Proc. of the 2016 International Symposium on Electromagnetic Compatibility - EMC EUROPE 2016, Wroclaw, Poland, September 5-9, 2016
Common Mode and Differential Mode
Characteristics of AC Motor for EMC Analysis
H. MILOUDI, A. BENDAOUD, M. MILOUDI*
**
APELEC Laboratory,
Djilali Liabes University
Sidi Bel Abbès, Algeria, e-mail:
*
E-mail: mohamed.miloudi@univ-sba.dz
Abstract — In Adjustable Speed Drives (ASD), high
frequency parasitic currents cause several unexpected
problems, such as premature deterioration of motor
winding insulation and ball bearings.
In order to understand and to mitigate electromagnetic
disturbance it is necessary to use a precise model of the
PWM inverter, the energy cable and the AC motor.
In this paper, an equivalent circuit of the three phase
induction motor for high frequencies is presented. The
proposed model details separately the common mode and
differential mode characteristics of the AC motor. The highfrequency model has been obtained by means of a frequency
domain analysis using an experimental setup and a
MATLAB model.
In order to verify extracted parameters, in-circuit
impedance measurements for the AC motor using an
Agilent 4294A Impedance Analyzer are done. The Measured
results basically verify the extracted data, while the
discrepancy between measured results and simulated results
is also analysed.
Keywords: Common Mode (CM), Differential Mode (DM),
High frequency, Induction machine, identification of AC
motor parameters
S. DICKMANN**, S. SCHENKE
Institute of Fundamentals of Electrical Engineering,
Helmut Schmidt University,
Hamburg, Germany
**
E-mail: Stefan.Dickmann@HSU-Hamburg.de
II. HIGH FREQUENCY MODEL FOR THREE PHASES
INDUCTION MACHINES
The asynchronous motor (induction motor) is the
most prevalent motor type in the industry. The models
proposed are essentially based on an experimental
procedure followed by extraction of the impedances from
these measures. So, we can have a behavioral
interpretation this machine.
Most developed models for similar studies are
generally valid for low and medium frequencies (<< 1
MHz) [5]. The electromagnetic conducted interference
(EMI) is classified into two types: differential mode
(DM) and common mode (CM). From this, the analysis
of the motor impedance is based on the observation of the
curves giving the variations of the motor impedance as a
function of the frequency found in two configurations:
the common mode and the differential mode.
The usual configuration of AC motor is shown in
figure 1.
Ɖ
I. INTRODUCTION
ƌ
Environmental electromagnetic pollution has been a
serious problem for electronic and electrical equipment
for years [1, 2]. The industrial PWM inverters are working
at a switching frequency between 500 Hz and 20 kHz,
EMI normative measurements extend from 150 kHz to 30
MHz.
The implementation of these modern components is
not used without some problems of electromagnetic
compatibility [3].
In Adjustable Speed Drives (ASD), every switching
operation of the power devices in the inverter imposes
high values of dV/dt for power cables and induction
motors. Such voltage variations cause high frequency
currents which flow between the motor phases
(Differential Mode currents) and also between motor
windings and the ground through stray capacitive links
(Common Mode currents).
The common mode current contributes to several
unwanted problems such as coupling to nearby systems
creating electromagnetic interference. It causes the
damaging of the machine bearings [4], bearing lubrication
and heating of the conduit carrying the three-phase
conductors, and it also decreases the lifetime of the motor
insulation.
Ɖ
>
Ő
Z
Ő
Ő
Fig. 1. Equivalent circuit per phase in high frequency of AC motor.
Where R : the resistance of a winding,
L: phase leakage inductance,
r: resistance representing eddy currents inside the
magnetic core and the frame,
Cp: capacitance representing the turn to turn
distributed capacitive coupling,
Cg: capacitance representing the winding to ground
distributed capacitive coupling [6, 7, 8, 9, 10,
17].
