regulated stably around its reference value in either current or voltage feedback control conditions with inverter phase shift control. The unity power factor operation is achieved when the inverter-to-rectifier phase shift angle is \(\delta=90^{\circ}\). The DAB converter efficiency is significantly improved when rectifier side R\({}_{\text{ac}}\) feedback control is regulated around its smaller normal value when a larger DC load resistance is connected in the test. The transformer winding current magnitude is greatly reduced when R\({}_{\text{ac}}\) feedback control is enabled when larger DC load resistance is connected to DC/DC converter output. The simulation and measurement results for TPS control matches well.