Mitigation Conducted Emission Strategy Based on Transfer Function from a DC-Fed Wireless Charging System for Electric Vehicles

Abstract

The large dv/dt and di/dt outputs of power devices in wireless charging system (WCS) in electric vehicles (EVs) always introduce conducted electromagnetic interference (EMI) emissions. This paper proposes a mitigation conducted emission strategy based on transfer function from a direct current fed (DC-fed) WCS for EVs. A complete test for the DC-fed WCS is set up to measure the conducted emission of DC power cables in a frequency range of 150 kHz–108 MHz. An equivalent circuit with high-frequency parasitic parameters for WCS for EV is built based on measurement results to obtain the characteristics of conducted emission from WCS. The transfer functions of differential mode (DM) interference and common mode (CM) interference were established. A judgment method of using transfer functions to determine the dominated interference mode responsible for EMI is proposed. From the comparison of simulation results between CM or DM and CM+DM interference, it can be seen that the CM interference is the dominated interference mode which causes the conducted EMI in WCS in EVs. A strategy of giving priority to the dominated interference mode is proposed for designing the CM interference filter. Finally, the conducted voltage experiment is performed to verify the mitigation conducted emission strategy. The conducted voltage of simulation and experiment is decreased respectively by 21.17 and 21.4 dBμV at resonance frequency 30 MHz. The conduced voltage at frequency range of 150 kHz–108 MHz can be mitigated to below the limit level-3 of CISPR25 standard (GB/T 18655-2010) by adding the CM interference filters.

1. Introduction

Wireless charging technologies, as an attractive alternative to cabled charging, are attracting widespread interest in the field of consumer electronics, medical implants and electric vehicles [1,2,3,4], due to their convenient and safe characteristics [5,6,7]. There are two kinds of power supply system in wireless charging system (WCS): alternating current fed (AC-fed) and direct current fed (DC-fed) system. DC-fed WCS is used in fast charging with high current and voltage and widely applied in electric vehicles (EVs) in future.

As for wireless charging for EVs, many researchers pay attention to improving the charging efficiency and electromagnetic compatibility (EMC). Some researchers adopt the method of optimizing the structure of the coupled coil pair, the compensation circuit and pulse width modulation (PWM) control strategy to improve the efficiency of wireless charging [8,9,10,11,12,13]. As for EMC, the two key considerations consist of electromagnetic emission and electromagnetic susceptibility (EMS). The electromagnetic emission of WCS mainly includes the emission of the electromagnetic field (EMF) generated by the coupling coils, the conducted emission and the radiated emission from the power cables.

As for electromagnetic emission for WCS, there are lots of research mainly focused on reducing the EMF which will exposure to humans. Different power levels of WCS have been researched to analyze the distribution characteristics of EMF. Some kinds of method were proposed to reduce magnetic field exposure, including adding a shield plate, optimizing coils shape and ferrite arrangement, matching impedance and adding a reverse magnetic field [14,15,16,17]. The fast switching of these power semiconductor devices such as MOSFET used in invertor of WCS is controlled by PWM, as result in generation of conducted EMI and low power quality. In addition some radiated EMI due to conducted-EMI may be generated to influence or even damage some onboard components such as sensors, analog devices, wireless devices of EVs, etc. Therefore, it is very significant to predict and suppress the conducted-EMI for WCS.

However, few research on conducted-EMI for WCS was presented previously. Although some studies on the conducted-EMI from high-voltage systems in EVs such as motor drive system, DC–DC converter and onboard charger have been carried out [18,19,20,21,22,23], the model and characteristics of the conducted-EMI for WCS are not yet proposed. In addition, filtering is usually used to mitigate the conducted-EMI. The analysis and design method of EMI filtering are always proposed based on constant source impedance and load impedance which are varied in practice. It may lead to inadequate mitigation and generation of new resonance due to impedance mismatch. In addition, the common mode (CM) and DM filters are designed separately by CM and DM interference propagation respectively. Then a combination of the CM and DM filters can result in bulky volume and high cost, and induce an unwanted resonance due to parameters of filter and high frequency parasitic parameters. On the other hand, the DM interference can lead to the CM interference, and the CM interference also can lead to the DM interference. The DM filter or CM filter can mitigate both of the CM and DM interference simultaneously. Therefore, a combination of the CM and DM filters cause filtering repeatedly, it means over design.

