conception optimale des

gilamonsterbirdsElectronics - Devices

Nov 24, 2013 (3 years and 7 months ago)

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Contribution à la modélisation et à la
conception optimale des
turboalternateurs de faible puissance


D. Petrichenko
,

L2EP, Laboratory of Electrotechnics and Power Electronics

Ecole Centrale de Lille




CNRT

Futurelec

Lille

2

Presentation plan


Introduction and problem definition


Developed approach


Software implementation


Applications


Conclusion and perspectives

Introduction

The objectives and problem definition

4

INTRODUCTION


Objectives

Objective
:

Creation

of

a

rapid

tool

used

in

optimal

electromagnetic

design

of

turbogenerators

of

power

of

10
-
100

MW
.

Collaboration
:


Jeu
mont
-
Framatome

ANP


Moscow

Power

Engineering

Institute

(M
.
P
.
E
.
I
.
)


CNRT

(Centre

National

de

la

Recherche

et

Technologie),

FUTURELEC
-
2

5

Introduction


Jeumont production

Jeumont production:


2
-
4
-
6
-
n pole turbogenerators


Power up to 1000 MW


Stator of a turbogenerator

4
-
pole rotor

6

Introduction


Turbogenerator particularities


Big number of input parameters

(up to 250):


complex geometry;


stator and rotor slots of different
configuration;


cooling system with ventilation
ducts;


complex windings.


Big number of physical
phenomena:


saturation phenomena;


mutual movement of stator and
rotor cores;


axial heterogeneity of the cores;


magnetic and electric coupling.


7

Introduction


existing methods


Assumptions to classical theory:


energy transformation


in
air
-
gap;


salient surfaces of magnetic
cores are replaced by non
-
salient;


only first harmonic of the
magnetic field is considered;


field factors of flux density in
the linear machine can be
applied to saturated
machine;


main field and leakage fields
of a saturated machine are
independent;


etc…

8

Introduction


existing methods


Finite element method

2D mesh of a generator

3
D mesh of a claw
-
pole machine

9

Introduction


calculation methods

Model speed

Model accuracy

Permeance networks


Conventional methods

Field calculation

Developed approach

Tooth contour method

Permeance network construction

Mode calculation

11

Developed approach


Principles


Axial heterogeneity


Network construction:


Air
-
gap


Tooth zones


Yoke zones


Electromagnetic coupling


Network equations


Operating modes calculation

12

Developed approach

Air
-
gap

Stator slots

Rotor slots

Stator teeth

Rotor teeth

Stator yoke

Rotor yoke


Linear



r
=1.0


Nonlinear



r

10.0 even for saturation


The direction of magnetic flux

is well defined.

1.
The surfaces of magnetic cores can be
considered
equipotential ones
!

2.
The air
-
gap zone is linear and can be
considered
independently

from magnetic
cores.

13

Developed approach


turbogenerator particularities

Axial view of the machine

Stator

Rotor

End winding effects

Duct effects

Lamination effects

14

Developed approach



turbogenerator particularities


Seven zones of influence of
axial heterogeinity:


Stator yoke


Stator teeth


Stator slots


Air
-
gap


Rotor slots


Rotor teeth


Rotor yoke


Axial structure of the
turbogenerator
must be
comprised

in the permeance
network in
-
plane in order to
calculate properly the winding
flux linkages.


The material properties must be
changed to reflect the influence
of the axial heterogeneity.

15

Developed approach



air
-
gap zone

Special Boundary Conditions:


The current is distributed regularly in the
wires.


All other currents in the magnetic system
are zero.


The permeability of the steel is infinite.

1.
The surfaces of magnetic cores can be considered
equipotential

for scalar magnetic potential.

2.
The air
-
gap zone is linear and can be considered
independently

from magnetic cores.






