Common mode (CM) conducted interference are predicted and compared with experiments in a motor drive system of Electric vehicles in this study. The prediction model considers each part as an equivalent circuit model which is represented by lumped parameters and proposes the parameter extraction method. For the modeling of the inverter, a concentrated and equivalent method is used to process synthetically the CM interference source and the stray capacitance. For the parameter extraction in the power line model, a computation method that combines analytical method and finite element method is used. The modeling of the motor is based on measured date of the impedance and vector fitting technique. It is shown that the parasitic currents and interference voltage in the system can be simulated in the different parts of the prediction model in the conducted frequency range (150 kHz30 MHz). Experiments have successfully confirmed that the approach is effective.
1. Introduction
Electric vehicles (EVs) are being actively research and development in recent years because they are an important way to deal with global environmental problems like global warming. EVs are characterized by motor drive systems, where electric power conversion is done by pulse width modulation (PWM) inverters
[1

3]
.
The PWM technique provides high control efficiency and can be easily implemented based on the modern integrated circuit. Nevertheless the fast rise time of the switching transient produce highfrequency common mode (CM) electromagnetic interference (EMI) which leads to several serious problems such as CM current flowing to the ground through the stay capacitance of the system, shaft voltage and bearing current in motor, deterioration of motor winding insulation, radiation of power line, etc
[4

6]
. The problems of EMI may affect work state of motor drive systems and their surrounding electric device
[7]
and these highly concern the safety of EVs. Therefore，it is necessary to establish an accurate CM conducted EMI model for evaluating the level of the CM EMI in the motor drive system. Researchers have conducted a number of EMI modeling studies on the motor drive system of EVs
[8

10]
and other industrial applications
[11

15]
. A piecewise linear insulated gate bipolar transistor (IGBT) behavior model for frequency simulation of motor drive EMI prediction have been proposed
[16]
. The inverter model is composed of a control circuit and a threephase IGBT module with parameters extracted from different device measurement. However, the control circuit and test procedure are complex. A physicsbased highfrequency model of power inverter including the IGBT unit cells, heat sink and connective printed circuit board (PCB) traces combined in a single electrical circuit is presented
[17]
. The IGBT model includes the highfrequency stray component superimposed on the wellknown Hefner IGBT model and the components is calculated using a 3D quasistatic finite element analysis. The invert model by this method is relatively accurate. Nevertheless, the geometric dimensions and the structural physical parameters of the IGBT have to be known first. A highfrequency modeling method, which takes into account phenomena such as skin effects, proximity effects and dielectric losses, is used to model power cables by the series association of n identical RLCG basic cells
[18]
. The parameter values in the model are obtained by measurement and specific date processing. Other Studies have adopted a fourport impedance matrix representation of the power line considered in CM and the impedance parameters value have been practically measured in various conditions by considering the relationship between the voltage and current of the ports
[19]
. However, the obtained deviation of the model by the two mentioned methods is depended on the measurement accuracy. A lumped RLC circuit is used to model a motor in the frequency range under 1 MHz
[20]
. The parameters in the model include the windingtoframe capacitance, windingtorotor capacitance and phase leakage inductance. The authors give a behavior model of AC motor
[21]
. The asymptotical and analytical methods are proposed to model the AC motor. Other alternative method
[22]
is proposed, including a finite element analysis
[23]
. However, with the frequency increasing above 1 MHz, all these methods are no longer suitable because of low accuracy.
This study aims to establish a prediction model of CM conducted interference for motor drive system of EVs. The highfrequency CM models of various parts of the system are proposed. First, the inverter model is presented. To model the inverter, a stray capacitor representing capacitive coupling between the IGBT and the heatsink and a CM voltage source, which takes into account the feature information of multiple interference sources, are used. This concentrated and equivalent method on the inverter can reduce the complexity of calculation simulation and it is easy to establish the model by experimental measurement. Second, a highfrequency CM model of the power line in EVs, using distributed parameter circuits calculated by combining the analytical method and finite element method (FEM), is detailed. This method can avoid the derivations error generated from measurements, however, the power line structures and parameters must be given at first. Third, a new approach based on vector fitting
[24]
is proposed to model a motor from 150 kHz to 30 MHz by using measured impedance date. Compared with the general modeling methods, this approach have a higher accuracy in a wide frequency range. At last, it will be shown that CM current and voltage can be predicted with a satisfactory accuracy using the proposed method.
2. Study System
The studied system (
Fig. 1
) is a motor drive system for EV applications. It is constituted of a direct current power supply, an industrial LISN, a threephase IGBT inverter, a permanent magnet synchronous motor (PMSM), and a threephase power line connecting the inverter to the motor. The complete system is placed on a copper plane to enable the EMI noise to circulate.