From the above proposed problems, firstly, it is necessary to build an equivalent circuit with high-frequency parasitic parameters for WCS for EV to predict the conducted-EMI for WCS. From which the practical EMI source impedance and load impedance can be taken into consideration. Secondly, the transfer functions of DM interference and CM interference were established to predict and determine the dominated interference mode responsible for EMI from WCS in EVs. Meanwhile, comparison of simulation results between CM or DM and CM+DM interference is performed to prove dominated interference mode. Then, a strategy of giving priority to the dominated interference mode is proposed for designing filter.

The organization of this paper is as follows. Session 2 shows a complete test for the DC-fed WCS, in order to measure the conducted-EMI of DC power cables in a frequency range of 150 kHz–108 MHz. In Section 3, modeling and simulation of the WCS for the conducted-EMI are presented. In Section 4, analysis and estimation for the conducted-EMI is performed based on the transfer function, and a judgment method of using transfer functions to determine the dominated interference mode responsible for EMI is proposed. Section 5 gives the method of designing the filters. In Section 6, the conducted voltage experiment for WCS is performed to verify efficiency and feasibility of the mitigation conducted-EMI strategy. In Section 7, conclusions and future works are proposed.

2. System Conducted-EMI Emission Measurement

2.1. Conducted-EMI Emission Setup

A complete test setup for conducted-EMI emissions from a DC-fed WCS on an EV in an EMI laboratory as shown in Figure 1 and mainly consists of a DC voltage source, DC power cables, standard line impedance stabilization networks (LISNs), a wireless charging controller, a couple of coils and an EMI-receiver. Measurements are performed to comply with the CISPR 25 standard which provides conducted EMI emission limits for vehicle components in a frequency range of 150 kHz to 108 MHz as shown in

Table 1. CISPR25 class3-average limits for conducted voltage.

Frequency/MHz	Limit/dB (μV)
0.15–0.30	70
0.53–1.8	50
5.9–6.2	45
26–28	36
30–88	36
88–108	30

. Two LISNs terminated with 50 Ω resistances provide DC power from a DC voltage source to the wireless charging controller using two shielded cables (2 m). The power invertor in a wireless charging controller with 425 V DC input is connected to coupling coils using two shielded cables (1.5 m). The WCS operates at a frequency of 85 kHz with a working gap of 150 mm and a system transmission power of 3.7 kW with a circular magnetic coupler. With this configuration, the total conducted-EMI noise voltage signals in DC cables can be picked up by any one of LISNs impedances connected to an EMI receiver.

2.2. Conducted EMI Experiment Results

The test platform as shown in Figure 2 is set up. Figure 3 shows the experimental results and it can be found that the conducted-EMI noise voltage of the wireless charging controller is dominant in a frequency range of 150 kHz–108 MHz and is not compliant with CISPR25 (GB/T 18655), as shown in Table 1. From Figure 3, it can be seen that the conducted voltage exceeds the limit requirement in the range of 500 kHz–2 MHz and 30 MHz–108 MHz. Therefore, it is necessary to build a high frequency circuit mode for analyzing the source and paths of conducted-EMI so as to predict the conducted-EMI emissions.

3. System Modeling and Analysis

3.1. The Construction of WCS

Without any physical connection in WCS, the power of 425 V DC voltage at the ground side is transmitted to the vehicle side and converted into the power of the 400 V DC for the battery. The designed system mainly consists of DC voltage source V_DC, filter capacitor C₇, full bridge invertor (S₁–S₄), coupled coils (primary coil L₁ and secondary coil L₂), LCC compensation, rectification and filtering and electric vehicle battery V_bat can be seen in Figure 4. The circuit parameters of WCS are designed and calculated, as shown in

Table 2. Circuit parameters of wireless charging system (WCS).

