An Improved Model for Circulating Bearing Currents in Inverter-Fed AC Machines

Full text

An Improved Model for Circulating Bearing
Currents in Inverter-Fed AC Machines
Michael Jaritz, Cornelius Jaeger, Matthias Bucher, Jasmin Smajic
IET Institute for Energy Technology
HSR University of Applied Sciences
CH-8640 Rapperswil, Switzerland
michael.jaritz@hsr.ch
Djordje Vukovic, Sebastian Blume
B&R Industrie-Automation AG
CH-8500 Frauenfeld, Switzerland
Abstract—In this paper, a general lumped parameter bear-
ing current model is presented. The lumped parameters are
derived from the analytical descriptions of the bearing current
paths and the numerical field simulations based on the finite
element method. The model considers frequency dependence.
The resulting model delivers the common mode current and
the circulating bearing current is determined by modeling the
magnetic coupling between the common mode current path and
the circulating bearing current path. The derived circuit can
be applied to AC machines and is verified by measurements
of a permanent magnet excited synchronous machine, which is
supplied by an off-the-shelf motor drive inverter.
Index Terms—Bearing currents, circulating bearing current,
common mode current, common mode voltage, magnetic cou-
pling, transmission ratio
I. INTRODUCTION
Although, the bearing current issue in electrical machines
is known for nearly 100 years [1], it is still a relevant ongoing
research topic. Failures caused by bearing currents lead to
heavy mechanical damages in electrical machines resulting
in high maintenance costs [2].
Pulse width modulated (PWM) drives, which use very fast
switching devices such as silicon carbide (SiC) or gallium
nitride (GaN) switches, in order to reduce the converter losses,
may even worsen the issue [3, 4]. These fast switching devices
generate a common mode (CM) voltage with a very high
du/dt, which leads to a CM-current with very high fre-
quency (HF) components [5]. The HF-CM-current is mainly
conducted through the stator-winding stator-core capacitance,
back to the source through the grounded machine housing (see
path 1 in Fig. 1). This causes the so-called circulating bearing
(CB) current [6–8]. The CB-current is an HF inductively
coupled current, which arises in the conductive loop formed
by the stator core-housing-non drive end (NDE) bearing-shaft-
rotor core-drive end (DE) bearing-housing (see path 2 in
Fig. 1). It is worth mentioning that there also exists other types
of bearing currents, such as the so-called electric discharge
machining (EDM) bearing currents or du/dt-currents (see
path 3 in Fig. 1). The EDM-currents are capacitively coupled
from the stator winding to the bearings. They are conducted
when the voltage across one of the bearings exceeds a certain
limit and a breakdown occurs. The du/dt currents are also
Stator winding
star point
Path 1
Path 3
iCM
Bearing (NDE)
Stator end
winding
Isolation
layer
Symmetry axis
Rotor
core (RC) Shaft (SFT)
Housing (H)
SEW-SFT
SEW-B
Cab
SEW-H uCM
Path 2
iCB
iCM
‘
iEDM ,
idu/dt
Bearing (DE)
SEW-SC
SEW-RC
SWA-SC
SWA-RC
Stator
core (SC)
Fig. 1. Simplified representation of the CM-current (iCM, iCM
0
, path 1),
the CB-current (iCB, path 2) and the EDM-currents (iEDM , idu/dt, paths 3)
paths and in an AC-machine. The excitation source of these currents is the
CM-voltage uCM. The definitions of the abbreviations are listed in Tab. I.
capacitively coupled from the stator winding to the bearings.
They are flowing as a displacement current through the
bearing capacitance [9, 10]. However, these currents are not
discussed in this paper.
In the current literature, the bearing currents are determined
with the help of equivalent lumped RLC-circuit models,
which represent the equivalent bearing current paths in the
electrical machine [5–13]. The RLC-parameters are derived
from analytical approximations of the machine geometry or
finite element method (FEM) based simulations [14, 15].
However, the magnetic interaction between the CM-current
and the CB-current is highly simplified in the existing models
[6, 8]. Therefore, in this paper, an improved lumped parameter
model, which accurately considers the magnetic coupling
between the CM-current and the CB-current is presented
and verified by measurements of a permanent magnetic syn-
chronous machine (PMSM). The calculations of all frequency
dependent lumped circuit elements, as well as the FEM based
derivation of the improved magnetic coupling parameters are
given.
