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

: In the commercialization process of wireless electric vehicle charging (WEVC), it is essential to ensure the interoperability between diverse WEVC systems due to the wide application of various coil conﬁgurations and compensation topologies. This paper proposes a novel electrical interoperability evaluation method based on impedance indices and corresponding feasible space in the complex plane. Firstly, the electromagnetic description of the coil system is introduced to reveal the energy ﬂow process of WEVC system. Further, two key impedance indices and their feasible space are derived and veriﬁed. Interoperability evaluation results show that the reference devices in Chinese WEVC standard GB/T 38775.6 and GB/T 38775.7 are able to achieve the requirements of power capability. Moreover, it is necessary to reduce the duty cycle of rectiﬁer when the battery voltage rises so as to narrow down the variation of load resistance and avoid dangerous working conditions. The proposed method can effectively evaluate the electrical interoperability of WEVC systems from different manufacturers under different power or distance levels before conducting experiments.


Introduction
Wireless electric vehicle charging (WEVC) is stepping onto the stage of commercialization. However, in order to promote the progress of WEVC technology, it is necessary to maintain the diversity of product designs. Currently, there are many well-established coil configurations and compensation topologies for WEVC system [1].
Interoperability of WEVC means that ground assemblies (GA) and vehicle assemblies (VA) produced by different WEVC manufacturers can transmit power and meet the performance and functional requirements. It also implies that systems under different power and ground clearance levels should operate with each other in accordance with certain rules. Tables 1 and 2 show the definition and interoperability requirements of power levels and ground clearance levels in exposure drafts of Chinese GB/T standard [2][3][4][5]. The magnetic coupling system (i.e., coil system) and compensation circuit are two key components of WEVC systems. As a result, magnetic interoperability and electrical interoperability are proposed in international standards such as SAE J2954 [6]. This paper focuses on electrical interoperability, which means that the compensation networks of GA and VA should work well with each other and meet the power and efficiency requirement. Figure 1 summarizes the interoperability for different compensation topologies in literatures [7][8][9][10][11][12][13]. As a topology with remarkable performance, the interoperability between LCC topology and other topologies receives extensive attention. Ali Ramezani et al. analyzed the LCC-S topology in the time domain and pointed out that the topology has the characteristics of output constant voltage and can realize zero voltage switching [10]. Ruikun Mai et al. analyzed the S-LCC topology and proved that it can realize weak communication control and input zero phase angle [11]. In addition, interoperation experiments 2 of 14 on LCC compensation and Parallel compensation are carried out and the results show that all combinations of LCC and Parallel can achieve power and efficiency requirements [12,13]. However, these studies apply different evaluation methods and criteria, and even different circuit structures, which makes it difficult to get a general conclusion.   Not supported Not supported Supported The magnetic coupling system (i.e., coil system) and compensation circuit are two key components of WEVC systems. As a result, magnetic interoperability and electrical interoperability are proposed in international standards such as SAE J2954 [6]. This paper focuses on electrical interoperability, which means that the compensation networks of GA and VA should work well with each other and meet the power and efficiency requirement. Figure 1 summarizes the interoperability for different compensation topologies in literatures [7][8][9][10][11][12][13]. As a topology with remarkable performance, the interoperability between LCC topology and other topologies receives extensive attention. Ali Ramezani et al. analyzed the LCC-S topology in the time domain and pointed out that the topology has the characteristics of output constant voltage and can realize zero voltage switching [10]. Ruikun Mai et al. analyzed the S-LCC topology and proved that it can realize weak communication control and input zero phase angle [11]. In addition, interoperation experiments on LCC compensation and Parallel compensation are carried out and the results show that all combinations of LCC and Parallel can achieve power and efficiency requirements [12,13]. However, these studies apply different evaluation methods and criteria, and even different circuit structures, which makes it difficult to get a general conclusion. To describe the electrical interoperability, the VA side impedance ZVA and the GA side impedance ZGA 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. To describe the electrical interoperability, the VA side impedance Z 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. This paper proposes a novel electrical interoperability evaluation method based on impedance analysis. Current and voltage limits of key components are transformed into constraints of circuit impedance parameters, and consequently, the power capability of the system can be evaluated by inclusion relationship between the feasible impedance space and operating impedance points. The method is based on a general circuit model for WEVC system so it can be applied to various circuit topologies with a very small amount of calculation. This paper proposes a novel electrical interoperability evaluation method based on impedance analysis. Current and voltage limits of key components are transformed into constraints of circuit impedance parameters, and consequently, the power capability of the system can be evaluated by inclusion relationship between the feasible impedance space and operating impedance points. The method is based on a general circuit model for WEVC system so it can be applied to various circuit topologies with a very small amount of calculation.
The paper is organized as follows. Section 2 introduces the electromagnetic description of a coil system and derives the power equation of WEVC system. In Section 3, key impedance indices and their feasible space are proposed to describe electrical interoperability. The method is applied and validated based on a set of interoperability experiments in Section 4. Finally, some conclusions and discussions are summarized in Section 5.