Symbol	Meaning	Value
VDC	DC power supply	425 V
L1, L2	Inductance of primary coil and secondary coil	226.4 µH
LM	Mutual inductance of primary coil and secondary coil	79.8 µH
Cƒ1, Cƒ2	Primary and secondary compensated capacitor	55.9 nF
Lƒ1, Lƒ2	Primary and secondary compensated inductance	62.7 µH
C1, C2	Primary and secondary compensated capacitor	21.4 nF/24.1 nF
C0	Rectifier inductance	34.3 µF
Lƒ3	Rectifier capacitor	131 µH
Vbat	Equivalent resistance	40 Ω

.

3.2. Simulation of the Electrical Characteristics of WCS

Based on the construction of the WCS in Figure 4, a WCS model is set up in Matlab/Simulink software to obtain the electrical characteristics of the WCS. The invertor circuit is driven by two pairs of sinusoidal pulse width modulation (SPWM) in complementary phase. The voltage and current for the battery are shown in Figure 5, respectively. It can be found that the current is 9.15 A and the voltage is 400 V to meet the 3.7 kW power requirement.

3.3. Parasitic Parameters

The parameters of the power component in WCS can be tested directly, such as when the self-inductance L₁ and L₂, mutual inductance L_M and distributed capacitance C₁₀ of the coils are measured by using the RC meter as shown in Figure 6a,b. Meanwhile, the parameters can also be obtained through modeling and simulation in ANSYS as shown in Figure 6c. The simulation results are in agreement with the measurement results, as shown in Table 2 and

Table 3. Parasitic parameters of WCS.

Symbol	Value	Symbol	Value
LP1, LP2	10 nH	RLf1, RLf2	0.03 Ω
LC0	50 nF	RLf3	1 μΩ
LP	0.2 μH	RL1/RL2	115 μΩ
LCf1, LCf2	10 nH	Cp1/Cp2	380 pF
LC1, LC2	8 nH	C3–C6	142 pF
Lcable1, Lcable2, Lcable3	1.76 µH	C10	21.4 nF
Rcable1, Rcable2, Rcable3	0.0524 Ω	C11/C12	80 pF
RS	0.1 Ω	C13	130 pF

.

From Figure 4, there are some parasitic parameters in inverter system in WCS. Among them, L_P1, L_P2 are inductances of connecting cables, L_P, R_S are the parasitic inductances and parasitic resistance of C₇, C₃–C₆ are the inter-electrode inductances of the MOSFET, R_L0, R_L1, R_L2, R_Lf1, R_Lf2 are the parasitic resistances of C₀, the coupling coils, L_f1 and L_f2, respectively. L_C0, L_Cf1, L_Cf2, L_C1 and L_C2 are the parasitic inductances of C₀, C_f1, C_f2, C₁ and C₂, respectively. L_cable1, L_cable2, L_cable3, R_cable1, R_cable2 and R_cable3 are the parasitic inductances and parasitic resistances on the connecting cable respectively. C₁₁, C₁₂ and C₁₃ are parasitic capacitances of primary coil, secondary coil and battery relative to the ground; C₁₀ is mutual capacitance of the coupling coils. C₁₄, C₁₅ are the parasitic capacitances of the two arms midpoint of the invertor relative to the ground.

It is necessary that the parasitic parameters should be extracted and determined for modeling of the WCS for the conducted-EMI. Some measurements for Z parameters and S parameters were made with time-domain reflectrometry and a vector network analyzer. A modeling method based on measurement-based model of the electromagnetic emissions is used to achieve high-frequency circuit model for element and system. The value of elements such as inductance or capacitance is regulated and determined by comparing between the simulation and measurement of Z parameters and S parameters [23], as shown in Table 3.

