A Novel Structure of Variable Inductance High-Frequency Transformer for Power Level Enhancement in Dual-Active-Bridge Converters

Abstract

This study presents a novel structure proposal of a variable inductance high-frequency transformer for enhancement power level of a dual-active-bridge (DAB) converter. The DAB converter is a solid-state transformer (SST) that requires high efficiency, power density, flexibility, and stability. Variable inductance facilitates achieving and extending maximum power levels. The proposed method adjusts the inductance based on the core insertion conditions of the transformer used in the DAB converter without requiring an additional inductor. The method was verified by analyzing the variable inductance characteristics of the transformer based on core insertion conditions via finite element analysis (FEA) and simulation and experiments within the variable inductance range.

1. Introduction

Recently, the demand for power conversion systems that offer high efficiency, power density, flexibility, and reliability has been increasing. To meet these demands, substantial research has focused on solid-state transformers (SST), which convert power using high-frequency conversion with semiconductor devices instead of the existing 50/60 Hz low-frequency transformer [1]. In particular, the introduction of new semiconductor materials such as gallium nitride (GaN) and silicon carbide (SiC) has revolutionized power conversion technology by providing higher efficiency and density. Dual-active-bridge (DAB) converters, commonly used as SSTs, are isolated bidirectional DC–DC converters [1,2,3,4]. DAB converters are widely used because of their simple structure and capability to transmit power using only phase shifts [5,6,7]. Consequently, it is used in various applications including renewable energy systems, DC grids, electric vehicles, energy storage systems (ESS), and data centers.

The DAB converter consists of a first full bridge and a second full bridge on both sides of a high-frequency transformer, and the transformer and additional inductor are connected in series to provide the inductance required for power conversion. The DAB converters transfer power using the phase shift between the primary and secondary full-bridge switches. However, using only the phase shift causes a high RMS current in the transformer [7,8,9,10,11]. Power semiconductors exhibit increased losses when the input and output voltage ratios of the DAB converter differ from the turns ratio of the transformer. If the voltage ratio differs from the turns ratio of the transformer, circulating currents may be generated, and be limited to the zero-voltage switching (ZVS) region [9]. These issues increase losses and reduce efficiency in power conversion. To achieve ZVS in a DAB converter, the inductor current should charge and discharge the parasitic output capacitance of the switch. The ZVS boundary is determined by the voltage conversion ratio M and phase shift ratio D of the primary and secondary switches. Additionally, large inductances are required to achieve ZVS under a wide load range, and achieving high efficiency at high loads requires minimal inductance [12]. However, the fixed inductance has a set load range and operating characteristics, and it must be redesigned or manufactured to deliver power that differs from the design value.

A method using a variable inductor and a variable transformer has been proposed [13,14,15,16,17,18,19]. This method improves power conversion efficiency and operating characteristics by changing the inductance. The variable inductance method adjusts the magnetic core’s saturation level by modifying the surrounding windings’ inductive impedance [14,18]. To achieve this, a DC bias current is used to change the inductance according to the control current. Using a variable inductor can extend the ZVS range at light loads and reduce the circulating current at medium loads, thereby improving the efficiency and power flow of the converter. However, this method, which uses a variable inductor with a DC bias current, requires a device that can conduct this current and necessitates an additional inductor. Additionally, the inclusion of a new transformer core structure and an external variable inductor increases the weight and volume, and potentially reduces efficiency. Recent studies on nonlinear inductors have focused on their behavior under real operating conditions, including temperature effects and power density optimization [20,21]. These works provide valuable insights into inductance variation mechanisms, particularly in DC–DC converters and switch-mode power supplies (SMPS). However, they primarily analyze inductors in conventional converter topologies, whereas this study investigates a novel high-frequency transformer with controllable inductance for dual-active-bridge (DAB) converters. By introducing an adjustable core insertion depth, our approach enables dynamic control of inductance without requiring additional external components.

In this study, a novel high-frequency transformer with variable inductance is proposed. The variable inductance is introduced by inserting a core into the transformer. Moreover, the required inductance for power conversion can be achieved using only the transformer without additional inductors, which improves power transmission. The power level of the DAB converter is enhanced by using the variable inductance transformer. The concept of the proposed transformer is verified through finite element analysis (FEA) and a prototype described in Section 2. Then, in Section 3, the proposed high-frequency transformer with variable inductance is applied to the DAB converter to verify the ZVS and output power characteristics. Finally, conclusions are drawn in Section 4.

