imfe presentation notes

7/29/2019 IMFE Presentation Notes

1/39

Modern Approachto IM Analysis

Alberti BianchiBolognani

FEMM introductionWinding definition

Meshing and solving

Postprocessing thesolution

Use of the LUA script

Indirect testsAnalysis

Indirect tests analysis

Noload test

Locked rotor test

Equivalent circuit

Computation of the motorperformance

Rotor FO AnalysisDynamic equations

Steadystate equations

In rotor flux refer. frame

Winding definition

Noload test

Computation under load

FO equivalent circuit

Torque vs speed curve

Rotor current distribution

1

A Modern Approach

to the Analysis

of Induction Motors

Luigi Alberti, Nicola Bianchi, and Silverio Bolognani

Electric Drive LaboratoryDepartment of Electrical EngineeringUniversity of PadovaPadova, Italy

June 2009




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





2

Outline

1 A brief introduction of using FEMM in electrical

machine analysis

2 Analysis using indirect tests

3 Analysis in the rotor flux reference frame



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





3

Outline


machine analysis





FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





4

A brief introduction

FEMM (Finite Element Method Magnetics)

it is very easy to be used,

it is organized so as to easily understand how a finiteelement method works,

it is freeware, so that anyone can download it anduse it.


2/39




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





5

2D field problem

In a 2D field problem

current density J = (0, 0, Jz) vector magnetic potential A = (0, 0, Az) magnetic field strength H = (Hx, Hy, 0) flux density B = (Bx, By, 0)

Induction motor section in the plane (x, y).




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





6

Problem definition

The first step is to define the problem:

Type: select a planar symmetry, i.e. the motorsection is studied in the plane (x, y);

Units: select the measure unity for drawing, e.g.

millimeter;

Frequency: select the frequency, e.g. equal to zerofor magnetostatic analysis;

Depth: select the length of the structure, along the zaxis, normal to the plane (x, y), e.g. Lz=100 mm.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





7

Steps of a finite element problem

The steps of a finite element problem are

preprocessing: preparing the field problem(using the editor femme.exe);

mesh: subdivision of the domain in small elements

(using triangle.exe); solution: solution of the field problem

(using fkn.exe);

postprocessing: analysis of the field solution andcomputation of integral quantities

(using the editor femmview.exe).



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





8

Preprocessing steps

Drawing- points

- segments- arcs

Mark- labels- groups

Properties- materials- boundary conditions

- circuits


3/39




Meshing and solving



Indirect testsAnalysisIndirect tests analysis

Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





9

Drawing

Points Segments Arcs

Example of drawing a stator slot.

IM drawing

Stator drawing

Air gap drawing

Rotor drawing




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





10

Marking the blocks

Labels

to give a name to the block; to assign the material properties, e.g. the electrical

conductivity, and the relative magnetic permeability;

to assign a current density to the block.

Label and material used.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





11

Marking the blocks

Stator Label

object label

lamination stack Fe

wedges Airslot no. 1 Cu1

slot no. 2 Cu2

slot no. 3 Cu3

... ...



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





12

Marking the blocks

Stator Groups

object label group

lamination stack Fe 1000

wedges Air 1000slot no. 1 Cu1 1001

slot no. 2 Cu2 1002

slot no. 3 Cu3 1003

... ... ...


4/39




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





13

Marking the blocks

Other Groups

object label group

air gap Air 0

rotor ... 10

Sketch of the rotor, as group 10.




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





14

Boundary conditions

Four main boundary conditions

Dirichlet: a given value of Az along a line.

Neumann: flux density lines normal to a line. Periodic: Az,segment1 = Az,segment2. Antiperiodic: Az,segment1 = Az,segment2.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





15

Boundary conditions

How to do

1 A boundary condition Az = 0 is defined in theproblem.

2 The external lines are selected.

3 The boundary condition is assigned.

Boundary condition assigned along

the outer periphery of the stator.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





16

Materials

The material of the objects can be defined or selected

from a given Material Library.

How to do

The appropriate material is assigned to the object:

1 Fe is assigned to stator and rotor laminations,

2 Cu is assigned to the stator slots,

3 Al is assigned to the rotor slots,

4 Air is assigned to the air spaces.


5/39




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





17

Sources

Current

Stator currents are defined as "circuit"

ideal current source connected to one or more blocks.

