# Modeling and Control Simulation of Power Converters in Automotive Applications
## 2 Electothermal Modeling and Control Algorithm
### AC/DC Converter Model and Control  
The study examines the totem pole configuration, a specific type of AC/DC converter with PFC [53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63]. In Figure 2, there are two SiC transistors (\(S_{D_{1}}\), \(S_{D_{2}}\)) and two GaN transistors (\(Q_{1}\), \(Q_{2}\)). The SiC components rectify the current at line frequency, replacing traditional diodes, while the GaN components perform fast switching at frequencies above 100 kHz. The circuit operates in two modes, depending on the polarization of the AC line voltage, as shown in the schematic in Figure 3. The activation of \(S_{D_{1}}\) and the deactivation of \(S_{D_{2}}\) together with the GaAs define the positive AC half-cycle. The modulation logic handles the negative AC half-cycle, with \(S_{D_{2}}\) active, by deactivating \(S_{D_{1}}\) and activating the GaAs. This cyclic interaction between phases produces the desired PFC effect, aligning the current with the AC supply voltage and eliminating reactive power. The SiCs handle the rectification, while the GaAs orchestrate the switching to obtain the correct voltage on the DC bus. Figure 4 shows a schematic of the complex control system of a totem pole-type AC/DC converter. The control is divided into various functional blocks that are crucial for the operation of the system. A second-order low-pass filter (LPF) separates the in-line and 90-degree offset components of the AC voltage. A phase-locked loop (PLL) calculates the phase compensation required to balance the current in the totem pole input connection with the supply voltage. The feedback controller mediator corrects errors between the actual voltage, \(V_{o}\), and the reference, \(V_{ref}\), for the DC bus; it also handles the AC \(I_{ac}\). Figure 1: Diagram illustrating the stages of power domain conversion in the reference device. Figure 2: Selected bidirectional PFC active rectifier circuit configuration. The modulation system, based on an inverse calculation mechanism, synchronizes the generation of the required AC voltage \(V_{ac}^{*}\) and the phase compensation \(\omega\) to ensure the effective operation of the system. \[ \begin{gathered} V_{Q}=\left[2\left(\frac{\hat{\omega}_{g}}{s^{2}+ \hat{\omega}_{g}^{2}}\right)\left(\frac{\omega_{g}}{s^{2}+\omega_{g}^{2}}\right) +\frac{s}{s^{2}+\hat{\omega}_{g}^{2}}\right]V_{g}\\ \hat{\omega}_{g}=\left(P+\frac{I}{s}+D\frac{Ns}{s+N}\right)V_{Q} \end{gathered}  \tag{1}\]  
Figure 5 highlights the importance of the second-order low-pass filter to obtain a signal with a 90-degree phase shift relative to the source voltage. This phase shift allows the phase-locked loop (PLL) block to accurately calculate the frequency required to synchronize the main voltage and current in the totem pole, achieving the desired PFC effect. The accurate measurement of the voltage on the DC bus depends on the control logic of the voltage and current feedback. Next, Figure 6 illustrates the internal configuration of the PLL block and how it processes input signals, such as \(\alpha\) and \(\beta\) from the LPF block. The result of this complex block is translated into carefully calculated trigonometric functions related to the \(\omega\) pulsation, which are fundamental for coordinating the complex dynamics of the system. Equation (1) shows the transfer functions of \(V_{Q}\) and the estimated network frequency/pulse, which are the outputs of the PLL system. Figure 4: Automatic control of a totem pole PFC converter. Figure 3: Current route during the changing operational states of the MOSFETs. The signal processing system is detailed in Figure 6. It is based on the Park transformation of the input signals to obtain components along the direct and quadrature axes. The goal is to cancel the quadrature component to achieve the desired PFC effect in the topen pole. A PID controller corrects any residual errors. This complex process identifies the impulse needed to control the current in the totem pole and, after integration, produces the angle for the Park transformation.