This document provides information about modeling a 3-phase AC motor for electric drive system simulation in PSpice. It includes the motor specifications, modeling of torque and back-EMF, a simplified 3-phase AC motor model, the equivalent circuit model, and parameter settings. Appendices provide details on measuring points, evaluation text, gate signals, model text, and simulation settings.

1. Concept Kit
Modeling of 3-Phase AC Motor
Drive Simulation
For Electric Drive Systems
[PSpice Version]
All Rights Reserved Copyright (C) Bee Technologies Inc. 2012 1

2. Contents
Slide #
1. Modeling of 3-Phase AC Motor Model
1.1 Manufacturer Specification......................................................................................................... 3
1.2 Torque and Back-EMF............................................................................................................... 4
1.3 Simplified 3-Phase AC Motor Model......................................................................................... 5
1.4 The 3-Phase AC Motor Equivalent Circuit................................................................................. 6
1.5 Parameter Settings..................................................................................................................... 7
2. Simulation Circuit of 3-Phase AC Motor Model................................................................................ 8
2.1 Phase Current Characteristics Under Load Variation................................................................ 9
2.2 Back-EMF Characteristics Under Load Condition..................................................................... 10
2.3 Speed and Torque Characteristics At 140Arms........................................................................ 11
2.4 Power Output and Efficiency Characteristics At 140Arms......................................................... 12
Appendix A: Measured Point of Simulation Circuit (1/2)........................................................... 13
Appendix A: Measured Point of Simulation Circuit (2/2)........................................................... 14
Appendix B: Evaluation Text...................................................................................................... 15
Appendix C: Gate Signal for Six-Step Control........................................................................... 16
Appendix D: 3-Phase AC Motor Model Text (1/2)..................................................................... 17
Appendix D: 3-Phase AC Motor Model Text (2/2)..................................................................... 18
Appendix E: Simulation Settings................................................................................................ 19
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3. 1.1) Manufacturer Specification
Motenergy, Inc (ME0913)
Motor Electrical Parameters
• Operating Voltage Range..........................0 – 72 V MAX
• Rated Continuous Current........................140 Arms
• Peak Stalled Current.................................400 Arms
• Voltage Constant.......................................50 RPM/V
• Phase Resistance (L-L).............................0.0125 Ω
• Phase Inductance......................................105uH at 120Hz, 110uH at 1kHz
• Maximum Continuous Power Rating……..17KW at 102V DC Battery Voltage
14.3KW at 84VDC Battery Voltage
12KW at 72VDC Battery Voltage
Motor Mechanical Parameters
• Rated Speed.............................................3000 RPM
• Maximum Speed.......................................5000 RPM
• Rated Torque............................................288 Lb-in
• Torque Constant.......................................1.6 Lb-in/A
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4. 1.2) Torque and Back-EMF
• The Torque are defined by :
 phe : u, v, w
Tu = KT ⋅ Iu
Vphe : Phase voltage applied from inverter to motor
Tv = KT ⋅ Iv (1)
VAC : Operating voltage range (Maximum voltage)
Tw = KT ⋅ Iw
VBAT : DC Voltage applied from battery
Te = Tu + Tv + Tw (2) Iphe : Phase current
At 140Arms (Rated Continuous Current) Tphe : Electric torque produced by u, v, w phase
KT = 1.6 Lb-in/A Te : Electric torque produced by motor
Ephe : Phase Back-EMF
Tphe = 1.6  140 = 224Lb-in
KE : Back-EMF constant
Te = 224*3= 672Lb-in KT : Torque constant
• The Back-EMF are defined by : ωm : Angular speed of rotor
Eu = KE ⋅ ω m
 1 Pound Inch equals 0.11 Nm
Ev = K E ⋅ ω m (3)
Ew = K E ⋅ ω m
At 5000 RPM (Maximum Speed)
Ephe ≈ VBAT (In an ideal motor, R and L are zero)
Ephe = 102V
KE = Ephe /ωm = 102 / 5000
KE ≈ 0.02V/RPM
All Rights Reserved Copyright (C) Bee Technologies Inc. 2012 4

5. 1.3) Simplified 3-Phase AC Motor Model
Frequency Response
110uH
105uH
BEMF1
R 1 L1
U 1 2
R 2 L2
BEMF2 Phase Resistance (L-L) : 0.0125Ω
V 1 2 Phase Inductance : 105uH
N 0 : 110uH
BEMF3
R 3 L3
W 1 2
Fig. 1 Scheme of the 3-Phase Model Fig.2 Phase-to-Ground
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6. RLL = 0.0125
PARAMET
0
0
LL = 105U
OUT-
OUT-
OUT+
OUT+
KE = 0.02
KT = 1.6
IN+
IN-
IN+
IN-
1.4) The 3-Phase AC Motor Equivalent Circuit
lim_w
0
0
lim_u
lim_v
mul
|Z| - Frequency Back-EMF Voltage
0
0
0
OUT+
OUT+
OUT+
OUT-
OUT-
OUT-
IN+
IN-
IN+
IN-
IN+
IN-
sp_w
sp_u
sp_v
0
0
0
0
0
0
Mechanical part
IN+
IN-
IN+
IN-
IN+
IN-
OUT+
OUT-
OUT+
OUT-
OUT+
OUT-
emf_w
emf_u
emf_v
emf_w
emf_u
emf_v
sp_w
sp_u
-
-
-
sp_v
+
+
+
E1
E2
E3
tw
tu
tv
+
+
+
-
-
-
0
0
0
TQSP 2 TQSP 2 TQSP 2
ew
eu
ev
Fig. 3 Three-Phase AC Motor Equivalent Circuit
• This figure shows the equivalent circuit of AC motor model that includes the |Z|-
U1
U2
U3
frequency part ,Back-EMF voltage part ,and Mechanical part.
1 1 1
n1
n3
n2
• The Back-EMF voltage is the voltage generated across the motor's terminals as the
windings move through the motor's magnetic field.
Vw
Vu
Vv
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0

