Energy and Power En gi neering, 2011, 3, 96-106
doi:10.4236/epe.2011.32013 Published Online May 2011 (
Copyright © 2011 SciRes. EPE
Application of Ant Colony Algorithm to the Analysis of
Common Mode EMI Model of DC Motor
Jinfeng Liu1, Xudong Wang1, Jiang Nan2
1School of Electrical & Electronic Engineering, Harbin University of Science & Technology,
Harbin, China
2Department of Electrical and Computer Engineering, Stevens Institute of Technology,
Hoboken, USA
Received December17, 2010; revised March 21, 2011; accepted March 31, 2011
The Electromagnetic Compatibility (EMC) of Direct Current (DC) motor windings is a system model which
is used to reflect the functional characters of the system in the whole EMC specified frequency (150 KHz -
30 MHz). For most motor designing process, it is always used to evaluate the inductance of windings in
lower or working frequency; however, when analyzing the conducted interference, it is necessary to take
some parameters in high frequency into account in building up the EMC model, such as the noticeable ca-
pacitance distributed among the windings or between windings and shells. Past research neglected the com-
mon-mode current generated by the high frequency interference within motor bearings coupled with shells,
since the parasitic capacitance of rotor core comes from armature windings supplied sufficient paths. In
EMC modeling process for DC motor problem, first, test the impedance of windings by experiments; then,
generate the equivalent circuit with overall parameters. At present, it is a difficulty that how to choose the
parameters. Most researchers preferred to adopt analytical calculation results, however, it could not reflect
the essence of the model since it requires many simplification. Based on this point, this paper adopted Ant
Colony Algorithm (ACA) with positive feedback to intelligently search and globally optimize the parameters
of equivalent circuit. Simulation result showed that the impedance of equivalent circuit calculated by this
algorithm was the same as experimental result in the whole EMC frequency. In order to further confirm the
validity of ACA, PSPICE circuit simulation was implemented to simulate the spectrum of common mode
Electromagnetic Interference (EMI) of equivalent circuit. The simulation result accords well with the ex-
periment result received by EMI receiver. So it sufficiently demonstrated correctness of ACA in the analysis
of high frequency equivalent circuit.
Keywords: Common Mode EMI, Motor Windings, Ant Colony Algorithm, PSPICE Simulation, EMI Receiver
1. Introduction
As the development of communication technology,
computer science, automatic control, vehicles, household
appliance, electric power industry and military, the re-
quirement of DC motors increased significantly. Since it
is the key component in the domains mentioned above,
the types and quantity of DC motors improved rapidly.
At the same time, the structure and control of DC motors
has changed significantly. However, as the key compo-
nent of many systems (such as electrical vehicles and
forklifts), the DC motors have become the serious inner
interference source of these systems, since when it oper-
ates, during the steering process and the unstable touch
between brush and commutator, there will generate tran-
sient voltage on the wires. These transient voltages will
invade into other components as conducted interference
through conductors [1]. As a result, it is essential to build
up a correct high frequency model of DC motors in order
to improve the electromagnetic compatibility of the sys-
tem. Jens Benecke from German built high frequency
The Key Science-Technology Project of Heilongjiang Province
(GB08A306). Youth Foundation of Harbin University of Science &
model of permanent magnet direct current motor with
12V low voltage, which contains three parts [2]. It was
not only complicate in modeling, but the parameters
were also hard to achieve. Meanwhile, Kohji Maki from
the United States utilized 3D electromagnetic field
analysis to build EMC simulation model of alternating
current (AC) motor [3] and French scholar C. Martis
built high frequency EMI model of permanent magnet
DC motor [4]. To improve precision and reduce com-
plexity of model, this paper takes the separately excited
DC motor produced by Liaoning Motor Maker as exam-
ple to build up the EMC model. In this process, besides
building up the physical model according to motor char-
acters, we need to set up the parameters of each element
in it. This paper adopted Ant Colony Algorithm to de-
termine the parameters in model. This Algorithm is a
new distributing evolution algorithm. It is strong in solu-
tion searching, adaptability and robustness; it could also
optimize the parameter collection process and make the
impedance of equivalent circuit in model equal to meas-
ured value.
