# 100 kW Three-Phase Wireless Charger for EV: Experimental Validation Adopting Opposition Method

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Charging Structure

## 3. System Modelling

#### 3.1. Electromagnetic Structure Description

^{2}. Hence TPP operates without any cooling considering the short operational time of the application and because of the mechanical constraints for the box, where the coils have been placed. The main parameters of the coils, from the Finite-Element-Analysis (FEA) design validation, are listed in Table 1.

#### 3.2. Control and Simulation Analysis

- At time $t={t}_{0}$, at the very beginning of the process, the system is at the starting condition. Considering the WPT inverter, it is possible to notice that the modulation depth is $m=1$. In this condition, the TPP primary side can be considered to be an open circuit. At the same time, the boost converter has a modulation index ${m}_{bst}=0$ or in another way can be considered to be an equivalent short circuit at the output of the WPT system. At the end of this state, all the bus capacitors are pre-charged and at a steady state.
- For $\Delta t=\Delta {t}_{1}$, the modulation index of the WPT inverter increases, following a linear ramp variation, till reaches the value of $m=0$. In this condition the output-phase voltages waveforms starting to be non-null till the end of the ramp, instant in which they reach the $50\%$ of pulse width. At the same time, the boost converter is forced to maintain the value of ${m}_{bst}=0$, still a short circuit see from diode bridge terminals. Within this status, the voltage at the battery side increases slightly due to the death time of the converter switches. However, side some more words are needed regarding the current evolution at the battery. In fact, replacing the AC physical dimensions with the corresponding DC Battery-side aspects in (2) and writing the DC current function of the other dimensions, the following relationship can be obtained:$${I}_{outDC}=\frac{4}{{\pi}^{2}}\frac{{V}_{in}}{{\omega}_{0}M}$$From (9) can be deduced that the current at DC output increases as the voltage at the primary side grows. The maximum is reached within ${m}_{H}=0$ at WPT inverter.
- For $\Delta t=\Delta {t}_{2}$, the modulation depth of WPT inverter reached $m=0$. Thus, the equivalent duty cycle is $50\%$ and the output-phase voltages become full square wave. In this condition, the boost remains still with ${m}_{bst}=0$ and as a consequence the voltage at the battery side remains low, while the current reaches the maximum. This state has been introduced to obtain a steady-state at the primary side, where the phase currents and the voltages are in phase thanks to the resonance of the WPT system.
- For $\Delta t=\Delta {t}_{3}$, the WPT inverter can be considered in steady state with modulation index $m=0$. In this portion of the analysis the boost increases its modulation depth from ${m}_{bst}=0$, following a linear ramp variation, to reach at the terminals of diode bridge a final DC value of ${V}_{outDC}\approx 380$ V. Considering now again the inductance model for the equivalent single-phase system [30], it is possible to rearrange the (2) highlighting the relationship between the output DC voltage and the input current of the electromagnetic system as:$${I}_{in}=2\frac{{V}_{outDC}}{{\omega}_{0}M}$$From the (10) it is clear that if the output voltage on the battery side increases, the current at the primary side grows too.
- For $\Delta t=\Delta {t}_{4}$, the boost converter reaches the final value for its modulation index (i.e., ${m}_{bst}=0.65$) which corresponds to the final value of the DC voltage at battery side ${V}_{outDC}\approx 380$ V. From (9) the DC after the diode bridge remains the same because of the full square wave at the primary side. However, the output current of the WPT inverter, thanks to (10) reaches a steady-state, as can be seen from Figure 7 due to the constant output voltage at the battery side. This is the final steady-state of the analysis. The output DC voltage and current reach the target values equivalent to a State-Of-Charge (SOC $\simeq 80\%$) of EV battery charge. In the fast-charging process, in fact, the charge will stop after having reached this SoC level.

## 4. Prototype System

#### 4.1. WPT Unit Realization

#### 4.2. Converter Design

## 5. Experimental Validation

#### 5.1. Experimental Setup

#### 5.2. Experimental Results

**a.**- Starting from a condition in which the low-side switch is in conduction state (Figure 13a) the phase voltage ${V}_{U}$ is zero and the phase current ${I}_{U}$ is negative.
**b.**- When ${S}_{n}$ is off the current flows through the parasitic capacitance ${C}_{p}$ and ${C}_{pn}$. The output voltage ${V}_{U}$ increase until the DC-link voltage is reached (Figure 13b).
**c.**- ${V}_{U}$ is equal to the DC-link voltage, the current forces the Schottky diode to pass in conduction mode. Then the current path in this period is provided by the diode (Figure 13c).
**d.**- The soft switching occurs when the high-side switch (S) is closed (Figure 13d) while the diode is in conduction mode.
**e.**- A duty cycle less than $42.5\%$ allow the ${V}_{U}$ to freely oscillate (Figure 13e). Due to the direction of the current ${I}_{U}$ the phase voltage decrease following the charging and discharging process of the parasitic capacitance.
**f.**- The high-side switch is turned on during the charging and discharging process of the parasitic capacitance. This led to a hard switching condition. The voltage across (S) differs from zero and the current has a positive value (Figure 13f).
**g.**- The high-side switch is on the state, keeping the ${V}_{U}$ at the DC-link level and the positive direction of the phase current ${I}_{U}$ (Figure 13g).

