EMMA IEEE

Transient Modelling of Squirrel-Cage
Induction Machine
Considering Air-Gap
Flux Saturation Harmonics
IEEE PAPER PRESENTATION In the subject of
EMMA (Electrical Machine Modelling and Analysis)
Prepared by
UTSAV YAGNIK (150430707017), M.E. Electrical,
SSEC, BHAVNAGAR

About the paper
 Authors :-
1. Xiaoping Tu , Senior Member, IEEE
2. Louis-A. Dessaint, Senior Member, IEEE
3. Roger Champagne , Fellow, IEEE
4. Kamal Al-Haddad, Fellow, IEEE
 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7,
JULY 2008.
EMMA IEEE by Utsav Yagnik
2

Outline
 Abstract 4
 Introduction 5
 The effects of air-gap flux saturation harmonics 8
 EMFs and currents of stator windings due to saturation harmonics 13
 Remedy to overcome 3rd harmonic component in EMF 14
 Equivalent circuit of rotor winding in presence of air-gap flux harmonics
15
 Electromagnetic torque 16
 Resolution procedure of the model 17
 Simulation Results 19
 Conclusion 30
3

Abstract
 A transient model of squirrel cage motor has been presented with air-gap
flux saturation harmonics.
 The winding magnetizing fluxes are directly calculated from the resultant
air-gap magneto motive force to avoid the use of complicated inductance
harmonics.
 The effect of fundamental and 3rd harmonic components of air-gap flux are
incorporated in the model by two saturation models.
 The machine parameters have been calculated considering the no load and
locked rotor condition.
 The model is useful to predict the machine transient states.
4

Introduction
It is necessary to understand the motor behaviour under saturated
conditions because…
 Proper utilization of magnetic material.
 To achieve temporary high efficiency or high torque, the machine is used
in saturated region practically.
 The effect of saturation influences some motor drive strategies such as
sensor less control methods or passivity based control method.
 It is well known that the currents will rise rapidly once saturation has
been reached to get more MMF.
 Also distortion in currents and voltage waveforms will also be observed
due to air-gap main flux saturation harmonics.
5

Introduction
 These flux saturation harmonics will create a EMF which will be
superimposed on normal EMF to distort the waveform and if load is also
connected then the current waveform will also be distorted.
 Under highly saturated conditions, the saturated harmonics which have
same frequency and speed as that of fundamental one, will have
significant amount of value and should be considered while modelling a
large scale operation of an squirrel cage induction motor.
 In this model saturation effects have been considered by incorporating the
magnetizing and mutual inductances in abc model of induction machine
but the saturation effects of 3rd harmonics are neglected fir rotor.
 This paper proposes the transient model of saturated squirrel cage
induction machine based on the assumption that air-gap flux saturation
harmonics are produced by the fundamental component of air-gap MMF.
6

Introduction
 Avoiding the use of inductance harmonics, a flux model is proposed,
where winding magnetizing fluxes are calculated using the resultant air-
gap MMF.
 The saturation effects are accounted by using two saturation factors, one
for fundamental and other for 3rd harmonic saturation factor.
 All parameters including the above two factors are obtained using Blocked
rotor test and no load test.
 The saturation effects on the electromagnetic torque have been included in
machine model to allow investigate the effects at any load.
 The resulting model is used to predict both steady state and transient
behaviour of the machine in wye and delta connections.
7

The effects of air gap flux saturation
harmonics
 Only the fundamental air-gap MMF is assumed to be responsible for the
saturation harmonics.
 The simulation results shows that the 3rd harmonics are dominant in
having effects on the saturation harmonics.
1. Fundamental air-gap MMF:
 The winding function represents the MMF distribution along the air-gap
per ampere current flowing in the winding.
 The winding function of a practical winding x can be expressed as…
8

 In the last equation
 𝑁 𝑝ℎ is series turn per phase
 𝑘 𝑤1 is the winding factor for the fundamental space component
 P is the number of poles
 𝜃 is the angular position along the inner surface of the stator
 𝛼 𝑥 is the magnetic axis angle of the winding x
 For a three phase machine, the magnetic axis angle of the stator is equal
to 0°, 120° and -120° for phase a , b and c respectively referring to the
magnetic axis angle of phase a.
harmonics
9

harmonics
 MMF in the air-gap produced by a machine winding is the product of its
winding function and the current flowing in it.
 The fundamental MMF can be expressed as
 Here, the LHS of above equation shows magnitude and angular position of
magnetic axis.
 The magnetic axe positions of rotor axis are different from stator and they
rotate with rotor which can be expressed as below.
10

harmonics
 The fundamental air-gap MMF is the vector sum of the fundamental stator
and rotor MMFs as below.
 The equivalent turns is a machine constant but instantaneous values
depend upon machine variables values at the given time. So, normalized
MMF is introduced for making the analysis simpler.
11

harmonics
2. Air-gap flux harmonics due to fundamental air-gap MMF:
 In most machines, the teeth are more saturated then core and so a
flattered air-gap flux density is observed as below…
12

