## 3 DAB LCC Resonant Converter TPS Control Validation
### Inverter and Rectifier Phase Shift PWM Modulator Implemented in Two Separate Control Hardware
Figure 29 shows the operation condition when the positive zero-crossing of the rectifier PWM sync signal aligns with the diode rectifier voltage signal after successful phase shift angle \(\delta\)(deg) auto-adjustment. In this condition, the rectifier phase shift PWM modulator gating signal output to the bridge power electronic switching devices is enabled. The DAB rectifier bridge phase shift PWM modulation performs similarly to the diode rectifier with smooth power on transition. Figure 29: DAB smooth startup transition stage (1): phase shift angle \(\delta\) (deg) auto-adjustment for rectifier PWM modulator smoothly enabled in diode rectifier operation condition. Power on Transition Stage (2)--Inverter-to-Rectifier Phase Shift Angle Auto-Adjustment for DAB Unity Power Factor Operation in Rectifier Phase Shift Open Loop Control  
In the power-on transition stage (2), inverter control is the same as in stage (1). The rectifier shift angle \(\beta\)s (deg) is smoothly reduced through the rate change limiting block to a smaller value setting (for example, \(\beta\)s = 40\({}^{\circ}\)) to improve the power factor angle auto-adjustment sensitivity. The rectifier AC power factor angle \(\varphi_{rec}(PF)\) is measured. The rectifier AC power factor angle is used to adjust \(\delta\) (deg) to minimize the rectifier AC power factor angle to achieve unity power factor operation of DAB bridges. Figure 30 shows the block diagram for the rectifier AC power factor angle measurement from phase difference detection of receiver coil AC current and rectifier AC current. The relationship of the fundamental frequency component of rectifier AC voltage and receiver coil current derived in (36) is rewritten as (43), which means that rectifier AC voltage lags the receiver coil current by 90\({}^{\circ}\). Utilizing (43), the peak instant of the fundamental frequency component of rectifier AC voltage can be detected by the negative zero crossing instant of the harmonic-free receiver coil current. \[\mathrm{I_{RX}}=\mathrm{j}\omega_{\mathrm{sw}}\mathrm{C_{2p}}\mathrm{V_{out \_ac}} \tag{43}\]  
The high order harmonics of rectifier AC current should be removed by bandpass filter centered at resonant frequency before its peak timing instant detection. The peak instant of the filtered rectifier current can be captured as the phase instant of the rectifier AC current. The AC power factor angle of the rectifier is calculated from the measured timing error as shown in (44), where \"fsw\" is the DAB converter resonant and switching frequency. The low pass filtered power factor angle is used for phase shift angle \(\delta\) auto-tuning adjustment purposes. \[\varphi(\mathrm{PF})_{\mathrm{rec}}=2\pi*\mathrm{fsw}*\Delta\mathrm{t_{rec}} \tag{44}\]  
Figure 31 illustrates the simulation results of inverter/rectifier AC voltage/current and receiver coil current for different inverter-to-rectifier phase shift angle \(\delta\) (deg) settings to achieve unity power factor operation. The unity power operation is achieved when the rectifier current peak time instant aligns with the negative zero crossing of the receiver coil current. DAB TPS Close Loop Control Stage with Inverter-to-Rectifier Phase Shift Angle Auto-adjustment for DAB Unity Power Factor Operation with Rectifier Feedback Control Enabled  
In the power-on transition stage (2), when the rectifier power factor angle is below the threshold setting, the startup process is transferred from stage (2) to the normal TPS closed-loop control stage. In the final TPS control stage, \(\mathrm{R_{ac}}\) feedback control regulation of \(\beta\)s angle is enabled. The inverter-to-rectifier phase shift angle \(\delta\) (deg) auto-adjustment for unity power factor operation of DAB continues to run to eliminate the accumulated phase timing draft in either the inverter PWM carrier signal or rectifier PWM carrier signal. The inverter battery voltage and current control are changed to the automatic CCCV mode setting based on battery voltage measurement and SOC status estimation.