Islot1: current source connected to first slot,

Islot2: current source connected to second slot,

Islot3: current source connected to third slot,

... and so on.

External circuits connected to the coil sides




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





18

Sources

Current density

An alternative is to assign a current density to the various

materials, e.g. to materials of the stator slots.

The peak value of current density in the slot is defined as

Jslot = kfill2Jc

With kfill = 0.4,With Jc = 6 Arms/mm2

It is Jslot = 3.4 A/mm2.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





19

Winding definition

Classical representation of the stator winding



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





20

Winding definition

Slot matrix

Matrix dimension is m Q The generic element kjq indicates the how much the

qth slot is filled by conductors of the jth p hase.

kjq = 1 means that the qth slot is completely filledby conductors of the jth phase;

kjq = 0.5 means that only 50% of the qth slot isfilled by conductors of the jth phase;

kjq = 0 means that no conductor of the jth phase iswithin the qth slot.

sign indicates the direction.


6/39




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





21

Winding definition

Definition of the labels of the stator slots.

Slots Matrix

q 1 2 3 4 5 6 7 8 9 10 11 12

a 0 0 1 1 0 0 0 0 -1 -1 0 0

b -1 -1 0 0 0 0 1 1 0 0 0 0

c 0 0 0 0 -1 -1 0 0 0 0 1 1




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





22

Winding definition

Current assignment

The current in the qth slot can be expressed as

Islot,q = ncka,qIa + kb,qIb + kc,qIcwhere

q 1 2 3 4 5 6 7 8 9 10 11 12

ka = 0 0 1 1 0 0 0 0 -1 -1 0 0

kb = -1 -1 0 0 0 0 1 1 0 0 0 0

kc = 0 0 0 0 -1 -1 0 0 0 0 1 1



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





23

Meshing and solving

Mesh of the structure



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





24

Flux line plot

Flux lines of the solved structure


7/39




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





25

Point property

Electric and magnetic quantities detected in the point P of

the solved structure.




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





26

Magnetic Flux

= Lz

line

Bndl

Magnetic flux computation from a line integration.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





27

Magnetic Flux

= Lz (Az,S Az,E)

Magnetic flux from magnetic vector potentialS

B ndS =

S

curlA ndS =

lS

A tdl



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





28

Flux linkages

Slots containing the coil sides of phase a

Az 1

Sslot

Sslot

AzdS


8/39




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





29

Flux linkages

a = ncLz

+ 1Sslot

Sslot,3

AzdS

+1

Sslot

Sslot,4

AzdS

1Sslot

Sslot,9

AzdS

1Sslot

Sslot,10

AzdS




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





30

Flux linkages

Using the slot matrix

q 1 2 3 4 5 6 7 8 9 10 11 12

ka = 0 0 1 1 0 0 0 0 -1 -1 0 0

kb = -1 -1 0 0 0 0 1 1 0 0 0 0

kc = 0 0 0 0 -1 -1 0 0 0 0 1 1

a = ncLz1

Sslot

Qq=1

Sslot,q

ka,qAzdS



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





31

Magnetic energy

The whole structure is selected

The magnetic energy

Wm = Lz

Sall

HdB

dS



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





32

Magnetic energy

The magnetic energy

Wm = Lz

Sall

HdB

dS

The magnetic coenergy

Wm = Lz

Sall

BdH

dS

The integral of A J

WAJ = Lz

Sall

AzJzdS


9/39




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





33

Scripts for the Preprocessing

The aim is to modify the current flowing in the coil, whose

sides are in the slots 3 and 10.

Coil sides in slot 3 and slot 10.




