# Optimizing Thermal Design of 75kW LLC Resonant Converters: Leveraging Variable Inductance for Electric Vehicle Converter Applications by Finite Element Analysis

Wai Keung Mo, Kasper M Paasch, Thomas Ebel

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Wai Keung Mo, Kasper M Paasch, Thomas Ebel. Optimizing Thermal Design of 75kW LLC Resonant Converters: Leveraging Variable Inductance for Electric Vehicle Converter Applications by Finite Element Analysis. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0311. hal-05079361

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Submitted on 22 May 2025

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# Optimizing Thermal Design of 75kW LLC Resonant Converters:
Leveraging Variable Inductance for Electric Vehicle Converter
Applications by Finite Element Analysis

Wai Keung Mo¹, Kasper M. Paasch², Thomas Ebel³

Centre of Industrial Electronics/ Department of Mechanical and Electrical Engineering

University of Southern Denmark / Alsion 2, 6400

Sønderborg, Denmark

E-Mail: wkmo@sdu.dk¹, Paasch@sdu.dk², ebel@sdu.dk³

URL: http://www.sdu.dk

## Acknowledgements

This work was supported by Interreg Deutschland-Danmark via the Smart Power Conversion project (ref.16-2,1-221). Find further information on Interreg Deutschland-Danmark on www.interreg5a.eu.

## Keywords

« Thermal design », « Reliability issues », « Magnetic device », « Finite element analysis », « Resonant converter ».

## Abstract

This paper presents a comprehensive analysis of a 75kW LLC resonant converter, focusing on magnetic design and efficiency. The work introduces a novel method for predicting temperature profiles, reducing the need for extensive testing, and saving time and costs.

## Introduction

The growing demand for electric vehicles has led to increased interest in resonant power converters. These converters offer high efficiency, power density, and reduced electromagnetic interference. Advances in semiconductor devices, materials, and thermal management are key to improving resonant converter performance. The transformer and inductor are critical components due to their impact on volume, power loss, and thermal management. This paper focuses on a thermal and power loss analysis of a 75kW phase-shift full-bridge LLC DC/DC resonant converter. A phase-shift active bridge converter is used to control energy flow through the series inductor,

Ls, using phase difference (ø) between v1 and v2. The power flow equation for the PS-active bridge is given in equation (1) below [1]

$$P_{12} = \frac{V_1 V_2}{2nL_s f} \frac{\phi}{\pi} \left(1 - \left|\frac{\phi}{\pi}\right|\right) \quad (1)$$

Where V1 and V2 are the peak voltage of v1 and v2, f is the converter switching frequency, n = Np / Ns is the transformer turns ratio and ø ranges from -π to π. The phase-shift active bridge (PS-AB) converter [2] [3] relies on the energy stored in the series inductor, Ls, to achieve zero-voltage switching (ZVS). However, ZVS can be lost under light load conditions. Adding an external series inductor can help maintain ZVS, but it can reduce efficiency at heavy loads. This paper introduces a novel resonant inductor with variable inductance to address this issue. A finite element simulation using ANSYS Maxwell and Icepak is conducted to analyze the thermal and power loss characteristics of the converter's components, including the switching devices, magnetic components, and capacitors. The goal is to optimize the design for power loss and thermal management, focusing on the transformer and inductor winding solutions.

## 75kW Phase-shift full Bridge (PS-FAB) LLC Resonant Converter

Unlike a phase-shift full active bridge (PS-FAB), a resonant active bridge operates at a variable switching frequency. As depicted in Figure 1, the input full bridge generates a square wave that is applied to the resonant tank. By adjusting the switching frequency, the resonant tank can be tuned to produce varying output voltages. A series resonant active bridge
<figure><img src="image_2.png" /><figcaption>Fig. 1: 75kW phase-shift full active bridge (PS-FAB) LLC DC/DC resonant converter</figcaption></figure>

leverages the energy stored in the transformer's magnetizing inductance, $L_m$, to achieve zero-voltage switching (ZVS). Ideally, the minimum current flowing through $L_m$ during the dead time should be independent of load conditions. However, in practice, it is influenced by the current passing through the magnetizing inductance. Therefore, the ratio of magnetizing inductance to series resonant inductance is critical for maintaining consistent ZVS.