2. Proposed Variable Inductance Transformer

The DAB converter has full-bridge switches on both the primary and secondary sides and uses a transformer for isolation and conversion ratio. The schematic of the DAB converter is shown in Figure 1. Typically, a DAB converter uses an additional inductor in series with the transformer to obtain the inductance required for power conversion. The fixed inductance of the additional inductor determines the load range and operating characteristics, and it can achieve the inductance required for power transmission. In this study, we aim to improve the operating characteristics and enhance the power level by using a high-frequency transformer with variable inductance to replace the fixed inductance of the additional inductor.

DAB converters generally use single-phase shift (SPS) modulation using the phase shift between the primary and secondary switches, as it is the simplest modulation technique and easily provides ZVS. In the SPS method, power is transferred through an inductor current flowing during the phase shift in the primary and secondary switches. The output power of a DAB converter is determined by the inductor current flow, which is controlled by the phase shift between the primary and secondary bridges [22]. The output formula of the DAB converter is expressed in (1).

$$P={\displaystyle \frac{n{V}_{in}{V}_{out}\varphi (\pi -\varphi )}{2{\pi }^2{f}_s{L}_{lk}}}$$

(1)

The output $P$ of the DAB converter is determined by the turns ratio of the transformer $n$, input voltage $V_{in}$, output voltage $V_{out}$, phase shift $\varphi$, switching frequency $f_s$, and leakage inductance $L_{lk}$. The output range of the DAB converter can be improved if the inductance changes under conditions wherein parameters other than the inductance are the same.

2.1. Conventional Variable Inductance Method

The conventional variable inductance method involves changing the fixed inductance of an additional inductor. This method highlights the benefits of variable inductance in DAB converters, such as improved efficiency, stability, and performance across a wide range of operating conditions. As shown in Figure 2, the inductance is altered by shifting the operating point of the B-H curve of the ferromagnetic material by applying a DC bias current to the control winding, thus changing the permeability and inductance of the core material. However, this method requires an external power source and an additional inductor to carry the DC bias current [13,14,15,16,17,18].

2.2. Proposed High-Frequency Transformer with Variable Inductance

If the inductance of the transformer used in the DAB converter can be varied, power can be transmitted without additional magnetic elements. Figure 3a,b shows the structure of the proposed high-frequency transformer with variable inductance. A variable inductance transformer consists of a transformer core, primary and secondary windings, and an inserted core. The material used for both the transformer and the inserted core is ferrite. This structure entails a core inserted between the primary and secondary coils, and the inductance varies depending on the position of the core. As the core passes through the space between the windings, the inductance changes, and the core can be inserted up to 50 mm. The proposed method can satisfy the inductance requirements for power transmission without requiring an additional inductor.

The inductance of a high-frequency transformer is influenced by the permeability and its insertion depth of the core. When a core with higher permeability than the air gap is inserted between the primary and secondary windings, the inductance increases. To quantify this relationship, an equivalent magnetic circuit model is applied. In this model, $l$ and $A$ represent the effective length and cross-sectional area of the air gap between the windings, respectively, while $l_c$ denotes the equivalent length of the inserted core. The parameters ${\mu }_0$ and ${\mu }_c$ correspond to the vacuum permeability and the permeability of the inserted core, respectively.

The inductance as a function of insertion depth can be expressed as follows:

$$L={\displaystyle \frac{{\mu }_0{N}^{2}A}{(l-l_c)}}+{\displaystyle \frac{{\mu }_c{\mu }_0{N}^{2}A}{l_c}}$$

(2)

In this equation, the first term represents the contribution of the remaining air gap, while the second term accounts for the additional inductance introduced by the inserted core. As the insertion depth increases, the inductance also increases.

Figure 4 shows the FEA simulation results of the magnetic flux density based on the position of the inserted core. It represents the central cross-sectional area of the proposed transformer and illustrates the interaction between thpe transformer core and the inserted core. When the core is inserted, the main flux generated in the transformer core leaks due to the influence of the inserted core, resulting in leakage flux. The leakage flux increases as the core is inserted deeper and has an opposite direction to the main flux. By adjusting the depth of the inserted core, the influence of the leakage flux can be controlled.

Figure 5 shows the FEA simulation results of magnetic flux density at different core insertion depths. As the auxiliary core insertion depth increases, the magnetic flux distribution is altered, leading to changes in localized flux density near the core edges. This variation is particularly noticeable in regions adjacent to the inserted core, where fringing effects become more pronounced. The increased flux concentration near the edges may result in higher eddy current losses in conductive materials nearby. The analysis confirms that while fringing effects are present, the overall impact on efficiency remains within an acceptable range.

The FEA simulation results in

Table 1. FEA simulation results of loss analysis according to core insertion depth.

