# Comparison of Resonant Converters for High-Power Inductive Wireless Power Transfer

Diego Castillo, Pablo Briceno, Antonio Sanchez-Squella, Hafte H Adhena, Alan J Watson

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Diego Castillo, Pablo Briceno, Antonio Sanchez-Squella, Hafte H Adhena, Alan J Watson. Comparison of Resonant Converters for High-Power Inductive Wireless Power Transfer. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0252. hal-05087243

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# Comparison of Resonant Converters for High-Power Inductive Wireless Power Transfer

Diego Castillo<sup>a</sup>, Pablo Briceno<sup>b</sup>, Antonio Sanchez-Squella<sup>a</sup>, Hafte H. Adhena<sup>b</sup>, Alan J. Watson<sup>b</sup>

Tel.: +44 / 07762129054

E-Mail:pablo.briceno@nottingham.ac.uk

URL: <sup>a</sup>https://www.usm.cl, <sup>b</sup>https://www.nottingham.ac.uk/

## ACKNOWLEDGMENT

This project has received funding from the European Union's EU Framework Programme for Research and Innovation Horizon 2020 under Grant Agreement No 955646.

*Index Terms*—Wireless Power Transmission, Modular Multilevel Converters (MMC), Cascaded H-Bridge, Railway power supply, Resonant converter.

*Abstract*—This paper focuses on the Modular Multilevel Converter (MMC) with integrated magnetics for an Inductive Power Transfer (IPT) system applied to a 1 MW high-speed train. The MMC achieves zero-voltage switching (ZVS) through duty cycle pattern modulation, and an improved capacitor voltage balancing algorithm to enhance reliability against inter-leg imbalances is presented. A comparison between the MMC and Cascaded H-bridge (CHB) with integrated transformers was studied. While the CHB converter excels in efficiency and performance, the MMC is particularly suited for handling higher currents. The study presents an IPT system with five H-bridged modules for the CHB with integrated transformers and five sub-modules per arm for the MMC. Maximum efficiency exceeds 94% at 1 MW, highlighting the strengths of both topologies in high-power applications.

## I. INTRODUCTION

In recent years, the need for efficient, safe, and convenient charging technologies has significantly increased due to the growing adoption of electric vehicles (EVs) and battery-based public transportation systems. One of the most promising solutions to meet this need is Inductive Power Transfer (IPT), a technology that allows the transfer of electrical energy without physical contact

through a loose magnetic coupling between two or more coils.

The application of IPT for charging light and medium electric vehicles up to 200 kW is currently well addressed [1]. However, the energy demand for charging batteries of trains, trams, or even ferries [2] is considerably higher than that of land vehicles, reaching the order of MW. This requires specific designs and innovative solutions in terms of coil design and power converters.

In the case of railways, nowadays, there are areas where electrification via overhead lines may not be feasible due to environmental restrictions or high construction and maintenance costs [3]. In these cases, wireless charging provides a viable technical solution, facilitating onboard battery charging without overhead lines. In [4], the scholars demonstrated the feasibility of 1 MW IPT applications specifically for high-speed trains experimentally.

Given the global push for more sustainable and electrified public transport systems, improvements in IPT efficiency for high-power applications, such as railways, will not only enhance operational performance but also significantly reduce infrastructure costs related to electrification. Additionally, addressing technical challenges such as stray electromagnetic fields and power density could pave the way for broader adoption of IPT systems in public transportation.

A crucial element for enabling the use of IPT is incorporating power electronics. In this regard, multilevel converters are being explored as potential solutions [5]–[7]. In addition to reducing the voltage or current stress of semiconductors, these converters can manipulate the input voltage of the resonant circuit, giving a chance to control the current at the primary circuit, enabling less complex control strategies than those of synchronised power converters [8] [9] or reducing the additional

<footnote><sup>a</sup>Universidad Tecnica Federico Santa Maria, <sup>b</sup>University of Nottingham</footnote>

<footnote><sup>a</sup>Vicuna Mackenna 3939, Santiago, Chile. <sup>b</sup>PEMC Building, Nottingham, UK.</footnote>
circuits on the power converts such as mentioned in [5]. A topic under discussion is the capabilities of these topologies to ensure a soft-switching operation over a wide load range without sacrificing efficiency, a matter in which the modulation strategy could be helpful.

