In this paper, a new three-winding planar transformer design with the integrated leakage inductor is proposed for a triple-active-bridge converter. It enables two output voltage levels: a high voltage (HV) output port and a low voltage (LV) output port. The primary and secondary windings are split unevenly in both side legs while the tertiary winding is connected in parallel. The unique winding configuration enables: (i) enhanced efficiency with low volume; and (ii) suppressed parasitic capacitances. Detailed transformer reluctance and loss models are developed in the design process. The core geometry is optimized using a reluctance-model-based mathematical computation. Moreover, comprehensive high-fidelity simulations are conducted to analyse the trade-offs among parasitic capacitances, losses, and inductances. The customized core and the non-overlapping winding boards are assembled, characterized, and tested under various power flow conditions.
Transformers play a vital role in power electronic systems to facilitate electrical energy transfer and provide galvanic isolation. A typical transformer is composed of a magnetic core, and two coupled windings that are connected to an input port and an output port . However, with the increasing demand for highly compact and integrated power electronic interfaces, multi-winding transformers have gained great attention to achieve the electrical integration with fewer component counts and capability of providing additional operation modes [2, 3]. Compared to the two-winding transformer, multi-winding transformer enables higher power density, reduced cost, and flexibility in different operation modes. For instance, various DC-DC converters can be integrated through a multi-winding transformer [3-6], in order to reduce volume, cost, and enhance power conversion efficiency.
Research has been conducted in multi-winding transformers in the literature [7-10]. A split-winding transformer structure is proposed in  to realize the multi-port integration. The minimum leakage inductance is achieved through a mathematical model. The leakage magnetic field energy is computed to screen out all possible winding configurations. Compared with simply interleaving primary and secondary windings in two winding transformers, this method is able to realize the traversal of all the possible configurations while maintaining low winding losses. However, in this design, the leakage inductance cannot be large enough to account for the required shim inductance in the phase-shifted based and resonant converters. Meanwhile, since the system is operated at low power and low switching frequency, the parasitic capacitance caused by the interleaved winding structure is ignored in the transformer design; while our proposed design considers a gallium nitride (GaN) based design, where transformer parasitics play a vital role in achieving desired converter operation. Furthermore, a Litz-wire based integrated transformer using EE-shape core is proposed in . The primary winding is located on one side of the EE cores while the secondary winding is placed on the other side. The tertiary winding is located above the secondary winding. The air gap between primary and secondary windings is utilized to ensure appropriate leakage inductances. However, the winding loss can be significant considering the monotonic magnetomotive force (MMF) distribution in each winding. Recently, a low-profile two-winding planar transformer is proposed in  using a split winding structure to reduce winding resistance while maintaining the required magnetizing inductance. The leakage inductance is controllable by adjusting the length of air gap or the cross-sectional area of the centre core leg. However, this proposed winding layer configuration is not applicable to a three-winding structure due to the unbalanced flux. In , a hand-wound three-winding transformer is proposed; however, the power rating and the performance is limited by the implementation of the Litz wires.
In addition, to achieve an optimal transformer design, prior efforts have been made using different analytical methods [11-13]. Using the concept of flux cancellation, an integrated transformer with leakage inductance is established and optimized in  based on the equivalent flux model. However, parasitic capacitances are not fully examined in this design process, which may lead to the distorted operation waveforms. In , a comprehensive approach considering the trade-off between the losses and footprint area is proposed for the PCB-integrated inductors and transformers. However, this approach cannot be used to design the integrated planar transformer with a three-winding structure due to the model limitations. Furthermore, the work in  discusses a systematic transformer design method using the genetic algorithm for medium-frequency applications, which satisfies all the design requirements with minimum iterations. However, this design approach might not be applicable to high-frequency wide bandgap GaN and SiC based converters.