To maximize output power, a four-parallel center-tapped output configuration with full-wave rectification is employed. This approach reduces the current flowing through individual output rectifiers. Similarly, the individual input current passing through the four LLC resonant inductors can be significantly decreased.

This paper focuses on the design of the 75 kW PS-FAB LLC DC/DC converter. The following table presents a selection of FB-LLC converter configurations, each optimized for specific requirements, suitable for finite element simulation.

<table><caption>Table 1: Electrical specification of PS-FAB-LLC converter</caption><thead><tr><th>Parameter</th><th>Test conditions</th><th>Chosen level</th><th>Units</th></tr></thead><tbody><tr><td colspan="4">Input characteristics</td></tr><tr><td>V<sub>m</sub></td><td>Input voltage</td><td>500 to 800</td><td>V</td></tr><tr><td colspan="4">Output characteristics</td></tr><tr><td>V<sub>o</sub></td><td>Output voltage</td><td>366</td><td>V</td></tr><tr><td>P<sub>o(max)</sub></td><td>Output power</td><td>75k</td><td>W</td></tr><tr><td>I<sub>o</sub></td><td>Output current</td><td>205</td><td>A</td></tr><tr><td colspan="4">System characteristics</td></tr><tr><td>η<sub>peak</sub></td><td>Peak efficiency</td><td>V<sub>in</sub>=800V, V<sub>out</sub>=366V, I<sub>o</sub>=205A</td><td>97 %</td></tr></tbody></table>

## Simulation results

A power loss analysis was conducted for the four main switches in the full bridge, eight output rectifiers, and magnetic components (four LLC series resonant inductors and four LLC transformers). All results are based on the following simulation conditions: $P_0$ = 75 kW, $V_0$ = 366 V, $I_0$ = 205 A, and individual transformer efficiency = 94%. Consequently, the individual output current flowing through the eight output rectifiers is 25.63 A, and the input current passing through the four resonant inductors is 54.5 A. Assuming equal current distribution among the output and input components, all simulation results were obtained using ANSYS Simplorer in conjunction with ANSYS Maxwell (for the simulation of nonlinear LLC transformer and LLC resonant inductor) illustrated in Fig. 2.

<figure><img src="image_3.png" /><figcaption>Fig. 2: Simulation result of output power curves</figcaption></figure>

## Converter Efficiency vs operation frequency

<figure><img src="image_4.png" /><figcaption>Fig. 3: Converter efficiency vs operation frequency ($P_0$=75kW, $V_0$=366V and $I_0$=205A)</figcaption></figure>

As shown in Figure 3, the converter achieves its highest efficiency of 97.1% at 60 kHz. Conversely, the lowest efficiency of 94.5% occurs at 180 kHz. The efficiency difference of
2.6% corresponds to a power loss difference of 2.13 kW.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Semi-conductors power loss vs operation frequency (Po=75kW, Vo=366V, Io=205A)</figcaption></figure>

Figure 4 presents two curves illustrating the total power loss of the four MOSFETs in the full bridge (blue) and the eight output rectifiers in the four center-tapped output configuration with full-wave rectification.

Across the operating frequency range of 60 kHz to 75 kHz, the power loss of the MOSFETs is marginally greater than that of the rectifiers. However, this disparity becomes significantly pronounced as the frequency increases to between 95 kHz and 150 kHz.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Four LLC resonant inductor power loss vs operation frequency.</figcaption></figure>

Figure 5 illustrates the total power loss of the four LLC resonant inductors, comprising both winding (Orange) and core (Blue) losses. As depicted, the total winding loss decreases from 24 W at 60 kHz to 8 W at 180 kHz.

<figure><img src="image_7.png" /><figcaption>Fig. 6: Total power loss of four LLC transformer vs operation frequency</figcaption></figure>

Figure 6 compares the total power loss of the four LLC transformers, separating winding and core losses. The total winding loss decreases from 34 W at 180 kHz to 18 W at 60 kHz. While core loss remains constant at approximately 0.5 W between 60 kHz and 140 kHz, it rises to 13 W at 180 kHz.