The studies in [11] have demonstrated that the
emission of motors, synchronous or asynchronous,
shows almost no dependence on the operating point. In
other hand, the HF model motor remains the same with
either low speed or high speed. This enables us to restrict
ourselves to identifying the machine in off-state.
978-1-5090-1416-3/16/$31.00 ©2016 IEEE
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Proc. of the 2016 International Symposium on Electromagnetic Compatibility - EMC EUROPE 2016, Wroclaw, Poland, September 5-9, 2016
III. EXEPRIMENTAL RESULTS
In this work, we propose a modeling method of the 3
phases motor based on an experimental approach. We can
say that these models reflect the radio frequency (RF)
behavior of the machine. The experimental tests have
been carried out on a 50 Hz motors of small size (0.25
kW), as reported in annex I.
The various experimental parameter values of the
model are measured with an Impedance Bridge
(HP4294A). These parameters are obtained by carrying
out 2 tests: one in common mode (CM) configuration and
the other one in differential mode (DM) configuration as
shown respectively in Figs. 2 and 3.
The impedance ZCM (Zpg) measured between the three
phase terminals connected together and the ground
terminal, with floating motor neutral [12].
0
Common mode impedance (Zpg)
-10
-20
-30
Phase [°]
-40
-50
-60
-70
-80
-90
-100 2
10
10
3
4
5
6
10
10
Fréquency (Rad/s)
7
10
10
Fig. 4. Measured common mode impedance ZCM of the induction motor
(magnitude and phase).
Also in this case the experimental results confirm the
frequency response of the impedance Zpp’ as shown in
Fig.5.
Fig. 2. Common mode test configuration [13].
10
8
Differential mode impedance Zpp'
The impedance ZDM (Zpp’) measured between the three
phase terminals connected together and the motor neutral,
with floating ground terminal [12, 14, 15].
10
Impedance ( Ω )
10
10
10
10
10
10
Fig. 3. Differential mode test configuration.
7
6
5
4
3
2
1
0
10 2
10
The common mode and the differential mode impedances
of the motor as functions of the frequency are shown in
Figs. 4 and 5 respectively.
3
4
10
10
5
10
Fréquency (Rad/s)
6
7
10
10
Magnitude
100
Differential mode impedance Zpp'
10
80
8
Common mode impedance (Zpg)
60
7
10
ig. 4. Measured
common mode impedance ZCM of the induction motor
(magnitude6 and phase).
40
10
10
20
Phase [°]
Impedance ( Ω)
10
5
0
-20
4
-40
10
10
10
3
-60
2
-80
-100 2
10
1
0
10 2
10
10
3
4
5
10
10
Fréquency (Rad/s)
Magnitude
6
10
10
3
10
4
5
10
10
Fréquency (Rad/s)
10
6
7
10
Phase
7
Fig. 5. Measured differential mode impedance ZDM of the induction
motor(magnitude and phase).
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Proc. of the 2016 International Symposium on Electromagnetic Compatibility - EMC EUROPE 2016, Wroclaw, Poland, September 5-9, 2016
IV. MODELING OF THE AC MOTOR
The high frequency model of the induction motor
consists of 3 differential mode impedances ZDM and 3
common mode impedances ZCM with connection to the
ground.
In the considered frequency range, the phase
resistance R is much smaller then the reactance of the
leakage inductance L. Therefore, in the following
considerations the stator resistance will be always
neglected. The impedances ZCM and ZDM can be
simplified:
A) Common Mode Characteristics
L(C P + C g ) s 2 +
A widely used equivalent circuit for the common
mode impedance is shown in Fig. 6.