2. EMC Model of Separately Excited DC
Motor Windings
The common-mode equivalent circuits mentioned in [5]
and [3] are applied to analyze and predict the over volt-
age on motor, shaft voltage/current and other negative
effect generated by common-mode voltage. Even use it
to analyze the common-mode circuit for leakage current,
it is only effective in frequency lower than 1MHz, hard
to face the requirement of EMI of whole conducted in-
terference frequency (150 kH2 - 30 MHz). The main dif-
ference between the high frequency common-mode
equivalent circuit of separately excited DC motors and
that of former ones is this model could be used to ana-
lyze and measure the emission intensity of common-
mode EMI and motor side common-mode EMI current in
the whole conducted interference frequency.
2.1. The Common Mode Current Coupled Path
of Separately Excited DC Motor
The excitation and armature windings in the slots of sta-
tor and rotor inside separately excited DC motor are
symmetrically distributed along the circle. That makes
the DC motor have plenty of electromagnetic coupled
inside and applied sufficient path for high frequency
EMI noise while there are electromagnetic and electrical
field inside the motor. Though there are many parasitic
parameters in motors, considered the separated power
supplement for excitation and windings, while the speed
control of motor is achieved by PWM controller on
windings, the armature windings is the main component
of the system to generate high frequency common mode
EMI. Accordingly, the parasitic capacity is mainly
achieved by measuring the armature windings. There are
mainly 3 types of parasitic capacity, the capacity from
armature windings to rotor core (Csa), the capacity from
armature windings to stator core (Csf), and the capacity
from excitation windings to stator core (Csg) [6].
According to the distribution of parasitic parameters of
separately excited DC motor, the common mode current
coupling path is showed in Figure 1, where Za and Zf
represents the resistance of unit length of armature and
excitation windings, respectively; Rb is the resistance of
Figure 1. Common mode current couple d path inside separately excited DC motor.
Copyright © 2011 SciRes. EPE
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bearing, Pa and Na, Pf and Nf is the positive and negative
node of power supplement to armature and excitation
windings, respectively, while the supplement to armature
windings is achieved through the power converter; icm is
large input common mode current, iacmk, ifcmk, igcmk (while
k = 1, 2,, n) is the common mode current of related
parasitic capacity flows each length unit.
Based on the analysis of the distribution of parasitic
capacity inside the motor showed in Figure 1 and motor
structure, armature winding is seriously affected by high
frequency interference, while excitation windings are
less affected when working under high quality power
supplement. Therefore, we can neglect the effect of ex-
citation windings to common mode current and only take
parasitic capacity into account when analyzing the com-
mon mode current path.
2.2. EMC Model Foundation of Separately
Excited DC Motor
The most effective method in discovering high frequency
characters of motor windings is multi-conductor and
multi-element conducting model. For specified DC mo-
tor, armature core is the homogeneous media in all direc-
tions and each rotor slot shares the same structure, the
path which winding turns and wire diameter is specified,
respectively; as a result, motor windings could be con-
sidered as a uniform conductor. In analyzing and meas-
uring the high frequency common-mode motor side cur-
rent of DC motors, we could adopt lumped parameter
model since it is simplified. This paper built up the EMC
model of DC motor windings based on the analysis of
separately excited DC motor accorded to former work,
which is showed in Figure 2.
In Figure 2, where La is the common-mode inductance
and Ca is parasitic capacity of armature windings; R
a is
the sum of eddy current effect of core and resistance of
Figure 2. High frequency common mode equivalent circuit
of separately excited DC motor.
armature windings; Lr is impedance of armature core; Cr
is the sum of parasitic capacity between armature wind-
ings and rotor slot and parasitic capacity among armature
core laminations; Rr is the sum of resistance of armature
laminations and resistance of motor bearing; Cf is the
parasitic capacity of armature windings coupled to exci-
tation windings core. After had this equivalent circuit,
we move on to calculate each parameter above according
to given characters of motor. Here we use Ant Colony
For the equivalent circuit showed in Figure 2, ac-
corded to circuit theory, it is easy to get the expression of
resistance of windings ZXY and the common-mode resis-
tance to earth ZXG as following:
aa aa
Zs RCs LCs
 (1)
aa aa
rr rr
rfrrf rrf
Zs RCs LCs
 
3. Ant Colony Algorithm
Ant Colony Algorithm, ACA, is a new evolution simu-
lated algorithm. It searches the optimized solution
through the evolution process of the group combined by
candidate solution. This algorithm adopts positive feed-
back mechanism in order to implement intelligent
searching and global optimization; meanwhile, it has
strong robustness [7].