## Curved -air gap LLC resonant inductor

The curved-air gap (CAG) solution offers a viable approach to realizing a variable inductance, which exhibits an inverse relationship with the load current. This allows the LLC resonant inductor to maintain an optimal quality factor (Q) throughout a broader range of load currents, thereby facilitating zero-voltage switching (ZVS).

$$Q = \frac{\sqrt{\frac{L_r}{C_r}}}{R_{ac}} \qquad (2)$$

$$f = \frac{1}{2\pi\sqrt{L_r C_r}} \qquad (3)$$

To achieve maximum efficiency, the operating frequency should be aligned with the resonant frequency, and an optimal Q factor must be realized. In this context, $C_r$ represents the resonant capacitor, $L_r$ the resonant inductor, and $R_{ac}$ the reflected load resistance.
<figure><img src="image_8.png" /><figcaption>Fig. 7: a. Effective inductance vs excitation current (h1=1mm) b. LLC resonant inductor with curved air gap solution (h1= air gap dimension and r4 = radius of spherical air gap)</figcaption></figure>

As depicted in Figure 7a, the effective inductance of the curved air-gap LLC resonant inductor reaches a maximum of 77.6 µH at an output current (Io) of 54.5 A. Subsequently, it decreases gradually to 1 µH at Io = 82 A.

<figure><img src="image_9.png" /><figcaption>Fig. 8: a. Effective inductance vs curved air gap dimensions (Io=54.5A) b. LLC resonant inductor with curved air gap solution (h1= air gap dimension and r4 = radius of spherical air gap)</figcaption></figure>

As illustrated in Figure 8a, the effective inductance of the curved air-gap LLC resonant inductor exhibits a maximum value of 75.7 µH when h1 = 1 mm and r4 = 1 mm. Subsequently, it decreases progressively to 1 µH as h1 increases to 38 mm and r4 expands to 22.5 mm.

Thermal analysis of the 75kW
phase-shift full bridge LLC DC/DC
resonant converter

To conduct a precise thermal analysis of the 75 kW PS-full bridge LLC DC/DC resonant converter, two distinct operating frequencies were selected: 90 kHz and 180 kHz.

The electrical circuit model is illustrated in Figure 1. It incorporates a center-tapped output rectifier and a full-wave rectification scheme. The corresponding finite element thermal models for the 180 kHz and 90 kHz operating frequencies are presented in Figures 9 and 12, respectively.

For the finite element thermal model, key components were chosen based on their performance characteristics. The WolfSpeed SiC diode (FFSH5065B) was selected for the output rectifier due to its high current capacity (50 A) and low switching losses. The main power switch was an Infineon SiC MOSFET (IMZA120R007M1Hb), known for its high current rating (225 A), low on-state resistance (7.5 mΩ), and reasonable switching losses.

For the LLC resonant inductor, a PQ65/54 core with five turns of disc-type coils was used at 180 kHz, while a PM114/93 core was employed at 90 kHz. Identical PQ65/54 cores were used for the LLC transformers in both cases.

KEMET KC-LINK surface-mount multilayer ceramic chip capacitors and Panasonic film capacitors were selected for the resonant and output capacitors, respectively.

# 1. Thermal simulation results

## a. CASE I (f=180kHz)

Despite a total power loss of 4.365 kW, natural air convection cooling proves insufficient for managing the thermal profile of the system. Forced air convection, utilizing eight 120x38x80mm fans, is essential to maintain acceptable component temperatures.