Electromagnetic Description of Coil System
This section discusses the essence of a coil system from the perspective of electromagnetism. No matter what coil configuration and compensation topology are used in a wireless charging circuit, the coil system can be regarded as a storage and transmission system of electromagnetic energy, as shown in Figure 3. This is a two-port system, and energy can flow into or out of the system via the two ports. When neglecting the coil loss, the power flow of the system at arbitrary time is described as below.
(1) P 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.  Regarding the coil currents i1, i2 as state variables, the state equations of the system can be derived according to the electromagnetism.
Firstly, flux linkage equations are where λ1, λ2 are the magnetic fluxes of coil 1 and coil 2, L1, L2 are self-inductances, and M is mutual inductance between the two coils. Secondly, electricity and magnetism are connected by Faraday's law: where e1, e2 are the voltages at port 1 and port 2. The last state equation is a variant of Equation (1): Regarding the coil currents i 1 , i 2 as state variables, the state equations of the system can be derived according to the electromagnetism.
Firstly, flux linkage equations are where λ 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. Secondly, electricity and magnetism are connected by Faraday's law: where e 1 , e 2 are the voltages at port 1 and port 2. The last state equation is a variant of Equation (1): Combining Equations (2)-(4), we can obtain the following expression: Integrating the above equation, we can get magnetic energy stored in the coil system: In W mag , 1 2 L 1 i 2 1 and 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).  Suppose that i1 and i2 are alternating currents with a phase difference φ12: where I1, I2 are the effective values of i1, i2 and ω is the angular frequency. In one current cycle, the energy transferred from port 1 to port 2 is: Therefore, the transmission power of any coil system can be expressed as: According to Equation (9), the determinants of transmission power are summarized as follows. (a) Coil current angular frequency ω, higher frequency can help achieve higher power density. (b) Mutual inductance M, which reflects the magnetic coupling characteristics between the coils. (c) Effective values of coil currents I1, I2, which reflect the power capacity of coils, compensation network and other power electronics on both sides. (d) Phase difference φ12 of coil currents, which reflects the degree of mutual induced energy transformed into effective transmission energy. When φ12 = ±90°, all the energy input from one port can output into the other port (the direction of energy flow depends on the sign of φ12). 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 φ12 = 90°, the power capacity is reduced by 13%, 29%, in the case of φ12 = 60°, 45°, and 30°, respectively. Suppose that i 1 and i 2 are alternating currents with a phase difference ϕ 12 : where I 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: Therefore, the transmission power of any coil system can be expressed as: According to Equation (9), the determinants of transmission power are summarized as follows. (a) Coil current angular frequency ω, higher frequency can help achieve higher power density. (b) Mutual inductance M, which reflects the magnetic coupling characteristics between the coils. (c) Effective values of coil currents I 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.

Definition of Key Impedance
With the help of circuit theory, the interoperability of WEVC system can be further evaluated. Figure 6 sketches a universal WEVC circuit model, including voltage source, coil system, compensation networks, and battery load. LP, LS, and M are self-inductance of GA coil, self-inductance of VA coil, and their mutual inductance. The model adopts the Ttype 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 {LP, LS, 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. Therefore, impedance is the key to analysing the power flow in WEVC circuit, and it is also an important indicator for judging the interoperability between GA and VA. A GA-VA pair which achieves interoperability means that the circuit impedance is controlled within a reasonable range under all possible charging conditions and possible coil inductance parameters {LP, LS, M}, so that power electronics will not exceed their safe operating area.
As indicated in Figure 6, ZS, ZP, and Zinv are the three key impedances. ZS includes the load, VA compensation network, and decoupled VA coil (i.e., LS-M). On the basis of ZS range, ZP includes mutual inductance branch additionally. Zinv is the input impedance of the inverter, including GA compensation network, coil system and the whole VA circuit.

Definition of Key Impedance
With the help of circuit theory, the interoperability of WEVC system can be further evaluated. Figure 6 sketches a universal WEVC circuit model, including voltage source, coil system, compensation networks, and battery load. L 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.

