This document describes a 3-phase AC motor model for simulation in SPICE. [1] The model simplifies the motor's behavior using equivalent circuits to represent the torque, back-EMF, and mechanical parts of the motor. Torque and back-EMF are defined based on phase currents and angular speed. [2] Key parameters like phase inductance, resistance, back-EMF constant, torque constant, and load current can be set to characterize different motors. [3] The complete equivalent circuit model combines the frequency response, back-EMF generation, and mechanical torque production to simulate 3-phase motor behavior in SPICE simulations.

1. 3-Phase AC Motor Model
Simplifies SPICE Behavior Model
[PSpice Model Version]
U1
1 AC_MOTOR
2
3
M 4 LL = 105U
N0 RLL = 0.0125
KE = 0.02
KT = 1.6
LOAD = 140
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2. 1) Torque and Back-EMF
• The Torque are defined by :
Tu K T Iu  phe : u, v, w
Vphe : Phase voltage applied from inverter to motor
T v K T Iv (1)
VAC : Operating voltage range (Maximum voltage)
T w K T 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
ωm : Angular speed of rotor
• The Back-EMF are defined by :
Eu KE m  1 Pound Inch equals 0.11 Nm
Ev K E m (3)
Ew K E 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
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3. 2) Simplified 3-Phase AC Motor Model
Frequency Response
AC Motor
110uH
105uH
BEMF1
R1 L1
U 1 2
R2 L2
BEMF2 Phase Resistance (L-L) : 0.0125Ω
V 1 2 Phase Inductance : 105uH
N0 : 110uH
BEMF3
R3 L3
W 1 2
Fig. 1 Scheme of the 3-Phase Model Fig.2 Phase-to-Ground
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4. 3) The 3-Phase AC Motor Equivalent Circuit
E1
eu + emf_u
PARAMETERS: PARAMETERS:
+
|Z| - Frequency -
- Back-EMF Voltage RLL = 0.0125 LOAD = 140
LL = 105U
lim_u KT = 1.6
Vu 0
U1 EMF_U ELIM_U KE = 0.02
n1 emf_u
U OUT+ IN+ IN+ OUT+
1
SP 2
sp_u OUT- IN- IN- OUT-
tu 0 0 lim_v
TQ
ELIM_V 0
E2 IN+ OUT+
ev +
+ emf_v IN- OUT-
-
- 0 lim_w
ELIM_W 0
Vv 0
U2 EMF_V IN+ OUT+
n2 emf_v
V OUT+ IN+ IN- OUT-
1
SP 2 sp_v OUT- IN- 0 Mechanical part
tv 0 0
TQ
torque
E3
ew + emf_w ETQ
+
-
- IN+ OUT+
IN- OUT-
Vw 0
U3 EMF_W
n3 emf_w U4 0 0 speed
W OUT+ IN+
AND3AMB
SP 2
1
sp_w OUT- IN-
tw sp_u ESP
0 mul
TQ
sp_v IN+ OUT+
sp_w IN- OUT-
0 0
N0
Fig. 3 Three-Phase AC Motor Equivalent Circuit
• This figure shows the equivalent circuit of AC motor model that includes the |Z|-
frequency part ,Back-EMF voltage part ,and Mechanical part.
• The Back-EMF voltage is the voltage generated across the motor's terminals as the
windings move through the motor's magnetic field.
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5. 4) Parameters Settings
Model Parameters:
LOAD : Load current each phase of motor [Arms]
U1 – e.g. LL = 125Arms, 140Arms, or 400Arms
AC_Motor
1
LL : Phase inductance [H]
LL = 105U
– e.g. LL = 10mH, 100mH, or 1H
2
3
M 4 RLL = 0.0125
N0 KE = 0.02
KT = 1.6 RLL : Phase resistance (Phase-to-phase) [Ω]
LOAD = 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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