Therefore, an equivalent circuit of the WCS with high-frequency parasitic parameters is built, and the symbol of parasitic parameters is marked by blue color as shown in Figure 7.

3.4. Noise Source

Fast switching of the MOSFETs of invertor causes large dv/dt and di/dt, as a result introduces conducted-EMI emissions. Therefore, the interference signal can be extracted from invertor arms. According to Figure 7, a circuit model with high-frequency parameters is built in Matlab/Simulink to obtain the noise source signals of CM interference and DM interference. The red blocks present the sensor of voltage or current, the green blocks present the collector of voltage or current. The noise source signals of CM interference and DM interference are shown in Figure 8, respectively.

3.5. Modeling and Simulation of the WCS for the Conducted-EMI

Computer Simulation Technology (CST) as an electromagnetic simulation software is used for modeling and simulation for EMC. The conducted and radiated emissions in the wide range frequency and time domains can be obtained by CST. A high-frequency circuit model for the WCS is established by CST to obtain the conducted interference voltage, as shown in Figure 9. The signals of the DM and CM interference sources U_CM and I_DM are obtained from Matlab/Simulink, as mentioned in Section 3.4. Because conducted interference voltage is an important indicator of conducted-EMI, the model of LISNs consist of R₁, R₂, C₈ and C₉ is built to obtain the conducted interference voltage by adding probe P1 and P2.

The conducted voltage simulation results are compared with the experimental results as shown in Figure 10. It can be found that the conducted voltage characteristics of simulation are basically same as those in the experiment. From Figure 10, it can be shown that the second harmonic appears at 170 kHz, the harmonic frequency interval is 85 kHz in the low frequency band, which is consistent with the switching frequency of MOSFET in invertor of WCS, the resonance phenomenon appears at 30 MHz and the amplitude of conducted voltage is similar before 30 MHz. Meanwhile, the conducted voltage in both cases exceeds CISPR25 (GB/T18655-2010) limits in the frequencies range of 500 kHz–2 MHz and 25 MHz–30 MHz. So in the frequencies range of 150 kHz–30 MHz, the high-frequency equivalent circuit of the WCS established by CST has a high accuracy in somehow. However, there is some difference between simulation and experiment results in the frequencies range of 30 MHz–108 MHz. Because some high-frequency parasitic parameters in the frequencies range of 30 MHz–108 MHz were not taken into consideration.

4. Analysis and Estimation for the Conducted-EMI

The DM propagation paths and the CM propagation paths for conducted-EMI emission model of the WCS are respectively carried out. The following simulations are based on the assumption that the S₁ and S₄ are conducting, S₂ and S₃ are non-conducting and the current flows through C₄ and C₅. The sources of the noises are injected at midpoint of the first arm due to the symmetry of the circuit.

4.1. Analysis for DM Propagation Paths

There is a parasitic capacitor C₁₀ between primary coil and secondary coil, so the DM interference current may exist in the secondary circuit. However, it depends on the bandwidth of high frequency transformer. This paper focus on the frequency range of 150 kHz–108 MHz, due to the larger capacitive reactance, we assume that the DM interference current mainly exists in the primary circuit. The DM propagation paths of the WCS are shown in Figure 11. The sequence in which the $I_{DM}$ flows through the components is as follows:

• Current loop I₁: $I_{DM}\to C_5\to L_{P2}\to \left({}_{R_S\to L_P\to C_9}^{R_2\to C_9\to C_8\to R_1}\right)\to L_{P1}\to I_{DM}$.
• Current loop I₂: $I_{DM}\to L_{f1}\to R_{Lf1}\to \left({}_{R_S\to L_P\to C_9}^{L_{C1}\to C_1\to L_{cable1}\to R_{cable1}\to L_1\to R_{L1}}\right)\to L_{P2}\to \left({}_{R_S\to L_P\to C_7}^{R_2\to C_9\to C_8\to R_1}\right)\to L_{P1}\to I_{DM}$.

