International Journal of Computer Architecture and Mobility (ISSN … Modelling... · International...

International Journal of Computer Architecture and Mobility

(ISSN 2319-9229) Volume 2-Issue 9, July 2014

Available Online at: www.ijcam.com

2D Modelling Induction Machine

Dahmane HACHI 1

, Badreddine NAAS 1, 2

, Bachir NAAS 1, 2

, AIDA Kamel, CHAHARA Belkacem

Faculty of Science and Technology, University of Djelfa, 17000 DZ, Algeria 1

Applied Automation and Industrial Diagnostic Laboratory (LAADI), Algeria 2 [email protected], [email protected], [email protected],

Abstract— In this study of the induction machine is

simulated using a 2D Finite elements methods by

FEMM. Its main goal is to find the best geometrical

structure. The simulations have been performed

using the magnetic vector potential A formulation

and have been limited to a magnetodynamic case.

The influence of the geometrical parameters and

there magnetic properties are taken account in order

to optimise the conception of the induction machine.

Keywords— induction machine IM, Finite element method

FEM, Magnetodynamic Finite Element Formulation.

I. INTRODUCTION

The asynchronous motor is currently the electric

motor whose use is most prevalent in the industry.

Its main advantage lies in the absence of sliding

electrical contacts, which leads to a simple, robust

and easy to build structure. The power range from a

few W to several MW. Directly connected to

industrial network with constant voltage and

frequency it runs at a slightly different speed

synchronous speed. This is the engine that is used

for producing virtually all the drives at a constant

speed. Thanks to the power electronics and control,

asynchronous motor also allows the realization of

variable speed drives. It takes place in the latter

area is growing.

Have an engine with minimum torque ripple,

economic and compact as possible, these are the

objectives that a manufacturer sets. But more often,

the manufacturer is forced to make a choice that

depends on the specifications imposed on it. Indeed,

the construction of a power machine is a function of

the intended application. The machine can operate

either below or above its power [2]. In the first case,

there will be oversized and it will be costly. In the

second case, we will under-sizing, which will result

in overheating of the coils etc..

This shows the construction of a specific

preliminary analytical calculation electrical

machines of any electrical machine presents certain

difficulties.

The terms of reference alone is not enough for the

manufacturer's sizing machine. In general, it is

necessary to be limited, in the preliminary

calculation to estimate a parameter based on the

data of a machine of the same type already built.

After the calculation of the main dimensions, one

calculates the various constraints (electrical,

magnetic, ...) in different parts of the machine. The

results must be located within the permissible limits

established by the experience of other existing

machines.

II. MODELLING INDUCTION MOTOR IN 2 D

Generally, an electromagnetic device comprises

several materials, some of which have nonlinear

characteristics. Furthermore, the electromagnetic

phenomena vary significantly within the structure.

Therefore, a complete analysis of the structure in

three dimensions (3D) is wasteful and costly in

terms of computation time. The use of 2D models is

particularly simple and effective choice is realistic.

In this case, the density of the magnetic excitation

potential and the current vector is perpendicular to

the cross section of the engine, which represents the

study plan and wherein the magnetic flux flows.

Furthermore, the vector potential has only one

component along (OZ) which is independent of the

third dimension (z) and the condition of the

Coulomb gauge is naturally satisfied in this case.

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( , )c ZJ J k et A A x y Ak

(1)

Other parts the contribution of the term (grad V) in

the induced currents, in this case can be neglected

because of the symmetry of the distribution of

currents in the induction apparatus in general.

Under these conditions, the vector equation

2 1 12( ) 0B B n projected onto the coordinate

axes gives rise to the following analytical

formulation:

1 1s

A A AJ

x x y y t

(2)

Harmonic regime: jt

So the equation

c s

AJ J grad V

t

is written:

1( ) srot rot A J A J

(3)

Equation (2) is the magnetodynamic equation in

transient magnetic vector potential term with source

term.

Depending on the areas treated, the distribution of

magnetic vector potential can be determined by the

following system of equation:

- In the air gap

1( ) 0rot rot A

(4)

- In the stator

1( ) srot rot A J

(5)

- In the rotor

1( ) 0

Arot rot A

t

(6)

Complex notation allows to pass from a spatio-

temporal problem to a problem of magneto complex

where time and space are decoupled. The

calculation of the potential in the steady state vector

is then effected by solving, in a given time, the

following equation:

1( ) 0s

eff

div grad A j g A J

(7)

III. MESH MACHINE

The generated mesh in the case of the machine

designed by the FEMM environment is shown in

Figure (1), it can be oriented by adjusting

parameters ways to obtain the desired fineness in

the thin regions such that the air gap.

