Transcript Modelling of Single-Phase Induction Motor with External

Modelling and Analysis of
Single-Phase Induction Motor
with External Rotor
Uma. R
Edited By
Sarath S Nair
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Presentation Outline
Introduction
 Why an external rotor?
 Equivalent circuit of rotor
 Lumped parameter equivalent circuit
 Mathematical model
 Role of conducting shell
 Steady state and dynamic analysis
 Summary
 References

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Introduction




Many domestic appliances require low-power
motors operating at constant speed that must start
under load(compressors, pumps etc)
Because of the reliability in operation the singlephase induction motor is one of the most widely
used types of AC machines
SPIM with external rotor is more advantageous for
low power application
Constant speed at different load can be easily
achieved by increasing the motor inertia, by using
an external rotor
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Why an external rotor?
Allows a higher stability in operation at different
loads due to higher inertia
 The fan blades can be attached directly to the
outside of the rotor, making the motor more
compact
 Heat generated within the rotor, is on the outside
and can be dissipated easily
 The start-up and operating characteristics of singlephase induction motors with external rotor can be
improved by covering the rotor with a conducting
shell joining the two end rings

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External rotor of an Induction motor
Fig1. axial half cross-section
Fig2. Fluxes in longitudinal section

L – laminations
Φσbx - leakage fluxes of bar

B - rotor cage bars
Φδx
-

R - end rings
Φex
- leakage

S - conducting shell
airgap flux
flux of shell
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Magnetic fluxes and Induced voltages
Φσbx= Lσb Ibx
 Σ Irk= kr Ibx
 Φσrx= kr Lσr Ibx

Φσrx= Lσr Irk
kr =1/(2sin2(Πp/Z))
The induced voltage by these fluxes equals the
resistive voltage drops on the path г b
jω(Φδx + 2 Φσbx + 2Σ Φσrx )= 2Rb Ibx +2Rr Σ Irk
On the path г e- (a closed path, consisting from two
"external bars“)
-jω(Φex + 2Σ Φσrx )= 2Re Iexwww.technologyfuturae.com
+2Rr Σ Irk
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Equivalent circuit of the Rotor
•
U1, U2 etc -the bar e.m.f.s

Each bar is represented by its complex impedance

Each ring by its ring-segment complex impedance
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Contd…

External shell

Due to the symmetry of the bar and ring segment
currents, a star equivalent of impedance & for the
ring segments can be established

equivalent impedance of a bar circuit is: without
external conducting shell

with external conducting shell
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Lumped parameter Equivalent Circuit
Assumptions
1. Only the fundamental space-harmonic component
of the air-gap flux distribution is considered.
2. A nonlinear resistor that is associated with the
total stator flux linkage models core loss in d and
q axis.
3. Stray losses, temperature effects and rotational
losses are neglected
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Mathematical Model

Mathematical model is described by the following
state-variable matrix equations:
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Contd…

Where the inductance terms are calculated using
the notations:

The induced voltages in the magnetising branch
are readily determined with:
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Contd…

Where

Torque equation is:
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Role of conducting shell


The ring impedance is especially high in small
external rotor motors, because of the increased
ring mean diameter
The external conducting shell
ensures a parallel way for the ring currents
 diminishes the equivalent ring impedance
 decreases the rotor resistance and the leakage
reactance
increases the cooling surface area
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Steady state and Dynamic analysis

A split phase induction motor with following
parameters are considered for analysis
o
o
o
o
o
o
o
Rated output power: 60 W
Rated frequency: 50 Hz
Rated speed: 2850 rpm
Rated voltage: 220 V
Stator main winding resistance:37.57 ohm
Stator auxiliary winding resistance: 56.83 ohm
Rotor resistance: 76.23 ohm
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Contd…

1) steady-state torque versus speed
for starting period
2) steady-state torque versus
speed for rated operating period
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Contd…
Fig(1)
Fig(2)

1) instantaneous torque versus speed for motor with extemal rotor
and without conducting shell

2) instantaneous torque versus speed for motor with extemal rotor
with conducting shell
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Contd…
Fig(1)
Fig(2)

1)Start-up speed response for motor with external rotor and without
conducting shell

2)Start-up speed response for motor with external rotor with
conducting shell
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Summary

This paper focused on a new construction of SPIM
with external rotor and conducting shell

An equivalent circuit for analysis and modelling of
the single-phase induction motor with external rotor
is derived.

The torque and speed characteristics of the motor
with and without the conducting shell is compared

A SPIM with external rotor and conducting shell
finds its application in compressors, pumps, air
conditioners etc
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References
[l] M. Popescu, “Analysis and Modelling of Single-Phase
Induction Motor with External Rotor for Domestic
Applications”, IEEE Trans. Ind. Appl.,2000,pp463-470
[2]P.C. Krause, 0. Waszynchuk, S.D. Sudhoff: Analysis of
Electrical Machinery, IEEE Press, New York, 1995
[3] S . D. Umans, “Steady-state, lumped-parameter model for
capacitor-run, single-phase induction motors”, IEEE Trans.
Ind. Appl., Vo1.32, no. 1, Jan/Feb 1996, pp.169-179
[4] E. Levi: “A unified approach to main flux saturation modelling
in D-Q axis models of induction machines”, IEEE Trans.
Energy Conv., Vol. 10, no.3, Sept. 1995,pp 455-461
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