DC/AC converter system with CM current pathways
Interference or noise flowing through heatsink, cable shielding layer, motor chassis and common ground is referred to as CM EMI. Note that in this study, only CM effects are considered, due to their dominant effects in EMI.
Fig. 1
shows the CM current paths (
I_{LISN}
and
I_{CM}
) of the system with the noise source located in the main circuit. The CM currents exist because the sum of three instantaneous voltages at the output of the inverter is not null and capacitive couplings to ground are distributed in the complete system.
3. Modeling
The aim of the modeling is to predict conducted emissions in a variablespeed drive system. The essential question that needs to solve in CM modeling is obtaining the equivalent circuit parameters of each part in the CM conducted EMI propagation paths.
Fig. 2
shows a simplified lumped element representation of the system. The CM equivalent circuits of the motor and power line need be precisely represented because these impedances have a significant influence on the level of conducted disturbances. The CM voltage source generated by the inverter should be carefully considered because the source is the reflex of the original EMI characteristics level in a system. In the following sections, we present several subsystem CM circuit models, such as the LISN model, inverter model, power line model, and motor model.
Lump element equivalent circuit of the system
 3.1 LISN Model
LISN is an industrial element for measuring the conducted interference in EMC standards. The parameters of the LISN circuit topology are provided by the manufacturers. In this study, LISN is located between a power supply and inverter for three functions: Firstly, to prevent incoming conducted disturbance from the power supply. Secondly, to maintain the stabilized impedance 50 ohms at the power electronics converter terminal in the wide frequency range, and finally to couple conducted interference voltage signal from the converter to the measuring receiver.
 3.2 Inverter model
Fig. 3
shows the inverter stage with the main stray capacitor
C_{cm}
representing capacitive coupling between the IGBT and the heatsink, and the voltages
V_{ag}, V_{bg}
and
V_{cg}
which are the output voltages of a leg of the inverter referenced to ground. In the common mode, the three inverter legs, generating the CM interference voltage, can be considered as a single voltage source
V_{cm}
. The model of
V_{cm}
and
C_{cm}
are presented in the following parts.
CM equivalent model of the inverter
 3.2.1 CM voltage source model
CM voltage generated by the inverter is expressed as
The system of impedances
Z_{LISN}
constitutes a voltage divider, which makes the point
P
and
N
(
Fig. 2
) on the DC source have the voltage potential of 1/2E and 1/2E, respectively. As a space vector pulse width modulation (SVPWM) method is used in this system with the regulated DC source voltage E, the turn on signals of the higher transistors (K
_{1}
, K
_{3}
, K
_{5}
) are shown as
Fig. 4(a)
. Each voltage (
V_{ag}, V_{bg}
and
V_{cg}
) has the value of 1/2E when the higher transistors are turned on, and 1/2E when the lower transistors (K
_{2}
, K
_{4}
, K
_{6}
) are turned on. Then, substituting each voltage (E/2 or –E/2) into (1), the CM voltage
V_{cm}
is illustrated as
Fig. 4(a)
. It can be observed that the voltage step of
V_{cm}
caused by the on/off of the switches are ±1/3E at every switching transient and this stairway voltage is particularly perturbing because it is constituted by six transients (
d_{v}/d_{t}
) per period.
CM voltage source modeling process
An electric vehicle industrial inverter supplied by the DC power source has been used in our experiments, its switching frequency was 7.5 kHz, and SVPWM strategy is used to generate the output voltages. The output voltages
V_{ag}, V_{bg}
and
V_{cg}
are experimentally determined by using an Agilent oscilloscope and three Agilent highvoltage probes (
Fig. 4(b)
). Then, the CM voltage
V_{cm}
is obtained by the equation (1), as shown in
Fig. 4(c)
.
The very essence of this modeling method for CM voltage source is that a stairway voltage is substituted for six switching elements by experimental measurements and subsequent calculations, and the characteristic of the CM EMI can be correctly described by the stairway voltage. Date from the CM voltage in
Fig. 4(d)
is stored in a memory module of simulation software where the date can be checked and edited. These data can be changed into a twoport model which represents the function of measured voltage through MAST language (
Fig. 4(e)
), then add the established model into component library. When building the CM conducted EMI circuit model of the variablespeed ac motor drive system in the simulation software, the established CM voltage source model should be invoked.
 3.2.2 Parasitic parameter Ccmmode
The capacitive coupling to ground in the converter is mainly due to the power module and its heat sink, as explained by the schematic representation of
Fig. 5(a)
. As the heat sink is connected directly to ground, this capacitance is a propagation path for the CM current.