In this work, a new three-winding planar transformer design is proposed for a three-port triple-active-bridge (TAB) converter. The primary and secondary windings of the transformer are split unevenly in both side legs. The reasons behind winding in two side legs are: (i) to compensate the magnetizing inductance reduction due to the proposed side-leg interleaved structure; (ii) to obtain a controllable leakage inductance; and (iii) to provide enough winding turns. The planar transformer with the proposed PCB winding configuration is utilized to improve the manufacturability, power density, and efficiency. A systematic transformer loss model, including both core and winding losses, is investigated. Magnetizing and leakage inductances are obtained from both the analytical model and simulation. In addition, a parasitic capacitance study is conducted. Consequently, a multi-objective optimization problem is formulated to optimize the integrated transformer design considering core geometry, losses, and inductances. The objective is to determine a set of core and winding specifications to achieve minimum transformer loss. It is worth mentioning that the traditional approach of using a three-winding transformer with a centre leg with twice width of the outer legs [4, 5] is not suitable in this case due to the inherently unbalanced flux distribution of the core. Finally, the optimal design is accomplished as a customized core, which is experimentally verified.
This manuscript is organized as follows: Section 2 discusses the basis of the three-winding transformer, including the reluctance model and study of the parasitic capacitance. Moreover, comprehensive high-fidelity simulations are conducted to analyse the trade-offs among parasitic capacitances, losses, and inductances. Thus, a transformer design optimization problem is formulated. The objectives are to minimize the total loss incurred in the transformer concerning the geometrical parameters and electrical parameters, and to achieve the smallest possible volume and weight. Section 3 presents the experimental results to validate the proposed transformer design. The Section 4 puts forward conclusions with relevant discussions.
2 INVESTIGATION OF THE THREE-WINDING TRANSFORMER
A conventional three-winding transformer  is composed of three non-interleaved windings across the centre leg using wire-wound configuration, as shown in Figure 1. However, this design has the following drawbacks: (i) the winding AC resistance is relatively large, leading to the increased loss with large amounts of winding currents, which significantly decreases the efficiency and may require a demanding thermal solution. More specifically, since the magnetomotive forces (MMFs) across each winding sum up in the end, the AC resistance would be substantially large in the middle point; (ii) the Litz wire-based winding configuration makes it difficult to achieve the leakage inductance control as it is highly sensitive to the relative displacement between primary and secondary windings, which is difficult to adjust precisely; (iii) the tertiary winding is made of copper bar and needs massive labour, making it difficult for manufacturing; (iv) the height of wire-wound transformer increases the volume of the system.
A split winding structure using EE core is proposed to resolve the aforementioned issues, as shown in Figure 2, where the primary and secondary windings of the transformer are split unevenly in both side legs; and the two tertiary windings are connected in parallel to maintain the flux balance. Note that the primary and secondary windings are asymmetrically interleaved on two legs, which is extremely difficult to achieve through a wire-wound transformer due to the complexity of the winding routings. Furthermore, this split winding configuration can help achieve a controllable leakage inductance while maintaining the sufficient magnetizing inductance for the converter operation.
As shown in Figure 2, top two boards 1 and 2 are composed of the primary and secondary windings while all the tertiary windings are located in the bottom board 3, where the distances between the boards are denoted as and . The layer change for the same winding is realized by the vias, while both left and right PCB layers with the same vertical height share the same PCB board. The width and height of side legs can be adjusted to reduce the core loss while maintaining enough magnetizing inductance. The increase of the thickness reduces the effective reluctance and core loss, however, it leads to a smaller window area. The width ratio between the center and side legs contributes to the core loss and the leakage inductance. The centre leg confines the leakage flux path, which is determined by the reluctance of the centre leg air gap. If the centre leg air-gap reluctance is large, less leakage flux will flow through it, resulting in smaller leakage inductance. Consequently, the leakage flux in the proposed magnetic structure is confined within the core instead of air. The confined flux can contribute to less radiated EMI and eddy current loss in the surrounding metals. With the increase in switching frequency (from 100 kHz to 500 kHz to 1 MHz), the reduction on radiated EMI and eddy current loss plays a key role in improving the system performance . The coupling structure between the primary and secondary windings gives additional control freedom in the mitigation of the common mode (CM) noise.
2.1 The planar transformer loss model
2.1.1 The core loss model
Considering the asymmetrical structure of the integrated transformer, a comprehensive transformer core loss model based on the proposed winding structure is established to achieve more accurate results using the magnetic equivalent circuit. This core loss model includes the leakage flux path from both windings and air gap, while splitting the location of magnetic flux path from the side legs and the centre leg. Three current sources are considered to form the equivalent magnetic circuit, where the reluctance is obtained from each leg piece to improve the accuracy of the model.
