contribution à la modélisation et à la conception optimale des turboalternateurs de faible...
TRANSCRIPT
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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
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Presentation plan
Introduction and problem definition Developed approach Software implementation Applications Conclusion and perspectives
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Introduction
The objectives and problem definition
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INTRODUCTION – Objectives
Objective:Creation of a rapid tool used in optimal electromagnetic design of turbogenerators of power of 10-100 MW.
Collaboration:
Jeumont-Framatome ANP
Moscow Power Engineering Institute (M.P.E.I.)
CNRT (Centre National de la Recherche et Technologie), FUTURELEC-2
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Introduction – Jeumont production
Jeumont production:• 2-4-6-n pole turbogenerators• Power up to 1000 MW
Stator of a turbogenerator
4-pole rotor
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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.
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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…
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Introduction – existing methodsFinite element method
2D mesh of a generator 3D mesh of a claw-pole machine
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Introduction – calculation methods
Model speed
Model accuracy
Permeance networks Conventional methodsField calculation
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Developed approach
Tooth contour method
Permeance network construction
Mode calculation
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Developed approach
Principles Axial heterogeneity Network construction:
Air-gap Tooth zones Yoke zones
Electromagnetic coupling Network equations Operating modes calculation
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Developed approach
Air-gap
Stator slots
Rotor slots
Stator teeth
Rotor teeth
Stator yokeRotor yoke
•Linearr=1.0
•Nonlinearr≥10.0 even for saturation•The direction of magnetic fluxis 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.
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Developed approach –turbogenerator particularities
Axial view of the machine
Stator
Rotor
Flux
End winding effects
Duct effects
Lamination effects
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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.
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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.
32
ln2 11
11 szz
z btgt
tb
Zone limits:
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Developed approach – air-gap zone
tz1
s
rtz2
bkm= 0
r
s bkm= tz2/4
r
s bkm= tz2/2
bkm= 3tz2/4s
r
Tooth contours air-gap permeance calculation
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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
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Developed approach – air-gap zone
A set of mutual air-gap characteristics
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Developed approach –magnetic system1. 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.
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Developed approach –magnetic system
Calculation of elements’ parameters
minblB eff The flux is supposed constant for the whole zone
6
4 231.
HHHhU elelm
The magnetic potentials of each small
element are calculated using trapezoidal formula:
elmUU .Total difference of potentials is found as a sum:
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Developed approach –magnetic system
Two-pole machine
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Developed approach – magnetic system
Teeth of different height – Variable Topology Model
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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
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Developed approach –system of equations
Equation setMagnetic permeance network
0
A
fAt
Magnetic circuit:
0
0
1
BE
t
BB
BB
E
t
EB
iA
dtiCdt
idLiR
dt
dAu
Electrical circuit:
tB
B
Wa
t
iWf
Magnetic & electrical coupling:
t
out
dt
dt
dJMM
0
0
Mechanical equations:
Bt
t
iWAU
UUM
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!
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Developed approach –Steady-state fixed rotor algorithm
1. Set stator and rotor currents
2. Calculate magnetic circuit
4. Obtain the EMF: jE
3. Obtain flux linkage
5. Solve the equation:
0 EIjxIRU 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!
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Implementation
Software implementation: TurboTCM
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Implementation – the core.Circuit specification.
Incidence matrices,permeance, mmf vectors,
parameter vector, etc.
Parser
Circuit builder
Elements&
Relations
COM
SOLVER
,
...
......
...
A
PT,T,1
ki,
P,11,1
aa
a
aa
,
......
......
......1
P
k
,,...,,...,, 21
t
Pk fffff …
Can be Matlab,VB program,C++ program orany other software.
Circuitdescription
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Implementation – component responsibilities
CircuitBuilderElectric circuit
CircuitBuilderMagnetic circuit
CircuitConnectorIntercircuit relations
Electric matrices Magnetic matricesAE – incidence matrixYE – permeance matrixZE – resistance matrixSE – sources vectoretc…
W – coupling matrixAM – incidence matrixYM – permeance matrixZM – resistance matrixSM – sources vectoretc…
Coupling equations:
dt
de
WiWf TE
CircuitBuilderThermal circuit?