This paper is organized as follows. In section II, the general
bearing current model is introduced and all governing equa-
tions for calculating the CM- and CB-currents are derived.
The derivation of the lumped RLC-parameters is given in
section III, where the main part of this section is concentrating
on the determination of the magnetic coupling parameters.
978-1-5386-6375-2/19/$31.00 ©2019 IEEE 225

TABLE I
DESCRIPTION OF THE USED ABBREVIATIONS IN FIG . 1 AND FIG . 2
Abbreviation Description
SW Stator winding
EW End winding region
SWA Part of the stator winding inside the stator core
SEW Part of the stator winding outside the stator core
SC Stator core
RC Rotor core
H Housing
B(NDE) Bearing non drive end
B(DE) Bearing drive end
SFT Shaft
Cab Grounding cable
Finally, in section IV the measured CM- and CB-currents are
verified with the currents delivered from the proposed model.
II. GENERAL COMMON MODE AND BEARING CURRENT
MODEL
Figure 2 (a) shows the equivalent lumped parameter model
according to Fig. 1. There, path 1 is related to the CM-currents
iCM and iCM
0, path 2 is related to the CB-current iCB and
path 3 is related to the EDM-current iEDM and du/dt-current
idu/dt. Since, the capacitor CSWA-SC is significantly bigger
than the other capacitors in the circuit (compare capacitances
in Tab. II), it can be safely assumed iCM ≈iCM
0. The
bearing resistance RB(NDE),(DE), as well as the non linear
impedance ZB(NDE),(DE) represent the combined values of the
bearing from the NDE-side and the DE-side. By assuming a
breakdown of both bearings at the same time (RB(NDE),(DE) ≈
0, ZB(NDE),(DE) ≈0), the CB-current becomes the dominating
current through the bearings [9] and the model can be reduced
to the model depicted in Fig. 2 (b). In this case, also path 3
is neglected. An even more compact model is shown in
Fig. 2 (c). Due to the frequency dependence of the lumped
circuit elements, the following analysis is carried out in
the complex frequency domain to determine the CB-current.
The currents ICM(jω)and ICB (jω), as well as the voltages
UCM(jω)and UCB (jω)are the complex representations of
their time domain signals iCM,iCB and uCM ,uCB, respectively
ωis the angular frequency. After solving the model in the
frequency domain, the spectral components of the currents
are finally transformed back into the time domain by using
the well known fourier series [16].
Applying Ohm’s law on the reduced bearing current model
in Fig. 2 (b) leads to
ICM(jω) = UCM(jω)
Zred(jω)(1)
where Zred is given as
Zred(jω) =ZEq (jω)+RSW(ω)+A(j ω)+RH(ω)+
+RCab(ω) + jωLCab (ω)
(2)
CSEW-SFT
CSEW-RC
CSWA-RC
Stator winding
star point
Rotor core Shaft
Housing
Path 1
Path 2
Path 3
Bearing
CSWA-SC CSEW-SC CSEW-H
CSEW-B(NDE),(DE)
CB(NDE),(DE)
iEDM,
idu/dt
RRC RSFT
RB(NDE),(DE)
RB(NDE),(DE)
RH
uCM
uCB1
uCB1
uCB2
iCB
RCab
RSC RRC
LCab
(a)
(b) (c)
ZB(NDE),(DE)
CSWA-SC CSEW-SC CSEW-H
Zred
iCM
iCM
‘
M
LRC LEW
uSFT
Stator winding
star point
Housing
Path 1 Path 1
RH
uCM
RCab
LCab
iCM
LSW
M
LSC
LSW RSW
REW
Path 2
uCB2
iCB iCB
RSC RRC
Path 2
LRC LEW
LSC
REW
RSW
uCM
iCM
iCM• ueDC,avg
L2
RCB
ZB(NDE),(DE)
Fig. 2. (a) Equivalent lumped parameter model according to Fig. 1. Path 1
is related to the CM-current iCM, path 3 is related to the circulating bearing
current iCB and path 3 is related to the EDM- and du/dt-currents iEDM
and idu/dt. (b) Reduced equivalent lumped parameter model and (c) compact
controlled source lumped parameter model, which is equivalent to (b) and
used for the verification in section IV.