3
2
ln
2
1
1
1
1





s
z
z
z
b
t
gt
t
b
Zone limits:

16

Developed approach



air
-
gap zone

t
z
1
s
r
t
z
2
b
km
= 0
r
s
b
km
= t
z2
/4
r
s
b
km
= t
z2
/2
b
km
= 3t
z2
/4
s
r
Tooth contours air
-
gap permeance calculation

17

Developed approach


air
-
gap zone

0,0E+00
2,0E-06
4,0E-06
6,0E-06
8,0E-06
1,0E-05
1,2E-05
1,4E-05
1,6E-05
-20,0
-15,0
-10,0
-5,0
0,0
5,0
10,0
15,0
20,0
Approximation
OPERA
Calculation zone

Comparison

18

Developed approach


air
-
gap zone

A set of mutual air
-
gap characteristics

19

Developed approach


magnetic system

1.
The permeability of the steel is high enough to consider magnetic surfaces equipotential !

2.
The direction of the flux in magnetic cores is well defined.

Variable parameter:
Number of layers per coil.
Variable parameter:
Number of yoke layers.
1
2
3
4
5
6
7
8
9
20

Developed approach


magnetic system

Calculation of elements’ parameters

min
b
l
B
eff




The flux is supposed constant for the whole zone

6
4
2
3
1
.
H
H
H
h
U
el
el
m



The magnetic potentials of each small element
are calculated using trapezoidal formula:



el
m
U
U
.
Total difference of potentials is found as a sum:

21

Developed approach


magnetic system

Two
-
pole machine

22

Developed approach



magnetic system

Teeth of different height


Variable Topology Model

24

Developed approach


electromagnetic
coupling


MMF sources


The values depend on the
ampere
-
turns which cross
the layer with the :


The first slot source


The second slot
source


The third slot source


The source of the yoke


Form the matrix
W
which
links together the
branches of electric circuit
and permeance network!

FMM
source 1

FMM
source 2

FMM
source 3

FMM
source 4

25

Developed approach


system of equations

Equation set

Magnetic permeance network



0









A
f
A
t

Magnetic circuit:

0
0
1














B
E
t
B
B
B
B
E
t
E
B
i
A
dt
i
C
dt
i
d
L
i
R
dt
d
A
u

Electrical circuit:







t
B
B
W
a
t
i
W
f
Magnetic & electrical coupling:









t
out
dt
dt
d
J
M
M
0
0


Mechanical equations:







B
t
t
i
W
A
U
U
U
M













2
1
Coupling matrix
W

allows to calculate:


MMF sources of the PN from the electric currents


Winding flux linkages from the fluxes of the PN
branches

The flux linkage already comprises
axial structure of the machine!

26

Developed approach


Steady
-
state fixed rotor algorithm

1. Set stator and rotor currents

2
. Calculate magnetic circuit

4. Obtain the EMF:









j
E
3. Obtain flux linkage




5
. Solve the equation:

0






E
I
jx
I
R
U
e




Various steady
-
state characteristics can be obtained directly or iteratively!

The flux linkage and EMF already take into account
the axial heterogeneity of the machine!

Implementation

Software implementation: TurboTCM

28

Implementation


the core.

Circuit specification.

Incidence matrices,

permeance, mmf vectors,

parameter vector, etc.

Parser

Circuit builder

Elements

&

Relations

COM

SOLVER

,
...
...
...
...
A
P
T,
T,1
k
i,
P
,
1
1
,
1
a
a
a
a
a

,
...
...
...
...
...
...
1
P
k





,
,...,
,...,
,
2
1
t
P
k
f
f
f
f
f



Can be Matlab,

VB program,

C++ program or

any other software.

Circuit

description

29

Implementation


component
responsibilities

CircuitBuilder

Electric circuit

CircuitBuilder

Magnetic circuit

CircuitConnector

Intercircuit relations

Electric matrices

Magnetic matrices

A
E



incidence matrix

Y
E



permeance matrix

Z
E



resistance matrix

S
E



sources vector

etc…

W


coupling matrix

A
M



incidence matrix

Y
M



permeance matrix

Z
M



resistance matrix

S
M



sources vector

etc…

Coupling equations:





dt
d
e
W
i
W
f
T
E









CircuitBuilder

Thermal circuit?