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





34

Motor data

The geometrical data

S_slot = 36.8 -- (mm2)

k_fill = 0.4

J_c = 6 -- (A/mm2)

J_slot = k_fill * sqrt2 * J_c

I_max = S_slot * J_slot



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





35

Current assignment

Current value

I_slot = I_max * (n / N_sim)

Current assignment to slot 3 and slot 10

modifycircprop("Islot", 3, +I_slot)

modifycircprop("Islot", 10, -I_slot)

analyse()



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





36

Current assignment

For given current

Ia = +4 -- current of the a-phase

Ib = -2 -- current of the b-phase

Ic = -2 -- current of the c-phase

Using the slot matrix, the computation of the current in

the qth slot beco mes

Islot[q] = ka[q]*Ia + kb[q]*Ib + kc[q]*Ic


10/39




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





37

Current assignment

Starting from d and qaxis values

Id = -3 -- Id is the d-axis current

Iq = +4 -- Iq is the d-axis current

the dq

abc transformation is used

I a = I d*cos(thetame) - Iq*sin(thetame)

Ib = (-Id/2 - Iq*sqrt(3)/2) * cos(thetame)

+ (-Id*sqrt(3)/2 + Iq/2) * sin(thetame)

Ic = (-Id/2 + Iq*sqrt(3)/2) * cos(thetame)

+ (+Id*sqrt(3)/2 + Iq/2) * sin(thetame)




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





38

Current density assignment

This is an alternative to assign the current.

After computing the current density

Islot = ka[q]*Ia + kb[q]*Ib + kc[q]*Ic

Jslot = Islot / S_slot

it is assigned to the slot block

modifymaterial("Cu" .. q, 4, Jslot)



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





39

Postprocessing

Slot cross area (slot 3):

groupselectblock(1003)

Sup = blockintegral(5)

clearblock()

Integral of Az (slot 3):

groupselectblock(1003)

intA3_r, intgA3_i = blockintegral(1)

clearblock()



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





40

Postprocessing

After selecting the whole domain

groupselectblock()

magnetic energy, coenergy, integral of A J are computed:Energy = blockintegral(2)

Coenergy = blockintegral(17)

AJ_intgr = blockintegral(0)


11/39




Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





41

Outline


machine analysis






Meshing and solving




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





42


Aim

The aim is to achieve a prediction of the induction motor

performance that is rapid and accurate at the same time.

Procedure

Analysis procedure combining a set of finite element (FE)

simulations with an analytical model of the induction

motor.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





43

Equivalent circuit

The finite element simulations are carried out to compute

the lumped parameters of the traditional equivalent

circuit.

Equivalent circuit of the threephase induction motor.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





44

Equivalent circuit

2D simulations

Using laminations, a twodimensional FE analysis is

generally satisfactory.

3D parametersThe threedimensional effects are analytically computed

and included in the model.

stator resistance, endwinding resistance and inductance, rotor ring resistance and inductance, skewing.


12/39




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





45

Equivalent circuit

Schematic model of the threephase induction motor.




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





46

Analysis procedure

Advantage of this procedure

The computation is rapid, since few FE simulationsare necessary,

The computation is accurate, since effects ofsaturation and eddy currents are considered in the

FE analysis,

This approach overcomes the limits of the completelyanalytical or completely numerical procedures.

The procedure yields a very easy implementation. The FE simulations required in the proposed

procedure can be carried out using any FE software.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





47

Analysis procedure

Scheme of the combined FEManalytical procedure



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





48

Analysis procedure

The steps of the analysis are

1 FE analysis at noload conditions: an accurate

prediction of the iron saturation.

2 From noload simulations, the maximum flux density

in stator path and iron losses are computed.

3 FE analysis at locked rotor: accurate prediction of

rotor current distribution.

4 Threedimensional parameters are computed

analytically and are added to the equivalent circuit.

5 The induction motor performance is predicted from

the equivalent circuit.

6 A further check of the operating points is carried out

using a direct FE analysis, deriving field sources

from the analytical model.


13/39




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





49

Noload tests

The motor is analyzed in the rotor reference frame

assuming a rotor slip equal to zero.

The frequency equals zero and magnetostatic FE

simulations are carried out.

x

1

Azx

+

y

1

Azy

= Joz




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





50

Current

The rms value of the current is fixed, e.g. Irms.

A suitable time instant is chosen, in order to assign the

threephase currents in the stator winding.

Currents assigned in the noload analysis

Phase Current Phase Current

A +2Irms -A 2Irms

B

2

2Irms -B +

2

2Irms

C

2

2Irms -C +

2

2Irms



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





51

Meshing

A careful mesh has to be performed in the iron lamination

and in the air gap, where the higher flux gradient is

expected.

Mesh for the noload simulation.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





52

Flux plot

A graphical verification.

