## 1 Introduction  
Nowadays, countries around the world are constantly seeking ways to utilize energy efficiently and reduce environmental impacts associated with carbon emissions. One of the most popular solutions today is using the smart grid, which provides a sustainable, reliable, economical, and environmentally friendly power grid [1]. The ability to connect electric vehicles (EVs) to the grid is one of the key features of a smart grid, which reduces emissions and fossil energy consumption. In a smart grid, EVs can be regarded as mobile energy storage. By connecting EVs to the grid, the overall energy utilization rate can be improved. Since power electronics technology has evolved rapidly in recent years, DC/DC converters have been widely used in EVs, energy storage systems, energy conversion systems, DC distributed power systems, and power transmission systems. Moreover, DC-DC converters even appear in applications such as inverters [2]. One of the most popular topologies used in the DC/DC converter is the dual active bridge (DAB). Due to the attractive characteristics such as zero-voltage switching (ZVS) of all power switches, near-minimal voltage and current stress, galvanic isolation with bidirectional power flow,low number of passive components as well as a high voltage conversion ratio [3; 4; 5; 6; 7; 8; 9], the DAB converter is widely used as the power interface for EVs in V2G systems. A DAB converter topology typically consists of a high-frequency transformer and two active full-bridge rectifiers, as shown in Figure 1. The DAB converter has bidirectional energy transmission characteristics, and it is commonly controlled by phase-shift control to change its transferred power. There are numerous phase-shift control methods applied to DAB converters. Generally, they can be categorized as SPS control, extended-phase-shift (EPS) control, dual-phase-shift (DPS) control, and triple-phase-shift (TPS) control. Among these control methods, the SPS control method is the most widely used due to its advantages, such as ease of implementation, simple algorithms used, soft switching capabilities, etc. In the SPS control method, diagonally opposite switches on each full-bridge are controlled to create a leading or lagging phase of the primary side voltage relative to the secondary side voltage of the transformer to control power flow direction and magnitude. The phase difference between the voltages on the primary side \(V_{P}\) and the secondary side \(V_{S}\), the so-called phase-shift angle, \(\theta\), is the only variable that can be controlled, as shown in Figure 2.  
When the control signal of the full-bridge rectifier on the primary side of the transformer is ahead of the control signal of the full-bridge rectifier on the secondary side of the  
Figure 1: The DAB converter topology. Figure 2: Control waveforms of SPS control. transformer, the energy is transferred from the DC bus to the energy storage (battery pack). Conversely, when the control signal of the full-bridge rectifier on the secondary side of the transformer precedes that of the full-bridge rectifier on the primary side of the transformer, energy is transferred from the energy storage to the DC bus. With the aim of achieving ZVS for power switches, auxiliary inductor \(L_{K}\) serves as a means of transferring and storing energy. However, the disadvantage of SPS is the occurrence of backflow power caused by the circulating current. There are periods during the power transfer process when the transformer's primary side voltage \(V_{P}\) and inductor current \(i_{LK}\) are in opposing directions, causing the energy stored in auxiliary inductor \(L_{K}\) to return to the input (DC bus), as the red area in Figure 3. As the transmission power remains constant, the greater the backflow power, the greater the required forward transmission power.