1. Introduction
High-power densities have become a design requirement for power conversion units, especially in high-restriction applications, such as offshore wind farms and traction systems [
1]. To accomplish this objective, heavy low-frequency transformers should be altered with high-power DC-DC converters comprised of lightweight and compact high-frequency transformers. However, when subjected to higher frequencies, one must contend with additional losses due to the eddy current in the magnetic core [
2], winding losses due to enhanced skin and proximity effects [
3], and parasitic elements, such as winding capacitance and leakage inductance [
4] producing excess switching losses, which are typically foremost at higher frequencies [
5].
Dual active bridge (DAB) converters are becoming extremely popular for use in high-power applications [
6].
Figure 1 depicts the equivalent circuit of a DAB converter in which the output signal of the input and output bridges is a square wave form with a nominal phase shift. This provides voltage to the inductance
LK, which is utilized as a power transfer element to shape the current [
7]. To accomplish zero-voltage switching (ZVS), the phase shift between the bridges must be greater than a specified value [
8], which results in a minimum value for the series inductance calculated as:
where
VDC and
Vout are the input and output DC voltages, respectively, and
is the phase shift between the primary and secondary voltages of the high-frequency transformer depicted as the key element of the DAB converter and is the ratio of the primary voltage to the secondary voltage.
Pout is the intended output power,
n is the number of turns of the high-frequency transformer, and
fs is the operating frequency, also known as the switching frequency.
This inductance, as seen in
Figure 1, may be viewed as an integrated leakage inductance,
Lk, in the high-frequency transformer, allowing for a reduction in the number and size of components [
9]. Consequently, it is crucial to precisely estimate the leakage inductance of a transformer during the design phase, as an inadequate leakage inductance causes a shift in the soft-switching area, which might have a negative impact on the converter’s efficiency. Similarly, high-leakage inductance is undesirable since it results in an undesired reactive power circulation inside the converter, which ultimately reduces the converter’s efficiency and output active power, but can widen the soft-switching zone to some extent.
Leakage inductance is a small inductive element which occurs due to improper coupling of flux between one winding and the other. Leakage inductances play a vital role in switching-based power supply resulting in less switching current in the device and the energy stored in it results in switch voltage spikes. Similarly, due to creation of EMI, switching losses increase and hence efficiency of the system decreases [
10,
11,
12,
13]. Furthermore, parasitic capacitances cause the infusion of currents due to high frequency, hence amplifying electromagnetic interferences (EMI) and can establish electrostatic connection with other circuit components. The system’s switching waveforms and efficiency can be improved by reducing two parameters, i.e., parasitic capacitance and leakage inductance [
14]. Switching frequency in modern technologies is increasing from kHz to MHz in order to minimize the size of inductive components and accurately estimate the high-frequency leakage inductance necessary for the appropriate design of a system. This is done in order to fulfil the requirements of the proper design of a system [
15].
Several research articles have been published on the calculation and analysis of leakage inductance on the planer and conventional core-type or shell-type transformer [
16,
17,
18,
19,
20,
21,
22,
23]. However, the major problem in these articles is the operation at low frequency. It is being concluded in most of the cases that leakage inductance is independent of frequency and current which is uniformly distributed. In fact, leakage inductance is reduced when frequency is increased [
24].
The size of passive components reduces with increase in frequency and hence help in the downsizing of a transformer. However, at higher frequencies, the parasitic components become dominant and accurate calculation of the parasitic parameters is required to achieve better results in resonant converters. Undesirable leakage inductances and parasitic capacitances can disrupt the design and create unwanted resonant frequencies, leading to voltage and current waveform distortion and reduced efficiency. This may also cause a disruption in the control system [
25]. High-frequency transformer design is a key step for proper working of isolated DC-DC choppers and appropriate core geometry and winding arrangements must be adopted to manage the factors depending upon its applications. Various transformer core geometries and winding configurations result in varying parasitic characteristics. It is vital to comprehend the parasitic parameters of different transformers and their applications require optimizing of these parasitic parameters [
26,
27].
Figure 2 depicts the schematic diagram of a single-phase 2D toroidal transformer.
In this article, the design of a toroidal transformer is conducted using ANSYS-Maxwell software, 2022 R2, (licensed for NUST, Pakistan) to recognize an FEM-based solution for various transformers. The main objective of this study is to design a high-frequency toroidal transformer in ANSYS-Maxwell, study the leakage inductance of different configurations of windings and use the designed toroidal transformer in a DAB converter.
Scope of the research article:
The scope of this research work is as follows:
A high-frequency toroidal transformer is developed using FEM instead of a shell-type or core-type for a dual active bridge (DAB) converter.
Leakage inductance is a major factor in reducing the power transfer in the DAB converter, therefore leakage inductance as a function of frequency is studied under different scenarios and minimized leakage inductance is obtained.
Other parameters, such as magnetic field lines, magnetic flux density and intensity are discussed and compared with the shell-type transformer. As a result, the best possible uniform parameters are obtained in the case of the toroidal transformer.
A reduced leakage-inductance-based toroidal transformer is used in a DAB converter and the simulated results are validated with the help of an experimental prototype.
4. Transformer’s Magnetic Flux Density, Intensity and Flux Lines
For the steady-state scenario, analysis of a magnetic field density (B), magnetic field strength (H) and magnetic flux lines (A) of a toroidal transformer proposed in this section have been discussed.
