This document describes a 3-phase AC motor model for simulation in SPICE. It includes: 1) Definitions of torque and back-EMF constants based on rated current and maximum speed. 2) A simplified 3-phase AC motor model showing the relationships between phase voltages, currents, torque, back-EMF, and angular speed. 3) An equivalent circuit diagram of the motor model including impedance, back-EMF voltage, and mechanical parts.

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3-Phase AC Motor Model
Simplifies SPICE Behavior Model
[LTspice Model Version]
Bee Technologies Inc.

2. • The Torque are defined by :
At 140Arms (Rated Continuous Current)
KT = 1.6 Lb-in/A
Tphe = 1.6  140 = 224Lb-in
Te = 224*3= 672Lb-in
• The Back-EMF are defined by :
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
1) Torque and Back-EMF
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wTw
vTv
uTu
IKT
IKT
IKT



mEw
mEv
mEu
KE
KE
KE






 phe : u, v, w
Vphe : Phase voltage applied from inverter to motor
VAC : Operating voltage range (Maximum voltage)
VBAT : DC Voltage applied from battery
Iphe : Phase current
Tphe : Electric torque produced by u, v, w phase
Te : Electric torque produced by motor
Ephe : Phase Back-EMF
KE : Back-EMF constant
KT : Torque constant
ωm : Angular speed of rotor
 1 Pound Inch equals 0.11 Nm
TwTvTueT 
(1)
(2)
(3)

3. 2) Simplified 3-Phase AC Motor Model
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Phase Resistance (L-L) : 0.0125Ω
Phase Inductance : 105uH
: 110uH
Frequency Response
105uH
110uH
Fig.2 Phase-to-GroundFig. 1 Scheme of the 3-Phase Model
AC Motor

4. 3) The 3-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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|Z| - Frequency
Back-EMF Voltage
Mechanical part
Fig. 3 Three-Phase AC Motor Equivalent Circuit

5. 4) Parameters Settings
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LOAD : Load current each phase of motor [Arms]
– e.g. LL = 125Arms, 140Arms, or 400Arms
LL : Phase inductance [H]
– e.g. LL = 10mH, 100mH, or 1H
RLL : Phase resistance (Phase-to-phase) [Ω]
– e.g. RLL = 10mΩ, 100mΩ, or 1Ω
KE : Back-EMF constant [V/RPM]
– e.g. KE= 0.01, 0.05, or 0.1
KT : Torque constant [Lb-in/A]
– e.g. KT= 0.1, 0.5, or 1
 1 Pound Inch equals 0.11 Nm
Model Parameters:
Fig. 4 Symbol of 3-Phase Induction Motor
• From the 3-Phase Induction Motor specification, the model is characterized by setting parameters
LL, RLL, KE, KT and LOAD.