Definition of Key Impedance
With the help of circuit theory, the interoperability of WEVC system can be further evaluated. Figure 6 sketches a universal WEVC circuit model, including voltage source, coil system, compensation networks, and battery load. LP, LS, and M are self-inductance of GA coil, self-inductance of VA coil, and their mutual inductance. The model adopts the Ttype 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 {LP, LS, 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. Therefore, impedance is the key to analysing the power flow in WEVC circuit, and it is also an important indicator for judging the interoperability between GA and VA. A GA-VA pair which achieves interoperability means that the circuit impedance is controlled within a reasonable range under all possible charging conditions and possible coil inductance parameters {LP, LS, M}, so that power electronics will not exceed their safe operating area.
As indicated in Figure 6, ZS, ZP, and Zinv are the three key impedances. ZS includes the load, VA compensation network, and decoupled VA coil (i.e., LS-M). On the basis of ZS range, ZP includes mutual inductance branch additionally. Zinv is the input impedance of the inverter, including GA compensation network, coil system and the whole VA circuit. Therefore, impedance is the key to analysing the power flow in WEVC circuit, and it is also an important indicator for judging the interoperability between GA and VA. A GA-VA pair which achieves interoperability means that the circuit impedance is controlled within a reasonable range under all possible charging conditions and possible coil inductance parameters {L P , L S , M}, so that power electronics will not exceed their safe operating area.
As indicated in Figure 6, Z 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.

Interoperability Evaluation Index I: Z inv
The role of Z 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.
According to Ohm's law of AC circuit, The input power can be expressed as where |Z inv | and ϕ(Z inv ) are the amplitude and phase of the impedance Z inv . From Equations (10) and (12), the amplitude constraints of Z inv are derived: In addition, in order to ensure the soft switching operation of the inverter, the phase of U inv is generally required to be ahead of I inv , which is essentially a constraint of ϕ(Z inv ).
With the help of the Z 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.

Interoperability Evaluation Index I: Zinv
The role of Zinv 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 Uinv_max and Iinv_max, respectively.
According to Ohm's law of AC circuit, The input power can be expressed as where |Zinv| and φ(Zinv) are the amplitude and phase of the impedance Zinv. From Equations (10) and (12), the amplitude constraints of Zinv are derived: In addition, in order to ensure the soft switching operation of the inverter, the phase of Uinv is generally required to be ahead of Iinv, which is essentially a constraint of φ(Zinv).
With the help of the Zinv amplitude constraints (13) and Zinv phase constraint (14), feasible impedance space of Zinv can be determined, and it can be transformed into a complex plane, as shown in Figure 7.

Interoperability Evaluation Index II: ZS/ZP
The power Equation (9) indicates that when diverse GAs and VAs are paired, the coil currents could change due to variation in circuit topology and parameters, even if the target power does not change. As a result, GA and VA coil currents may exceed their limit. Based on this fact, the role of ZS/ZP 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 Zinv is completely determined by GA, whereas the feasible space of ZS/ZP is determined by GA and VA together.
Assume that the maximum currents of GA and VA coils are IP_max and IS_max, respectively.
From Equation (19), the feasible impedance space of ZS/ZP is determined, and it can also be transformed into the complex plane, as shown in Figure 9.

Interoperability Evaluation Index II: Z S /Z P
The power Equation (9) indicates that when diverse GAs and VAs are paired, the coil currents could change due to variation in circuit topology and parameters, even if the target power does not change. As a result, GA and VA coil currents may exceed their limit. Based on this fact, the role of Z 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.
Assume that the maximum currents of GA and VA coils are I P_max and I S_max, respectively.
According to Kirchhoff's voltage law, . I P Z P + . I S Z S = 0.
Hence, |I P |/|I S | = |Z S /Z P |, ϕ(I P , I S ) = −ϕ(Z S /Z P ), where |Z S /Z P | and ϕ(Z S /Z P ) are the amplitude and phase of Z S /Z P . The transmission power can be expressed as From Equations (15) and (18), the amplitude constraints of Z S /Z P are derived: From Equation (19), the feasible impedance space of Z S /Z P is determined, and it can also be transformed into the complex plane, as shown in Figure 9. Figure 10 shows the steps of interoperability evaluation using Z 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.  Figure 10 shows the steps of interoperability evaluation using ZS/ZP, which is similar to Figure 8. The main difference is that ZS/ZP 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., Mmax case and Mmin case.