The value of
C_{cm}
(
Fig. 5(b)
) is determined using an impedance analyzer. The impedances
Z_{ag}, Z_{bg}
, and
Z_{cg}
are measured between each leg of the inverter and the ground as shown in
Fig. 5(c)
. The measured impedances are capacitive until 25 MHz, beyond 25 MHz, turning to inductive because of parasitic inductance introduced during measurement. In fact, this inductance does not exist in the system, so it can be neglected. Therefore,
Z_{ag}, Z_{bg}
, and
Z_{cg}
are assimilated to an identical capacitance
C_{cm}
equal to 267 pF from 150 kHz to 30 MHz. The impedance frequency characteristics comparison of
Z_{ag}
and Ccm is illustrated in
Fig. 5(d)
.
Parasitic parameter C_{cm} extraction process
 3.3 Power line model
Power line spread paths of CM conducted disturbances in motor drive system. In order to predict the EMI level produced by the system, a highfrequency equivalent circuit model should be established for the power line.
Three crosslinked polyethylene insulated cables are used in the study, the geometrical and physical parameters of single phase cable are shown in
Fig. 6(a)
, the conductor of cable is composed of 19 bundle mutual insulation copper wires, therefore, the variation of inductance and resistance with frequency by skin effect is neglected here; the shielding layer is connected to both the heatsink of the inverter and the shell of the PMSM, space between the cables is 50mm.
A power line can be viewed as a three conductor transmission line guided by transmission line theory,
Fig. 6(b)
shows per meter length model of the power line. Mutual capacitance
C_{M}
of two conductors is considered to be zero in theory because of the shielding layer existing in each phase cable; and the value of mutual inductance
L_{M}
, which is much less than self inductance because the space between the cable is large, can be neglected. All conductors are considered in parallel for the CM current propagation paths in the power line and the power line CM model can be described as
Fig. 6(c)
.
In this section, we have proposed power line CM model (
Fig. 6(c)
) obtained by the seriesassociation of N identical RLC basic cells. The analytic method is applied to calculate both the resistance parameters and the inductance parameters and FEM is employed to determine the capacitance parameters.
Power line CM model process
 3.3.1 Inductance parameters
The analytic method model to calculate selfinductance of single cable is shown in
Fig. 7
. The outer conductor and inner conductor represent the conductor and the shielding layer of the cable, respectively, the outer conductor has negligible thickness, and the current is uniformly distributed inside the inner conductor.
Inductance parameters calculation model a=3.25 mm, b=4.55mm
The current density inside the inner conductor is
The magnetic flux density within the inner conductor at any radius
ρ
such that 0 ≤
ρ
≤
a
, from Ampere’s law, is
The flux enclosed in the region between
ρ
and
ρ
+
dρ
, the unit length in the
z
direction is
As only a fraction of the total current is enclosed by the contour at radius
ρ
, the flux linkages are
Thus, the total flux linkages within the inner conductor are
Hence, the inductance per unit length of the inner conductor due to the flux inside it is
Next, determine the inductance due to the flux between the two conductors. The flux density in the region
a
≤
ρ
≤
b
is
The flux passing through the region between
ρ
and
ρ
+
dρ
, the unit length in the
z
direction is
The total flux linkages are
Thus, the contribution to the selfinductance by these flux linkages is
In the region
b
≤
ρ
, the magnetic flux density is zero. Hence, the total inductance per unit length of the insulated cable is
 3.3.2 Capacitance parameters
For calculating the capacitance between the conductor and shielding layer, The FEM model of the phase cable is created in Maxwell 2D (
Fig. 8
). Calculating the capacitance from FEA is related to the electrostatic energy
W^{C}
. The first step is to assign a voltage
U
_{1}
to the conductor; the shielding layer in the volume
V
is grounded. FEA programme discretizes problem volume
V
into triquetrous element as shown in
Fig. 8
and then solves the Laplace equation to get the electric field
E
_{1}
and the displacement field
D
_{1}
according to (13).
FEM model for capacitance computation
Where,
Ф_{c}
is the electric scalar potential. The same procedure is applied to shielding layer in succession; in the end,
W^{C}
_{12}
which is stored in the electric field associated with the capacitance between the conductor and shielding layer can be obtained from (14).
Since the energy can also be expressed
Where
C
represents the capacitance between conductor and shielding layer, further combing the (14) and (15), we can get
C
as
 3.3.3 Resistance parameters
The resistance parameters of the perunitlength conductor are defined as
The
RLC
parameters of the EMI model of the power line are computed using the aforementioned setup, and the equivalent circuit model of the perunitlength power line (1m) is shown in
Fig. 9
.