Core Depth	Parameter	Joule Loss	Iron Loss	Hysteresis Loss	Total Loss
$0 \mathrm{m}\mathrm{m}$	Transformer Core	$0.0000 \mathrm{W}$	$0.9425 \mathrm{W}$	$0.9425 \mathrm{W}$	$6.0156 \mathrm{W}$
	Inserted Core	$0.0000 \mathrm{W}$	$0.5614 \mathrm{W}$	$0.5614 \mathrm{W}$
$10 \mathrm{m}\mathrm{m}$	Transformer Core	$0.0000 \mathrm{W}$	$0.9060 \mathrm{W}$	$0.9060 \mathrm{W}$	$9.4733 \mathrm{W}$
	Inserted Core	$0.0586 \mathrm{W}$	$1.4623 \mathrm{W}$	$1.4038 \mathrm{W}$
$20 \mathrm{m}\mathrm{m}$	Transformer Core	$0.0000 \mathrm{W}$	$0.8782 \mathrm{W}$	$0.8782 \mathrm{W}$	$12.9341 \mathrm{W}$
	Inserted Core	$0.2111 \mathrm{W}$	$2.3553 \mathrm{W}$	$2.1442 \mathrm{W}$
$30 \mathrm{m}\mathrm{m}$	Transformer Core	$0.0000 \mathrm{W}$	$0.8676 \mathrm{W}$	$0.8676 \mathrm{W}$	$14.3120 \mathrm{W}$
	Inserted Core	$0.2707 \mathrm{W}$	$2.7104 \mathrm{W}$	$2.4397 \mathrm{W}$
$40 \mathrm{m}\mathrm{m}$	Transformer Core	$0.0000 \mathrm{W}$	$0.8485 \mathrm{W}$	$0.8485 \mathrm{W}$	$14.0887 \mathrm{W}$
	Inserted Core	$0.2322 \mathrm{W}$	$2.6737 \mathrm{W}$	$2.4415 \mathrm{W}$
$50 \mathrm{m}\mathrm{m}$	Transformer Core	$0.0000 \mathrm{W}$	$0.8317 \mathrm{W}$	$0.8317 \mathrm{W}$	$13.5059 \mathrm{W}$
	Inserted Core	$0.1844 \mathrm{W}$	$2.5448 \mathrm{W}$	$2.3604 \mathrm{W}$

show the impact of the core insertion depth on different loss components. As the insertion depth increases, the inserted core exhibits higher iron loss and hysteresis loss, while the transformer core loss remains relatively stable. This analysis highlights the influence of magnetic flux distribution on loss characteristics.

Figure 6 shows a prototype of the variable inductance transformer. The transformer proposed in this study is based on the EE 118 core and its inductance is adjusted by inserting an EE 7091 core. The transformer and insert core are composed of ferrite, and the coil is constructed from Litz wire. The specifications are summarized in

Table 2. Specification of Variable Inductance Transformer.

Parameter	Value
Transformer Core Type	$\mathrm{EE} 118 (118\times 86.5\times 35.5 \mathrm{m}\mathrm{m}$)
Transformer Core Magnetic Material	PM11
Inserted Core Type	$\mathrm{EE} 7091 (70\times 45.5\times 19.5 \mathrm{m}\mathrm{m}$)
Inserted Core Magnetic Material	PM11
Winding Type	Litz wire
Primary (1st) Winding Turns	29
Secondary (2nd) Winding Turns	18
Turns Ratio	1.61 (29:18)

.

The core is inserted between the primary and secondary coils of the high-frequency transformer, and the inductance varies depending on its position. The insertion depth of the auxiliary core is a critical parameter in determining the inductance adjustment range and is constrained by the spacing between the transformer windings and the structural design of the core. In this study, the maximum insertion depth set in this study is 50 mm.

The inductance changes as the core moves through the space between the windings. The core can be inserted up to 50 $\mathrm{m}\mathrm{m}$, and the change in inductance depending on the insertion position is illustrated in Figure 7. The inductance varies from 97.5 $\mathsf{\mu }\mathrm{H}$ to 29.7 $\mathsf{\mu }\mathrm{H}$, with a variation range of approximately 70%.