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Implementation – software structure
Electric circuit parameters
Turboalternator parameters
Electric circuit description
Winding description
Magnetic circuit description
Electric part equations
0
...
...
0
1
BE
t
BB
BB
B
E
t
EB
iA
dtiCdtid
L
iRdt
d
u
Au
Coupling equations
tB
B
Wa
t
iWf
Magnetic part equations 0
A
fAt
SOLVER
Calculation results
Input data specification
Equation preparation: C++
Parser
Circuit builder
Elements&
Relations
TCMLib
Matlab solver and results
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Implementation –Matlab solver
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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).
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Implementation –Various characteristic calculation
0 0.2 0.4 0.6 0.8 1 1.2 1.40.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Is, p.u.
Us,
p.u.
Load diagram: If=I
fnom
PF=0.8, underexcited
PF=1PF=0.8, overexcited
0 500 1000 1500 2000 2500 3000 3500 4000 4500100
200
300
400
500
600
700
800
900
Is, A
If,
A
Regulation characteristic, Us=Usnom
PF=0.8, underexcited
PF=1
PF=0.8, overexcited
0 0.2 0.4 0.6 0.8 1 1.2 1.40
0.2
0.4
0.6
0.8
1
1.2
1.4
V-curves for Us=U
snom
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 characteristicsRegulation characteristics
Variation of xd and xq parameters
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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 45 500
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
1Air-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
1.5Air-gap flux density
Angular position, rad
B,
T
0 10 20 30 40 500
1
2
Harmonic orders
B,
T
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Applications
Small machineTwo pole turbogeneratorFour pole turbogenerator
Optimization application: screening study
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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
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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
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Application –Two pole machine of 3000 VA
Experimental bench and the results in dynamics
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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
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Application –Two pole turbogenerator – no-load case
Errmax=2.41%
Errmax=1.03%Errmax=16.46%
Errmax=7.11%
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Application – Two pole turbogenerator – load cases
0 0.2 0.4 0.6 0.8 1 1.2 1.40.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Is, p.u.
Us,
p.u.
Load diagram: If=I
fnom
PF=0.8, underexcited
PF=1PF=0.8, overexcited
0 0.2 0.4 0.6 0.8 1 1.2 1.40
0.2
0.4
0.6
0.8
1
1.2
1.4
V-curves for Us=U
snom
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
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Application – Two pole turbogenerator – load cases
0 500 1000 1500 2000 2500 3000 3500 4000 4500100
200
300
400
500
600
700
800
900
Is, A
If,
A
Regulation characteristic, Us=U
snom
PF=0.8, underexcited
PF=1
PF=0.8, overexcited
Regulation characteristicsVariation of xd and xq parameters
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Application –Four pole turbogenerator
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Application –Four pole turbogenerator
Material properties were unknown Linear modelisation fit completely In nonlinear case – the error was significant
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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 Xd and Xq Air-gap flux densities Etc…
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Application –Response surface study Objective: Demonstrate the use of TurboTCM together
with an optimization supervisor. Variables:
hs1 – stator tooth height (±10%) bs1 – stator tooth width (±10%) Di1 – stator boring diameter (±5%) Tp1 – rotor pole width (±10%)
Responses: KhB3 – 3rd order harmonic of air-gap flux density KhE3 – 3rd order harmonic of stator EMF KhE1 – the fundamental of the no-load stator EMF If – excitation current in no-load
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Application – Response surface study results
KhB3 for Tp1 min KhB3 for Tp1 max
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Application – Response surface study results
KhE3 for different Tp1 KhE1 for different Tp1
If for Di1 min for different Tp1 If for Di1 max for different Tp1
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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
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Conclusion and perspectives
General conclusion and perspectives
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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.
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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.
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Thank you for attention!
Any questions?