Interoperability Evaluation Based on Chinese WEVC Standard
In the Chinese standard for WEVC, a set of reference devices is developed with the aim to test the interoperability of market-developed devices. The reference devices include one reference GA applied to all power and ground clearance levels (WPT1~WPT3, Z1~Z3), and nine reference VAs for WPT1~WPT3, Z1~Z3, respectively [3,4]. If the marketdeveloped device can pair up with reference devices and achieve safe charging at expected power and relative positions, it will pass the interoperability test and get market access.
However, the interoperability test between reference devices and market-developed devices requires a large cost, so it is generally carried out after the design stage. As a result, the interoperability test can hardly help improve the design of market-developed devices. This section will apply the interoperability evaluation method to reference devices, so that R&D engineers of WEVC could use it to evaluate the interoperability between their devices and reference devices, and improve their design at the early stage.

Feasible Impedance Space of Reference Devices
The double-sided LCC compensation topology is adopted in the reference devices of Chinese standard due to its good performance. The circuit diagram is shown in Figure 11, and the current and voltage limits are listed in Table 3.  Figure 10 shows the steps of interoperability evaluation using ZS/ZP, which is similar to Figure 8. The main difference is that ZS/ZP 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., Mmax case and Mmin case.

Interoperability Evaluation Based on Chinese WEVC Standard
In the Chinese standard for WEVC, a set of reference devices is developed with the aim to test the interoperability of market-developed devices. The reference devices include one reference GA applied to all power and ground clearance levels (WPT1~WPT3, Z1~Z3), and nine reference VAs for WPT1~WPT3, Z1~Z3, respectively [3,4]. If the marketdeveloped device can pair up with reference devices and achieve safe charging at expected power and relative positions, it will pass the interoperability test and get market access.
However, the interoperability test between reference devices and market-developed devices requires a large cost, so it is generally carried out after the design stage. As a result, the interoperability test can hardly help improve the design of market-developed devices. This section will apply the interoperability evaluation method to reference devices, so that R&D engineers of WEVC could use it to evaluate the interoperability between their devices and reference devices, and improve their design at the early stage.

Feasible Impedance Space of Reference Devices
The double-sided LCC compensation topology is adopted in the reference devices of Chinese standard due to its good performance. The circuit diagram is shown in Figure 11, and the current and voltage limits are listed in Table 3.

Interoperability Evaluation Based on Chinese WEVC Standard
In the Chinese standard for WEVC, a set of reference devices is developed with the aim to test the interoperability of market-developed devices. The reference devices include one reference GA applied to all power and ground clearance levels (WPT1~WPT3, Z1~Z3), and nine reference VAs for WPT1~WPT3, Z1~Z3, respectively [3,4]. If the market-developed device can pair up with reference devices and achieve safe charging at expected power and relative positions, it will pass the interoperability test and get market access.
However, the interoperability test between reference devices and market-developed devices requires a large cost, so it is generally carried out after the design stage. As a result, the interoperability test can hardly help improve the design of market-developed devices. This section will apply the interoperability evaluation method to reference devices, so that R&D engineers of WEVC could use it to evaluate the interoperability between their devices and reference devices, and improve their design at the early stage.

Feasible Impedance Space of Reference Devices
The double-sided LCC compensation topology is adopted in the reference devices of Chinese standard due to its good performance. The circuit diagram is shown in Figure 11, and the current and voltage limits are listed in Table 3.  By using the method introduced in Section 3.2. and substituting the data in Table 3 into the equations, the feasible Zinv space can be obtained, as displayed in Figure 12. The feasible Zinv 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.  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. Figure 11. Reference GA-VA circuit. By using the method introduced in Section 3.2. and substituting the data in Table 3 into the equations, the feasible Z 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.  By using the method introduced in Section 3.2. and substituting the data in Table 3 into the equations, the feasible Zinv space can be obtained, as displayed in Figure 12. The feasible Zinv 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.  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. Similarly, the feasible Z 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.

An Application Example: Evaluate Interoperability between Reference GA and VA
As a reference device for interoperability test, the reference GA-VA pair is supposed to be interoperable. Therefore, the Zinv and ZS/ZP 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.
Since the parameters of the compensation network have been listed in the standard documents, it will not be repeated here. It is worth mentioning that the battery load and rectifier can be regarded as a load resistance, and its value depends on the operating condition of battery and rectifier. As stated in the standard document, the battery voltage range is set to 320~450 V. Assuming that the duty cycle of the rectifier D = 100% regardless of whether the battery voltage is at the maximum or minimum, and the load resistances are: Accordingly, the impedance points of reference GA-VA pair are scattered over the impedance space, as shown in Figures 14-17. Figures 14 and 15 are Zinv and ZS/ZP points at minimum battery voltage. It can be found that all Zinv and ZS/ZP points are within their feasible range at corresponding power levels, except that a ZS/ZP point at WPT3/Z1 (Mmin) is out of the range slightly. The out-ofrange point means when the reference GA-VA pair (WPT3/Z1) operates at minimum battery voltage and minimum coupling position, the GA coil current IP can exceed its limit slightly (3% estimated). Fortunately, the current margin of coil will ensure the normal operation of the system.