2.1.2 PCB winding loss
Regarding the PCB winding, the winding loss is mainly determined by the MMF distribution, which means that the winding layer structure needs to be carefully considered. The MMFs are suppressed using the interleaved winding structure, where the primary and secondary windings are asymmetrically placed in both side legs. For , the proposed winding structure along with the MMF distribution is demonstrated in Figure 4.
Moreover, only the bottom two layers have the non-interleaved windings in the left leg, and the top two layers in the right leg have non-interleaved windings. This kind of winding configuration takes the advantage of interleaving to reduce the winding loss while maintaining the flexibility of magnetizing and leakage inductances control.
Meanwhile, the winding loss can be further reduced by settling the layer thickness less than the skin depth, which allows the effective cross-section area to be increased. Considering the high current rating, the tertiary windings can be split into two parts and wound around the side legs to maintain the flux balance.
2.2 The parasitic capacitance study
The parasitic capacitance of the planar transformer can lead to many issues, including the winding current/bridge voltage waveform distortion, unexpected voltage gain, increased EMI noise, and reduced power conversion efficiency. This is in particular of significant importance in wide bandgap GaN and SiC semiconductor-based converters, as the slew rate of turn-on and turn-off of switches is very high. The converter zero-voltage-switching operation is sensitive to the transformer parasitic capacitance. Thus, it is necessary to conduct a thorough study on the parasitic capacitance mitigation based on the proposed transformer structure. The simplified equivalent parasitic circuit is shown in Figure 5. The inter-winding capacitance refers to the parasitic capacitance between primary and secondary windings, which has little effect in distorting the waveforms; however, the intra-winding capacitance contributes to the waveform distortion.
2.3 System level co-design
Considering all the aforementioned factors, a comprehensive system level transformer co-design is achieved. First, the turns ratio evaluation is conducted to investigate the relation between the parasitic capacitance and the circulating power, as shown in Figure 6. OBJ is denoted as the current objective function, which is three winding current RMS square summation. It is observed that both the objective function (formed by the circulating power) and the winding loss function are negatively related to the turns ratio. A high turns ratio between primary/secondary and tertiary windings is needed to integrate with different energy sources. For instance, the onboard charger and the auxiliary power module for electric vehicle applications can be integrated using the proposed structure: 400 V for HV output port-1 (secondary) and 12 V for LV output port-2 (tertiary). On one hand, higher step-down turns ratio help reduce the circulating energy in the tank. On the other hand, increasing turns ratio leads to increasing the parasitic capacitance due to the increased overlapping area. It is worth mentioning that although more winding turns lead to more winding resistance, considering the reduced winding current, the winding loss is in fact reduced. In other words, the control burden can be relieved with the high step-down turns ratio. Thus, the turns ratio 16:16:1 for the primary/secondary/tertiary is selected considering conduction loss and manufacturing capability, which can be realized by stacking two 8 layers PCBs. PCBs with more than 8 layers are not preferred due to the high manufacturing cost, especially for high-power applications.
Apart from turns ratio, the overlapping area between adjacent layers contribute to the parasitic capacitance and winding loss. A series of simulation studies are conducted in ANSYS to analyse the relationship between the overlapping area, winding loss, magnetizing inductance, core loss, and parasitic capacitance. Windings with 5.5 mm PCB trace width with 3 oz copper thickness are selected in the study. The transformer 3D model for high fidelity simulation model is shown in Figure 7.
A high-fidelity simulation is conducted, where the PCB trace model is directly extracted from the PCB layout software. The parameter variations on the PCB trace overlapping between the primary and secondary windings are achieved using the ANSYS optimetrics analysis. It is observed that the core loss is not varied in a large range with different overlapping displacements. However, with the decrease of the PCB overlapping area, the copper loss increases due to the non-negligible proximity effect while the parasitic capacitances are reduced. Moreover, the displacement range is not only determined by the PCB trace width, but also is related to the core geometry, where the minimum clearance requirement between the core and the winding board needs to be satisfied. The window area inherently confines the maximum trace width. To better understand the trade-offs, two cases of the PCB winding configurations are selected and manufactured for the laboratory testing, which are marked in red and green colour in Figure 8. The green colour case refers to the fully non-overlapping and the red colour case refers to the fully overlapping.
