## 3 DAB LCC Resonant Converter TPS Control Validation
### Inverter and Rectifier Phase Shift PWM Modulator Implemented in Two Separate Control Hardware  
Figure 27 illustrates the inverter phase shift PWM modulators and rectifier phase shift PWM modulation signal connections when the inverter and rectifier phase shift control is to be implemented in two separate control hardware. The initial unknown random inverter-to-rectifier phase shift angle \(\delta\_\)init (random) in the rectifier PWM modulator is generated because of the phase timing difference of inverter Leg 1 and rectifier Leg 1 PWM carrier signals, which cannot be controlled. The inverter-rectifier phase shift angle \(\delta\) is a control variable which can be adjusted using a self-tuning algorithm for TPS control. The inverter-to-rectifier phase shift angle \(\delta\) is applied to remove the effect of unknown \(\delta\_\)init and to achieve the desired smooth power-on startup transition performance and unity power factor operation of the DAB converter in regular battery wireless charging operation. DAB Converter TPS Control Smooth Poweron Startup Transition with Inverter-to-Rectifier Phase Shift Angle Auto-Adjustment Scheme  
Figure 28 shows the function block diagram for the inverter-to-rectifier phase shift angle \(\delta\)(deg) auto-adjustment scheme to be implemented in the same high-timing resolution rectifier FPGA of the PWM modulator with two power-on DAB converter startup transition stages added. The transition stage (1) is to smoothly enable the rectifier phase shift PWM modulator in the DAB converter diode operation condition. The DAB converter power on startup  
Figure 28: Function block diagram for DAB smooth startup transition from stage (1) to stage (2) and to the final TPS stage. Figure 27: TPS phase shift PWM modulator signal connections when TPS control in separate inverter and rectifier control hardware. process starts at diode rectifier operation with rectifier side PWM gating signals disabled. The inverter phase shift control is enabled for CC mode operation with a very small charging current to establish the rectifier side AC voltages for diode bridge operation. The rectifier phase shift angle is fixed to \(\beta\)s = 180\({}^{\circ}\). The rectifier PWM carrier signal timing is auto-adjusted to match the diode rectifier timing with the inverter-to-rectifier phase shift angle change. Therefore, the rectifier phase shift control is enabled smoothly from diode bridge operation. Once the rectifier phase shift PWM modulator is enabled, the startup process transfers to the transition stage (2). The transition stage (2) is to achieve inverter and rectifier unity power factor operation with phase shift angle \(\delta\) (deg) auto-adjustment. A smaller rectifier phase shift angle is applied in an open loop condition in this stage. The inverter phase shift control operates at the same condition as the transition stage (1). The inverter-to-rectifier phase shift angle is auto-adjusted to minimize the measured rectifier power factor angle to achieve unity power factor operation. Once the DAB converter runs in unity power factor operation, the start-up transition stage (2) is completed, and TSP control is transferred to the regular power transfer operation stage. Power on Transition Stage (1)--Smoothly Enable Rectifier Phase Shift Control in Diode Bridge Operation Condition  
In the power-on transition stage (1), the rectifier phase shift PWM modulator runs internally when its output gating signals are disabled. The rectifier PWM sync signal is constructed internally in the rectifier PWM modulator FPGA by subtracting the gating signal g_T7 from g_T5. The rectifier phase shift PWM modulator starts with \(\beta\)s (deg) = 180\({}^{\circ}\). The positive zero crossing timing difference of the PWM sync signal and diode rectifier AC voltage is used to auto-adjust \(\delta\) (deg) setting until \(\Delta\delta\) below its maximum threshold.