An Application Example: Evaluate Interoperability between Reference GA and VA
As a reference device for interoperability test, the reference GA-VA pair is supposed to be interoperable. Therefore, the Z 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.
Since the parameters of the compensation network have been listed in the standard documents, it will not be repeated here. It is worth mentioning that the battery load and rectifier can be regarded as a load resistance, and its value depends on the operating condition of battery and rectifier. As stated in the standard document, the battery voltage range is set to 320~450 V. Assuming that the duty cycle of the rectifier D = 100% regardless of whether the battery voltage is at the maximum or minimum, and the load resistances are: Accordingly, the impedance points of reference GA-VA pair are scattered over the impedance space, as shown in Figures 14-17. Figures 14 and 15 are Z 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.       Figures 16 and 17 are Z 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.    As the battery voltage rises, reducing the duty cycle can narrow down the variation of load resistance, so that the Zinv and ZS/ZP points can get closer to minimum Ubat situation. Figures 18 and 19 ( The figures show that all points return to their feasible range. This analysis proves the significance of introducing a controlled rectifier into the WEVC system. It also proves that the reference devices provided by Chinese standard are able to achieve the requirements of power capability.  As the battery voltage rises, reducing the duty cycle can narrow down the variation of load resistance, so that the Z inv and Z S /Z P points can get closer to minimum U bat situation. Figures 18 and 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 π sin 0.56 · π 2 U bat_max 2 P out at U bat_max , D = 56%.
The figures show that all points return to their feasible range. This analysis proves the significance of introducing a controlled rectifier into the WEVC system. It also proves that the reference devices provided by Chinese standard are able to achieve the requirements of power capability. As the battery voltage rises, reducing the duty cycle can narrow down the variation of load resistance, so that the Zinv and ZS/ZP points can get closer to minimum Ubat situation. Figures 18 and 19 ( The figures show that all points return to their feasible range. This analysis proves the significance of introducing a controlled rectifier into the WEVC system. It also proves that the reference devices provided by Chinese standard are able to achieve the requirements of power capability.  Full power tests are conducted to demonstrate the interoperability of the reference GA and VA devices. Table 4 lists the output power achieved in the lab, including all power and ground clearance levels. The tests cover the extremum of coupling conditions and battery voltages, and all results show sufficient power capability.

Conclusions and Discussions
A wireless electric vehicle charging system includes coils, compensation networks, and converters. No matter what coil configurations and compensation topologies are adopted, the coil system can be regarded as a storage and transmission system of electromagnetic energy. Two types of energy are stored dynamically in the system, including the energy of self-induced flux and energy of mutual induced flux. The former flows in to one side of the coil, whereas the latter flows through both sides and transfer power from one to the other. Accordingly, frequency, amplitudes, and phase difference of coil currents, as well as the mutual inductance of coils are determinants of transmission power.
Various coil configurations and compensation topologies bring about the problem of interoperability, which means ground assemblies (GA) and vehicle assemblies (VA) can Full power tests are conducted to demonstrate the interoperability of the reference GA and VA devices. Table 4 lists the output power achieved in the lab, including all power and ground clearance levels. The tests cover the extremum of coupling conditions and battery voltages, and all results show sufficient power capability.

Conclusions and Discussions
A wireless electric vehicle charging system includes coils, compensation networks, and converters. No matter what coil configurations and compensation topologies are adopted, the coil system can be regarded as a storage and transmission system of electromagnetic energy. Two types of energy are stored dynamically in the system, including the energy of self-induced flux and energy of mutual induced flux. The former flows in to one side of the coil, whereas the latter flows through both sides and transfer power from one to the other. Accordingly, frequency, amplitudes, and phase difference of coil currents, as well as the mutual inductance of coils are determinants of transmission power.
Various coil configurations and compensation topologies bring about the problem of interoperability, which means ground assemblies (GA) and vehicle assemblies (VA) can achieve a wireless power transmission that meets the performance and functional require-ments, especially the power requirement. This paper proposes an electrical interoperability evaluation method based on two impedance indices. Z 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.