# Electrical Interoperability Evaluating of Wireless Electric Vehicle Charging Systems Based on Impedance Space

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## Abstract

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## 1. Introduction

_{VA}and the GA side impedance Z

_{GA}are defined in SAE J2954, as presented in Figure 2. Several recommended parameters for GA side impedance are derived based on the performance of reference devices. The analysis in the SAE standard is of great value for the evaluation and optimization of interoperability. Nevertheless, it cannot reflect the influence of circuit constraints (such as coil current, DC input voltage) on electrical interoperability.

## 2. Electromagnetic Description of Coil System

_{1}and P

_{2}mean the power flow at port 1 and port 2. If the power flows into the system from port 1, P

_{1}is positive, otherwise it is negative. The same rule applies to port 2. W

_{mag}refers to the magnetic energy stored in the system, and dW

_{mag}/dt shows the change rate of magnetic energy.

_{1}, i

_{2}as state variables, the state equations of the system can be derived according to the electromagnetism.

_{1}, λ

_{2}are the magnetic fluxes of coil 1 and coil 2, L

_{1}, L

_{2}are self-inductances, and M is mutual inductance between the two coils.

_{1}, e

_{2}are the voltages at port 1 and port 2.

_{mag}, $\frac{1}{2}{L}_{1}{i}_{1}^{2}$ and $\frac{1}{2}{L}_{2}{i}_{2}^{2}$ are the energy of the self-induced flux in coil 1 and coil 2, respectively. These two parts of energy only flow back and forth on one side, but not to the other side. Mi

_{1}i

_{2}is the energy of a mutual induced flux, which can flow from one side to the other, as shown in Figure 4. In a current cycle, when port 1 inputs energy to the coil system, port 2 outputs energy from the coil system (or vice versa).

_{1}and i

_{2}are alternating currents with a phase difference φ

_{12}:

_{1}, I

_{2}are the effective values of i

_{1}, i

_{2}and ω is the angular frequency. In one current cycle, the energy transferred from port 1 to port 2 is:

_{1}, I

_{2}, which reflect the power capacity of coils, compensation network and other power electronics on both sides. (d) Phase difference φ

_{12}of coil currents, which reflects the degree of mutual induced energy transformed into effective transmission energy. When φ

_{12}= ±90°, all the energy input from one port can output into the other port (the direction of energy flow depends on the sign of φ

_{12}). Otherwise, there will be some energy backflow, which means that the power transmission capacity declines, as shown in Figure 5. Compared with an ideal situation φ

_{12}= 90°, the power capacity is reduced by 13%, 29%, in the case of φ

_{12}= 60°, 45°, and 30°, respectively.

## 3. Evaluation Indices of Electrical Interoperability

#### 3.1. Definition of Key Impedance

_{P}, L

_{S}, and M are self-inductance of GA coil, self-inductance of VA coil, and their mutual inductance. The model adopts the T-type equivalent circuit of mutual inductance to realize a decoupled connection of GA and VA circuits. In addition to the design of coils on both sides, coil inductance parameters {L

_{P}, L

_{S}, M} are also affected by the relative position between the coils. As a result, compensation networks are introduced into both sides of charging system so as to compensate the reactive power generated by coil system.

_{P}, L

_{S}, M}, so that power electronics will not exceed their safe operating area.

_{S}, Z

_{P}, and Z

_{inv}are the three key impedances. Z

_{S}includes the load, VA compensation network, and decoupled VA coil (i.e., L

_{S}-M). On the basis of Z

_{S}range, Z

_{P}includes mutual inductance branch additionally. Z

_{inv}is the input impedance of the inverter, including GA compensation network, coil system and the whole VA circuit.

#### 3.2. Interoperability Evaluation Index I: Z_{inv}

_{inv}is to convert a safe operating area of the inverter into a safe impedance area of the circuit. Assume that the maximum voltage and current of the inverter are U

_{inv_max}and I

_{inv_max,}respectively.

_{inv}| and φ(Z

_{inv}) are the amplitude and phase of the impedance Z

_{inv}.

_{inv}are derived:

_{inv}is generally required to be ahead of I

_{inv}, which is essentially a constraint of φ(Z

_{inv}).