From Figure 11, it can be seen that the DM interference current passes through the LISNs and the power cables which connects with the DC voltage source. So it is possible that the DM interference current may not only flow on the DC power cables but can also affect the quality of the DC voltage source.

The equivalent circuit of the DM interference paths is shown in Figure 12. From Figure 12, it can be seen that Z₁, Z₂, Z₃, Z₄ and Z₅ represent part of circuital impedance, respectively. And the function was given by Equations (1)–(5). The relationship between the output noise energy and the input noise energy in the system is given by the transfer function in Equation (6). Then, a Bode-diagram for the transfer function is drawn, as shown in Figure 13. From (6) and Figure 13, some DM interference elements in the frequencies range of 150 kHz–180 MHz can be illustrated.

$$Z_1=R_1+\frac{1}{s{C}_8}+\frac{1}{s{C}_9}+R_2$$

(1)

$$Z_2=\frac{1}{s{C}_7}+s{L}_P+R_S$$

(2)

$$Z_3=s{L}_{f1}+R_{Lf1}+\frac{1}{s{C}_1}$$

(3)

$$Z_4=s{L}_{cf1}+\frac{1}{s{C}_{f1}}$$

(4)

$$Z_5=\frac{1}{s{C}_1}+s{L}_{cable1}+R_{cable1}+s{L}_1+R_{L1}$$

(5)

$$\begin{array}{l}\hfill G(S_1)=\frac{V_{RD}}{V_{DM}}=\frac{Z_1//Z_2}{(Z_1//Z_2)+\left[Z_3+(Z_4//Z_5)\right]//C_3+Z_{LP1}+Z_{LP2}}·\frac{Z_{R1}}{Z_1}\\ =\frac{3.75e^{-32}{s}^4+7.5e^{-26}{s}^3+3.875e^{-}{}^{20}{s}^2+2.5e^{-15}{s}^5+1.25e^{-9}}{2.25e^{-63}{s}^9+6.75e^{-57}{s}^8+2.255e^{-48}{s}^7+6.75e^{-42}{s}^6+6.9e^{-36}{s}^5+2.7e^{-30}{s}^4+4.525e^{-25}{s}^3+1.575e^{-19}{s}^2}\end{array}$$

(6)

From Figure 13, it can be also seen that the DM conducted voltage is −10 dBμV at 150 kHz. Along with the frequency increasing, the magnitude of the DM conducted interference voltage is rapidly declining. Thus, the DM interference mainly exists at the low frequency band.

4.2. Analysis for CM Propagation Paths

Similarly, there are four different CM propagation paths as shown in Figure 14, it can be found that the CM interference current passes the LISNs and the power cables connected to the DC voltage source. The sequence in which the $I_{CM}$ flows through the components is as follows:

• Current loop I1: $I_{CM}\to \left({}_{L_{P1}\to R_1\to C_8}^{C_5\to L_{P2}\to R_2\to C_9}\right)\to ground\to I_{CM}$;
• Current loop I2: $I_{CM}\to \left({}_{C_5}^{E_1\to R_{L1}}\right)\to C_{11}\to ground\to I_{CM}$;
• Current loop I3: $I_{CM}\to E_1\to C_{10}\to \left({}_{R_{l2}\to C_{12}}^{E_2\to E_3\to V_{bat}\to C_{13}}\right)\to ground\to I_{CM}$;
• Current loop I4: $I_{CM}\to C_{P1}\to ground\to I_{CM}$.

Among them, $E_1$ is a path of $L_{f1}\to R_{Lf1}\to L_{C1}\to C_1\to L_{cable1}\to R_{cable1}\to L_1$; $E_2$ is a path of $L_2\to L_{cable2}\to R_{cable2}\to C_2\to L_{C2}\to L_{f2}\to R_{Lf2}$ and $E_3$ is a path of $R_{Lf3}\to L_{f3}\to L_{cable3}\to R_{cable3}$.