So far, few studies have evaluated the performance of multilevel converters in high-power applications [10]. Only Cascaded H-Bridge (CHB) [11] [12] and Modular Multilevel Converter (MMC) [13] topologies have been tested in prototypes. This work has studied these topologies, as shown in Fig. 1, and improvements in the modulation strategy for MMC have been proposed. The focus is on the efficiency and performance of the topologies, evaluating their ability to provide efficient and reliable energy transfer under demanding operating conditions. For this purpose, thermal models of the semiconductors will be considered in the PLECS software, taking into account the conduction and switching losses.

In Section II of this article, the main characteristic of each power converter is listed under Zero Voltage Switching operation. In Section III, the simulation results and analyses of those are mentioned. The last section corresponds to the Conclusion, where the main results and analyses are highlighted.

## II. POWER CONVERTER

The IPT system comprises an inverter, a compensated resonant network, and a rectifier. Typically, series-series (SS) and series-parallel (SP) compensated configurations are widely adopted, especially in high-power applications [14], due to their simple structure and independence in compensating for coupling and load conditions [15]. These configurations exhibit better efficiencies than other topologies [16]. However, LCC-S compensation is selected for both converters, taking advantage of the fact that both topologies integrate the resonant inductors into the primary IPT compensation network, reducing the number of components and improving the converter's power density. In Fig. 2, the IPT system selected for wireless charging is shown.

### A. MMC With Integrated Magnetics

In [13], is proposed an MMC with *N* sub-modules (SM) per arm with integrated magnetics and a complex strategy scheme to ensure ZVS for all switches over a wide range of operations.

With the digital modulation scheme, each SM can operate at only one of three duty cycle values. These are 100%, 0%, or 50%. For each leg of the proposed MMC system, during a switching period, a SM number is assumed to operate at *D* = 100%, b SM number

<figure><img src="image_2.png" /><figcaption>Fig. 1: Converter topologies to compare. (a) MMC [13]. (b) RIIT-MI [11].</figcaption></figure>

operates at *D* = 0%, and c SM number operates at *D* = 50%, where it must be satisfied that *a* + *b* + *c* = 2*N*. Each combination of *a*, *b*, and *c* defines a duty cycle pattern that results in different average voltages across the capacitors and varying output voltages, depending on how these values are distributed relative to the main bus voltage.

The number of duty cycle patterns generated depends on *N*. For example, with *N* = 3, there are 12 duty cycle
<figure><img src="image_3.png" /><figcaption>Fig. 2: IPT LCC-S System.</figcaption></figure>

patterns, and with $N = 5$, there are 32. Figure 3 shows the 32 values that the inverted voltage $V_{inv}$ can have, being this the main disadvantage of the MMC as it is not possible to fine tune the inverted voltage regulation. There are several solutions such as adding a DC-DC converter to the MMC input or increasing $N$ to have more operating points.

<figure><img src="image_4.png" /><figcaption>Fig. 3: Duty-cycle pattern number versus output voltage amplitude.</figcaption></figure>

In an MMC, it is necessary to maintain the capacitor voltages in the SMs at equal or similar values, which requires control. This is called capacitor voltage balancing. In [13], a balancing algorithm is proposed that compares and assigns duty cycles based on the sum of the upper arm voltages ($V_{1u} + V_{2u}$) versus the sum of the lower arms ($V_{1l} + V_{2l}$).