_{inv}amplitude constraints (13) and Z

_{inv}phase constraint (14), feasible impedance space of Z

_{inv}can be determined, and it can be transformed into a complex plane, as shown in Figure 7.

_{inv}. Note that Z

_{inv}is merely one of the evaluation indices, and it mainly evaluates the power capability of the inverter.

#### 3.3. Interoperability Evaluation Index II: Z_{S}/Z_{P}

_{S}/Z

_{P}is to convert current limitations of GA and VA coils into safe impedance area of the circuit. An important difference between the two evaluation indices is that the feasible space of Z

_{inv}is completely determined by GA, whereas the feasible space of Z

_{S}/Z

_{P}is determined by GA and VA together.

_{P_max}and I

_{S_max,}respectively.

_{S}/Z

_{P}| and φ(Z

_{S}/Z

_{P}) are the amplitude and phase of Z

_{S}/Z

_{P}.

_{S}/Z

_{P}are derived:

_{S}/Z

_{P}is determined, and it can also be transformed into the complex plane, as shown in Figure 9.

_{S}/Z

_{P}, which is similar to Figure 8. The main difference is that Z

_{S}/Z

_{P}evaluates the power capability of the GA-VA coil pair. In addition, it is recommended that the evaluation process should be carried out twice, i.e., M

_{max}case and M

_{min}case.

## 4. Interoperability Evaluation Based on Chinese WEVC Standard

#### 4.1. Feasible Impedance Space of Reference Devices

_{inv}space can be obtained, as displayed in Figure 12. The feasible Z

_{inv}space of WPT1~WPT3 appears as a similar shape, which is a part of a circle. As the power level increases, the feasible space shrinks significantly.

_{S}/Z

_{P}space can also be obtained based on Equation (19). Note that different mutual inductances result in different feasible Z

_{S}/Z

_{P}space, so the feasible Z

_{S}/Z

_{P}spaces at Z1(M

_{max}, M

_{min}), Z2(M

_{max}, M

_{min}), Z3(M

_{max}, M

_{min}) are displayed separately. In addition, transmission power is also involved in Equation (19). The feasible Z

_{S}/Z

_{P}spaces are displayed in Figure 13. They all appear a shape of circular segment. The increase of power and the decrease of mutual inductance lead to a decrease in the area of the feasible space.

#### 4.2. An Application Example: Evaluate Interoperability between Reference GA and VA

_{inv}and Z

_{S}/Z

_{P}points of the reference GA-VA pair should be within their corresponding regions. In the following part, the impedance points will be calculated according to the circuit parameters and test conditions published in the standard.

_{inv}and Z

_{S}/Z

_{P}points at minimum battery voltage. It can be found that all Z

_{inv}and Z

_{S}/Z

_{P}points are within their feasible range at corresponding power levels, except that a Z

_{S}/Z

_{P}point at WPT3/Z1 (M

_{min}) is out of the range slightly. The out-of-range point means when the reference GA-VA pair (WPT3/Z1) operates at minimum battery voltage and minimum coupling position, the GA coil current I

_{P}can exceed its limit slightly (3% estimated). Fortunately, the current margin of coil will ensure the normal operation of the system.

_{inv}and Z

_{S}/Z

_{P}points at maximum U

_{bat}and 100% rectifier duty cycle. There are 2/18 Z

_{inv}points and 16/18 Z

_{S}/Z

_{P}points out of range. This result indicates that as the battery voltage rises, if the controller does not regulate down the duty cycle of rectifier, Z

_{inv}and Z

_{S}/Z

_{P}will deviate from the ideal operating state, and cause voltages and currents to exceed the safe range.

_{inv}and Z

_{S}/Z

_{P}points can get closer to minimum U

_{bat}situation. Figure 18 and Figure 19 are Z

_{inv}and Z

_{S}/Z

_{P}points at maximum U

_{bat}and 56% rectifier duty cycle. Under such conditions the load resistance is

## 5. Conclusions and Discussions

_{inv}is adopted to ensure the safety of the inverter, and Z

_{S}/Z

_{P}is adopted to make sure the coil currents are within their limits. Feasible ranges of Z

_{inv}and Z

_{S}/Z

_{P}are obtained based on a set of reference devices in Chinese standard. The results of interoperability evaluation and experiments show that the reference devices are able to achieve the requirements of power capability. Moreover, it is necessary to reduce the duty cycle of the rectifier when the battery voltage rises so as to narrow down the variation of load resistance and avoid dangerous working conditions.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Energy flow at different φ

_{12}in a current cycle (M = 10 μH, I

_{1}= 10 A, I

_{2}= 10 A).