This part of the interference current may generate conducted-EMI from DC power cables at ground side and battery side in EVs, so it is significant to predict the CM interference of WCS. An equivalent circuit of the CM interference paths is shown in Figure 15, R_L2 and L2 are divided equally into RL2-1, RL2-2 and L2-1, L2-2. In Figure 15, you can see Z₁, Z₂, Z₃, Z₄ and Z₅ and Z₆ which represent a part of circuital impedance, respectively. And the function was established by Equations (7)–(12). The relationship between the output noise energy and the input noise energy in the system is given by transfer function in Equation (13). Then, the bode-diagram of the transfer function is drawn, as shown in Figure 16. From Equation (13) and Figure 16, some CM interference elements in the frequencies range of 150 kHz–180 MHz can be illustrated.

$$Z_1=(R_1+\frac{1}{s{C}_8}+s{L}_{P1})//(s{L}_{P2}+\frac{1}{s{C}_9}+R_2+\frac{1}{s{C}_5})$$

(7)

$$Z_2=s{L}_{2-2}+R_{2-2}+R_{bat}$$

(8)

$$Z_3=s{L}_{2-1}+R_{2-1}+s{L}_{cable2}+R_{cable2}+s{L}_{f2}+R_{Lf2}+s{L}_0+R_{L0}+\frac{1}{s{C}_2}+s{L}_{C2}+s{L}_{cable3}+R_{cable3}$$

(9)

$$Z_4=s{L}_{cf1}+R_{Lf1}+\mathrm{s}{L}_{C1}+\frac{1}{s{C}_1}+s{L}_{cable1}+R_{cable1}+s{L}_{C1}+R_{L1}$$

(10)

$$Z_5=(Z_2//Z_3)+Z_{C13}$$

(11)

$$Z_6=\left[(Z_5+Z_4)//Z_{C5}\right]+Z_{C11}$$

(12)

$$\begin{array}{l}G(S_2)=\frac{V_{RC}}{V_{CM}}=\frac{(Z_6//Z_{CP1})R_1}{{(Z_1//Z_6//Z_{CP1})}^2(Z_{CP1}+Z_{C8}+R_1)}\\ =\frac{7.32e^{-3}{s}^4+2.446e^5{s}^3+2.078e^1{}^0{s}^2+4.4418e^{14}{s}^5}{7.294e^4{s}^7+1.23e^{12}{s}^6+1.56e^{17}{s}^5+6.631e^{21}{s}^4+9.4e^{25}{s}^3}\end{array}$$

(13)

It can be seen that the magnitude of the CM interference voltage is between −5 dBμV and 0 dBμV in the frequency range of 150 kHz–108 MHz, which is much higher than DM interference.

In summary, from the view of Bode diagram and transfer function, it can be seen that the DM interference is not obvious and decreases along with the increase of frequency. The CM interference exists in all frequency bands and the magnitude of interference is relatively higher. Therefore, the CM interference has a great influence for the conducted interference of the WCS.

4.3. Simulation Results for CM and DM Conducted Voltage

The conducted interference measured by LISNs appears as conducted voltage. And the comparison between the one mode and CM+DM conducted voltage are shown in Figure 17. The black curve represents the conducted voltage of the CM+DM mode simulation, the red curve represents the DM conducted voltage and the blue curve represents the CM conducted voltage. It can be seen that some resonances appear at the same frequency 170 kHz, 430 kHz, 1.6 MHz, 30 MHz and the amplitude of those resonances are similar in the CM+DM waveform and CM waveform. However, in all frequency bands, the DM conducted voltage is smaller than that in CM+DM, especially at 30–108 MHz. Meanwhile the resonance point is shifted. Thus, from the view of conducted voltage, the CM waveform of the conducted voltage are better to represent the CM+DM waveform in fact.