7. 1.5) Parameters Settings
Model Parameters:
LOAD : Load current each phase of motor [Arms]
U 1 – e.g. LL = 125Arms, 140Arms, or 400Arms
M E0913
1
LL : Phase inductance [H]
LL = 105U
M
– e.g. LL = 10mH, 100mH, or 1H
2 4 R L L = 0 .0 1 2 5
N 0 KE = 0 .0 2
3 KT = 1 .6 RLL : Phase resistance (Phase-to-phase) [Ω]
LO AD = 140 – e.g. RLL = 10mΩ, 100mΩ, or 1Ω
KE : Back-EMF constant [V/RPM]
– e.g. KE= 0.01, 0.05, or 0.1
Fig. 4 Symbol of 3-Phase Induction Motor KT : Torque constant [Lb-in/A]
– e.g. KT= 0.1, 0.5, or 1
 1 Pound Inch equals 0.11 Nm
• From the 3-Phase Induction Motor specification, the model is characterized by setting parameters
LL, RLL, KE, KT and LOAD.
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8. 2) Simulation Circuit of 3-Phase AC Motor Model
V1 S1 D 1 S3 D 3 S5 D 5
102V U P + + D M O D _01 VP + + D M O D _01 W P + + D M O D _01
- - - - - -
0 0 0 U 1
M E0913
R U U 1
R V 2
M
4
V
N 0
N 0 R W W 3
N 0
RU, RV, RW: 173.75m
V2
102V
LL = 105U
S2 D 2 S4 D 4 S6 D 6 R L L = 0 .0 1 2 5
U D + + D M O D _01 VD + + D M O D _01 W D + + D M O D _01 K E = 0 .0 2
K T = 1 .6
- - - - - -
LO AD = 140
0 0 0
0
• Fig.5 Analysis of motor operation powered by
U P U D VP VD W P W D
alternating voltage variation involves using the
model of three-phase induction motor.
U 2
VP
U P
W P
VD
U D
W D
G D R V
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9. 2.1) Phase Current Characteristics Under Load Variation
- Simulation Results
500A
Load 50Arms
0A
- 500A
0s 5 0 0 ms
500A I ( RU) / SQRT( 2 )
Ti me
Load 140Arms
0A
- 500A
0s 5 0 0 ms
500A I ( RU) / SQRT( 2 )
Ti me Load 200Arms
0A
- 500A
0s 5 0 0 ms
I ( RU) / SQRT( 2 )
Ti me  Reference of Phase U
Fig. 6 Current Characteristics under load Condition
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10. 2.2) Back-EMF Characteristics Under Load Condition
- Simulation Results
200V
Load 50Arms
100V
0V
- 100V
- 200V
0s 5 0 0 ms
200V V( X_ U1 . EU)
Ti me
Load 140Arms
100V
0V
- 100V
- 200V
0s 5 0 0 ms
200V V( X_ U1 . EU)
Ti me
Load 200Arms
100V
0V
- 100V
- 200V
0s 5 0 0 ms
V( X_ U1 . EU)
Ti me  Reference of Phase U
Fig. 7 Back-EMF Characteristics under load Condition
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11. 2.3) Speed and Torque Characteristics At 140Arms
- Simulation Results
4 . 0 KV
The Load 140(Arms) is Rated Continuous Current
3 . 0 KV
( 4 6 4 . 1 4 6 m, 3 . 2 3 1 1 K)
RPM 2 . 0 KV
1 . 0 KV
SEL > >
0V
V( X_ U1 . s p e e d )
1 . 0 KV
Tphe: Electric torque produced by each phase
Lb-in 0 . 5 KV
( 4 4 6 . 4 8 6 m, 2 2 3 . 7 2 8 )
0V
0s 5 0 0 ms
V( X_ U1 . t u )
Ti me  Reference of Phase U
Fig. 8 Speed and Torque Characteristics at Load=140Arms
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12. 2.4) Power Output and Efficiency Characteristics At 140Arms
- Simulation Results
2 0 KW
At Load=140Arms, Power Output ≈ 13.7 [KW]
( 9 6 0 . 6 1 6 m, 1 3 . 6 6 2 K)
Watt 1 0 KW
SEL > >
0W
RMS( V( RU: 1 , N0 ) ) * RMS( I ( RU) )
100
At Load=140Arms, Efficiency ≈ 82 [%]
( 9 6 2 . 5 0 0 m, 8 1 . 9 4 1 )
[%] 50
0
0. 5s 1. 0s
100* ( ( RMS( V( U, N0 ) ) * RMS( I ( RU) ) ) / ( RMS( V( RU: 1 , N0 ) ) * RMS( I ( RU) ) ) )
Ti me  Reference of Phase U
Fig. 9 Power Output and Efficiency Characteristics at Load=140Arms
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