**Figure 13.**Feasible impedance space of Z

_{S}/Z

_{P}under different power and ground clearance levels.

GA: WPT1 | GA: WPT2 | GA: WPT3 | |
---|---|---|---|

VA: WPT1 | 3.7 kW | 3.7 kW | 3.7 kW |

VA: WPT2 | 3.7 kW | 7.7 kW | 7.7 kW |

VA: WPT3 | 3.7 kW | 7.7 kW | 11.1 kW |

GA: Z1(100–150 mm) | GA: Z2(100–210 mm) | GA: Z3(100–250 mm) | |
---|---|---|---|

VA: Z1(100–150 mm) | Supported | Supported | Supported |

VA: Z2(140–210 mm) | Not supported | Supported | Supported |

VA: Z3(170–250 mm) | Not supported | Not supported | Supported |

WPT1 | WPT2 | WPT3 | |
---|---|---|---|

U_{inv_max} | 840 V | 840 V | 840 V |

I_{inv_max} | 45 A | 45 A | 45 A |

I_{P_max} | 65 A | 65 A | 65 A |

I_{S_max} | 35 A | 50 A | 75 A |

Power Class | Z Class | M_{max}, U_{bat_min} | M_{max}, U_{bat_max} | M_{min}, U_{bat_min} | M_{min}, U_{bat_max} | ||||
---|---|---|---|---|---|---|---|---|---|

U_{bat}(V) | P_{bat}(kW) | U_{bat}(V) | P_{bat}(kW) | U_{bat}(V) | P_{bat}(kW) | U_{bat}(V) | P_{bat}(kW) | ||

WPT1 | Z1 | 320.1 | 3.25 | 451.4 | 3.31 | 320.2 | 3.25 | 450.9 | 3.30 |

Z2 | 319.8 | 3.24 | 449.7 | 3.28 | 320.5 | 3.26 | 449.9 | 3.29 | |

Z3 | 320.8 | 3.27 | 450.3 | 3.30 | 321.3 | 3.27 | 450.8 | 3.30 | |

WPT2 | Z1 | 321.4 | 6.57 | 451.1 | 6.49 | 319.7 | 6.51 | 449.3 | 6.47 |

Z2 | 319.5 | 6.62 | 447.2 | 6.64 | 319.7 | 6.62 | 446.7 | 6.62 | |

Z3 | 319.7 | 6.49 | 452.1 | 6.55 | 319.2 | 6.48 | 452.4 | 6.53 | |

WPT3 | Z1 | 319.6 | 10.03 | 449.5 | 10.02 | 319.5 | 10.02 | 449.6 | 9.97 |

Z2 | 319.5 | 9.92 | 451.5 | 9.93 | 321.7 | 10.06 | 447.9 | 9.75 | |

Z3 | 319.3 | 9.91 | 451.3 | 10.02 | 321.5 | 10.03 | 449.1 | 9.83 |

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**MDPI and ACS Style**

Shi, B.; Yang, F.; Wei, B.; Ouyang, M.
Electrical Interoperability Evaluating of Wireless Electric Vehicle Charging Systems Based on Impedance Space. *World Electr. Veh. J.* **2021**, *12*, 245.
https://doi.org/10.3390/wevj12040245

**AMA Style**

Shi B, Yang F, Wei B, Ouyang M.
Electrical Interoperability Evaluating of Wireless Electric Vehicle Charging Systems Based on Impedance Space. *World Electric Vehicle Journal*. 2021; 12(4):245.
https://doi.org/10.3390/wevj12040245

**Chicago/Turabian Style**

Shi, Bingkun, Fuyuan Yang, Bin Wei, and Minggao Ouyang.
2021. "Electrical Interoperability Evaluating of Wireless Electric Vehicle Charging Systems Based on Impedance Space" *World Electric Vehicle Journal* 12, no. 4: 245.
https://doi.org/10.3390/wevj12040245