It may happen that $V_{1u}$ and $V_{2l}$ increase to $V_{bus}$ and $V_{1u}$ and $V_{2l}$ decrease to 0 V or vice versa. This condition cannot be reversed by the algorithm. Therefore,

<figure><img src="image_5.png" /><figcaption>Fig. 4: Capacitor voltage balancing block diagram, based on [13].</figcaption></figure>

a modification of the original balancing algorithm is made, performing the comparison and allocation per leg, as shown in Fig. 4. The disadvantage of this modification is that there are cases where the inverted voltage is not symmetrical, thus increasing the THD of the voltage signal. However, this does not affect the amplitude of the voltage and the resonant circuit filters out the harmonics.

## B. Resonant Inductor Integrated-Transformer-Based Multi-Inverter (RIIT-MI)

In [11], a CHB topology with High-Frequency transformers called Resonant Inductor Integrated Transformer (RIIT-MI) is proposed to improve the IPT power rating without compromising performance while enabling ZVS over a wide range of operations by changing
the modulation strategy. However, incorporating high-frequency transformers (HFTs) in two of three modules compromises the power distribution and the modularity feature.

Hybrid modulation employs multiple modulation schemes for the inverters, which include Full-Bridge Phase Shift Control (FB-PSC), Half-Brisge Duty Cylce Control HB-DCC, and BPC. The FB-PSC scheme provides twice the voltage gain ($G_{ac-dc}$) compared to the HB-DCC scheme. In contrast, the BPC scheme has no voltage gain. To avoid the dc bias voltage across the RIIT, only symmetrical FB-PSC and BPC schemes are applied to \#2 \sim \#n inverters. However, \#1 inverter can also operate at the HB-DCC scheme. Although all the inverters can use the same gate signals, hard switching occurs at light loading with a small $\alpha_i$ or $D_1$. Fig. 5 shows the n+1 possible operating modes with the hybrid modulation scheme.

<figure><img src="image_6.png" /><figcaption>Fig. 5: Voltage gain $G_{dc-ac}$ as a function of duty cycle $D_1$ and phase shift $\alpha_1$ for different modes of operation.</figcaption></figure>

For the design of the converter, advantage should be taken of the LCC-S compensation, which has the characteristic of maintaining a constant voltage at the output, thus reducing the sensitivity of $G_{dc-ac}$ to load variations. It is advisable to operate in the \#n mode, since the HB-DCC scheme has lower switching losses compared to the FB-PSC scheme. In this \#n mode, inverter 1 operates with HB-DCC and inverters \#2 \sim \#n operate in FB-PSC.

### III. SIMULATIONS AND ANALYSIS

#### A. Key parameters of prototype

Obtaining accurate parameters for high-power IPT systems is challenging due to the limited availability of experimental prototypes in the literature, as most

reported systems are designed for low-power applications. This lack of data necessitates the use of theoretical models and the adaptation of components to high-power scenarios. Therefore, the parameters used in the simulations presented in this section are based on estimations of the prototype described in [13] and [11], and these have been scaled up for higher power levels.

1) Resonant tank: Both topologies share the resonant tank and operate at a resonance frequency of $f_0 = 61.5$ kHz. The IPT system includes a set of resonant and filtering components, as detailed in Table I. The parasitic resistances of the high frequencies capacitors are obtained from the datasheets.

<table><caption>TABLE I: Resonant tank specifications.</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th></tr></thead><tbody><tr><td>Operating frequency</td><td>$f_0$</td><td>61.5 [kHz]</td></tr><tr><td>Primary filtering capacitor</td><td>$C_p$ & ESR</td><td>267.89 [nF] & 0.858 [mΩ]</td></tr><tr><td>Resonant capacitor</td><td>$C_f$ & ESR</td><td>24.44 [nF] & 9.375 [mΩ]</td></tr><tr><td>Secondary filtering capacitor</td><td>$C_s$ & ESR</td><td>37.73 [nF] & 6.105 [mΩ]</td></tr><tr><td>Self-inductance of transmitting coil</td><td>$L_p$ & $R_p$</td><td>299 [μH] & 0.3355 [Ω]</td></tr><tr><td>Self-inductance of receiving coil</td><td>$L_s$ & $R_s$</td><td>710 [μH] & 0.0750 [Ω]</td></tr></tbody></table>

2) RIIT-MI Converter: The RIIT-MI converter uses five inverters connected in parallel at the DC input ($n = 5$) with a voltage of $V_{bus} = 1150$ V in mode \#5. Each inverter is coupled to a resonant inductor integrated transformer (RIIT) with a turns ratio of $n_{pi} : n_{si} = 2 : 1$. The table II presents the key parameters of the RIITs used in this topology.