Simulation results demonstrate that an air flow speed of 70 cfm can effectively reduce power losses to 50W. However, localized hot spots may persist, particularly in the LLC resonant capacitors, marked with a red circle, situated near the gate-drive transformers and main switches, as illustrated in Figure 10. The overall temperature of the output film capacitors remains around 22°C.
<figure><img src="image_10.png" /><figcaption>Fig. 9: Finite element thermal model of PS-FAB LLC resonant converter (center tapped output with full-wave rectification)</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 10: Temperature profiles of the output film capacitors and LLC resonant capacitors (Ceramic capacitors)</figcaption></figure>

The semiconductor device with the highest temperature, marked with a yellow circle, is the main switch MOSFET, located near the gate driver transformers as indicated in Figure 11. This MOSFET is operating well above its junction temperature limit of 175°C, resulting in permanent damage. The elevated temperature of the MOSFET also contributes to increased heat dissipation in the adjacent resonant capacitor, as shown in Figure 9.

<figure><img src="image_12.png" /><figcaption>Figure 11: Maximum temperature simulation of semiconductor devices (Power MOSFET and output rectifiers) under Po=75kW.</figcaption></figure>

a. CASE II (f = 90kHz)

<figure><img src="image_13.png" /><figcaption>Figure 12: Finite element thermal model for f=90kHz</figcaption></figure>

The system's highly efficient 96.9% efficiency rating at 90kHz results in an overall power loss of 2.32kW. Despite using only one heat sink for the eight output rectifiers, natural air convection cooling is insufficient to maintain acceptable component temperatures, which must not exceed 175 °C for junction temperature limit. Forced air convection, utilizing eight 120x38x80mm fans, is therefore necessary to ensure the system's reliable operation.
Simulation results show that an air flow speed of 70 cfm can reduce power losses to 5W. However, localized hot spots of 22.9°C may still occur in the output film capacitors near the PCB edge, as depicted in Figure 13. The overall temperature of the LLC resonant ceramic capacitors remains at 21.8°C.

<figure><img src="image_14.png" /><figcaption>Fig. 13: Temperature profiles of the output film capacitors and LLC resonant capacitors (Ceramic capacitors)</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 14: Maximum temperature simulation of semiconductor devices (Power MOSFET and output rectifiers) under $P_o=75\,\text{kW}$.</figcaption></figure>

The semiconductor device with the highest temperature is the main switch MOSFET, located near the gate driver transformers as indicated in Figure 14. This MOSFET operates within normal parameters. However, its elevated temperature of

$109^\circ\text{C}$ also leads to increased heat dissipation in the adjacent resonant capacitor, as shown in Figure 13.

<figure><img src="image_16.png" /><figcaption>Fig. 15: Power MOSFET body temperature against volumetric flow rates</figcaption></figure>

As illustrated in Figure 15, a minimum volumetric flow rate of $4 \, \text{m}^3/\text{s}$ is necessary to prevent the body temperature of four individual power MOSFETs from exceeding the maximum junction temperature specified by the power semiconductor manufacturer. Furthermore, the proximity between the four power MOSFETs and the cooling fans is a critical factor in achieving adequate thermal management. As illustrated in Figure 16, a minimum volumetric flow rate of $2.6 \, \text{m}^3/\text{s}$ is required to ensure that the body temperature of the eight output rectifiers remains below the maximum junction temperature specified by the power semiconductor manufacturer.

<figure><img src="image_17.png" /><figcaption>Fig. 16: Output rectifier body temperature against volumetric flow rates ($\text{m}^3/\text{s}$)</figcaption></figure>
Moreover, the spatial arrangement of the eight output rectifiers in relation to the cooling fans significantly influences the effectiveness of thermal management.

<figure><img src="image_18.png" /><figcaption>Fig. 17: Core and winding temperatures of LLC resonant inductor</figcaption></figure>

Comparing the winding losses of the LLC resonant inductor at 60 kHz and 90 kHz, it is evident that increasing the switching frequency to 90 kHz can effectively mitigate thermal issues by reducing winding losses. While this may result in a slight increase in overall losses, it offers a favourable balance between efficiency and thermal management when compared to lower frequencies.

As highlighted in Section III, the LLC resonant inductor's power loss of 17W at 90 kHz can lead to localized hotspots within the disc-type winding coil and terminals. These hotspots may result in operating temperatures approaching 140°C, as depicted in Figure 17. To prevent overheating and ensure the long-term reliability of the inductor, the use of Class H insulation is essential.

