# Numerical Analysis of the Cooling Performance in a 7.2 kW Integrated Bidirectional OBC/LDC Module
## 2 Development of the Numerical Model  
### Circuit Simulation Model of the Integrated Module  
A circuit diagram of the developed 7.2 kW integrated bidirectional OBC/LDC module is shown in Figure 2. In this circuit, the totem-pole PFC and buck converter were implemented as bridgeless and synchronous rectification types, respectively. These operate as follows: When the AC voltage is  
Figure 1: Numerical analysis method used for the 7.2 kW integrated bidirectional onboard battery charger/low-voltage DC–DC converter (OBC/LDC) module developed in this study.  
positive, the PFC stores energy in the inductor and switches Q3-Q5 are turned on. Later, when Q3-Q5 are switched off, the energy stored in the inductor is discharged and the current flow passes through switches Q1-Q2 and Q6. The PFC control block is configured based on the duty cycle of the current (Equation (1)) and the voltage-current (Equation (2)) relationships as follows [24]:  
\[G_{i}=\frac{i_{L}}{d}=\frac{CV_{DC}+2(1-D)I_{L}}{(LC)s^{2}+\left(\frac{k}{k} \right)+\left(1-D\right)^{2}}\approx\frac{V_{0}}{sL}, \tag{1}\]  
\[G_{v}=\frac{v_{o}}{i_{L}}=\frac{(1-D)V_{DC}-LI_{L}}{CV_{0}s+2(1-D)I_{L}}\approx \frac{1}{sCV_{0}}. \tag{2}\]  
The DC-DC converter in the circuit is represented as a series resonant converter (SRC) in which the primary and secondary circuits are separated using a transformer. In the forward direction, the AC voltage is converted to a DC voltage using switches Q7 and Q8, whereas in the reverse direction, the voltage is converted using switches Q20-Q23. The output voltage in the forward direction is determined by the high- or low-battery-voltage setpoints, which depend on the winding ratio, resonance point, and operating frequency of the transformer. This circuit was designed to generate a constant output voltage by aligning the resonance point and operating frequency to 300 kHz. In addition, the system was configured to respond to a broad range of output voltages depending on the number of windings.  
The SRC resonance-type circuit is configured through a serial connection with a transformer ratio of 12:14:1, based on the output in the high- and low-voltage directions at the primary side. The equivalent model was constructed based on this configuration. The output voltage can be predicted as follows [25]:  
\[V_{convert}=G_{sw,g}G_{resonant,g}N_{s}/N_{p}, \tag{3}\]  
Figure 2: Circuit diagram of the designed 7.2 kW integrated bidirectional OBC/LDC module.  
The resonant gain graph of the SRC resonant circuit can be defined as follows. Note that the \(m\) value was omitted because, unlike the LLC circuit, the SRC circuit has only one inductor:  
\[G_{resonant,g}=\frac{F_{x}^{2}(m-1)}{\sqrt{1+jQ\left(\frac{1}{F_{x}}-F_{x}\right) ^{2}}} \tag{4}\]  
where \(F_{x}\) is the ratio of the resonance frequency and switching frequency and Q (Equations (5) and (6)) is the quality factor, which is defined as follows:  
\[Q=\frac{\sqrt{L_{r}/C_{r}}}{R_{ac}}, \tag{5}\]  
\[R_{ac}=\frac{8}{\pi^{2}}\frac{N_{s}^{2}}{N_{p}^{2}}R_{L}. \tag{6}\]  
Using Equations (4) to (6), the resonant gain of the SRC circuit can be expressed as shown in Figure 3, where the maximum output voltage can be 467 V. Therefore, it is necessary to control the step-up and step-down through the introduction of the buck converter to stabilize the battery.  
The buck converter reduces the voltage based on the output voltage of the DC-DC converter. The inductor voltage is applied when the switch turns on and the amount of current increases. In contrast, when the switch turns off, the operating mode disconnects the input power. The control block of the buck converter circuit maintains a high stability by enabling constant current (CC) operation during charging. Then, when discharging, the constant voltage (CV) control method is used instead to improve the overall efficiency.