and
A(jω) = 1
jω(CSWA-SC +CSEW-SC +CSEW-H).(3)
The governing equations for the magnetic coupling between
path 1 and path 2 are obtained as
UCB1(jω) = jωLSW (ω)ICM(jω)−jωM (ω)ICB (jω)(4)
UCB2(jω) = jωM (ω)ICM (jω)−jωL2(ω)ICB(jω)(5)
where, M(ω)is the frequency dependent mutual inductance,
LSW(ω)is the frequency dependent self inductance of the
stator winding and L2(ω)is the frequency dependent self
inductance of the CB-current path 2, which is given by
L2(ω) = LSC(ω) + LRC (ω) + LEW(ω).(6)
By substituting ICB with
ICB(jω) = UCB2(jω)
RCB(ω)(7)
226

TABLE II
EQUI VALE NT CI RC UIT C APACI TANC ES
Location Capacitance (pF) FEM method
CSEW-SC 209.71 3D
CSEW-RC 6.00 3D
CSEW-H 113.04 3D
CSEW-B(NDE),(DE) 3.71 3D
CSEW-SFT 11.81 3D
CSWA-SC 46407.77 2D
CSWA-RC 3.50 2D
in (4) and (5), leads to
UCB1
(jω)=jωLSW (ω)ICM(j ω)−jωM (ω)UCB2 (jω)
RCB(ω)(8)
UCB2(jω) = jωM (ω)RCB (ω)
RCB(ω) + jωL2(ω)ICM (jω)(9)
where
RCB(ω) = RSC (ω) + RRC(ω) + REW (ω).(10)
Inserting (9) in (8), results in
UCB1(jω) = ICM (jω)ZEq(jω)(11)
where
ZEq(jω) = jωLSW (ω) + ω2M2(ω)
RCB(ω)+jωL2(ω).(12)
Finally, by the substituting (9) in (7), the complex transfer
characteristic of ICB is obtained as
GICB (jω) = ICB(jω)
ICM(jω)=jωM (ω)
RCB(ω) + jωL2(ω)(13)
with
M(ω) = ueDC,avgL2(ω)(14)
and ueDC,avg is the magnetic transmission ratio. Notice: Equa-
tions (1) and (13) are represented by the model in Fig. 2 (c).
The derivations of the lumped frequency dependent parame-
ters of the reduced bearing current model is presented below.
III. DER IVATIO N OF T HE CM- A ND CB-CURRENT
CIRCUIT LUMPED PARAMETERS
A. Derivation of the RLC-circuit elements
The FEM based derivation of the capacitances, as well as
the resistance and the inductance of the end winding region
LEW and REW, is performed in the same way as presented
in detail in [8]. The resistive and inductive stator core and
rotor core parameters RSC,RRC ,LSC and LRC are analytically
obtained according to [17]. The derived values are listed in
Tab. II, respectively shown in Fig. 3. In addition, the measured
CM-impedance ZCM,meas is depicted in Fig. 3.
Frequency f (Hz)
|Z | (Ω), R (Ω), L (H)
101102103104105106107108
10-8
10-6
10-4
10-2
100
102
104
106
REW
RSC
RRC
ZCM,meas
LSC
LRC
LEW
Fig. 3. Finite element method obtained (LEW, REW), analytically ob-
tained (LSC, LRC , RSC, RRC ) and measured (ZCM,meas) frequency dependent
lumped parameters of the reduced bearing current model.
B. Derivation of the magnetic coupling parameters
To obtain the mutual inductance M(ω)(see (14)), only
an eddy-current analysis would be not sufficient, since the
source current of this model flows as a displacement current
through a capacitive path (the capacitive coupling between
the stator winding and the stator core). Thus, a Full-Maxwell
field analysis including inductive and capacitive couplings
should be performed. This analysis would be too demanding
in terms of CPU time and memory and has considerable
stability problems as the considered frequency range goes
from RF- (MHz) towards low frequencies (Hz). To avoid the
mentioned difficulties the following method is applied in this
work.