3.1. Principle of ACA
Suppose there are m parameters to optimize, denoted as
p1, p2, pm, for any one among them pi (1 i m), set it as
N possible non-zero value, combined set Qpi. Then, all
the ants leave the formicary for food, and each ant starts
from set Qpi based on the pheromone
j(Qpi) of each ele-
ment in set and state transition probability
randomly choose one and only one element in set Qpi
independently. State transition probability and phero-
mone are calculated by (3) and (4), respectively.
jP N
QtnQt Q
 i
where ρ is the duration indice of residue information and
1-ρ is the volatility;
is the increased phero-
mone on j
th element caused by all the ants in this loop.
This increase is determined by the difference of analyti-
cal and concrete output, the smaller the difference be, the
more the pheromone increases [8].
After all ants finished choosing elements in the set,
they get the food source. Then adjust the pheromone of
each element. This process will be repeated until the op-
timized solution would be found or reach the iteration
times [9].
3.2. Parameter Selection Based on ACA
The mechanism of ACA path searching shows that there
is essential effect from parameter selection to the per-
formance of ACA. However, there is no theory support
for parameter setting. Thus we need to get the optimized
solution by experience through repeated matching and
adjustment [10]. The scale of solution space N and num-
ber of ants K are close related to the efficient of opti-
mized solution searching, accuracy and global superior-
ity of solution, and other optimization function. If the
optimized solution is dense in parts, it is better to choose
large N. The selection of K is related to N, the larger N is,
the lager K is required, meanwhile, it should take the
time complexity of the algorithm into account in the se-
lection of K [11]. Normally, the duration indices of resi-
due information is 0.5
1 and 0.7 is optimized; total
pheromone value Q is 1 Q 10 000 and has little effect
to algorithm. Since the selection range of Q is much lar-
ger than that of
, in practical, we set
randomly first,
than calculate the value of Q; after get a value of Q, re-
in order to get a more optimized solution. Re-
peat this process by times, the optimized parameter
group would be finally reached [12].
3.3. Implementation of ACA in EMC Modeling
of DC Motor
The common-mode current equivalent circuit of sepa-
rately excited DC motor shows that there are 7 parame-
ters need to set by ACA. According to the characters of
motor, set up the candidate solution group (7 × 30), that
is the set Qpi required by ACA, where m = 7, N = 30.
Figure 3 shows the flowchart of setting the parameter in
equivalent circuit using ACA.
Based on experience and experiment result, we have
following conclusion about ACA parameter selection:
maximized number of loops NcMAX = 1000, duration
indices of residue information ρ = 0.7, total pheromone
Q = 700, number of ants M = 150, deviation E is limited
to 0.1 (the smallest error allowed by algorithm). At the
beginning, the original pheromone of each element in the
set (1 j N) and , put all
the ants into the formicary. Each ant choose the solution
space according to state transition probability, and then
take the parameter each ant chose into the H function and
get the vector coefficient. After that, use freqs() function
to calculate the amplitude and frequency output response
of simulated filter constructed by these vector coeffi-
cients, the frequency bandwidth of this function is 150
kHz - 30 MHz. The pheromone of each ant will be ad-
justed by the difference of analytical output and simulate
output. After all the ants reached food sources, record the
deviation of optimized solution; if the deviation faces the
requirement, stops calculating, or continue. If all 150
ants after 1000 loops of searching could not reach the
requirement, we should reconsider whether ACA is suit-
able for this type of problems.
4. Experiment and Simulation
4.1. Experiment Analysis
In order to get the high frequency EMI model of motor,
it is necessary to achieve the amplitude and frequency
characters of resistance of motor through experiment.
Then equal it into a lumped-parameter circuit to make
the analytical impedance of equivalent circuits the same
as tested impedance of windings. We adopted Agilent
4249A precision impedance analyzer produced by
Agilent Technology to test the impedance of motor. Its
scale range is from 40 Hz to 110 MHz, covered the fre-
quency bandwidth talked in this paper. Use that analyzer
to test the short and open circuit impedance of XQ-7A2
separately excited DC motor. The testing principle
showed in Figure 4(a) and (b).
Figure 5(a) and (b) showed the test result of ampli-
tude and frequency characters of short and open circuit
impedance when DC motor operates in 150 kHz - 30
MHz frequency bandwidth.
From the figure we found it is necessary to take the
parasitic parameters related with common-mode signals
inside the motors into account when setting up the high
frequency common-mode equivalent circuit of separately
excited DC motor.
4.2. Analysis of High Frequency Model of DC
In order to achieve the parameters of equivalent circuit,
we adopted ACA to optimize the selection of parameter
group. The training curve showed in Figure 6. After 200
times of training, the result reached the accuracy re-
quirement. The parameters of output equivalent circuit
showed in Table 1.