## Reliability issue of power semiconductors

Concerning power semiconductors, particularly SiC MOSFETs and rectifiers, our simulations indicate potential reliability issues. Under conditions of high switching currents, with power losses of 500W per MOSFET and 250W per rectifier (as shown in Fig. 4), these components

may be prone to thermal cycling and mechanical deformation.

<figure><img src="image_19.png" /><figcaption>Fig. 18: Main switch SIC MOSFET operates at f =180kHz and the output power =75kW (Vo=366V, Io=205A) (deformation=2.7%)</figcaption></figure>

Although the maximum displacements observed (43.4 µm for MOSFETs and 6.16 µm for rectifiers), as shown in Figures 18 and 19, may appear insignificant, they can gradually impair heat dissipation from the attached heat sinks. This occurs due to a positive feedback loop, where rising temperatures result in additional deformation, leading to a reduction in heat transfer efficiency.

NormalizedDeformation = 0.0555555556

<figure><img src="image_20.png" /><figcaption>Fig. 19: Output SIC rectifier operates at f=180kHz and the output power =75kW (Vo=366V, Io=205A) (deformation = 5.6%)</figcaption></figure>
Given these simulation findings, we recommend further investigation into the long-term reliability of these components under high-power conditions.

Compared to identical SiC MOSFETs operating at 180 kHz, these devices operating at 90kHz exhibit a less power loss (250W per each), leading to lower temperatures and reduced deformation. As shown in Figure 20, the maximum MOSFET displacement is 17 µm, while the output SiC rectifier remains undeformed.

<figure><img src="image_21.png" /><figcaption>Fig. 20: Main switch SiC MOSFET operates at f =90kHz and the output power =75kW (Vo=366V, Io=205A) (deformation=6.7%)</figcaption></figure>

## Conclusions

This paper presents the design and analysis of a 75 kW PS-FAB LLC DC/DC converter. Despite achieving a peak efficiency of 97.1% at 60 kHz, thermal management remains a significant challenge, particularly at higher frequencies. Given the 75kW output power level, a minimum volumetric flow rate of 4m3/s is required to ensure that the body temperature of the four power MOSFETs and eight output rectifiers remain below the maximum junction temperature specified by the power semiconductor manufacturer.

Finite element simulations revealed potential reliability concerns for the power semiconductors, especially the MOSFETs, under high switching currents.

While forced air cooling is essential, optimizing the switching frequency and component selection

can mitigate thermal issues. The use of a curved air-gap LLC resonant inductor is beneficial for maintaining zero-voltage switching across a wider load range. However, further investigation into the long-term reliability of the power semiconductors under high-power conditions is recommended.

## References

[1] Michon, M.; Duarte, J.L., “A three-port bi-directional converter for hybrid fuel cell systems,” Proceedings of the the IEEE Power Electronics Specialists Conference, pp4376-4742,2004.

[2] Yu, S.Y.; Chen, R., “Survey of Resonant Converter Topologies”, Texas Instrument Power Supply Design Seminar 2018.

[3] Hangseok Choi, “Analysis and design of LLC resonant converter with integrated transformer,” APEC 2007, pp-1630-1635.

[4] E. Stenglein, M. Albach, “Analytical calculation method for the non-linear characteristic of ferrite-cored inductors with stepped air gap”, Springer, Electrical Eng (2017) 99: 421-429

[5] W.K.Mo, K.M Paasch, T.Ebel, “Single-stage Single Switch curved air gap PFC integrated flyback transformer design”, 2023 17th CPE-POWERENG.

[6] W.K.Mo, K.M Paasch, T.Ebel, “Single-stage, single-switch curved air gap power factor correction integrated flyback transformer design for lighting equipment power applications”, EPE 2023

[7] A.Ibrahim, J.P.Ousten, “PowerCycling issues and challenges of SiC-MOSFET power modules in high temperature conditions”, Microelectronics reliability volume 58, Mrach 2016, page 204-210.

[8] Pei Sheng Liu, Jin Xin Huang, “Reliability analysis of power MOSFET”, 15th International Conference on Electronic Packing Technology, 2014, page 912-916.
<figure><img src="image_22.png" /></figure>