## 2 DAB DC/DC Resonant Converter TPS Close Loop Control Scheme
### Mathematical Formulation of DAB TPS Control Method
#### 2.2.4 DAB LCC Resonant Converter Rectifier AC Voltage Phase Measurement from Receiver Coil Current  
For LCC resonant converter, the receiver coil voltage and current are sinusoidal signals at resonant frequency, and the phase relationship between transformer winding voltage and current can be utilized to measure the phase rectifier AC voltage at resonant frequency. The resonant frequency component of rectifier AC voltage can be derived as (36) utilizing resonant condition (14), which means that the phase of rectifier AC voltage lags the receiver coil current by \(90^{\circ}\).  
\[V_{ac\_rec}=\frac{1}{j\omega_{\text{sw}}C_{2s}}(I_{RX}-I_{ac\_rcrc})-j\omega_{ \text{sw}}L_{1s}*I_{ac\_rec}=\frac{1}{j\omega_{\text{sw}}C_{2s}}I_{RX} \tag{36}\]DAB TPS Close Loop Control Scheme for Unity Power Factor Operation of Inverter and Rectifier at Optimized Resonant Circuit AC Load Resistance  
Figure 5 shows the proposed TPS control scheme to achieve unity power factor operation of the DAB converter at optimized resonant circuit AC load resistance in the wireless charging system. The battery charging voltage/current feedback control is implemented to control the inverter phase shift angle \(\beta\)p. The resonant circuit AC load resistance Rac feedback control is applied to regulate the rectifier phase shift angle \(\beta\)s. The inverter-to-rectifier phase shift angle \(\delta\) is set to 90\({}^{\circ}\) for unity power factor operation of the DAB inverter and rectifier bridges.  
The inverter phase shift angle \(\beta\)p changes the inverter AC output voltage pulse-width and the input AC voltage of the resonant circuit so that the power from the inverter to the rectifier can be regulated. In CC mode control, the battery current feedback is applied to regulate the power from the inverter to the rectifier. In CV mode control, the battery voltage feedback is applied to regulate the power flow from the inverter to the rectifier.  
For the inverter phase shift control, in CC mode battery charging operation, the DC/DC converter DC output current is regulated around the charging current reference by the proportional and integral (PI) control. The feedback current is the battery charging current measured after the load side filter capacitor. In CV mode charging, the DC/DC inverter output voltage is regulated around the target voltage. The feedback voltage is measured as the battery DC voltage.  
The rectifier phase shift control regulates the resonant circuit AC load resistance Rac to match its optimized value. In the control algorithm implementation, the Rac feedback signal is calculated as a function of the rectifier phase shift angle \(\beta\)s and DC load resistance using (11), assuming the rectifier runs at unity power factor. The DC load resistance signal is estimated from the ratio of battery voltage over battery charging current. When the charging current is approaching zero, Rac feedback control is disabled because DC load resistance (R\({}_{\text{dc}}\)) estimation is inaccurate. In this condition, the rectifier phase shift angle is set to its maximum value at \(\beta\)s = 0.5 and \(\beta\)s (deg) = 180. The change rate of the rectifier phase shift is limited to smooth out the dynamic transition caused by the phase shift command sudden change.  
The proposed DAB resonant DC/DC converter TPS close loop control scheme can be implemented for all DAB resonant circuit topologies. However, the optimized AC load resistance value and the optimized inverter-to-rectifier phase shift angle setting to achieve  
Figure 5: DAB resonant DC/DC converter TPS control scheme.  
unity power factor operation are to be decided by both the resonant circuit topology and the resonant circuit parameter.