# Finite Element Analysis-Aided Optimization of Rectangular Coil Assemblies Applied in Electric Vehicle Inductive Chargers

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Performance Evaluation of Coil Assemblies

#### 2.1. Efficiency Analysis

#### 2.2. Leakage Magnetic Field Analysis

## 3. Influence of Geometric Parameters

#### 3.1. Overall Design of Coil Assembly Pair

#### 3.2. Evaluation of FOMs

#### 3.2.1. Calculation of Coil ESR

#### 3.2.2. Evaluation of LMF and Efficiency Performance

#### 3.2.3. Impact of Geometric Parameters

- 1.
- With the increase in interlayer distances, (${d}_{w-f}$ and ${d}_{f-Al}$), $FO{M}_{LMF}$ is reduced, whereas $FO{M}_{effi}$ is enhanced.

- 2.
- Increasing the coil size ($A$ or $B$) or the ferrite-coil size difference ($dif{f}_{w-f}$) has the same impacts as increasing ${d}_{w-f}$.

- 3.
- Adding a ferrite ring, i.e., a protrusion along the outer contour of the ferrite layer, improves both FOMs. By contrast, the impact of ${w}_{ring}$ is insignificant.

- 4.
- The stability of $M$ against coil misalignment can be enhanced via increasing the average turn size of the TX coil. By contrast, increasing the average turn size of the RX coil improves $M$ but has a negligible impact on its stability. In a practical IPT system, higher stability of $M$ means a lighter burden on the power converters, which is favorable. Therefore, the RX coil dimensions should be near the maximum allowable values and the TX coil size should be determined based on the maximum allowable variation of mutual inductance.

- 5.
- Increasing the coil pitch ($p$) is beneficial for improving both FOMs, and the impact is significant. However, for the RX coil, a larger $p$ implies that the maximum allowable turn number is reduced, which can possibly lead to a lower $FO{M}_{effi}$. For the TX coil, a larger $p$ means either the turn number or the average turn size is smaller. The possible consequence is either lower $FO{M}_{effi}$ or lower stability of $M$, both of which are undesirable. Meanwhile, a lower boundary should be assigned to size of the RX coil’s innermost turn. When the innermost turn is so small that its contribution to mutual inductance is far outweighed by its contribution to coil ESR, increasing the turn number not only results in a higher consumption of copper but also lowers $FO{M}_{effi}$.

- 6.
- When the size of the outermost turn is fixed, increasing the turn number before the size of the innermost turn becomes excessively small is beneficial for improving both FOMs. When the size of the innermost turn and the ferrite core parameters are fixed, both FOMs are decreased after $N$ exceeds a threshold, which is mainly attributable to the increase in eddy loss due to the short distance between the copper winding and the ferrite core boundary. By adding a ferrite ring, the eddy loss can be effectively suppressed, and the maximum allowable size of the outermost turn is increased.

#### 3.2.4. Constraints and Design Parameters

- On the TX side: $A$, $B$, $p$, $dif{f}_{w-f}$;

- On the RX side: $p$, $dif{f}_{w-f}$, $N$.