CM Equivalent circuit of the power line
 3.4 Motor model
PMSM is a main propagation path for CM conducted emission of the drive system. In order to predict the EMI level, a highfrequency equivalent circuit model should be established for the motor. In this section, vector fitting (VF) method is proposed to model the PMSM with high accuracy from 150 kHz to 30 MHz, using measured impedance date.
 3.4.1 Vector fitting technique
Vector fitting
[24]
is widely used for fitting a rational function for frequency domain response; it also is an accurate, robust, and efficient method. By applying vector fitting, the rational function of motor obtained by experimental date can be approximated a transfer function
f
(
s
) as
The terms
r_{k}
and
p_{k}
are the residues and poles, respectively, they could be real or complex conjugate pairs while
d
and
e
are real. In this paper,
s
is equivalent to
j·ω
for motor impedance application where ω is the angular frequency.
Then, we convert the rational approximation given by (18) into an equivalent circuit using in simulating software. It can be divided into several subcircuits in terms of the order of the function as follows.
1) Equivalent circuit for d and e
A
RL
series circuit (
Fig. 10(a)
) will be used to synthesize the parameters
d
and
e
in function
f
(
s
). The values of
R
and
L
are
2) Equivalent circuit for real poles
The impedance rational expression for a real pole and residue is
A simple
RC
parallel circuit (
Fig. 10(b)
) is used to replace the rational function with one real pole. Comparing the circuit impedance with (20), the values of
R
and
C
are
3) Equivalent circuit for a complex conjugate pole pair
The complex conjugate pole pair can be expressed by the impedance rational as
Where pkc and
are complex conjugate pole pair and rkc and
are the residue pair. The equivalent circuit composed of
RLC
for representing (22) is shown in
Fig. 10(c)
and the values of these parameters are
Equivalent circuit
With the subcircuits obtained above, the total impedance of
f
(
s
) is represented by connecting subcircuits in series.
 3.4.2 CM impedance measurement and modeling
For the CM conducted emission of the system, the three phases of the motor are considered in parallel and the CM parameters of motor (
Z_{CM}
) are identified by inspecting the input impedance measured between the motor three phase winding connected together and the motor frame, as shown in
Fig. 11
. The CM impedance is obtained by using an impedance analyzer in the frequency range from 150 kHz to 30 MHz.
Schematic for testing Z_{CM}
In consideration of a tradeoff between the accuracy and the complexity of the equivalent circuit by using VF models, 4order approximation is used to model the CM impedance of the motor winding with a corresponding circuit topology shown in
Fig. 12
. The parameter values of the transfer function for 4order approximation are given in
Table 1
and the component values of the circuit are given in
Table 2
.
4order VF model
Parameter values for 4order transfer function
Parameter values for 4order transfer function
Component values for 4order CM equivalent
Component values for 4order CM equivalent
The simulated and experimental results of CM impedance are shown in
Fig. 13
. This curve shows that the
Z_{CM}
impedance is almost capacitive when the frequency is below 6 MHz. when the frequency is increasing, the antiresonance occur at the frequency point 7 MHz as the phase angle at this point is 0° and the impedance behaviour is changing from capacitive to inductive. The comparisons of magnitude and phase date shows that the simulation results of 4order equivalent circuit match the experimental results well in the entire bandwidth for both the magnitude and phase of the
Z_{CM}
.
Measurement and simulation results for motor CM model
4. Model Simulation and Experimental Verification
 4.1 EMI simulation
The CM simulation model of the motor drive system is shown in
Fig. 14(a)
. Where
Z_{LISN}
represents the LISN module; the inverter module is consist of the CM excitation source and parasitic capacitance between the semiconductors and heat sink; the models of the power line and PMSM are characterized by
Z_{Power}
line and
Z_{Motor}
, respectively.
All the circuit modules are incorporated into the circuit simulation software and the detailed circuit simulation model of the motor drive system for CM EMI level is shown in
Fig. 14(b)
. The transient emulation type has been selected and simulation computing time is 200 μs with simulation step size 0.1 ns. The CM conducted emission voltage
V_{LISN}
and current
I_{CM}
would be simulated and calculated to compare with the results measured on the experimental bench. Where VLISN can be expressed as:
EMI CM model simulation of a motor drive system
 4.2 EMI measurement
To validate the effectiveness of the EMI models proposed in this paper, we establish the experimental measurement platform of the motor drive system used in EVs. The setup of the experimental facilities is shown in
Figs. 15(a)
and
(b)
.