Starting from the second Maxwell equation in its complex
form [18]
∇ ×
→
H=
→
J+jω
→
D(15)
and taking the divergence on both sides
∇ · (∇ ×
→
H) = ∇ ·
→
J+∇ · jω
→
D(16)
results in
0 = ∇ ·
→
J+∇ · jω
→
D(17)
and finally in
∇ ·
→
J=−∇ · jω
→
D.(18)
where
→
His the magnetic field and
→
Dis the electrical flux
density. After introducing the material relations, (18) can be
written as
∇ ·
→
Eσ=−∇ · jω
→
E(19)
where
→
Eis the electrical field, σis the electrical conductivity
and is the electrical permittivity. By comparing the material
coefficients results in
|σ|DC ⇐⇒ |ω·|AC .(20)
227

Stator
coil
Housing
(b)
View 2
Air box
View 2
Axis of symmetry
∂NΩ
∂DΩ
∂NΩ
∂NΩ∂N1Ω1
∂N1Ω1
Ω
Shaft
Rotor core
Housing
Bearing (NDE)
CB-current loop
Stator
core Bearing
(DE)
(c)
Shaft
Rotor core
Housing
(a)
Insulation
layer
IDC, ∂N2Ω1, S
Outlet
φ = 0, ∂D1Ω1
10°
Stator coil
JSW
Insulation
layer
View 1
Stator
core
Insulation
layer
Stator
core
Stator coil
∂N1Ω1
JSW
∂N1Ω1
∂N1Ω1
∂N1Ω1
Inlet
Inlet
Ω1
Ω1
SIDC, ∂N2Ω1
φ = 0
∂D1Ω1
Outlet
∂N1Ω1∂N1Ω1
View 1
Breakout view
inside the stator core
Breakout view
inside the stator core
∂N1Ω1
Fig. 4. A 10 ◦section of the PMSM is modeled in 3D. (a) View 1 of the 3D-SCD-FEM model of the investigated PMSM. The stator coil is shown within
a breakout view of the stator core. (b) View 2 of the 3D-SCD-FEM model of the investigated PMSM. Only the Stator coil (orange), the stator core (grey),
the insulation layer (yellow) and a part of the housing (green) is needed for solving the SCD-BVP. (c) Axis symmetric 3D-FEM model, where all parts of
the PMSM are modeled for solving the MS-BVP.
By using the interpretation (20) the capacitive displacement
current can be replaced with equivalent conduction current
that has an identical path and the same current density. Having
this mathematical conversion a 10 ◦section of the PMSM is
modeled in 3D. The current density distribution of this current
source can be determined by solving the three dimensional
stationary current distribution (SCD) boundary value problem
(BVP). The 3D-SCD-BVP is defined in the computational
domain Ω1as [19]
∇ · (σDC · ∇ϕ) = 0 in Ω1⊆R3(21)
ϕ= 0 on ∂D1Ω1(22)
→
n·σDC · ∇ϕ= 0 on ∂N1Ω1(23)
→
n·∇ϕ=IDC
σDC ·Son ∂N2Ω1(24)
and finally, solving for the current density results in
→
JSW=−σDC ∇ϕwith σDC =ω·AC.(25)
The declarations of the 3D-SCD-BVP are depicted in
Fig. 4 (a) and (b). The DC-current IDC is applied at the surface
Sof the inlet (boundary ∂N2Ω1) and the scalar electrical
potential ϕis applied at the top of the outlet (boundary
∂D1Ω1). The boundary ∂N1 Ω1(blues lines) is applied on all
conducting outer surfaces, which means, no current density
component perpendicular to the conducting surfaces exists.
In order to solve the 3D-SCD-BVP in the Ω1domain, only
the stator coil, the stator core and parts of the housing are
modeled, as can be seen in Fig. 4 (a).