Z pg =
2 ⋅ C g s( L ( C p +
Ɖ
ƌ
Z pp' =
Ɖ
>
Ő
Z
Ő
Cg
2
L
s +1
R
) s2 +
(5)
L
s + 1)
R
(6)
Ls
ª
º
Cg 2 L
«L( Cp + ) s + s +1»
2
R
¬«
¼»
Ő
V. ANALYSIS OF THE MOTOR IMPEDANCES
Fig. 6. Equivalent circuit for common mode impedance Zpg
The common mode impedance can be given by the
following relations :
Z pg =
VCM ( p )
I CM ( p )
(1)
The configurations of AC motor given in Fig. 6 and
Fig. 7 have been verified by plotting the frequency
response of the common mode and differential mode of
impedances. The Fig. 8 and Fig. 9 show the comparison
between the experimental results and the simulation
results respectively for the common mode and differential
mode.
8
10
experimental
simulation
7
10
(2)
6
10
5
Impedance (Ω )
º
ª R⋅ L
R⋅ r
L
(Cp +Cg )s2 +(
(Cp +Cg )+
)s +1»
«
R+ r
R +r
»¼
« R+ r
Zpg = ¬
ª R⋅ L
º
Cg
Cg
R⋅ r
L
2⋅Cg s «
(Cp + )s2 +(
(Cp + )+
)s +1»
R
r
R
r
R
r
+
+
+
2
2
¬«
¼»
B) Differential Mode Characteristic
10
4
10
3
10
2
10
A widely used equivalent circuit for the differential
mode impedance is shown in Fig. 7.
1
10
0
Ɖ
10 2
10
ƌ
3
4
10
5
10
10
Fréquency (Rad/s)
10
6
7
10
Magnitude
Ɖ
>
Z
Ő
0
Ő
Ɖ͛
experimental
simulation
-10
-20
-30
Fig. 7. Equivalent circuit for differential mode impedance Zpp’.
-40
Z pp '
Phase [°]
The differential mode impedance can be given by the
following relations :
-50
-60
V ( p)
= DM
I DM ( p )
(3)
-70
-80
-90
Zpp' =
ªL º
(R⋅ r) « s +1»
¬r
¼
ª R⋅ L
º
Cg
Cg
R⋅ r
L
(R+ r) «
(Cp + ) s2 +(
(Cp + ) +
)s +1»
2
2 R +r
R+ r
¬«R+ r
¼»
-100 2
10
(4)
3
10
4
5
10
10
Fréquency (Rad/s)
6
10
10
7
Phase
Fig. 8. Simulation and experimental results for common mode
impedance
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Proc. of the 2016 International Symposium on Electromagnetic Compatibility - EMC EUROPE 2016, Wroclaw, Poland, September 5-9, 2016
The common mode impedance has a pole in the
origin, two complex conjugate zeros and two complex
conjugate poles. The zeros and poles natural frequencies
are respectively f1 and f 2 given by:
­
° f 1 = 2π
°°
®f =
° 2
°
2π
°¯
1
L (C + C g )
1
C
§
·
L¨ C + g ¸
2 ¹
©
(7)
The corresponding Bode plot shown in the figure 8
indicates that at DC the circuit of the common mode
impedance behaves as an open circuit. As we increase the
frequency, the impedance of the capacitor Cg dominates
and decreases linearly with frequency at –20 dB/decade,
and the phase angle equals -90° until the first resonant
frequency f1.
For the differential mode, at the frequency f1, the
impedance of the inductor (L) equals that of the capacitor
(C+Cg). As frequency is further increased, the impedance
of the parasitic capacitances (C+Cg/2). decreases until
there magnitude equals that of the inductor. This occurs
at the self-resonant frequency of the inductor f2.
10
10
Impedance (Ω)
10
10
10
8
7
experimental
simulation
6
5
We can see that for low frequencies the inductor
dominates, and the impedance increases at +20
dB/decade while the angle is +90°. The impedance of the
parasitic capacitance decreases until its magnitude equals
that of the inductor. This occurs at the self-resonant
frequency of the inductor f2.
After this frequency the magnitude of the impedance
of the parasitic capacitance dominates and increases at 20 dB/decade, while the phase angle approaching -90°.
There is a very good accordance between the
experimental results and simulation results of the
proposed model in both magnitude and phase [16].