Comparison of simulate and test result of short and
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Figure 3. Flowchart of circuit parameters set by ACA algorithm.
Copyright © 2011 SciRes. EPE
Figure 4. Test scheme of DC motor windings.
Figure 5. Comparison of DC motor windings characters.
Figure 6. Training curve of ACA algorithm.
Table 1. Setting DC motor equivalent circuit parameters by
ACA algorithm.
Resistance Capacitor/pF Inductance/μH
Ra/mRr/KCa C
r C
f L
a L
Value 21.339.822 424 210 12.11.6
open circuit impedance showed in Figure 7(a) and (b).
From this figure we found that in high frequency (higher
that 20 MHz), the difference between simulated and
tested result is higher than that in low frequency, how-
ever, in the whole frequency domain, the simulated and
tested result of common-mode impedance for DC motor
are quite similar. Consequently, the equivalent circuit
which its parameters are selected by Ant Colony Algo-
rithm would reflect the common-mode impedance of
separately excited motors correctly.
Figure 8(a) and (b) shows the difference between
simulated and experiment error of short and open circuit
It is clear that for the frequency higher than 20 MHz,
the error of simulated result is bigger, since in high fre-
quency the dielectric constant, permeability and other
parameters of the medium inside motors are function of
frequency, not constant. That makes the parasitic capac-
ity and inductance is not constant in the whole frequency.
Accordingly, it will cause simulation error in high fre-
quency that adopted constant value of parasitic capacity
and inductance in the model [13].
5. Analysis and Simulation of Interference
Source in Separately Excited DC Motor
5.1. Analysis of Interference Source
When separately excited DC motors operation, since
102 J. F. LIU ET AL.
Figure 7. Compare the simulation result with experiment
result of DC motor windings.
during the steering process, the terminal voltage and
current of motor will generate periodic pulsation, there
would be sufficient high frequency component of voltage
in motor [14]. Figure 9 shows the equivalent circuit of
steering process of DC motor. Set up the function of
steering current and conducted interference source based
on this equivalent circuit, then use numerical method
MATLAB to get the interference solution in time domain
Figure 9 takes the steering process with one group of
brushes as example to analyze. The black rectangular on
top and bottom are brushes. The state showed in figure is
mutation state of steering component; as the rotation
direction of armature windings marked in figure, the coil
x and n are in the state of steering. As a result, Rs and Ls
are the coil resistance and leakage inductance in two se-
ries branches, respectively; is is the steering current of
Figure 8. Error curve of simulation result.
Figure 9. Equivalent circuit of DC motor commutation.
Copyright © 2011 SciRes. EPE
mutation component, since the circuit is symmetric, it is
sufficient to analyze one branch only; rx and ry are con-
tact resistance between brush and two commutating
segments, respectively; meanwhile, ix and iy are the cur-
rent flows into commutating segments through brush,
respectively. Two ua branches are the two paralleled ar-
mature winding branches and ua is the back electromo-
tive force of armature branch, and ia is the current in this
According to Kirchhoff law, the voltage function of
brush circuit showed in top of Figure 9 can express as:
iii (6)
When motor operating, the total outside voltage drop
is composed by the contact voltage drop of the pair of
brush uc and the back electromotive force of the branch
ua, accordingly:
uu u (8)
Based on electric machine theory, the back electromo-
tive force of armature ua is a certain constant when the
motor rotates stable. Accordingly, the effect from ua to
conducted electromagnetic interference is negligible.
That reveals the transient voltage when motor operating
mainly comes from the contact voltage drop of brushes,
especially by the end of the commuting process. The
acute changes of contact voltage drop become the main
resource of conducted interference in the motor. From
Figure 6 we found:
uriri (9)
Suppose the contact between commutating segment
and brushes is ideal, the contact resistance is:
where Rd is the contact resistance when commutator
contact with brush completely, Tk is the mutation period
of DC motor, expressed as:
 (12)
where bk is the width of commutator. Dk and Da are the
diameter of commutator and armature, respectively; vk
and va are the linear velocity of the surface of commuta-
tor and armature, respectively [19]. Here the rated speed
of motor is 1400 rpm, then take parameter Dk = 360 mm,
bk = 100 mm into Equation (12), get the rated operation
steering period is around 38.4 ms.