The simulation result of the conducted voltage is consistent with the change of the transfer function by bode diagram. Therefore, from Figure 16 and Figure 17, it can be concluded that the CM interference is mainly responsible for the conducted-EMI from the DC power cables of WCS.

5. Filters Design and Experiments

The passive filter design method is used to determine the values of the major components in the EMI filter. From above discussion, the conducted interference of the WCS comes mainly from CM interference. Therefore, giving priority to designing the CM filter is taken into account to mitigate the conducted-EMI in WCS in EVs. Then, designing DM filter is considered if necessary.

5.1. Calculating Parameters in EMI Filters

The first step is to determine required filter attenuation for CM conducted-EMI and the CM conducted voltage in blue curve as shown in Figure 18. The CM attenuation $A_{CM}$ is calculated by the Equation (14):

$$A_{CM}=A_{nCM}-A_{ST}+m$$

(14)

here, $A_{nCM}$ is amplitude of the maximum conducted voltage; $A_{ST}$ is the limits of standard CISPR25 (GB/T 18655-AVE) level 3; m is the safety margin (6 dBμV).

It can be seen from Figure 18, the conducted voltage obtained from the experimental all meet the standard limit in the frequency range of 150 kHz–500 kHz and partially meet standard in the frequencies range of 500 kHz–2 MHz. However, it all exceeded standard in the frequencies range of 30 MHz–108 MHz. Among them, the maximum conducted voltage appears at 30 MHz. Therefore, the frequency point at 30 MHz is selected as a target attenuation frequency and expressed as $f_{aim}$. The conducted voltage at 30 MHz is 51.17 dBμV and the $A_{ST}$ is 36 dBμV. So, the target attenuation of CM conducted interference can be obtained as $A_{CM}$ = 51.17 − 36 + 6 = 21.17 dBμV.

The second step is to specify the filter corner frequency. It is determined by the target attenuation frequency. Thus, the corner frequency can be specified by the Equation (15):

$$f_0=\frac{f_{aim}}{{10}^{\frac{A_{CM}}{S}}}$$

(15)

where, S is the slope rate of the decay ramp of 40 db/dec. So the $f_0$ is equal to 54.55 MHz.

The CM inductance $L_C$ and CM capacitance $C_Y$ can be calculated by Equation (16):

$$L_C={(\frac{1}{2\pi f_0})}^2\times \frac{1}{2C_Y}$$

(16)

Obviously, there is much possibility for the combination of L_C and C_Y. According to Equation (16), it can be seen that C_Y and L_C are inversely proportional to each other. Generally, assuming that the constant value of C_Y is 500 nF, the value of L_C can be calculated as 265 μH. The filter series connected between LISNs and WCS as shown in Figure 19.

5.2. Topology Selection of CM Filter

In order to select the best filter topology with considering the volume and weight of the filter, CL, LC and CLC topology are designed and modeled in CST. The conducted voltage of simulation results with three types filters are shown in Figure 20.

In Figure 20, the conducted voltages of different topology circuits with LC, CLC and CL are displayed by three colors. There are some harmonic in the low-frequency bands, the value of the conducted voltages of Nth harmonic (2th = 170 kHz, 3th = 255 kHz, 4th = 340 kHz, 5th = 425 kHz) and 1 MHz are listed in

Table 4. The value of conducted voltage in three circuits of WCS.

Circuit with Filter	Value of Conducted Voltage (dBμV)					Characteristic
	170 kHz	255 kHz	340 kHz	425 kHz	1 MHz
LC filter	61.12	43.91	43.91	47.14	55.18	With new resonance, fewer components
CLC filter	56.48	36.86	37.83	36.32	24.70	Good mitigation, more components and volume
CL filter	38.57	18.26	18.03	14.43	6.36	Better mitigation, fewer components

. It is obvious that the smallest value of conducted voltage and harmonic content appears in the circuit with CL filter. The conducted voltage by using LC filter is good after 2 MHz, but it causes a new resonance and still exceeds the standard at 1 MHz. Although the mitigation of the conducted voltage by using CLC filter is also well, the cost and volume of the CLC are larger than others. Therefore, the CL topology is the best choice for CM filter due to the best suppression, the smallest number of components, the smallest volume and weight, compared with LC and CLC topology.