2.3. Zero-Voltage Switching Operation of DAB Converter

The DAB converter is an isolated, bidirectional DC–DC converter that utilizes Zero-Voltage Switching (ZVS) to minimize losses in both primary and secondary switches. ZVS is activated at the switch turn-on, allowing the inductor current to charge and discharge the parasitic output capacitance of the switches. The ZVS boundary, as depicted in Figure 8, is defined by the operating conditions of the primary switch (3) and secondary switch (4) which correspond to the voltage conversion ratio M and the phase shift ratio D [23].

$$D>{\displaystyle \frac{M-1}{2M}}$$

(3)

$$D>{\displaystyle \frac{1-M}{2}}$$

(4)

Utilizing a variable inductance transformer improves the power level and achieves ZVS operation. Replacing the fixed inductor with a variable inductance transformer can be used as an additional control parameter for the efficient power transfer of the converter.

3. Simulation and Experimental Results

Figure 9 shows the ZVS operating point as the inductance changes. Cases 1 to 3 represent the inductance change conditions when the voltage conversion ratio is the same for each phase shift. In the DAB converter, the ZVS operating point can be changed when the inductance changes under the condition that other parameters are the same. In each case, the power level increases for a constant voltage conversion ratio as the inductance decreases. Therefore, the power level rises from 41.9 $\mathrm{W}$ to 299 $\mathrm{W}$ with the inductance change. The change in inductance increases the power level and the ZVS operating point. The variable inductance can be used as a parameter for ZVS operation.

Figure 10 shows the simulation waveform under case 2 conditions. When the inductance changes from 97.5 μH to 29.7 μH, the inductor current increases, satisfying the ZVS condition at the secondary switch’s turn-on. As the inductance decreases, the secondary voltage increases, increasing the voltage conversion ratio. The simulation results show that the voltage conversion ratio increases, the power is improved, and the ZVS condition can be achieved by changing the inductance.

Figure 11 shows the experimental configuration of the DAB converter using a variable inductance transformer. A DC power supply and a DC load were used, the waveform was monitored with an oscilloscope, and the power was measured with a power analyzer. The DAB converter used a SiC MOSFET, and the switching frequency was 100 kHz. The variable inductance transformer utilized the inductance characteristics that change depending on the core insertion position. The power transfer characteristics were confirmed when the core insertion position was changed, and the inductance was changed under the same conditions as the remaining parameters and experimental conditions. The specifications of the DAB converter are presented in

Table 3. DAB Converter Specification.

Parameter	Unit	Value
Input Voltage	V	100
Output Voltage	V	40~62.5
Switching Frequency	kHz	100
Leakage Inductance	μH	29.7~97.5
Dead Time	ns	380
Load Resistance	Ω	25

, and the experimental equipment used in this study is presented in

Table 4. Experimental Equipment Details.

Equipment Name	Manufacturer	Model Number
DC Power Supply	Faith (Shenzhen, China)	FTB9120-1000-40
Oscilloscope	Tektronix (Beaverton, OR, USA)	DPO3034
Power Analyzer	N4L (Leicester, UK)	PPA4530
DC Load	Faith (Shenzhen, China)	FT68206AL-1200-180

.

Figure 12 shows the output power of the DAB converter according to the core insertion position of the variable inductance high-frequency transformer. The inductance of the transformer changes according to the core insertion position, and the experimental results show that the power supply range of the DAB converter is improved from 42 W to 259 W, depending on the position of the inserted core. The operating waveform of the DAB converter is shown in Figure 13. Under the case 2 conditions, the experimental results are the same as the simulation results, confirming that the variable inductance transformer can expand the power and achieve ZVS in the DAB converter.

4. Conclusions

This study proposes a high-frequency transformer with variable inductance by inserting auxiliary cores into the primary and secondary windings. The core-inserted variable inductance transformer can satisfy the leakage inductance requirement using only the transformer without additional inductors. The magnetic characteristics of the transformer that change with the inserted core were analyzed through finite element analysis (FEA), and a prototype was fabricated to verify the inductance change experimentally according to the core insertion.

The proposed variable inductance transformer was applied to a DAB converter to verify its operation. The effectiveness of the proposed transformer was verified by experimentally applying it to a widely used DAB converter. The proposed method improved the ZVS operation of the DAB converter and extended the output power range. By improving the ZVS operation, the variable inductance transformer can be applied to a wide load range and can achieve high efficiency in the DAB converter.

This paper presents a method to improve the output of the DAB converter by using a novel structure of a variable inductance high-frequency transformer with inserted cores. The proposed variable inductance high-frequency transformer can achieve the inductance required for power transmission by inserting the core into the existing transformer structure without connecting additional inductors. Based on the analysis, the core-inserted variable inductance high-frequency transformer is expected to be the most attractive regarding the wide inductance variation range. This paper provides a method to achieve the required inductance in power conversion devices by using the existing transformer without additional magnetic elements. The results of this paper focus on improving the operational stability of the DAB converter and contributing to the degree of freedom and wide operating range.