Flux lines at noload


14/39




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





53

Flux linkages

Flux linkage is computing from the magnetic vector

potential Az as

m = Lstk1

Sslot

Q

q=1

Sq

AzdS

Average flux linkage is

m =2

3

a

b2 c

2




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





54

Noload voltage

The noload voltage is estimated as:

E0 = 0 m

0 5 10 150

50

100

150

200

250Noload test

Stator current (Arms

)

Phase

tophase

volta

ge

(V)

Comparison between measured and predicted voltage.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





55

Noload voltage

E0 (V) 31 38 45 52I0 (A) 0.34 0.42 0.49 0.56

E0 (V) 60 67 76 83I0 (A) 0.65 0.73 0.83 0.92

E0 (V) 94 101 107 113

I0 (A) 1.05 1.11 1.22 1.30E0 (V) 120 128 135 141I0 (A) 1.40 1.54 1.71 1.86

E0 (V) 147 151 156 158I0 (A) 2.05 2.21 2.42 2.55

E0 (V) 162 165 169 170I0 (A) 2.73 2.93 3.16 3.31



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





56

Magnetic energy

Magnetic energy

Wm =

vol

B0

H dB dvol

Magnetic coenergy

W

m =

vol

H0 B

dH dvol

Integral of Az Jz

WAJ =

vol

A J dvol

Wm = Wm only when no saturation occurs. Always WAJ = Wm + Wm.


15/39




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





57

Magnetic energy

0 2 4 6 8 10 120

2

4

6

8

10No load test

Stator current (A)

Magneticenergy(J)

Wm = int H.dB

0.5 * int A.J

Magnetic energy as a function of the current.




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





58

Magnetizing inductance

from flux linkages

Lm =mI0

from magnetic energy

Lm =2

3

2Wm

I02

from integral of A J

Lm =2AJ

3I02



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





59


0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2

1.4No load test

Stator current (A)

Fluxlinkage(V

s)Inductance(H)

FluxInductance

Flux linkage and inductance.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





60


0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7No load test

Stator current (A)

Magnetizzinginductance(H)

from

from Wm

from A.J


When saturation occurs,

the two energy computations yield different results.


16/39




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





61

Iron losses resistance

Flux density in the stator teeth Bt and in the stator back

iron Bbi are extracted from the field solution.

Their peak values are expressed as a function of the

stator flux linkage.

From the material specific losses khy and khy in (W/kg),

the iron losses are estimated as

Pfe = kmagg

khy

f

50B2 + kec

f

50

2B2

G




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





62

Iron losses resistance

The iron losses resistance is computed as:

R0 = 3E2

Pfe= 3

(m)2

Pfe

0 2 4 6 8 10 120

0.5

1

1.5

2x 10

4 No load test

Stator current (A)

R0

R0 corona

R0 denti

R0 tot

Noload resistance as a function of the stator current.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





63

Locked rotor test

The analysis is carried out in the rotor reference frame.

The simulation frequency is the rotor frequency fr = s f.

A magnetodynamic analysis is carried out

1

2Azx2

+2Azy2

= JszjrAz

In locked rotor analysis, a linear iron is assumed, so that

the superposition of the effects can be applied.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





64

Current

The current are assigned according to the complex

notation.

Phase Current Phase CurrentA +

2Irms -A

2Irms

B

2

2Irmsj

6

2Irms -B +

2

2Irms+j

6

2Irms

C

2

2Irms+j

6

2Irms -C +

2

2Irmsj

6

2Irms


17/39




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





65

Meshing

A careful mesh has to be performed in the rotor bars,

where current are induced, and in the air gap as well.

Mesh in the locked rotor simulation.




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





66

Flux plot

A graphical verification.

Flux plot with frequency 50 Hz.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





67

Magnetic energy

0 10 20 30 40 500

0.05

0.1

0.15

0.2

0.25

Rotor frequency (Hz)

E

nergyand

coenergy(J)

int H.dBint B.dHint A.J

Magnetic energy as a function of the rotor frequency.

Since the problem is linear, magnetic energy Wm and

coenergy Wm coincide: Wm = W

m =WAJ

2.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





68

Rotor Joule losses

Selecting the rotor bars, the Joule losses are computed.