VI. IDENTIFICATION OF AC MOTOR PARAPETERS
The parameters of the proposed circuit of the
induction motor (Fig. 1) are obtained by identification
procedures and experimental data for common mode and
differential mode configuration at low and high
frequencies.
According to the characteristic of the magnitude, it’s
found that two characteristic frequencies are extracted
from the common mode impedance. The first frequency
denoted f1 represents the natural frequency of Zpg
numerator that minimizes impedance (common-mode
impedance of the resonance). The second frequency
denoted f2 is obtained and the denominator defines the
resonance impedance (resonance impedance of the
differential mode).
At low frequency, in common mode configuration
(experimental results shown in Fig.4); the common mode
impedance Zpg is almost purely capacitive [17, 18], and
the capacitance Cg can be evaluated by:
4
Cg =
3
10
(8)
The capacitance C and inductance L can be obtained
2
10
by solving the following equations (7).
1
10
In order to calculate the value of resistance R, we can
used the relation 5 or 6, we chose one point [ f1 Z wg ].
In Table 1, the values of two characteristic
frequencies are reported.
0
10 2
10
1
2 ⋅ ω1 ⋅ Z pg
10
3
10
4
5
10
Fréquency (Rad/s)
10
6
10
7
Magnitude
100
TABLE I.
RESONANT
FIFFERENTIAL IMPEDANCE
experimental
simulation
80
f1
40
MODE
AND
(resonant frequency of
4.25154090000e+04
common mode impedance)
20
Phase [°]
COMMON
Resonant frequencies (Hz)
60
f 2 (resonant frequency of
0
7.14369660000e+04
differential mode impedance)
-20
In Table 2, the values of the high frequency
parameters of the motor are reported.
-40
-60
-80
-100 2
10
FREQENCIES
10
3
4
5
10
10
Fréquency (Rad/s)
10
6
10
7
Phase
Fig. 9. Simulation and experimental results for differential mode
impedance.
Cg
C
L
R
r
TABLE II.
Parameters of AC motor
0.125*10e-8 F
2.8221e-10 F
0.0145 H
8.1242e+03 Ω
5Ω
PARAMETERS OF AC MOTOR
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Proc. of the 2016 International Symposium on Electromagnetic Compatibility - EMC EUROPE 2016, Wroclaw, Poland, September 5-9, 2016
The common mode impedance has a pole in the
origin, two complex conjugate zeros and two complex
conjugate poles. The zeros and poles natural frequencies
are respectively f1 and f 2 calculated in (7).
The differential mode impedance has one zero and a
pair of complex conjugate poles.
VII. CONCLUSION
ZĞĨĞƌĞŶĐĞƐ
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[11]
[12]
In this work we proposed methods and model for the
estimation of induction motor equivalent circuit
parameters. A comparison between the computed and
measured values is provided and discussed for an AC
induction motor.
The proposed model for simulating EMC behaviour
of induction machines is parameterized in the frequency
range from 100 Hz up to 10 MHz. It is shown that the
distribution of the common-mode impedance in the
simulation model is very similar to that in the
experimental result.
The common-mode impedance can be got considering
that the capacitance Cg coupling the winding to ground,
so we can represent the path of common-mode current by
this capacity.
In the next work we’ll propose a new method based
on Particle Swarm Optimization (PSO) algorithm, and
model of AC motor in the frequency range from a few
kHz up to 100 MHz.
[1]
[10]
[13]
[14]
[15]
[16]
[17]
[18]
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ANNEX I: AC MOTOR CHARACTERISTICS
VEM motors GmbH
weight
6.8 Kg
Frequency
50 Hz
60 Hz
Voltage
230/400 V
275/480V
Power
0.25 kW
0.3 kW
Current
1.36/0.78 A
1.4/0.8 A
speed
1370/1400 min-1
1660/170 min-1
Cos ij
0.72
0.68
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