Figure 8 shows an input voltage simulation waveform for analysis.
Boundary conditions for the design of a toroidal transformer, geometric dimensions, and attributes of all materials utilized are defined in the model using the 2D environment of ANSYS MAXWELL.
Table 3 shows the electrical data that was used in the transformer study and design.
Figure 9 depicts the magnetic flux density of a toroidal transformer as designed in the ANSYS MAXWELL 2D environment.
The magnetic field strength is also determined by the research study.
Figure 10a depicts a high magnetic field at the core, whereas
Figure 11 depicts homogenous magnetic flux lines. Excessive stress and strain on the winding is obvious from
Figure 10b, which can cause insulation to degrade or even deform [
32], whereas the toroidal transformer showed less winding stress compared to the shell-type.
5. Leakage Inductance of a Toroidal Transformer
To compare the computation and finite element analysis (FEA) simulation, the magnetic core of ferrite material was chosen. Using Ansys/Maxwell, the FEA simulation was conducted using 2D rotational symmetry.
At low frequency, the magnetic field strength (H) within the conductors was linearly distributed. As the frequency increased, the high-frequency eddy current effect led the current density to be nonuniform in the cross section of the conductor, and the majority of the currents concentrated on the conductor’s surface [
24]. As the number of layers grew, the proximity effect accelerated the movement of conductor currents toward the surface. As illustrated in
Figure 12, the magnetic field strength (H) developed the “concave form” at high frequency, particularly for a large number of layers.
Consequently, the leakage inductance was drastically decreased as the frequency increased. Comparing the high-frequency leakage inductances of the four distinct winding layouts, parametric FEM simulations encompassing a broad range of frequencies were conducted up to 300 kHz. The resultant leakage inductances were then compared to those derived by Equations (8)–(10). The following formulae can be used to determine the leakage inductance for a DAB converter [
33,
34].
Similarly, leakage inductance associated with the leakage flux of a winding can be determined by [
35];
where,
L11 = Self-inductance of winding 1
L22 = Self-inductance of winding 2
LM = Mutual inductance due to one winding on the other.
Table 4 briefly describes the details of the toroidal transformer defined for different cases as described in detail below. High-frequency leakage inductances for the four different winding configurations were compared. DAB converter-based leakage inductance is analytically calculated using Equation (8).
5.1. Case: 1
In this scenario, the current density distribution at 50 kHz and the investigated winding arrangement, illustrated in
Figure 13 consisted of 5 and 120 foil conductors in the primary and secondary winding respectively, two layers and one turn per layer, with a foil thickness of 1.2 mm. All the geometrical dimensions were kept constant while the operating frequency was swept from 50 Hz to 300 kHz. An analysis was performed of the inductance behavior of overlapping windings in cases where they were not entirely distributed around the ring core, and they were not fully overlapped.
The leakage inductance waveforms in
Figure 14 show more significant variation when the coils are in different situations. The individual leakage of each coil was more prominent when it was tightly wounded, and the other coil was more dispersed over the core. On the other hand, when the coils were overlapped and wound close to each other, the leakage was small, consistent with the concept that the leakage flux is intense when the turns of a winding are together, but if another winding is placed overlapping the first one, the secondary winding strongly links with the primary, decreasing its leakage flux. Leakage inductances referred to the primary side were 1.93 and 1.85 uH at 1 kHz and 1 MHz, respectively. The reduction in leakage inductance was 5%.
5.2. Case: 2
In case 2, Primary winding consisted of 15 turns while secondary turns consisted of three layers overlapping each other and contained 375 turns covering the whole core of the transformer as shown in
Figure 15. Since the number of turns were 15 and 375, respectively, one turn of primary coil was placed for 25 turns of secondary coil. The distance between the core and primary and between the primary and secondary winding was the same.
The analysis of the leakage inductance graphs in
Figure 16 represents more significant variation when the coils are in different situations. To cover the core of a transformer, the primary winding is increased and the secondary winding correspondingly increases. Comparing the leakage inductance of the primary side and secondary side, the leakage inductance represents that due to the less-turns ratio, the flux created on the primary results in a completely induced current on the secondary, resulting in less leakage inductance while the flux due to the secondary current results in more flux and hence less current is generated on the output, hence more leakage inductance is produced. Leakage inductance in this scenario was 6.65 at 1 kHz and 5.98 uH at 1 MHz, reducing the leakage inductance by 11%.
5.3. Case: 3
In case 3, 24 turns, covering half of the toroid core of the transformer, were winded on the primary while four layers of secondary winding contained 600 turns, as depicted in
Figure 17. The leakage inductance waveform in
Figure 18 gives us information about the primary flux linkage with the secondary, hence resulting in minimized leakage inductance while the flux created due to the secondary is not completely induced in the primary flux, therefore resulting in higher leakage inductance in comparison with the primary leakage inductance. Leakage inductance at 1 kHz and 1 MHz was 9.5 and 8.2 µH, respectively. The reduction was approximately 14%.
After studying various cases of the toroidal transformer, it was observed that case 3 resulted in less leakage inductance due to an increased number of turns on the primary side and an assumption can be made that proper winding, covering the area of the core and a decreased distance of winding from the core resulted in proper coupling of flux between the two windings and therefore less leakage inductance was produced.