EMFs and currents of stator windings
due to saturation harmonics
 Like the fundamental component of the magnetic flux density, the third
harmonic also produces the machine windings by linking the
corresponding space harmonic component of the machine winding. And
the equivalent circuit looks like below…
13

Remedy to overcome the third
harmonic component in EMF
 To overcome the problem of third harmonic producing the EMF, the stator
windings must be connected in manner as below …
14

Equivalent circuit of rotor winding in
presence of airgap flux harmonics
15

Electromagnetic torque
 As discussed earlier, the saturation harmonics produce useful torque in
squirrel cage machine.
 when the stator windings are wye-ground connected or delta connected,
identical third harmonic currents circulate in the three stator windings.
 These three identical currents will produce a third harmonic MMF with a
fixed axis but a pulsating amplitude in the airgap.
 The interaction between this MMF and the third harmonic rotor MMF will
produce a pulsating torque at six times the fundamental frequency.
 Since this torque is very small, and its average value is zero, it does not
have much effect on the machine performance and is neglected in the
analysis.
16

Resolution procedure of the model
 All of the model equations are expressed in terms of the normalized MMFs
and the machine parameters, such as the machine constant KM and the
machine saturation factors ksat1 and ksat3.
 The machine electrical parameters depend on the machine construction
and can be obtained by using appropriate tests.
 However, the normalized MMFs are calculated from the machine winding
instantaneous currents, which cannot be directly obtained. This section is
devoted to a procedure of resolving the machine currents by combining the
model’s electrical and mechanical equations
17

Resolution procedure of the model
 Once the variables are resolved, the model is ready to be simulated.
 The state variables λx,1 can be initialized to very small values (but not
zero) to facilitate the starting of simulation. The state variables λx,3, the
rotor position θr, and the rotor speed ωr are set to zero.
 The basic machine electrical parameters and the saturation factors ksat1
and ksat3 are obtained from the conventional no-load and locked rotor
tests.
 The machine constants KM and A are directly calculated from the
conventional electrical machine parameters.
 This model uses non-iterative approach to finding parameters which is
time saving on part of simulation.
18

Simulation Results
19

Simulation Results
 Distortion of phase voltage waveform with wye connection under highly
saturated condition. (a) Experimental & (b) Simulation.
20

Simulation Results
 Measured and simulated magnetization characteristics for the
fundamental and third harmonic components.
21

Simulation Results
 Distortion of the phase current waveform with wye connection with
neutral to ground at VL-L = 1.55 pu. (a) No load. (b) Full load = 12 N · m.
22

Simulation Results
 Amplitudes of fundamental and third harmonic currents of the machine
winding with wye connection with neutral to ground. (a) No load. (b) Full
load.
23

Simulation Results
 Distortion of the phase current waveform of the induction machine with
delta connection at VL-L = 1.55 pu. (a) No load. (b) Full load.
24

Simulation Results
 Amplitudes of fundamental and third harmonic currents of the machine
windings with delta connection. (a) No load. (b) Full load.
25

Simulation Results
 Phase current and machine torque with wye connection with neutral to
ground from the light load to the full load at VLL = 1.44 pu. (a)
Experiment. (b) Simulation.
26

Simulation Results
 Torque produced by fundamental and third harmonic components of air-
gap flux from the light load to the full load at VLL = 1.44 pu.
27

Simulation Results
 Transient state simulation results containing the saturation third
harmonic with Direct online start.
28

Simulation Results
 Transient state simulation results containing the saturation third
harmonic with External fault in phase A.
29

Conclusion
 A transient model of a squirrel-cage induction machine, including air-gap
saturation flux harmonics, is presented.
 The model is based on a flux model, which analyses the machine with the
aid of the MMF and flux rather than the inductance. The fundamental and
third harmonic saturation components are taken into account by using
two saturation factors, which are obtained from the conventional no-load
and locked rotor tests, with access to the stator neutral point. Including
the effects of the saturation harmonics in the torque, the model can be
used to simulate the machine performance under any load condition.
 The simulation and experimental tests show that distortion of winding
voltage and current waveforms of saturated machines is well predicted by
the model.
 The model can be used to predict the machine transient states under a
high supply voltage, such as direct online start and external phase faults.
30

Conclusion
 In principle, the effects of the higher order saturation harmonics such as
fifth, seventh, etc., can be incorporated using the same approach.
 However, the saturation parameters for these harmonics are difficult to
experimentally obtain from the machine winding terminals and would
require search coils installed in the stator. Also, the simulation and
experimental results show that the saturation third harmonic plays a
predominant role; therefore, modelling of the third harmonic component is
enough for most induction machines.
31

THANKYOU
32

EMMA IEEE

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