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
2,0E06
4,0E06
6,0E06
8,0E06
1,0E05
1,2E05
1,4E05
1,6E05
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
Vcurves 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
Airgap 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
Airgap 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
Vcurves 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!
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