Fig. 1 Mesh of finite elements ¼ induction motor

IV. THE FIELD LINES

It is often useful to start the analysis by the display

of the field lines. Examination of field maps is a

good way to check if the results are reasonable. One

can see how the distribution of the flux varies with

time by changing the phase of the sources. Fig. 2

shows the distribution of the field lines in the

magnetic circuit. Although we note the presence of

the poles. The distribution lines are nearly

symmetrical relative to the axes of the poles. The

field flux penetrates into the magnetic circuit of the

armature (rotor) and left regularly.




Fig.2 the field lines of the induction machine 5.5 KW

In Fig. 3 we represent the distribution of the

induction in the motor, it also substantially

symmetrical. It shows saturated motor areas.

Fig. 3 Distribution of the induction in asynchronous machine 5.5 KW

V. ELECTROMECHANICAL CHARACTERISTIC

In subtitle is going to represent the mechanical and

electrical characteristics of both the machine

- Magnetic induction

- Couple depending on frequency

A. Electromagnetic Torque

Fig.4 expressed the torque variation as a function of

frequency machine while giving case of frequency

variation

Fig. 4 Torque variations depending on frequency machine 5.5 KW

B. normal and tangential components of the induction and

field:

There is shown the form of the induction field and

the terminal of the gap of machine. We can observe

that the diagram induction and real and imaginary

field has a quasi-sinusoidal, but the sum of the

diagram give us a new diagram is not sinusoidal.

Fig. 5 the form of the induction in asynchronous machine 5.5 KW




Fig. 6 the form of the magnetic field in asynchronous machine 5.5 KW

VI. INFLUENCE OF FREQUENCY

To study the influence of the frequency of the

electromagnetic force, we took machine as an

example Fig. 7 figure showing the form of the

deformation field line increasing frequency

.

(a) (b)

(c)

Fig. 7 (a, b, c) The Field lines for f = 5, 10 Hz and 20 respectively for the

machine 5.5 KW

VII. TEST OF OPEN CIRCUIT (NO LOAD)

The simulations are performed at zero frequency,

assuming that work in the framework of the rotor.

This corresponds to a sliding of the rotor equal to

zero.

We took the machine to see the distribution of the

induction field.




Fig. 8 The Distribution of induction form in induction machine 5.5 KW for

f = 0 Hz

Fig. 9 The form of the induction in ASYNCHROUNS machine of 5.5 KW for

f = 0 Hz

FIG. 10 THE FORM OF THE MAGNETIC FIELD IN ASYNCHRONOUS

MACHINE 5.5 KW FOR F = 0 HZ

VIII. TEST OF BLOCKED ROTOR

These test are performed assuming a blocked rotor and

imposing a fixed current in the stator slots. Simulation is

performed with the rotor frequency 50 Hz .We took the

machine to see the distribution of the induction field.

Fig. 11 Distribution of magnetic induction in induction machine 5.5 KW for

f = 50 Hz




Fig. 12 The form of the induction in ASYNCHROUNS machine of 5.5 KW for f = 50 Hz

FIG. 13 THE FORM OF THE MAGNETIC FIELD IN ASYNCHRONOUS MACHINE 5.5 KW FOR F =50 HZ

IX. CONCLUSIONS

Exploiting FEMM requires us how torque is

calculated. The finite element complex magneto

dynamic is an instant calculation for rotor position,

but the value provided by the software is

approximate; Indeed, it would make several

simulations for different positions and average,

which proves to be a tedious process by the number

of resolution to make.

REFERENCES

[1] R.Kechroud, « contribution à la modélisation

des machines électriques par la méthode des

éléments finis associée aux multiplicateurs de

Lagrange”, Thèse de doctorat d’état, ENP,

Avril 2002.

[2] M. Liwschitz, L. Maret « Calcul des machines

électriques ».Tome 1et 2 edition Bordas 1967.

[3] Kostenko « Machines électriques », Tome 2,

Edition Mir, 1978.




[4] A. Curchod et L. Vellard «Mémento

d’éléctrotechnique », Edition Dunod, 1950 .

[5] BOUCHARD, R.P, OLIVIER, G, “Conception

de moteurs asynchrones triphasés”, édition de

l’école polytechnique de Montréal, 1997

[6] S. R. H. HOOLE, « Rotor motion in the

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[7] T. W. PRESTON, A. B. J. REECE, P.S.

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471-473.

[8] D. RODGER, H. C. LAI, P. J. LEONARD, «

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[9] A. A. ABDELRAZEK, J. L. COULOMB, M.

FÉLIACHI, J. C. SABONNADIÈRE,

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[10] E. VASSENT, G. MEUNIER, J. C.

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