The mutual inductance MDC, as well as the CB-current loop
inductance L2,DC are obtained by solving the 3D magneto-
static (MS)-BVP, which is given in the computational domain
Ωas [19]
∇ × 1
µ∇×
→
A=
→
JSW in Ω⊆R3(26)
→
n×
→
A= 0 on ∂DΩ(27)
→
n×∇×
→
A= 0 on ∂NΩ(28)
where
→
A is the magnetic vector potential and µis the magnetic
permeability. At the axis of symmetry, only a tangential
component of the vector potential is non-zero (boundary
∂DΩ) and there exists no magnetic field outside the air box
(boundary ∂NΩ), as shown in Fig. 4 (c). For solving the 3D
MS-BVP in the Ωdomain, all parts of the PMSM are included
(see Fig. 4 (c)). Finally, the magnetic transmission ratio ueDC
is calculated as [20]
ueDC(ω) = MDC(ω)
L2,DC(ω).(29)
The close invariance in frequency of the magnetic coupling
parameters is clearly shown in Fig. 5. Thus, the mean value
of ueDC(ω)(see Tab. III) is used for calculating M(ω)in (14)
with
ueDC,avg =mean(ueDC(ω)) .(30)
IV. MEA SU RE ME NT A ND S IM UL ATIO N RE SU LTS
In the following, the simulated CM- and CB-
currents are verified with measurements on a PMSM
(8LSP96.R2015P644-3, [21]), which is driven by a inverter
based motor drive (ACS880-01-061A-3, [22]). The main
parameters of the motor drive system are listed in Tab. IV
228

TABLE III
AVERAGED MAGNETIC COUPLING PARAMETERS
Parameter Value
L2,DC,avg 2.36 ×10−1H
MDC,avg 3.85 ×10−2H
ueDC,avg 1.64 ×10−1
Frequency f (Hz)
101102103104105106107108
10-2
10-1
100
L in (H), M in (H), ue (-)
L2,DC
MDC
ueDC
Fig. 5. FEM obtained mutual inductance MDC, self inductance of the CB-
current loop L2,DC (see Fig. 4 (c)) and the magnetic transmission ratio ueDC.
and the measurement circuit is depicted in Fig. 6. The
investigated PMSM is equipped with a hybrid bearing on
its NDE-side, which is bypassed with a copper stripe for
measuring the CB-current iCB,meas. The CB-current probe
(CP031A), as well as the CM-current probe (CP031), [23]
have a bandwidth of 100 MHz respectively a sensitivity of
1 mA/div and 10 mA/div. Further, the test machine has
been mounted isolated from the ground and only a defined
single point at the housing provides the grounding. The shaft
voltage uSFT,meas is measured on the DE-side with respect
to the housing and the measured CM-voltage uCM,meas is
obtained by measuring all phase-to-ground voltages and
calculating the mean value. Further, the phase-to-ground
voltages are measured as close as possible to the machine in
order to exclude the influence of the supply- and grounding
cables on the measurement of uCM,meas. The machine is
operated under no-load conditions.
For verifying the proposed CB-model, the circuit in Fig. 2 (c)
is used and Zred is replaced by the measured CM-mode
impedance ZCM,meas (see Fig. 3), which is obtained by
electrically connecting the endings of the stator winding and
measuring the impedance related to the grounded point of
the housing. The depicted period of uCM,meas in Fig. 7 (a) is
transformed into its spectral components and input into the
frequency depended model. The considered frequency range
is between 30 Hz and 5 MHz.
Figure 7 shows all measured values according to Fig. 6 and
the simulated CM-current iCM,sim, as well as the simulated
CB-current iCB,sim. Figure 8 shows the waveforms of the
TABLE IV
DATA SHEE T PARA ME TER S OF T HE IN VE STI GATE D PMSM [21] AND T HE
US ED MOT OR D RIV E IN VERT ER [22]
Parameters PMSM
Nominal speed nN(rpm) 1500
Nominal torque MN(Nm) 350
Nominal power PN(W) 54 978
Nominal current (RMS) IN(A) 107.3
Parameters motor drive inverter
Nominal power PN(W) 30 000
Nominal current (RMS) IN(A) 61
Stator winding
star point
A
A
V
V
Hybrid
bearing (NDE)
Stator end
winding
Isolation
layer
Symmetry axis
Shaft (SFT)
Housing (H)
Copper
stripe
uCM
RCab
LCab
uSFT,meas
iCB,meas
Bearing (DE)
iCM
iCM,meas
uCM,meas
Rotor
core (RC)
Stator
core (SC)
Fig. 6. Measurement setup for measuring the CM-current iCM,meas, the CB-
current iCB,meas, the CM-voltage uCM,meas and the shaft voltage uSFT,meas.
zoom area in Fig. 7. The time range is exemplary chosen
where the shaft voltage is low and a maximal CB-current
occurs. By comparing the measured and the simulated first
maximal peak values of the CM-currents in Fig. 8 (c) (see
regions Y1and Y2) the relative error is 14.7 % for the
negative peak and 11.7 % for the positive peak. The relative
error in case of the CB-currents in Fig. 8 (d) (see regions
X1and X2) is 38.6 % for the negative peak and 15.8 % for
the positive peak. The higher deviation of the CB-current
can be explained by the fact that the bearing resistance is
assumed to be zero during the breakdown and the impedance
of the additional copper stripe in the bearing current circuit
is neglected as well. Therefore, the assumed impedance
of the CB-current circuit is too low and the calculated
CB-current is too high, which results in a higher deviation.
