This document discusses 3-phase induction motors. It describes the construction of 3-phase induction motors, including their stator windings and two types of rotors: squirrel cage and wound rotor. It explains how the rotating magnetic field is generated by the 3-phase currents in the stator windings, causing the rotor to turn. Equivalent circuits are presented to model the motor, including per-phase and Thevenin equivalent circuits. The torque-speed curve and effect of varying rotor resistance are described. Methods for determining motor parameters from tests are provided.

1. 3-Phase Induction Motors
EE 340

2. Where does the power go?
• The electric energy generated purchased by
consumers for different needs. This energy is
converted to different forms:
– Lighting (indoor/outdoor – CFL, incandescent,
LED, Halogen…)
– Heating (electric water heaters, clothes dryers,
electric stoves and ovens)
– power supply of electronic devices (computers,
TV, DVD, battery chargers, home automation,
etc…)
– Industrial (arc furnaces, welders, manufacturing
processes….)
– Conversion to mechanical power by motors
(pumps, fans, HVAC, refrigeration – compressors,
power tools, food processors, escalators,
elevators, ….)

3. Types of Electric Motors

4. 3-Phase induction machine construction
• 3 stator windings (uniformly
distributed as in a synchronous
generator)
• Two types of rotor:
– Squirrel cage
– Wound rotor (with slip rings)

5. The rotating magnetic field
• The basic idea of an electric motor is to generate two magnetic fields:
rotor magnetic field and stator magnetic field and make the stator field
rotating. The rotor will constantly be turning to align its magnetic field
with that of the stator field.
• The 3-phase set of currents, each of equal magnitude and with a phase
difference of 120o, flow in the stator windings and generate a rotating
field will constant magnitude.

7. The rotating magnetic field
• Consider a two-pole. The 3-phase stator coils
are placed 120o apart. Once connected to the
source, the currents in three coils will be
balanced and symmetrical,
• The magnetic flux density generated by these
currents stator at any arbitrary moment is
given by

8. The rotating magnetic field
• The net magnetic field has a constant magnitude and rotates
counterclockwise at the angular velocity ω.
• The stator rotating magnetic field can be represented by a
spinning magnet.
• For a two pole machine,
• For a p-pole machine,
)(
60
1
)()( rpmnrpsfHzf sme 
)(
120
)(
2
)( rpmn
p
rpsf
p
Hzf sme 

9. Principle of Operation
• https://www.electrical4u.com/working-
principle-of-three-phase-induction-motor/

16. Per-phase equivalent circuit
• Motor Slip
• R1 and R2: stator and rotor winding resistances
• X1 and X2: stator and rotor winding leakage reactances
• Xm: magnetizing reactance
• Rc: core loss resistance
• Rotor winding parameters are referred to the stator side
s
ms
n
nn
s



17. Power flow diagram
]/)1([3
3
)/(3
/3
3
2
2
2
2
2
2
2
2
2
2
1
1
2
1
SSRIPPP
RIP
SRIP
REp
RIP
RCLAGconv
RCL
AG
Ccore
SCL






18. Simplified per-phase equivalent circuit
• Core loss is embedded with friction, windage and stray-load loss
mindRCLAGconv
syncindAG
RCL
SCL
SSRIPPP
SRIP
RIP
RIP






/)1(3
)/(3
3
3
2
2
2
2
2
2
2
2
2
1
2
1

19. Thevenin equivalent circuit
and torque-slip equation
 2
2
2
2
2
2
2
1
11
1
)()/(
/3
)(,,
XXSRR
SRVP
XX
X
RRXX
XX
X
VV
THTHsync
TH
sync
AG
ind
M
M
THTH
M
M
TH










20. Torque-speed curve
 2
2
2
2
2
2
)()/(
/3
XXSRR
SRVP
THTHsync
TH
sync
AG
ind




Operating region:
≈ linear curve

21. Effect of varying rotor resistance
(by adding external resistance to wound rotor)

22. Motor speed control by variable frequency (VFD)

23. Determining motor circuit parameters
• DC Test (or use Ohm-meter)
• Locked-rotor Test
• No-load Test
Measuring Vφ, I1, P, Q
→ R1+R2, X1+X2
Measuring V, I → R1
Measuring Vφ, I1, P, Q
→ R1, X1+Xm

24. Rules of thumb for dividing stator and rotor leakage
reactances
• Cross section of squirrel cage rotor bars (NEMA Class A,B,C,D)

25. Motor Specifications

26. Problems
• 7.4
• 7.5
• 7.7*, 7.8, 7.10
• 7.14, 7.15
• 7.18
• 7.19