Experiment setup for the motor drive system
To simulate the actual mounting structures of the motor drive system in a car, the converter case is connected to the car body, which is replaced by the ground plane in the experimental platform. The ground plane comprises a galvanized steel plain sheet with a thickness of 1.2 mm, an area of 2400mm ´ 1000 mm, and a height of 1000 mm from the ground. Traction battery, as the DC power supply, is connected to the input terminal of LISN
_{1}
and output terminal of this device is connected to inverter. The PMSM (45kW) motor was fed by a threephase voltagesource inverter through a 3m shielded power line. The driving circuit of the inverter is power by a 12V battery through LISN
_{2}
connection to reduce the interference generated by the 12V battery; the start and end of inverter operation is controlled by the host computer through the CAN highway. Current have been measured using a FCC F331 current probe (bandwidth=10 kHz250 MHz) and the common mode EMI voltage
V_{LISN}
is obtained as:
Where
V_{1}
and
V_{2}
are, respectively, the voltages measured at 1–traction battery 320 V, 2–LISN1, 3–inverter, 4–power line, 5– PMSM, 6–test stand, 7–ground plane, 8–LISN
_{2}
, 9–12 V storage battery, 10–computer, 11–CAN highway the terminals of the LISN
_{1}
.
The simulated and experimental common mode current in the power line shielding layer and motor chassis are presented in
Fig. 16(a)
. Discrepancies between the simulation and experimental results are observed at some frequency ranges, such as 4 MHz to 5 MHz, with an error greater than 10 dB. However, the comparison of the simulation and measurement results indicates good conformance with errors less than 10 dB in the most of the frequency ranges. Therefore, the comparison results show the validity of the proposed power line model and motor model in CM conducted emission.
Fig. 16(b)
shows the simulated and the measured results of CM conducted EMI at the terminal of the LISN ports. The comparison of the results in the range 750 kHz to 20 MHz indicates performance that corresponds to errors less than 5 dB, and the difference between the simulation and experimental results are observed at some frequency ranges, with an error no more than 10 dB. Therefore, the comparison results show the good behavior of the proposed inverter and LISN CM models.
Comparison between measurement and calculation
These curves show that all impedances and CM source are accurately determined and our method is efficient in predicting CM conducted EMI for the motor drive system.
5. Conclusion
A pragmatic methodology is described in the paper to predict the CM conducted perturbation in a motor drive system of EVs. An equivalent circuit model has been proposed based on a representation of the full system. The model is reduced to the only described propagation, largely responsible for the major disturbances generated by these devices. Minimizing the complexity of the model make model easy to establish. The processing methods for the inverter consist of two steps: the CM voltage source is obtained by concentrating the output voltage waveform of each leg as one waveform; the stray capacitance has been identified by measurement. The CM model of the power lines based on transmission line model is used and the parameter extraction method in the model combines analytical method and FEM. The processing methods focuses on the motor CM parameters in the prediction model, establishes a highfrequency equivalent circuit model with high accuracy from 150 kHz to 30 MHz based on VF technique. The simulation and measurement results proved that the proposed model effectively describes the CM EMI levels of the motor drive system. The obtained model of the system would be used to design a CM filter for the reduction of conducted CM interference in EVs in future studies. While inserting a CM filter in a modeling such as presented herein, it is possible to design its component to obtain the desired attenuation with actual impedance. Lastly, this method is well matched to represent the CM current flowing in any part of the system: inverter, power line or motor chassis.
Acknowledgements
This work has been supported by the National Natural Science Foundation of China (51177183) and Application Development Planned Program (cstc2013yykfa60001) of Chongqing, China
BIO
YongMing Yang received a M.Sc. degree and a Ph.D. degree in electrical engineering from Chongqing University, Chongqing City, China, in 1987 and 1999. Since 1987, she has served at Chongqing University as a Lecturer (1988), an Associate Professor (1996) and a Professor (2002). Her current research interests are the preventive diagnostic techniques and online monitoring techniques for power equipment.
HeMeng Peng was born in Henan Province, China, in 1989. He received his B.S. degree in electrical engineering from Chongqing University, Chongqing, China, in 2009. He is currently working toward the Ph.D degree at the State Key Laboratory of Power Transmission Equipment & System Security and New Technology, China. He current research interests include vehicle electromagnetic compatibility.
QuanDi Wang was born in Anhui Province, China, in 1954. She received her Ph.D in Electrical Engineering from Chongqing University, Chongqing, China, in 1998. She is currently a professor at the College of Electrical Engineering, Chongqing University, China. Her main research interests include the simulation and numerical computation of electromagnetic field, and vehicle EMC prediction.
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