# Analytical Selection of Leakage Inductance for Single-Phase Dual Active Bridge Converters
## 5 Results  
The parameters for the dual active bridge (DAB) converter were determined to fulfill the specific needs of the Level-1 electric vehicle (EV) charging station. It is important to note that the charging voltage varies depending on the level of the EV charging system [25; 26]. For example, a Level 1 charging station typically has a charging voltage ranging from 200 to 400 V. Higher levels of charging stations, such as Level 2 and above, operate at significantly higher voltages, with Level 3 and DC fast charging stations delivering voltages from 400 V up to 800 V or more. Additionally, the average rectified voltage derived from a 120 V AC input is around 108 V.  
The efficacy of the presented method was evaluated through a comparative analysis using a Matlab Simulink 2022b software with the conventional SPS and dual-phase shift (DPS) [27] control methods. This assessment involved employing converters with identical parameters, facilitating a thorough examination of their performances under identical conditions. The leakage inductance was determined through the proposed analytical formula outlined in Equation (30) for a 1.5 kW converter for the developed power controller-based modulation method. The key parameters of the converter included input and output voltages of 108/250 V, a leakage inductance of 33.3 \(\mu\)H, and a switching frequency of 30 kHz, as illustrated in Table 4.  
The power controller underwent comprehensive testing across various load conditions to evaluate its performance. Figure 10 illustrates the steady-state primary side voltage (green), secondary side voltage (blue), and current (red) waveform at 20%, 60%, and full load, providing insights into its performance across different load levels. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Proposed Law** & **SPS Method** \\ \hline Volume & 94,310.6 mm\({}^{3}\) & 170,677.1 mm\({}^{3}\) \\ Weight & 301.56 g & 573.24 g \\ Core Losses & 9.72 W & 15.14 W \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of transformer characteristics: Proposed Method vs SPS-Based Method. The proposed method was compared to the SPS and DPS techniques at 0.6 pu of load, as shown in Figure 11. The analysis of reactive power and inductor current waveforms revealed that the proposed method effectively eliminates circulating power and significantly reduces inductor current under the same load conditions. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Value** & **Unit** \\ \hline Rated Power (\(P_{\text{{r}}nal}\)) & 1500 & Watt \\ Input/Output Voltages & 108/250 & Volt \\ Switching Frequency (\(f_{s}\)) & 30 & kHz \\ Inductor (\(I_{e}\)) & \(33.3\times 10^{-6}\) & Henry \\ \hline \end{tabular}
\end{table} 
Table 4: Parameters for 1.5 kW DC/DC converter. Figure 10: _Cont._  
A scale-down laboratory prototype with a power rating of 350 W was constructed, as shown in Figure 12. The voltages and switching frequency were kept constant to facilitate accurate comparison with theoretical predictions. The TMS320F28335 microcontroller (Texas Instruments, Dallas, TX, USA) was employed for control and operation. Furthermore, the leakage inductance was calculated from (30) to be 130.61 uH to ensure optimal performance. To evaluate the effectiveness of the developed power controller, a comprehensive test was carried out. Initially, the connected load was set to 20% of the converter's full load capacity. Subsequently, the load was abruptly increased to reach the full capacity of the designed converter. Figure 13 illustrates the transition in active power from 0.2 per  
Figure 11: Inductor current and reactive power. unit to full load. Remarkably, even as the load conditions changed, the reactive power of the first harmonic components remained at zero during steady-state conditions. A comparative experiment was carried out to assess the efficacy of the developed method against the SPS and DPS modulation techniques.