However, the proposed model shows good agreement with
the measurement results in time response.
V. CONCLUSION
In this paper, an improved lumped parameter circulating
bearing current model is presented and verified by measure-
ments on a permanent magnet excited synchronous machine.
The derivations of the frequency dependent lumped param-
eters are given and a detailed finite element based method
for deriving the magnetic transmission coefficient from the
geometry of the electrical machine is carried out. The relative
error between the peaks of the circulating bearing current
of the proposed model and measurements is in the range
of 15.8 % and 38.6 %, whereas the waveforms show good
agreement in time response.
229

0 5 10 15 20 25 30
Time t (ms)
-400
-200
0
200
400
Voltage (V)
uCM,meas
0 5 10 15 20 25 30
Time t (ms)
-20
-10
0
10
20
(a)
(b)
(c)
(d)
Voltage (V)
0 5 10 15 20 25 30
Time t (ms)
-20
-10
0
10
20
Current (A)
0 5 10 15 20 25 30
Time t (ms)
-10
-5
0
5
10
Current (A)
Zoom area
Zoom area
Zoom area
Zoom area
uSFT,meas
iCM,meas
iCB(NDE),meas
iCM,sim
iCB,sim
Fig. 7. (a) Measured CM-voltage uCM,meas. (b) Measured SFT-voltage
uSFT,meas. (c) Measured and simulated CM-currents iCM,meas and iCM,sim.
(d) Measured and simulated CB-currents iCB,meas and iCB,sim. The yellow
zoom area is used for Fig. 8.
(a)
(b)
(c)
(d)
10.005 10.01 10.015 10.02
Time t (ms)
-200
-100
0
100
200
Voltage (V)
10.005 10.01 10.015 10.02
Time t (ms)
-3
-2
-1
0
1
2
Voltage (V)
10.005 10.01 10.015 10.02
Time t (ms)
-20
-15
-10
-5
0
5
10
15
20
Current (A)
10.005 10.01 10.015 10.02
Time t (ms)
-7
-5
-3
-1
0
1
3
5
7
Current (A)
uCM,meas
uSFT,meas
iCM,meas
iCM,sim
iCB,sim
iCB,(NDE),meas
X1
Y1
X2
Y2
Fig. 8. Zoom area of the measured and simulated curves given in Fig. 7.
The peaks in the regions Y1, Y2, X1and X2are used for the evaluation.
REFERENCES
[1] P. L. Alger and H. W. Samson, “Shaft currents in electric machines,”
Journal of the American Institute of Electrical Engineers, vol. 42,
no. 12, pp. 1325–1334, Dec 1923.
[2] RENOWN-ELECTRIC. (2018) Avoiding Motor Shaft Voltage &
Bearing Current Damage. [Online]. Available: https://www.magnetec.
de/fileadmin/pdf/bearing-current- damage-guide.pdf
[3] D. Han, S. Li, W. Lee, W. Choi, and B. Sarlioglu, “Trade-off between
switching loss and common mode EMI generation of GaN devices-
analysis and solution,” in IEEE Appl. Power Electron. Conf. Expo.
(APEC), March 2017, pp. 843–847.
[4] K. Euerle, K. Iyer, E. Severson, R. Baranwal, S. Tewari, and N. Mohan,
“A compact active filter to eliminate common-mode voltage in a SiC-
based motor drive,” in IEEE Energy Convers. Congr. Expo. (ECCE),
Sept 2016, pp. 1–8.
[5] S. Ogasawara and H. Akagi, “Modeling and damping of high-frequency
leakage currents in PWM inverter-fed AC motor drive systems,” IEEE
Trans. Ind. Appl., vol. 32, no. 5, pp. 1105–1114, Sept 1996.