## 4. Optimization of Coil Assembly Pair

#### 4.1. Validation of the Accuracy of FEA

#### 4.2. Constraints and Predetermined Parameters

#### 4.3. Manual Optimization of a Coil Assembly Pair

#### 4.4. Experimental Results

## 5. Discussions

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Dai, X.; Li, X.; Li, Y.; Hu, A.P. Maximum Efficiency Tracking for Wireless Power Transfer Systems with Dynamic Coupling Coefficient Estimation. IEEE Trans. Power Electron.
**2018**, 33, 5005–5015. [Google Scholar] [CrossRef] - Zhu, G.; Gao, D.; Lin, S. Leakage Magnetic Field Suppression Using Dual-Transmitter Topology in EV Wireless Charging. J. Power Electron.
**2019**, 19, 625–636. [Google Scholar] - Mohammad, M.; Choi, S.; Elbuluk, M. Loss Minimization Design of Ferrite Core in a DD-Coil-based High-Power Wireless Charging System for Electrical Vehicle Application. IEEE Trans. Transp. Electrif.
**2019**, 4, 957–967. [Google Scholar] [CrossRef] - Budhia, M.; Covic, G.A.; Boys, J.T.; Huang, C.-Y. Development and Evaluation of Single Sided Flux Couplers for Contact-less Electric Vehicle Charging. In Proceedings of the 2011 IEEE Energy Conversion Congress and Exposition, Phoenix, AZ, USA, 17–22 September 2011. [Google Scholar]
- Tang, Y.; Zhu, F.; Ma, H. Efficiency Optimization with a Novel Magnetic-Circuit Model for Inductive Power Transfer in EVs. J. Power Electron.
**2018**, 1, 309–322. [Google Scholar] - Otomo, Y.; Igarashi, H. A 3-D Topology Optimization of Magnetic Cores for Wireless Power Transfer Device. IEEE Trans. Magn.
**2019**, 55, 1–5. [Google Scholar] [CrossRef] [Green Version] - Al-Saadi, M.; Valtchev, S.; Gonçalves, J.; Crăciunescu, A. New Analytical Formulas for Coupling Coefficient of Two Inductively Coupled Ring Coils in Inductive Wireless Power Transfer System. In Proceedings of the 7th EAI International Conference, GreeNets 2020, Harbin, China, 27–28 June 2020; pp. 117–127. [Google Scholar]
- Yilmaz, T.; Hasan, N.; Zane, R.; Pantic, Z. Multi-Objective Optimization of Circular Magnetic Couplers for Wireless Power Transfer Applications. IEEE Trans. Magn.
**2017**, 53, 1–12. [Google Scholar] [CrossRef] - Hariri, A.; Elsayed, A.; Mohammed, O.A. An Integrated Characterization Model and Multiobjective Optimization for the Design of an EV Charger’s Circular Wireless Power Transfer Pads. IEEE Trans. Magn.
**2017**, 53, 1–4. [Google Scholar] [CrossRef] - Bosshard, R.; Kolar, J.W. Multi-Objective Optimization of 50 kW/85 kHz IPT System for Public Transport. IEEE J. Emerg. Sel. Topics Power Electron.
**2016**, 4, 1370–1382. [Google Scholar] [CrossRef] - Kim, M.; Park, S.; Jung, H.-K. Numerical Method for Exposure Assessment of Wireless Power Transmission under Low-Frequency Band. J. Magn.
**2016**, 21, 442–449. [Google Scholar] [CrossRef] [Green Version] - Park, S. Evaluation of Electromagnetic Exposure During 85 kHz Wireless Power Transfer for Electric Vehicles. IEEE Trans. Magn.
**2018**, 54, 1–8. [Google Scholar] [CrossRef] - Lu, M.; Ngo, K.D.T. A Fast Method to Optimize Efficiency and Stray Magnetic Field for Inductive-Power-Transfer Coils Using Lumped-Loops Model. IEEE Trans. Power Electron.
**2018**, 33, 3065–3075. [Google Scholar] [CrossRef] - Sampath, J.P.K.; Alphones, A.; Vilathgamuwa, D.M. Coil optimization against misalignment for wireless power transfer. In Proceedings of the 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC), Auckland, New Zealand, 5–8 December 2016; pp. 1–5. [Google Scholar]
- Wang, X.; Sun, P.; Deng, Q.; Wang, W. Evaluation of AC Resistance in Litz Wire Planar Spiral Coils for Wireless Power Transfer. J. Power Electron.
**2018**, 18, 1268–1277. [Google Scholar] - Yashima, Y.; Omori, H.; Morizane, T.; Kimura, N.; Nakaoka, M. Leakage magnetic field reduction from Wireless Power Transfer system embedding new eddy current-based shielding method. In Proceedings of the 2015 International Conference on Electrical Drives and Power Electronics (EDPE), Tatranska Lomnica, Slovakia, 21–23 September 2015; pp. 241–245. [Google Scholar]
- Zhu, G.; Gao, D. Finite Element Analysis-Aided Performance Improvement of Circular Coil Assemblies Applied in Electric Vehicle Inductive Chargers. In Proceedings of the 2021 International Conference on Wireless Power Transfer, 34th International Electric Vehicle Symposium and Exhibition (EVS34), Nanjing, China, 25–28 June 2021. [Google Scholar]

**Figure 1.**Optimization methodologies commonly adopted in the literature. (

**a**) Analytical, equation-based optimization. (

**b**) Finite element analysis-based optimization.

**Figure 3.**Overall design of the coil assemblies and the magnetic flux paths. (

**a**) Front view. (

**b**) Top view. (

**c**) Magnetic flux paths.

**Figure 5.**Simulated FOMs. The solid line with triangular dots, dashed line with triangular dots and solid line with circular dots denote $FO{M}_{effi}$, $FO{M}_{effi2}$ and $FO{M}_{LMF}$, respectively. For the sake of clarity, the units of the vertical-axis quantities are omitted.

**Figure 6.**Comparisons between simulated and measured coil ESR. (

**a**) ESR versus $N$. (

**b**) ESR versus ${d}_{w-f}$. (

**c**) ESR versus ${d}_{w-Al}$ (distance between copper wire and aluminum plate).

**Figure 8.**Geometric parameters of the initial and optimized coil assemblies (the aluminum plate is not shown). The coils are made of 600-strand Litz wires.

**Figure 9.**Experimental setup. (

**a**) Coil assembly pair and magnetic field analyzer. (

**b**) Optimized TX coil. (

**c**) Initial TX coil. (

**d**) Measurement of power, efficiency and the inverter’s output voltage.

**Figure 10.**Configuration of the IPT prototype and the voltage or current waveforms. Input power and output power are measured before the SiC-based inverter and after the SiC-based rectifier, respectively.

