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:

Jeumont-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 methodsFinite element method

2D mesh of a generator 3D mesh of a claw-pole machine

9

Introduction – calculation methods

Model speed

Model accuracy

Permeance networks Conventional methodsField 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 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.

13

Developed approach –turbogenerator particularities

Axial view of the machine

Stator

Rotor

Flux

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.

32

ln2 11

11 szz

z btgt

tb

Zone limits:

16

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

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 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.

20

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:

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 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!

26

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!

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

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

29

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?

30

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

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 1.40.4

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

Applications

Small machineTwo pole turbogeneratorFour 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

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Application –Two pole turbogenerator – no-load case

Errmax=2.41%

Errmax=1.03%Errmax=16.46%

Errmax=7.11%

41

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

42

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

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 Xd and Xq Air-gap flux densities Etc…

46

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

47

Application – Response surface study results

KhB3 for Tp1 min KhB3 for Tp1 max

48

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

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?