30

Implementation


software structure

Electric circuit

parameters



Turboalternator parameters



Electric circuit

description



Winding



description



Magnetic circuit

description



Electric


part equations



0

...

...

0

1































B

E

t

B

B

B

B

B

E

t

E

B

i

A

dt

i

C

dt

i

d

L

i

R

dt

d

u

A

u





Coupling equations















t

B

B

W

a

t

i

W

f



Magnetic part equations







0



















A

f

A

t





SOLVER



Calculation results





Input data specification

Equation preparation: C++

Parser

Circuit builder

Elements

&

Relations

TCMLib

Matlab solver and results

31

Implementation


Matlab solver

32

Implementation


Graphical User Interface

Allows:


Set up a project:


Rated data;


Geometrical descriptions;


Winding descriptions;


Axial configuration;


Simulation parameters;


Perform the Model generation:


Generate magnetic permeance
network;


Generate electric circuits;


Generate coupling matrices;


Perform some calculations:


Machines’ characteristics;


Operating mode calculation;


Save the project and prebuilt model
for further use from the command
line or scripts (optimization).


33

Implementation


Various characteristic calculation

0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
I
s
, p.u.
U
s
, p.u.
Load diagram: I
f
=I
f
n
o
m
PF=0.8, underexcited
PF=1
PF=0.8, overexcited
0
500
1000
1500
2000
2500
3000
3500
4000
4500
100
200
300
400
500
600
700
800
900
Is, A
If, A
Regulation characteristic, U
s
=U
s
n
o
m
PF=0.8, underexcited
PF=1
PF=0.8, overexcited
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
V-curves for U
s
=U
s
n
o
m
If, p.u.
Is, p.u.
Ps = 0.80p.u.
Ps = 0.70p.u.
Ps = 0.60p.u.
Ps = 0.50p.u.
Ps = 0.40p.u.
Ps = 0.30p.u.
Ps = 0.20p.u.
Ps = 0.10p.u.
Ps = 0.00p.u.
V
-
shaped characteristics.

Time: 12 minutes on Pentium IV

Load characteristics

Regulation characteristics

Variation of x
d

and x
q

parameters

34

Implementation


Each operating mode output

-1
-0.5
0
0.5
1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
-600
-400
-200
0
200
400
600

Air gap flux density in no
-
load and rated cases

Ampere
-
turns distribution in the zones

-1
-0.5
0
0.5
1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
-1500
-1000
-500
0
500
1000
1500

0
5
10
15
20
25
30
35
40
45
50
0
0.5
1
Harmonic orders
B, T
-4
-3
-2
-1
0
1
2
3
4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Air-gap flux density
Angular position, rad
B, T

-4
-3
-2
-1
0
1
2
3
4
-1.5
-1
-0.5
0
0.5
1
1.5
Air-gap flux density
Angular position, rad
B, T
0
10
20
30
40
50
0
1
2
Harmonic orders
B, T

Applications

Small machine

Two pole turbogenerator

Four pole turbogenerator

Optimization application: screening study

36

Application


Two pole machine of 3000 VA


S = 3000 VA


V = 220 V


PF = 0,8


p = 1


24 stator slots


16 rotor slots irregularly distributed


Shaft with a separate BH
-
curve

37

Application


Two pole machine of 3000 VA


100 positions


Excitation current of 20 A (saturated mode)


Time of calculation in OPERA RM: 3h25min


Time of calculation in TurboTCM:
18.3 seconds


Gain in calculation time:
672.13 times

Comparison with finite element calculations (OPERA RM),

taking rotation into account

38

Application


Two pole machine of 3000 VA

Experimental bench and the results in dynamics

39

Application


Two pole turbogenerator


Several machines were
tested:


Power of 31
-
67 MVA


Voltage of 11
-
13.8 kV


Frequency of 50
-
60 Hz


Power factors of 0.8
-
0.9


No
-
load and short circuit
cases were compared with
experimental results


In most cases errors do not
exceed 3.5 %

No
-
load

Short circuit

40

Application


Two pole turbogenerator


no
-
load case

Err
max
=2.41%

Err
max
=1.03%

Err
max
=16.46%

Err
max
=7.11%

41

Application



Two pole turbogenerator


load cases

0
0.2
0.4
0.6
0.8
1
1.2
1.4
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
I
s
, p.u.
U
s
, p.u.
Load diagram: I
f
=I
f
n
o
m
PF=0.8, underexcited
PF=1
PF=0.8, overexcited
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0
0.2
0.4
0.6
0.8
1
1.2
1.4
V-curves for U
s
=U
s
n
o
m
If, p.u.
Is, p.u.
Ps = 0.80p.u.
Ps = 0.70p.u.
Ps = 0.60p.u.
Ps = 0.50p.u.
Ps = 0.40p.u.
Ps = 0.30p.u.
Ps = 0.20p.u.
Ps = 0.10p.u.
Ps = 0.00p.u.
V
-
shaped characteristics.

Time: 12 minutes on Pentium IV

Load characteristics

42

Application



Two pole turbogenerator


load cases

0
500
1000
1500
2000
2500
3000
3500
4000
4500
100
200
300
400
500
600
700
800
900
Is, A
If, A
Regulation characteristic, U
s
=U
s
n
o
m
PF=0.8, underexcited
PF=1
PF=0.8, overexcited
Regulation characteristics

Variation of x
d

and x
q

parameters

43

Application


Four pole turbogenerator

44

Application


Four pole turbogenerator


Material properties were unknown


Linear modelisation fit completely


In nonlinear case


the error was significant



45

Application


Different machines


conclusion


The tool was validated on several types of machines:


Small 2 pole synchronous machine


Two
-
pole turbogenerator


Four
-
pole turbogenerator


No
-
load, short circuit and load characteristics are
easily obtained.


It’s possible to obtain special values from the results:


Electromagnetic torque


Parameters X
d

and Xq


Air
-
gap flux densities


Etc…

46

Application


Response surface study


Objective:
Demonstrate the use of TurboTCM
together with an optimization supervisor
.


Variables:


h
s1



stator tooth height (
±
10%)


b
s1



stator tooth width
(
±
10%)


D
i1



stator boring diameter (
±
5%)


T
p1



rotor pole width (
±
10%)


Responses:


K
hB3



3
rd

order harmonic of air
-
gap flux density


K
hE3



3
rd

order harmonic of stator EMF


K
hE1



the fundamental of the no
-
load stator EMF


I
f



excitation current in no
-
load

47

Application



Response surface study results

K
hB3

for T
p1

min

K
hB3

for T
p1

max

48

Application



Response surface study results

K
hE3

for different T
p1

K
hE1

for different T
p1

I
f

for D
i1

min for different T
p1

I
f

for D
i1

max for different T
p1

49

Application


Response surface study. Conclusion.


TurboTCM can be easily coupled with
Experimental Design Method


Different influence factors can be quantified


The full factorial design was performed:


81 experiments were lead


It takes 25 minutes on a PC Pentium IV 2GHz.


Optimization can be performed using our tool

Conclusion and
perspectives

General conclusion and perspectives

51

Conclusion


The main idea:
exploit the particularities of a machine to
minimize the number of the network elements.


Axial heterogeneity:


taken into account on the stage of the network construction;


the model is not a 2D model any more!


Flexible and adaptive PN construction, treating:


complicated geometries;


irregular slot structure and distribution.


Fixed rotor algorithm


rapid steady
-
state calculations.


Software TurboTCM is modular, scalable and flexible:


taking into account different machine configurations;


different modes of use;


easy coupling with optimization software.


The results are validated for several different types of machines.


52

Perspectives


Expand the approach and software to other
types of electrical machines.


Implementation of additional methods of air
-
gap permeances calculation.


Further development and extension by
multiphysical phenomena:


Thermal circuit coupling;


Vibroacoustic analysis.


Taking into account the Eddy
-
currents and
hysteresis effects.

Thank you for attention!

Any questions?