[6] A. Muetze and A. Binder, “Calculation of Circulating Bearing Currents
in Machines of Inverter-Based Drive Systems,” IEEE Trans. Ind.
Electron., vol. 54, no. 2, pp. 932–938, April 2007.
[7] S. Chen and T. A. Lipo, “Circulating type motor bearing current in
inverter drives,” IEEE Ind. Appl. Magazine, vol. 4, no. 1, pp. 32–38,
Jan 1998.
[8] C. Jaeger, I. Grinbaum, and J. Smajic, “Numerical Simulation and
Measurement of Common-Mode and Circulating Bearing Currents,” in
22nd. Int. Conf. Elect. Mach. (ICEM), Sept 2016, pp. 486–491.
[9] D. Schr ¨
oder, Leistungselektronische Schaltungen: Funktion, Auslegung
und Anwendung. Springer-Verlag, 2008.
[10] T. Plazenet, T. Boileau, C. Caironi, and B. Nahid-Mobarakeh, “An
overview of shaft voltages and bearing currents in rotating machines,”
in IEEE Ind. Appl. Soc. Annu. Meeting, Oct 2016, pp. 1–8.
[11] Fei Wang, “Motor Shaft Voltages and Bearing Currents and Their Re-
duction in Multilevel Medium-Voltage PWM Voltage-Source-Inverter
Drive Applications,” IEEE Trans. Ind. Appl., vol. 36, no. 5, pp. 1336–
1341, Sept 2000.
[12] S. Chen, T. A. Lipo, and D. Fitzgerald, “Modeling of Motor Bearing
Currents in PWM Inverter Drives,” IEEE Trans. Ind. Appl., vol. 32,
no. 6, pp. 1365–1370, Nov 1996.
[13] D. F. Busse, J. M. Erdman, R. J. Kerkman, D. W. Schlegel, and
G. L. Skibinski, “The Effects of PWM Voltage Source Inverters on
the Mechanical Performance of Rolling Bearings,” IEEE Trans. Ind.
Appl., vol. 33, no. 2, pp. 567–576, Mar 1997.
[14] A. Bubert, J. Zhang, and R. W. D. Doncker, “Modeling and measure-
ment of capacitive and inductive bearing current in electrical machines,”
in Brazilian Power Electron. Conf. (COBEP), Nov 2017, pp. 1–6.
[15] J. hoon Jun, C. kyu Lee, and B. il Kwon, “The analysis of bearing
current using common mode equivalent circuit parameters by FEM,” in
Int. Conf. Elect. Mach. Syst., vol. 1, Sept 2005, pp. 49–51 Vol. 1.
[16] I. N. Bronstein, J. Hromkovic, B. Luderer, H.-R. Schwarz, J. Blath,
A. Schied, S. Dempe, G. Wanka, and S. Gottwald, Taschenbuch der
Mathematik. Springer-Verlag, 2012, vol. 1.
[17] P. M¨
aki-Ontto et al., “Modeling and reduction of shaft voltages in
AC motors fed by frequency converters,” Ph.D. dissertation, Helsinki
University of Technology; Teknillinen korkeakoulu, 2006.
[18] P. Leuchtmann, Einf ¨
uhrung in die elektromagnetische Feldtheorie.
Pearson Studium M¨
unchen, 2005.
[19] J. Smajic and National Agency for Finite Element Methods and
Standards, How to Perform Electromagnetic Finite Element Analysis.
NAFEMS, 2016.
[20] M. Albach, Grundlagen der Elektrotechnik 1. Pearson Studium
M¨
unchen, 2004.
[21] B&R−Industrial Automation. (2018) PMSM technical data.
[Online]. Available: https://www.br-automation.com/de-ch/produkte/
antriebstechnik/synchronmotoren-8ls/kuehlart- p/baugroesse-9/
8lsp96ee015ffgg-3/
[22] ABB Ltd. (2018) ACS880 Catalog 3AUA0000118315 RevN DE(3).
[Online]. Available: https://new.abb.com/drives/de/
frequenzumrichter-fuer-niederspannung/industrial- drives/
acs880-single- drive-frequenzumrichter/acs880-01
[23] Teledyne Lecroy. (2016) Current Probes. [Online]. Available: http:
//cdn.teledynelecroy.com/files/pdf/current-probes-ds.pdf
230
Powered by TCPDF (www.tcpdf.org)