Furthermore, the trade-off between the trace overlapping displacement and the winding resistance needs to be analysed. Note that the AC resistance is determined by the effective conduction area, which is related to the current density. Figure 9 illustrates the FEA simulation results of the current density distribution in the PCB windings. It is observed that the current density increases when the non-overlapping-structure is implemented. As can be seen from Figure 9a, the split structure merits the parasitic capacitance because of the minimum overlapping area. However, the current vector is concentrated in the adjacent terminals between the primary and secondary windings, which results in lower effective conduction area and higher winding resistance. In Figure 9b, the current density is distributed along with all the sections, which leads to a lower winding resistance.
2.4 Transformer design optimization
Considering the proposed transformer performance model including loss, inductance, and parasitic capacitance, a multi-objective optimization process is conducted to achieve the optimal design. The fixed design parameters are winding turns, turns ratio, magnetizing and leakage inductances, as well as core materials. Given the operation frequency (100 kHz), PC95 from TDK is selected due to its lowest core loss density at 100 kHz. In order to identify the candidates in terms of loss, volume and weight, the tuning variables for the optimization process are selected as effective volume, air gap length, cross-sectional area, core geometry, magnetizing and leakage inductance, width and thickness of PCB winding, as well as winding layer distribution. The flowchart describing the transformer optimization process is shown in Figure 10.
Figure 11a shows the 3D surface of magnetizing inductance with two independent variables from geometry parameters. Given the fixed value of air gap length, the requirement for the minimum magnetizing inductance applies an additional restriction for the transformer design, which helps define the optimal solution with air gap length iteration. The shim inductance design target is 18–20 μH from the power transfer requirement.
Thus, the core geometry dataset is computed using the optimization method, given different dimension constraints. As indicated, there is a trade-off among the volume, magnetizing inductance, and core loss. Due to the plotting variable limitations, two factors, core loss and magnetizing inductance, are plotted using the simplified winding model, as shown in Figure 11b. The selected core geometry has a balanced performance in core loss and magnetizing inductance. Given the desired magnetizing inductance range, the core volume is minimum compared to other adjacent core options.
2.5 Towards very high switching frequency operation
Increasing switching frequency further beyond 100 kHz can potentially reduce the core size of the transformer leading to a highly compact design. However, the winding loss at higher switching frequencies can be substantially increased. In a conventional centre-leg-wound transformer , the leakage inductance is achieved using the energy stored in the air gap between adjacent winding boards, as demonstrated in Figure 12. Thus, it is difficult to implement the interleaved winding structure as it significantly reduces the maximum achievable leakage inductance. Unlike the proposed transformer design, the conventional centre-leg-wound transformer cannot achieve an asymmetrical winding structure to maintain the desired leakage inductance.
To illustrate the effectiveness of the proposed three-winding transformer design at higher switching frequencies, a frequency sweep is conducted to analyse the AC winding resistance. The sweep ranges from 100 kHz to 1 MHz with a step size of a 100 kHz. Figure 13 shows the comparison between the proposed side-leg-wound transformer and the conventional centre-leg-wound transformer counterpart with similar specifications. The Y-axis units represent the percentage increase in AC resistance compared to the 100 kHz design.
A significant increase in AC resistance is observed in the conventional centre-leg-wound transformer when increasing the switching frequency. This would affect heavily on the transformer conduction losses and thermal performance. Meanwhile, the proposed side-leg-wound transformer is able to keep the AC resistance variation minimal with the increased frequency due to the interleaved asymmetric winding structure. This result suggests that the proposed transformer design process is extendable to high frequency operation, that is, 500 kHz to 1 MHz.
3 EXPERIMENTAL VERIFICATIONS
The detailed geometrical parameters of the proposed transformer core are shown in Figure 14a. Given the customized core dimensions, two cases of the winding designs are achieved: non-overlapping and fully overlapping. The finished board thickness is around 4 mm with immersion silver technique, where the dielectric layer thickness is maximized considering the manufactory capability. The layer change terminals are minimized as they reduce the effective winding turns. The assembled integrated planar transformer is shown in Figure 14b. The copper bars are utilized as the spacers and connectors.