<table><caption>TABLE II: RIIT specifications.</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th></tr></thead><tbody><tr><td>Turns ratios of RIITs</td><td>$n_{pi} : n_{si}$</td><td>2:1</td></tr><tr><td>Leakage inductance of RIIT</td><td>$L_{ri}$ & $R_{L_{ri}}$</td><td>6.25 [μH] & 44.2 [mΩ]</td></tr></tbody></table>

3) MMC: The MMC converter consists of 5 sub-modules (SM) per arm ($N = 5$) and operates with an input voltage of $V_{bus} = 4000$ V. The submodules incorporate SM capacitors of $C_{SM} = 150$ μF with an
ESR of 1.5 mΩ. The parameters of the arm inductors are presented in Table III.

<table><caption>TABLE III: Arm inductor specifications.</caption><thead><tr><th></th><th>L<sub>1u</sub></th><th>L<sub>1l</sub></th><th>L<sub>2u</sub></th><th>L<sub>2l</sub></th></tr></thead><tbody><tr><td>Inductance [μH]</td><td>90</td><td>90</td><td>90</td><td>90</td></tr><tr><td>Mutual inductance M<sub>1ul</sub><br/>& M<sub>2ul</sub> [μH]</td><td colspan="2">65</td><td colspan="2">65</td></tr><tr><td>Equivalent L<sub>1</sub> [μH] &<br/>R<sub>ac</sub> [mΩ]</td><td colspan="4">25 & 164.2</td></tr><tr><td>Equivalent L<sub>armDC</sub> [μH]<br/>& R<sub>DC</sub> [mΩ]</td><td colspan="2">310 & 61.1</td><td colspan="2">310 & 61.1</td></tr></tbody></table>

## B. Efficiency

The power loss of the IPT system consists of inverter loss, primary compensation loss, self-inductance of the transmitter and receiver coils, secondary compensation loss, and rectifier loss. The inverter loss consists of conduction loss ($P_{con,inv}$) and switching loss ($P_{sw,inv}$), while the rectifier loss only includes conduction loss ($P_{con,rect}$) as it is a passive diode rectifier. The losses are obtained from the thermal model provided by the manufacturer and loaded as a Look-Up Table chart into Plecs. Switching losses of the free-wheeling diode are not considered. The loss of the compensated resonant network includes conduction losses in $L_1$, $C_f$, $C_p$, $L_p$, $L_s$, and $C_s$.

In the case of the arms inductors and power transformers, the losses are estimated based on the design presented in [11] and [13], respectively. In the case of an inductance, this resistance will be the alternating current resistance $R_{ac}$, and for capacitors, it will be the equivalent series resistance (ESR). These values are obtained from the datasheets provided by the manufacturers. The experimentally measured values from the authors of [4] are used for the receiver and transmitter coils. Based on the previous analysis, the conversion efficiency of the IPT system can be determined by calculating the ratio of the output power to the sum of the output power plus the total power losses. The total losses include both the conduction losses in all components and the switching losses in the semiconductors.

1) *Comparison of Efficiency:* The efficiency of the RIIT and MMC converters shown in Fig. 6 corresponds to steady-state conditions. Across the four sampled output power levels, the RIIT converter (red curve) demonstrates better performance than the MMC (blue curve). This is primarily because the conduction and switching

losses in the RIIT converter are lower than in the MMC, as shown in Fig. 7. The main reason for this difference is that the MMC has twice as many active switches as the RIIT converter. Additionally, as the output power increases in the MMC, the proportion of conduction losses starts to match the switching losses. At 1 MW, losses are split 50% conduction and 50% switching, which reduces the overall efficiency of the converter.