Parameter | Value |
---|---|

Copper conductivity | $5.8\times {10}^{7}$ S/m |

Aluminum conductivity | $2.7\times {10}^{7}$ S/m |

Litz wire diameter | 2.45 mm |

Litz wire strand diameter | 0.1 mm |

Litz wire strand number | 600 |

${\mu}_{r}$ of ferrite | 2200 |

Coil excitation current | 20 A (peak) |

Excitation frequency | 85 kHz |

Parameter | Value |
---|---|

$p$ | 3 |

$A$ | 270 |

$B$ | 270 |

${d}_{w-f}$ | 3 |

${d}_{f-Al}$ | 2 |

$dif{f}_{w-f}$ | 10 |

$dif{f}_{f-Al}$ | 5 |

${h}_{ring}$ | 0 |

${W}_{ring}$ | 5 |

TX aluminum plate size | 300 × 300 × 5 |

RX aluminum plate size | 600 × 600 × 2 |

Ferrite core thickness | 5 |

Air gap height | 130 |

**Table 3.**Predetermined geometric parameters and constraints of the coil assembly pair. The unit of all parameters is mm.

Parameter | Value |
---|---|

Air gap | 160 |

TX aluminum plate dimensions | 560 × 560 × 2 |

RX aluminum plate dimensions | 1000 × 700 × 2 |

TX ferrite core dimensions | ≤490 × 490 × 5 |

RX ferrite core dimensions | ≤360 × 360 × 5 |

Turn number | ≤18 |

Coil misalignment | 0 to 100 |

Parameter | Initial TX | Initial RX | Optimized TX | Optimized RX |
---|---|---|---|---|

${d}_{f-Al}$ (mm) | 1.5 | 1.5 | 3 | 3 |

${\mathrm{h}}_{rng}$ (mm) | 0 | 0 | 7 | 7 |

Self-inductance ($\mathsf{\mu}\mathrm{H}$) | 481.32 | 223.35 | 203.25 | 127.04 |

DC resistance ($\mathrm{m}\mathsf{\Omega}$) | 141.0 | 79.8 | 88.9 | 67.5 |

ESR at 85 kHz ($\mathrm{m}\mathsf{\Omega}$) | 616.0 | 295.1 | 184.2 | 139.0 |

Series capacitance (nF) | 7.47 | 15.64 | 17.76 | 27.41 |

Coupling coefficient | 0.107 to 0.138 | 0.137 to 0.187 | ||

Coupling coefficient (simulated) | 0.102 to 0.133 | 0.129 to 0.181 | ||

Mutual inductance ($\mathsf{\mu}\mathrm{H}$) | 35.1 to 45.1 | 22.0 to 30.1 | ||

$FO{M}_{effi}$ | 6780 to 11,193 | 18,924 to 35,425 | ||

Litz wire length (m) | 55.4 | 36.8 |

Parameter | Value |
---|---|

Litz wire strand diameter (mm) | 0.1 |

Litz wire strand number | 600 |

Ferrite material | PC40 |

Room temperature (°C) | 23–26 |

DC load resistance (Ω) | 15 and 20 |

Inverter phase shift angle (degree) | 180 (fixed) |

Input DC-link voltage (V) | 100–300 (adjustable) |

Inverter switching frequency (kHz) | 85 (fixed) |

Output power (W) | 600 |

Inverter switching device | Cree C3M0075120J |

Rectifier diode | Rohm SCS220 |

$\mathbf{DC}\text{}\mathbf{Load}\text{}\mathbf{Resistance}\text{}\left(\mathbf{\Omega}\right)$ | Initial Design | Optimized Design |
---|---|---|

15 | $3.17\text{}\mathsf{\mu}\mathrm{T}$ | $2.94\text{}\mathsf{\mu}\mathrm{T}$ |

20 | $3.25\text{}\mathsf{\mu}\mathrm{T}$ | $3.11\text{}\mathsf{\mu}\mathrm{T}$ |

Reference | Inclusion of Ferrite Core | Inclusion of Aluminum Shield | Number of Parameter Sweeps | Analytical or Numerical | Impact of Design Parameters Explicitly Shown |
---|---|---|---|---|---|

[14] | No | No | Not applicable | Analytical | No |

[9] | Yes | No | Not applicable | Analytical | No |

[13] | Yes | No | Small | Analytical | No |

[10] | Yes | No | Large | Hybrid | No |

[8] | Yes | No | Large | Numerical | No |

This work | Yes | Yes | Moderate | Numerical | Yes |

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**MDPI and ACS Style**

Zhu, G.; Gao, D.
Finite Element Analysis-Aided Optimization of Rectangular Coil Assemblies Applied in Electric Vehicle Inductive Chargers. *World Electr. Veh. J.* **2021**, *12*, 219.
https://doi.org/10.3390/wevj12040219

**AMA Style**

Zhu G, Gao D.
Finite Element Analysis-Aided Optimization of Rectangular Coil Assemblies Applied in Electric Vehicle Inductive Chargers. *World Electric Vehicle Journal*. 2021; 12(4):219.
https://doi.org/10.3390/wevj12040219

**Chicago/Turabian Style**

Zhu, Guodong, and Dawei Gao.
2021. "Finite Element Analysis-Aided Optimization of Rectangular Coil Assemblies Applied in Electric Vehicle Inductive Chargers" *World Electric Vehicle Journal* 12, no. 4: 219.
https://doi.org/10.3390/wevj12040219