Since during the commuting process of DC motor, the
transient current affects seriously to sensitive compo-
nents, the effect from voltage drop is negligible and
Equation (5) is changed into:
 (13)
Take (6), (7), (10) and (11) into (13), we have the
function of commuting current is in time domain:
skk kk
da ds
ttTtTt t
 
5.2. Simulation of Interference Source
Equation (14) is a typical first order differential equation
and we can use solution command ode45 in MATLAB to
get is in time domain. Set up the starting steering current
is(0) = 10A, steering period Tk = 38.4e – 3 s, time slot t =
0.5e – 7 s, from former simulation result, we have the
parameters of motor: Ls = 121 μH, Rd = 21.3 m, ia =
10A. With the help of above, we have the solution of
steering current is in time domain, and the curve showed
in Figure 10.
From the commutating current we could see that the
current changed rapidly during the steering process, and
this rapid change would cause transients of contact volt-
age between brush and commutator, even generate elec-
tric sparks.
Figure 10. Curve of commutating current.
Copyright © 2011 SciRes. EPE
104 J. F. LIU ET AL.
Take (6), (7), (10) and (11) into (9), we have the func-
tion of contact voltage of DC motor:
kk kk
Tt tTtt
 
The first order differential function of contact voltage
 
22 22
ckk kk
da ds
Ri Ri
Tt Tt
Take the solution of is in time domain got from nu-
merical analysis into (15) and (16) we could get the solu-
tion of conducted interference emission source uc in time
domain. Figure 11 shows the curve of contact voltage uc
and changing rate of contact voltage duc in time domain.
The Figure 11 reveals that the contact voltage changed
as soon as the steering process starts, even after the proc-
ess finished the contact voltage is still almost 1 V, and
the changing rate reached high voltage of 1500 V by the
end of the steering process and make it the main inter-
ference source in motor operation.
6. Result and Discussion
The measurement of common mode conducted interfer-
ence is to observe voltage on 50 resistance regulated
by the linear impedance stabilizing network, LISN,
through EMI receiver. There are 2 functions of LISN,
one is to apply the 50 resistance in order to keep the
comparability of measuring result, the common mode
interference in certain frequency band could be observed
through the voltage on that resistance; the other one is to
divide the measured circuit and background noise on the
power grid, in order to reduce the interference from
power grid to result.
Connect motor windings with 12 V DC power supply
to make it operate stably, while serial connect LISN by
the side with DC bus; its equivalent circuit is showed in
Figure 12. Cs is the coupled capacity from motor wind-
ings to the ground. Consequently, we get the curve of
spectral with impedance of 50 to the ground and it is
showed in Figure 13.
Figure 13 shows that without the control of power
switch, common-mode conducted interference will be
generated during the motor operates, especially in the
frequency of 150 kHz, the jamming intensity increased
rapidly, and will hold a certain high intensity even
reached 11 MHz.
Figure 14 is the simulation model based on PSPICE
circuit simulation software. In this figure, E1 is the high
frequency interference source. This model adopted the
activity simulation model in PSPICE. Activity simulation
model is an extension of traditional controlled source
described by mathematical calculation. Common activity
models are saved in ABM.olb [17]. In the simulation
model showed in Figure 14, the high frequency inter-
ference source of DC motor is modeled by HIPASS. In-
put the high frequency interference source in this model
as the controlled source. Meanwhile, set a probe on the
terminal of 25 resistances which represents LISN, then
set up the analysis type as alternating analysis in setting
window, and the scale range as 150 kHz - 30 MHz.
Figure 15 shows the comparison of simulated and ex-
periment spectrum of LISN side common-mode voltage
from PSPICE circuit simulation software. From the
comparison we could find that simulated spectral curve
could follow the experiment one correctly, proved the
accuracy of the DC motor model and analysis of inter-
ference source.
Figure 11. Curve of conduc te d interference sourc e.
Figure 12. Equivalent circuit of common mode test.
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Figure 13. Actual spectrum measurement of DC motor.
Figure 14. Model of circuit simulation.
7. Conclusions
Contemporary research about the equivalent circuit of
separated excited DC motor in all EMC frequency is not
sufficient. The work this paper accomplished was to re-
search the high frequency common-mode equivalent
circuit of separately excited DC motor based on the re-
search of inner principle of DC motor and steering proc-
ess, and determine the parameters by Ant Colony Algo-
rithm. This equivalent circuit could be used for analysis
and measuring of the motor side common-mode con-
ducted EMI emission power and EMI current. Further-
more, the similarity of simulation and experiment result
has proved its correctness.
8. References
Figure 15. Spectrum contrast between simulation and ex-
periment of common mode conducted interference in DC
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