From Figure 20, by adding the CL topology CM filter, the conducted voltage in the frequency 150 kHz–108 MHz can be decreased to below the limits of standard GB/T 18655-AVE level 3 and the harmonic wave is obviously suppressed. In addition, it is unnecessary to design DM filters.

6. Experimental Verification

6.1. Electrical Experiment of WCS in EVs

An experimental system is built to validate the rightness and feasibility of the proposed design method, as shown in Figure 21. Figure 21a shows a wireless charging system with power of 3.7 kW. The secondary charging coil is installed on the chassis, and the primary charging coil is installed under the ground. The WCS transfer power to the battery. Figure 21b shows the visual information on the instrument panel when the electric vehicle is charging. From Figure 21b, the voltage and current of fast charging are 400 V and 9 A, in addition, the outside temperature is −3 °C, and the mileage for current power reaches 148 km, so the WCS that we built can achieve the charge normally.

6.2. Conducted Emission Experiments

A conducted emission experiments is setup when the WCS is working. Then, a CL filter is added in the WCS which is shown in Figure 2, so as to validate the attenuation effect of the conducted emission from DC-fed WCS. According to the filter structure designed in Section 5, the CL topology CM filter is added at DC input terminals inside of the controller. Then, Figure 22 shows the conducted voltage on the primary DC power cable after adding the CL filter. From Figure 22, the mitigation of the conducted voltage in low frequency band is obvious, the conducted voltage is lower than the limit of CISPR 25 (GB/T18655) in all frequency bands, as result in meeting the standard requirements.

The conducted voltage measured in the experiment without filter is $A_{\mathrm{e}1}$, after adding the CL filter, the conducted voltage is $A_{\mathrm{e}2}$, and the actual attenuation at 30 MHz can be expressed as Equation (17):

$$A_{\mathrm{e}1}-A_{\mathrm{e}2}=43.6-22.2=21.4 dB\mu V$$

(17)

At 30 MHz, the expected attenuation for CM filter with CL topology is 21.17 dBμV, and the experimental attenuation is 21.4 dBμV, from which a good consistence is achieved. It means that the mitigation of the proposed CM filter with CL topology is accurate, and shows the effectiveness and feasibility of only adding the CM filter as well. From the experiments results in Figure 22, based on giving priority for designing CM filter, the mitigation conducted emission strategy is suitable and feasible.

7. Conclusions

A mitigation conducted emission strategy based on transfer function from a DC-fed WCS for EVs is proposed. An equivalent circuit model with high-frequency parasitic parameters for the DC-fed WCS for EVs is built based on measurement. The characteristics of conducted emission from DC power cables is obtained in a frequency range of 150 kHz–108 MHz by measurement and simulation. The transfer functions of DM interference and CM interference were established. A judgment method of using transfer functions to determine the dominated interference mode responsible for EMI is proposed. Compared with the simulation results of the mitigation of DM interference, it can be seen that the CM interference is the dominated interference mode and responsible for the conducted EMI from DC power cables of the WCS. A strategy of giving priority to the dominated interference mode is proposed for designing the CM interference filter. The conducted voltage of simulation and experiment is decreased respectively by 21.17 dBμV and 21.4 dBμV at resonance frequency 30 MHz. By adding the CL topology CM filter, the conducted voltage in the frequency 150 kHz–108 MHz can be decreased to below the limits of standard CISPR25 (GB/T 18655-AVE) level 3. In the future, the equivalent circuit model for the DC-fed WCS should be improved in the frequency 30 MHz–108 MHz.