# Analytical Selection of Leakage Inductance for Single-Phase Dual Active Bridge Converters
###### Abstract  
The single-phase dual active bridge (DAB) DC/DC converter is a vital component in modern power electronics systems, facilitating efficient bidirectional power transfer between various energy sources and loads. One of the critical aspects in the design of such converters is the selection of an appropriate leakage inductance, as it significantly affects the circulating power within the converter. This study investigates the influence of inductance on the reactive power flow and introduces an analytical formula for calculating the necessary leakage inductance based on the specified rated power of the DAB converter. By employing the inductance values determined through the proposed formula, the developed power control-based modulation method, implemented in discrete time, successfully achieves zero reactive power caused by the first harmonic components under all load conditions. This selection of leakage inductance optimizes the performance of the converter ensuring efficient power delivery across various applications. The applicability of this method extends to various DAB applications, including electric vehicles, integration with asynchronous microgrids, and aerospace systems.  
active/reactive power controller; leakage inductance; dual active bridge; DC/DC converter +
Footnote †: journal: Applied  
the focus was on selecting the best leakage inductance for a three-phase multilevel DAB converter used in wind turbine installations. Both studies [12; 13] utilized a thorough brute-force optimization technique, which, while robust, was noted for being computationally intensive and requiring considerable time to execute. In the study [14], a sophisticated methodology for optimizing leakage inductance was detailed, which was specifically designed for a three-phase DAB converter used in utility applications. This method uniquely blended the analytical expressions for power and current specific to the three-phase DAB converter with the capabilities of numerical solvers to accurately identify the most effective leakage inductance value. While this technique achieved results more expediently than the exhaustive brute-force method utilized in the studies [12; 13], it fell short of providing a thorough analysis of variations in the leakage inductance relative to changes in the design parameters. This highlights a need for flexibility in the optimization process to ensure its applicability across various system designs. Therefore, selecting an appropriate leakage inductance is essential for optimal DAB converter performance across various modulation schemes. The strategic selection of the leakage inductance not only improves the efficiency but also enhances the reliability and durability of the converter system. Furthermore, optimizing the design of DAB converters can lead to better adaptability in power systems, ensuring more stable and robust power supply solutions in advanced technological applications.  
This study explores the optimization of leakage inductance in single-phase DAB converters to enhance their performance. An analytical formula was developed to identify the ideal leakage inductance. Additionally, a power controller was designed to independently manage the active and reactive powers of the first harmonic components of the voltages and currents in the converter. Implementing the analytical formula to determine the optimal leakage inductance ensured that the power controller effectively eliminated reactive power caused by the first harmonic components under various operating conditions. By adopting this approach, this study demonstrated a significant reduction in inductor current compared to conventional modulation methods. Furthermore, this optimized strategy allowed for a substantial decrease in the size of the leakage inductance when compared with that of the conventional method, thus not only enhancing the converter's efficiency, but also its compactness and applicability in space-constrained applications such as electric vehicles and portable devices.