Pjr =1

2AlLstk

SAl

Jz JzdS


18/39




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





69

Torque

Selecting the rotor, the torque is computed

from Maxwell stress tensor,

T = Lstk

lgap

BrB0

dl

as ratio between rotor losses and synchr. speed

T = Pjr2f/p




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





70

Torque

Torque comparison

0 10 20 30 40 500

0.05

0.1

0.15

0.2

0.25Locked rotor test

Rotor frequency (Hz)

Torque

(Nm)

from Maxwell tensorfrom rotor losses

Torque comparison



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





71

Rotor parameters as a function of the frequency

The equivalent resistance is computed from the Joule

losses

Req =Pjr

3I2

The equivalent inductance is computed from the

magnetic energy

Leq =2

3

Wm

I2



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





72


Transformation of the circuit

Ll,2D = LmLeq(Lm Leq) (Req/)2

(Lm Leq)2 + (Req/)2

Rr,2D = ReqLm + Ll,2DLm Leq


19/39




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





73


0 10 20 30 40 505.4

5.45

5.5

5.55

5.6

5.65

5.7

Frequency (Hz)

Rotorresistance()

Rotor resistance versus rotor frequency

0 10 20 30 40 500

0.002

0.004

0.006

0.008

0.01

Frequency (Hz)

Rotorinductance(H)

Leakage inductance versus rotor frequency




Meshing and solving





Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





74

3D parameters

The 3D parameters considered are:

Rs stator winding resistance;

Lew end winding leakage inductance;

Rring rotor ring resistance;

Lring rotor ring leakage inductance.

Lsk rotor skewing.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





75

Equivalent circuit

Equivalent circuit with variable parameters.

When all the parameters are computed, the equivalent

circuit is solved to compute the motor performance.

Mechanical power, torque, electrical power, current,

losses, power factor and so on ...



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





76

Noload performance predictions and measurements

Test Prediction Test Prediction

V (V) 75.8 75.8 107 107Io (A) 0.84 0.82 1.23 1.18

Po (W) 9.1 9.6 15.3 14.7V (V) 120 120 135 135Io (A) 1.4 1.34 1.7 1.6

Po (W) 19.4 20 26.4 25


20/39




Meshing and solving



Indirect tests

AnalysisIndirect tests analysis

Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





77

Power (V = 120 V, f = 50 Hz)

0 0.2 0.4 0.6 0.8 10

500

1000

1500

2000

slip

Electricpower(W)

Electrical power versus slip.

0 0.2 0.4 0.6 0.8 10

100

200

300

400

500

600

slip

Meccpower(W)

Mechanical power versus slip.




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





78

Efficiency and power factor (V = 120 V, f = 50 Hz)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

slip

Efficiency

Efficiency versus slip.

0 0.2 0.4 0.6 0.8 1

0.4

0.5

0.6

0.7

0.8

0.9

1

slip

Cosphi

Power factor versus slip.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





79

Torque and input current

0 0.2 0.4 0.6 0.8 10

2

4

6

8

10

12From equivalent circuit

slip

Torque(N

m)Current(A)

Torque (Nm)

Current (A)

FE Analysis

Torque and stator current versus slip

(V = 120 V, f = 50 Hz).



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





80

Working point test

Scheme of the combined FEManalytical procedure


21/39




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





81

Low frequency supply (f = 8.33Hz)

0 0.2 0.4 0.6 0.8 10

1

2

3

4

slip

Torque(Nm)Current(A)

Torque

Current

FE Analysis

Current and torque versus slip

0 0.2 0.4 0.6 0.8 10

20

40

60

slip

Meccpower(W)

0 0.2 0.4 0.6 0.8 150

100

150

200

slipElectricpower(W)

Power versus slip




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





82

High frequency supply (f = 300Hz)

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

slip

Torque(Nm)Current(A)

Torque

Current

FE Analysis

Current and torque versus slip

0 0.2 0.4 0.6 0.8 10

200

400

600

800

slip

Meccpower(W)

0 0.2 0.4 0.6 0.8 10

500

1000

slipElectricpower(W)

