ee-362 electromechanical energy conversion-ii …
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EE-362 ELECTROMECHANICAL ENERGYCONVERSION-II
Equivalent Circuit of Induction Machines
Ozan Keysan
keysan.me
Office: C-113 • Tel: 210 7586
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Assume the rotor is stationary (s=1):
Then the frequency of rotor currents:
Machine just behaves just like a transformer(secondary short-circuited)
Stator winding: Primary winding of the transformer
Rotor bars: Secondary winding of the transformer
=fr fs
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Equivalent Circuit, Rotor Stationary (s=1)
Same as a transformer with secondary side short-circuited
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Assume now the rotor starts rotating (with )
Rotor induced voltage reduces (as the frequencydi�erence between rotor and stator reduces)
Nr
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Assume now the rotor starts rotating (with )
Rotor induced voltage reduces (as the frequencydi�erence between rotor and stator reduces)
Therefore current reduces,
but not that much, because the rotor sideimpedance reduces with reduced rotor currentfrequency ( jwL)
Nr
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Stator Side Equivalent Circuit
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Rotor Side Equivalent Circuit
Rotor side impedances can be modi�ed to transfer these to the statorside
For curious students: P.C.Sen, Principles of Electrical Machines and PowerElectronics, Section 5.7, Derivation of the equivalent circuit of inductionmachines
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Equivalent Circuit with Referred Rotor
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Determination of Equivalent Circuit Parameters
Equivalent tests for induction machines:
Open-circuit Test = No-Load Test
Short-circuit test = Locked Rotor Test
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Locked-Rotor Test
Rotor kept stationary with a mechanical locking system
Apply a small voltage (10-15% of the rated) to obtain rated currentand measure:
Input Power
Input Voltage
Current
= 0 → s = 1nr
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Locked-Rotor Test
Neglect the parallel branch and s = 1, the circuit becomes:
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Locked-Rotor Test
Measure using an ohm-meter, assume
Assume
= = ( + )Pphase
Ptotal
3I21r1 r′
2
r1(dc)
= 1.1r1(ac) r1(dc)
= =V1
I1
Zeq ( + + ( +r1 r′
2)2 X1 X ′
2 )2
‾ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√
=X1 X ′
2
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No-Load Test
Run the motor at no-load, applying rated voltage
Again measure:
Input Power
Input Voltage
Current
≃ → s ≃nr ns0
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No-Load Test
Rotor-side is open-circuited (s=0), the series branch (R1,X1) can alsobe neglected:
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No-Load Test
, �nd
, �nd
But, how about mechanical friction and windagelosses?
Get a few measurements at di�erent voltages and speeds toestimate the friction.
= =Pphase
Ptotal
3
V2
1
Rc
Rc
= = //V1
I1
Zeq Rc Xm Xm
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Example:
Estimate the parameters of a 30 kW, 50 Hz, Delta-connected, 415 V,3-phase machine, if the test results are as follows:
Locked-Rotor Test:
Input Power: 6.4 kW
Line Current: 77 A
Line Voltage: 130 V
Resistance between two lines: 0.293 Ω
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Example:
Estimate the parameters of a 30 kW, 50 Hz, Delta-connected, 415 V,3-phase machine, if the test results are as follows:
No-Load Test:
Input Power: 1.65 kW
Line Current: 22.8 A
Line Voltage: 415 V
Friction and windage losses: 1.15 kW
Assume =X1 X ′
2
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