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Induction Machines
EE 340
Spring 2012
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)
– Conversion to mechanical power by motors (pumps, fans, HVAC, refrigeration – compressors, power tools, food processors, escalators, elevators, ….)
– power supply of electronic devices (computers, TV, DVD, battery chargers, home automation, etc…)
– Industrial (arc furnaces, welders, manufacturing processes….)
Power Demand – Individual Customer
MW and MVAR loading on a feeder
System load: 24-hours
0
1000
2000
3000
4000
5000
6000
1 2 3 4 5 6 7 8 910 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Syst
em L
oad
(MW
)
Hour of Day
System load: 4-month period
0
1000
2000
3000
4000
5000
60006
/1/2
00
8
6/8
/20
08
6/1
5/2
00
8
6/2
2/2
00
8
6/2
9/2
00
8
7/6
/20
08
7/1
3/2
00
8
7/2
0/2
00
8
7/2
7/2
00
8
8/3
/20
08
8/1
0/2
00
8
8/1
7/2
00
8
8/2
4/2
00
8
8/3
1/2
00
8
9/7
/20
08
9/1
4/2
00
8
9/2
1/2
00
8
9/2
8/2
00
8
Time (mm/dd/yy)
Syst
em
de
man
d (
MW
)
Types of Electric Motors
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)
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 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.
The rotating magnetic field
• Consider a simple 3-phase stator containing three coils, each 120o apart. Such a winding will produce only one north and one south magnetic pole; therefore, this motor would be called a two pole motor.
• Assume that the currents in three coils are:
• The magnetic flux density in the stator at any arbitrary moment is given by
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 as a north pole and a south pole.
• For a two pole machine,
• For a p-pole machine,
)(60
1)()( rpmnrpsfHzf sme
)(120
)(2
)( rpmnp
rpsfp
Hzf sme
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
nns
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
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
Thevenin equivalent circuit and torque-slip equation
2
2
2
2
2
2
2
1
11
1
)()/(
/3
)(,,
XXSRR
SRVP
XX
XRRXX
XX
XVV
THTHsync
TH
sync
AGind
M
MTHTH
M
MTH
Torque-speed curve
2
2
2
2
2
2
)()/(
/3
XXSRR
SRVP
THTHsync
TH
sync
AGind
Operating region: ≈ linear curve
Effect of varying rotor resistance (by adding external resistance to wound rotor)
Motor speed control by variable frequency (VFD)
Determining motor circuit parameters
• DC Test
• 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
Rules of thumb for dividing stator and rotor leakage reactances
• Cross section of squirrel cage rotor bars (NEMA Class A,B,C,D)
Motor Specifications
Problems
• 7.4
• 7.5
• 7.7*, 7.8, 7.10
• 7.14, 7.15
• 7.18
• 7.19