Power versus slip



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





83

Tests and computations comparison

Test Cal Test Cal Test Cal

V (V) 42 42 52 52 60 60

f (Hz) 9 9 11.5 11.5 13.1 13.1

s (%) 46 46 30.3 30.3 30 30

I (A) 3.8 3.7 3.8 3.9 4.2 4.3Pe (W) 270 250 311 301 400 390P0 (W) 7.6 7.2 10.5 10.3 15 13

T ( Nm) 2.2 2.2 2.2 2.1 2.6 2.5Pm (W) 67 66 111 106 151 142



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





84

Tests and computations comparison

Test Cal Test Comp Test Cal

V (V) 213 213 218 218 220 220

f (Hz) 288 288 275 275 272 272

s (%) 6 6 1.7 1.7 1 1

I (A) 3.1 2.8 1.3 1.2 0.78 0.75Pe (W) 1030 930 430 407 220 215P0 (W) 120 90 62 50 40 46

T (Nm) 0.45 0.42 0.2 0.19 0.12 0.11Pm (W) 760 710 340 320 157 167


22/39




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





85

Conclusions

It can be affirmed that the proposed procedure allows an

effective model of the induction motor to be built.

By means of such a model, a satisfactory prediction ofthe induction motor performance is achieved.




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





86

Outline


machine analysis





FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





87

Stator and rotor voltages

stator

vsa = Rsisa +dsa

dt

vsb = Rsisb +dsb

dt

vsc = Rsisc +dsc

dt

rotor

vra = Rrira +dra

dt= 0

vrb = Rrirb +drb

dt= 0

vrc = Rrirc +drc

dt= 0



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution



Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





88

Stator voltage in the dsqs reference frame

Space phasor of stator voltage

vss = Rsiss +

dssdt

Space phasor of stator flux linkage

ss = Lsiss + LMi

sr

sd = Lsisd + LMirdsq = Lsisq + LMirq


23/39




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





89

Rotor voltage in the drqr reference frame

Space phasor of rotor voltage

vrr = Rrirr +

drrdt

= 0

Space phasor of rotor flux linkagerr = Lr

irr + LMirs

rd = Lrird + LMisdrq = Lrirq + LMisq




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





90

In a generic dgqg reference frame

The stator quantities:multiplied by ejg = ejgt,

The rotor quantities:multiplied by ej(

emg) = ej(

emg)t,

they are expressed in the generic reference frame dgqg.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





91

Speed of the dgqg reference frame

if g = 0,the reference frame dgqg is fixed with respect to the

stator reference frame;

if g = em,

the reference frame d

g

q

g

rotates at the electricalspeed of the rotor (i.e., at the speed em = pm),hence it is fixed with respect to the rotor reference

frame;

if g = ,the reference frame dgqg rotates at the synchronous

speed.



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





92

In the dgqg reference frame

Stator and rotor voltages

vsd = Rsisd +dsd

dt gsq

vsq

= Rs

isq

+dsq

dt+

g

sd

and

0 = Rrird +drd

dt (g me)rq

0 = Rrirq +drq

dt+ (g me)rd


24/39




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





93

dgqgaxis equivalent circuits

d and qaxis dynamic circuits of the inductio n motor

(with g = ).




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





94

Using the space phasor notation

Voltage equation

vs = Rsis +dsdt

+ gs

0 = Rrir +dr

dt

+ (g

em)r

Dynamic circuit using the space phasors (g = ).



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





95

Using the space phasor notation

Highlighing leakage inductances

s = Lslis + LM(is +ir)

andr = Lrlir + LM(is +ir)

Dynamic circuit using the space phasors, Tform

(g = ).



FEMM introduction

Winding definition

Meshing and solving

Postprocessing the

solution




Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





96


The speed of the dgqg reference frame is g = .

Stator voltage

vs = Rsis + s

Rotor voltage

0 = Rrir + ( em)ror

0 =Rrsir + r

slip

s = em


25/39




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





97


Voltage equations

vs = Rsis + Lslis + LM(is +ir)

0 =Rr

sir + Lrlir + LM(is +ir)

Steadystate equivalent circuit, using Tform (g = ).




Meshing and solving



Indirect tests


Noload test

Locked rotor test

Equivalent circuit





Winding definition

Noload test





98


It is possible to introduce an arbitrary constant c in the

voltage equations

vs =

Rs

is +

Ls

is +

cLM

ir

c

0 = c2Rr

s

irc

+ c2Lrirc

+ cLMis

By rearranging the value of c, it is possible to express the

voltage equations in different ways.

Modern Approachto

imfe presentation notes

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