<figure><img src="image_7.png" /><figcaption>Fig. 6: Comparison of dc-dc efficiency.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7: Loss comparison of MOSFETs.</figcaption></figure>

In Fig. 9, the breakdown of losses for output powers of 280 kW and 1 MW is shown. One interesting aspect to highlight is the comparison of the integrated inductor
<figure><img src="image_9.png" /><figcaption>Fig. 8: Reference tracking comparison between RIIT and MMC converter.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 9: Power loss breakdown at different power levels. (a) RIIT 280 kW. (b) RIIT 1 MW. (c) MMC 280 kW. (d) MMC 1 MW.</figcaption></figure>

losses between both topologies. In the case of the RIIT-MI, the system features 4 transformers (RIIT), which account for 1.64% and 10.75% of the total losses at 280 kW and 1 MW, respectively. Meanwhile, in the MMC, the losses in the arm inductors ($L_{arm}$) contribute to 4.73% and a significant 23.92% of the total losses at the same power levels.

Another key aspect is the analysis of the losses in

the transmitter ($R_p$) and receiver ($R_s$) coils. At 280 kW, these coils account for approximately 80% of the total losses. However, as the output power increases to 1 MW, the percentage of these losses decreases. This is because the current in the primary coil remains relatively constant, making the losses in the coils less relevant as the output power grows.

Finally, it is worth mentioning that the losses in the filters ($C_p, C_s, C_f$) remain constant across all analyzed cases. These losses are practically negligible, with minimal contribution to the total losses, highlighting their insignificant impact on the overall system efficiency.

### C. Primary-side control

The purely resistive load has been modified to an RL load with a 2800 V DC voltage source in series. In Fig. 8, the reference tracking performance of both converters is shown.

For the MMC (red curve), the dynamics of a reference change are influenced by the duty cycle patterns, as the capacitor voltage ($V_c$) depends on the pattern. Therefore, depending on the next pattern, the capacitors will charge or discharge, which represents the main difficulty in the dynamic response of the system. For example, the simulation started with pattern #10, which shares the same $V_c$ as pattern #4, preventing a sharp dynamic response. However, the change from pattern #3 to #6 at 55 ms results in a variation from 800 V to 1143 V, leading to high power surges during the transition. If both patterns share the same voltage in the SM, the transition is smoother. Otherwise, high currents are generated that could exceed the limits of the electronic components.

In contrast, the RIIT converter (blue curve) shows smaller oscillations in its dynamic response. However,
the voltage gains at which the converter operates could hinder smooth switching for small values of $α_1$, ranging from 32.5° to 50.5°. This could affect its performance under certain operating conditions.

Additionally, with the selected configuration, the MMC only has six discrete operating values, which makes it difficult to follow other references precisely. This highlights the need for an additional DC/DC converter to achieve finer voltage gain control.

## IV. CONCLUSION

This study exhibits the characteristics of two multi-level resonant converter topologies for IPT systems in high-power railway applications. Although the RIIT-MI outperforms the MMC in terms of overall efficiency, the MMC stands out for its ability to handle higher currents, making it particularly suitable for applications requiring higher power demands. However, the design of the MMC is primarily optimized to operate at discrete voltage levels, which limits its operational range without an additional converter at the output to adjust voltages continuously. On the other hand, the dynamics of the MMC largely depend on the charging or discharging of submodule capacitors when switching duty cycle patterns. This can negatively affect system response in variable load scenarios or dynamic operating conditions. Despite this limitation, the MMC's duty cycle patterns ensure soft switching over a wide operating range, significantly reducing switching losses. In contrast, although the RIIT also employs ZVS, it cannot guarantee this operation across its entire range, which could limit its effectiveness under certain load conditions. Nevertheless, its modular architecture and ability to maintain better overall energy efficiency make it an attractive option for high-power railway applications that prioritize efficiency.

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