As can be seen from Figure 15, the tertiary winding board with 4 layers in parallel forms a "W" shape PCB trace, where the left leg winding is connected in parallel with the right leg to increase the ampacity. Moreover, since the adjacent layer is not utilized, the intra-winding capacitance is reduced in the tertiary winding.
The impedance analyser Keysight E4990A with a wide frequency range of 20 Hz to 120 MHz is utilized to characterize the transformer. Both open and short circuit tests are conducted for the overlapping and non-overlapping winding boards.
One-layer tape-based air gap is employed to obtain the required leakage inductance. Thus, the parasitic capacitances, the leakage inductance, and the magnetizing inductance can be extracted using the equivalent model. With open circuits in both secondary and tertiary windings, and are measured across the primary winding. With short circuits in both secondary and tertiary windings, are measured across the primary winding. The measured results are summarized in Table 1.
The measured intra-winding capacitances are consistent with the FEA based estimations. It is observed that higher parasitic capacitances are formed in the non-split winding board. The intra-winding capacitance is reduced to 0.3 nF in the split winding structure.
The three-winding transformer is tested with a GaN based three-port DC-DC converter, with one input power source and two output loads. It enables two output voltage levels: 400 V for HV output port-1 (secondary) and 12 V for LV output port-2 (tertiary). As shown in Figure 16, the tertiary winding current is measured as 39.3 A. The power distribution of this testing condition is: = 2095 W, = 290 W, where refers to the high voltage output port and refers to the low voltage output port. The HV load resistance is 47 and the LV load resistance is 0.33. It is observed that there is some ringing in the tertiary bridge voltage, which is caused by the parasitic capacitance in the tertiary side.
Moreover, the power conversion efficiency of the proposed transformer is measured using the Tektronix PA3000 power analyser. To analyse the transformer loss, a subtraction-based method is implemented. First, all winding current RMS values are measured. By subtracting the semiconductor loss and capacitor loss from the total power loss, the transformer efficiency is obtained, as shown in Figure 17.
The thermal images of the transformer and the hardware prototype operating in G2B mode with a power rating of 2.5 kW are shown below, which include the side-view of the transformer to capture the thermal distribution across all three transformer PCBs. In Figure 18a, the highest temperature of the proposed transformer is observed to be 39.1 °C located at the middle board of the transformer stack with the forced air cooling. The core temperature is observed to be 28.4 °C. In Figure 18b, the thermal image of the entire hardware prototype (top-view) is illustrated. The LV side circuit uses bottom-cooled switches without heatsink. The highest temperature is observed to be 33.9 °C at the LV side trace due to the ohmic losses induced by high currents.
Furthermore, a comprehensive comparison between the simulation and the experiment is investigated, as shown in Table 2. The transformer loss from the experiment is obtained through the loss breakdown as it is difficult to measure the winding and core loss separately. The transformer loss from the simulation is obtained through ANSYS, where the core loss is 10 W and the winding loss is 72 W. It can be observed that the error is less than 10%.
Moreover, a comparative study of transformer loss between the proposed transformer design and other existing studies, as shown in Table 3. Note that the design space parameters including turns ratio, power rating, and volume in the multi-winding transformer and the optimization objective varies in different cases.
In this work, a new three-winding planar transformer design is proposed, which can be used within any three-port isolated converter. It enables two output voltage levels with high step-down ratios. Detailed transformer reluctance and loss models are developed to synthesize a systematic design approach. Moreover, co-simulation is conducted to analyse the relationships among parasitic capacitances, losses, and inductances. The optimized three-winding transformer design is achieved considering the trade-off among the loss, magnetizing and leakage inductances, parasitic capacitance, and volume. The customized core and the non-overlapping winding board are assembled and tested. The proposed transformer is tested up to 2.5 kW with the peak efficiency of 98%. It is reported that the error between the simulation and the experiment is less than 10%. The proposed transformer design process is extendable to very high frequency operation, that is, 500 kHz to 1 MHz.
This work has been partially sponsored by the Maryland Innovation Initiative Grant, which is gratefully acknowledged.
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