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

1. 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

2. Presentation plan • Introduction and problem definition • Developed approach • Software implementation • Applications • Conclusion and perspectives

3. 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 Stator of a turbogenerator Jeumont production: • 2-4-6-n pole turbogenerators • Power up to 1000 MW 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 3D mesh of a claw-pole machine

9. Introduction – calculation methods Field calculation Permeance networks Conventional methods Model speed Model accuracy

10. 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 • Linear • r=1.0 Stator slots Rotor slots Stator teeth • Nonlinear • r≥10.0 even for saturation • The direction of magnetic fluxis well defined. Rotor teeth Stator yoke Rotor yoke • The surfaces of magnetic cores can be considered equipotential ones! • The air-gap zone is linear and can be considered independently from magnetic cores.

13. Stator Flux Rotor Developed approach –turbogenerator particularities Axial view of the machine 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. Zone limits: 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. • The surfaces of magnetic cores can be considered equipotential for scalar magnetic potential. • The air-gap zone is linear and can be considered independently from magnetic cores.

16. Developed approach – air-gap zone Tooth contours air-gap permeance calculation

17. Developed approach – air-gap zone Calculation zone Comparison

18. Developed approach – air-gap zone A set of mutual air-gap characteristics

19. Developed approach –magnetic system • The permeability of the steel is high enough to consider magnetic surfaces equipotential ! • The direction of the flux in magnetic cores is well defined.

20. Developed approach –magnetic system Calculation of elements’ parameters The flux is supposed constant for the whole zone The magnetic potentials of each small element are calculated using trapezoidal formula: 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

23. FMM source 1 FMM source 2 FMM source 3 FMM source 4 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!

24. Magnetic circuit: Electrical circuit: Magnetic & electrical coupling: Mechanical equations: Developed approach –system of equations Magnetic permeance network Equation set • 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!

25. 3. Obtain flux linkage 4. Obtain the EMF: 5. Solve the equation: Developed approach –Steady-state fixed rotor algorithm 1. Set stator and rotor currents 2. Calculate magnetic circuit The flux linkage and EMF already take into account the axial heterogeneity of the machine! Various steady-state characteristics can be obtained directly or iteratively!

26. Implementation Software implementation: TurboTCM

27. COM Parser SOLVER Can be Matlab, VB program, C++ program or any other software. Elements&Relations Circuit builder … Implementation – the core.Circuit specification. Circuitdescription Incidence matrices, permeance, mmf vectors, parameter vector, etc.

28. Implementation – component responsibilities CircuitBuilder Thermal circuit? CircuitBuilder Electric circuit CircuitBuilder Magnetic circuit CircuitConnector Intercircuit relations Electric matrices Magnetic matrices W – coupling matrix AE – incidence matrix YE – permeance matrix ZE – resistance matrix SE – sources vector etc… AM – incidence matrix YM – permeance matrix ZM – resistance matrix SM – sources vector etc… Coupling equations:

29. Electric circuit Turboalternator parameters parameters Electric circuit Winding Magnetic circuit description description description Magnetic part equations Electric part equations ( ) t F = L × × j + A f t = × j u A TCMLib B E E × F = A 0 Y d B + × + R i ... B dt = u Parser B Coupling equations t d i ò B + × + - × 1 ... L C i dt B = × f W i dt B 0 t × = A i 0 t Y = × F W B E B Elements&Relations a SOLVER Calculation results Circuit builder Implementation – software structure Input data specification Equation preparation: C++ Matlab solver and results

30. Implementation –Matlab solver

31. 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).

32. Implementation –Various characteristic calculation Regulation characteristics Load characteristics V-shaped characteristics. Time: 12 minutes on Pentium IV Variation of xd and xq parameters

33. Implementation –Each operating mode output Air gap flux density in no-load and rated cases Ampere-turns distribution in the zones

34. Applications Small machine Two pole turbogenerator Four pole turbogenerator Optimization application: screening study

35. 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

36. Application –Two pole machine of 3000 VA Comparison with finite element calculations (OPERA RM), taking rotation into account • 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

37. Application –Two pole machine of 3000 VA Experimental bench and the results in dynamics

38. 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

39. Application –Two pole turbogenerator – no-load case Errmax=7.11% Errmax=2.41% Errmax=16.46% Errmax=1.03%

40. Application –Two pole turbogenerator – load cases Load characteristics V-shaped characteristics. Time: 12 minutes on Pentium IV

41. Application –Two pole turbogenerator – load cases Variation of xd and xq parameters Regulation characteristics

42. Application –Four pole turbogenerator

43. Application –Four pole turbogenerator • Material properties were unknown • Linear modelisation fit completely • In nonlinear case – the error was significant

44. 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…

45. 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

46. Application – Response surface study results KhB3 for Tp1 min KhB3 for Tp1 max

47. 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

48. 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

49. Conclusion and perspectives General conclusion and perspectives

50. 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.