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematization of the final EV battery charging application for the WPT system under analysis.

**Figure 2.**Schematization of the test-bench for the experimental validation for the WPT system under analysis.

**Figure 10.**(

**a**) Power test-bench with WPT structure, WPT inverter and boost converter and chiller. (

**b**) Control bench, supply and measurement system.

**Figure 11.**Measured phase voltages (${V}_{u},{V}_{v},{V}_{w}$) and phase currents (${V}_{u},{V}_{v},{V}_{w}$) (${I}_{u},{I}_{v},{I}_{w}$) on the primary side of WPT unit and measured voltage (${V}_{DCout}$) and current (${I}_{DCout}$) at output DC terminals of the WPT unit.

**Figure 12.**Measured phase-to-phase voltages (${V}_{uv},{V}_{vw},{V}_{wu}$) and phase currents (${I}_{u},{I}_{v},{I}_{w}$) on the primary side of WPT unit and at output DC side.

**Figure 14.**(

**a**) Voltage and current waveforms at the limits of hard commutation. (

**b**) Voltage and current waveforms reaching the limit of ZVS.

Three-Phase System Preliminary Values | ||
---|---|---|

Parameter | Variable | Value |

Working frequency | ${f}_{0}$ | 85 kHz |

DC input voltage | ${V}_{DC}$ | 580 V |

Litz wire cross section | ${S}_{\u2300}$ | 56 mm^{2} |

Coils external diameter | ${D}_{coils}$ | 710 mm |

Transmitter-Receiver airgap | ${z}_{0}$ | 50 mm |

Transmitter self-inductance | ${L}_{PH}$ | 23.28 μH |

Receiver self-inductance | ${L}_{ph}$ | 23.28 μH |

Mutual inductance | ${M}_{3ph}$ | 9.43 μH |

Resonant Capacitor | ${C}_{ph}$ | 170 nF |

Three-Phase System Measured and Testing Values | ||
---|---|---|

Parameter | Variable | Value |

Resonance Frequency | ${f}_{0}$ | 82.37 kHz |

Transmitter self-inductance | ${L}_{PH}$ | 23.46 μH |

Receiver self-inductance | ${L}_{ph}$ | 23.46 μH |

Error FEA vs manufactured inductance | ${e}_{\%}$ | 1% |

Mutual inductance | ${M}_{3ph}$ | 8 μH |

Converter Reactive Components | ||
---|---|---|

Parameter | Variable | Value |

DC-Link Bulk capacitors | ${C}_{DC\_Link}$ | 40 μF |

Fast SMD DC-Link capacitor | ${C}_{DC\_Fast\_smd}$ | 4.7 nF |

Fast Film DC-Link capacitor | ${C}_{DC\_Fast\_film}$ | 1.8 μF |

Output Filter capacitor | ${C}_{DC\_out}$ | 3 μF |

Parasitic Mosfet capacitance | ${C}_{p}$ | 2.5 nF |

Mosfet Stray Inductance | ${L}_{Stray}$ | 15 nH |

Measured Values of Electrical Quantities of the System | ||
---|---|---|

Parameter | Variable | Value |

Supply voltage | ${V}_{DC\_supply}$ | 580.49 V |

Supply current | ${I}_{DC\_supply}$ | 14.83 A |

Supply Power | ${P}_{DC\_supply}$ | 8.61 kW |

WPT Input DC current | ${I}_{DC\_input}$ | 192.12 A |

WPT Input Power | ${P}_{DC\_input}$ | 111.52 kW |

WPT Output DC voltage | ${V}_{DC\_output}$ | 378.87 V |

WPT Output DC current | ${I}_{DC\_output}$ | 277.19 A |

WPT Output DC Power | ${P}_{DC\_output}$ | 104.96 kW |

Boost Output DC current | ${I}_{Boost\_output}$ | 177.29 A |

Boost Output DC Power | ${P}_{Boost\_output}$ | 102.91 kW |

WPT efficiency | ${\eta}_{WPT}$ | 94.12% |

Boost efficiency | ${\eta}_{Boost}$ | 98.05% |

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**MDPI and ACS Style**

Colussi, J.; La Ganga, A.; Re, R.; Guglielmi, P.; Armando, E. 100 kW Three-Phase Wireless Charger for EV: Experimental Validation Adopting Opposition Method. *Energies* **2021**, *14*, 2113.
https://doi.org/10.3390/en14082113

**AMA Style**

Colussi J, La Ganga A, Re R, Guglielmi P, Armando E. 100 kW Three-Phase Wireless Charger for EV: Experimental Validation Adopting Opposition Method. *Energies*. 2021; 14(8):2113.
https://doi.org/10.3390/en14082113

**Chicago/Turabian Style**

Colussi, Jacopo, Alessandro La Ganga, Roberto Re, Paolo Guglielmi, and Eric Armando. 2021. "100 kW Three-Phase Wireless Charger for EV: Experimental Validation Adopting Opposition Method" *Energies* 14, no. 8: 2113.
https://doi.org/10.3390/en14082113