emma ieee

Transient Modelling of Squirrel-Cage Induction

Machine Considering Air-Gap

Flux Saturation HarmonicsIEEE PAPER PRESENTATION In the subject of

EMMA (Electrical Machine Modelling and Analysis)Prepared by

UTSAV YAGNIK (150430707017), M.E. Electrical,SSEC, BHAVNAGAR

EMMA IEEE by Utsav Yagnik

2 About the paper

Authors :-1. Xiaoping Tu , Senior Member, IEEE2. Louis-A. Dessaint, Senior Member, IEEE3. Roger Champagne , Fellow, IEEE4. Kamal Al-Haddad, Fellow, IEEE

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008.


3 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


4 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.


5 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.


6 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.


7 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.


8 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…


9

In the last equation

is series turn per phase is the winding factor for the fundamental space component P is the number of poles is the angular position along the inner surface of the stator 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 and -120 for phase a , b and c respectively referring to the magnetic axis angle of phase a.

The effects of air gap flux saturation harmonics


10 The effects of air gap flux saturation 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.


11 The effects of air gap flux saturation 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.


12 The effects of air gap flux saturation harmonics2. 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…


13 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…


14 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 …


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


16 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.


17 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


18 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.


19 Simulation Results



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



Measured and simulated magnetization characteristics for the fundamental and third harmonic components.



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.



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



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.



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



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.



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.



Transient state simulation results containing the saturation third harmonic with Direct online start.



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


30 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.


31 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.


32

THANK YOU

emma ieee

Documents