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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

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2 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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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

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5 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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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.

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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…

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8 Introduction – existing methods Finite element method 2D mesh of a generator3D mesh of a claw-pole machine

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9 Introduction – calculation methods Model speed Model accuracy Permeance networksConventional methodsField calculation

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Developed approach Tooth contour method Permeance network construction Mode calculation

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11 Developed approach Principles Axial heterogeneity Network construction: Air-gap Tooth zones Yoke zones Electromagnetic coupling Network equations Operating modes calculation

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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.

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13 Developed approach – turbogenerator particularities Axial view of the machine Stator Rotor Flux End winding effects Duct effects Lamination effects

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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.

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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. Zone limits:

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

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17 Developed approach – air-gap zone Calculation zone Comparison

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

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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.

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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:

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21 Developed approach – magnetic system Two-pole machine

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22 Developed approach – magnetic system Teeth of different height – Variable Topology Model

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23 Approach – electromagnetic coupling Magnetic shells approach: The shell is stretched on the sort of winding

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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

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25 Developed approach – system of equations Equation setMagnetic permeance network Magnetic circuit: Electrical circuit: Magnetic & electrical coupling: Mechanical equations: 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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26 Developed approach – Steady-state fixed rotor algorithm 1. Set stator and rotor currents 2. Calculate magnetic circuit 4. Obtain the EMF: 3. Obtain flux linkage 5. Solve the equation: 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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28 Implementation – the core. Circuit specification. Incidence matrices, permeance, mmf vectors, parameter vector, etc. Parser Circuit builder Elements & Relations COM SOLVER … Can be Matlab, VB program, C++ program or any other software. Circuit description

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29 Implementation – component responsibilities CircuitBuilder Electric circuit CircuitBuilder Magnetic circuit CircuitConnector Intercircuit relations Electric matricesMagnetic 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: CircuitBuilder Thermal circuit?

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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 EB iA dtiC id L iR d u Au Coupling equations t B B W a t iWf Magnetic part equations 0 A fA t SOLVER Calculation results Input data specification Equation preparation: C++ Parser Circuit builder Elements & Relations TCMLib Matlab solver and results

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31 Implementation – Matlab solver

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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).

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33 Implementation – Various characteristic calculation V-shaped characteristics. Time: 12 minutes on Pentium IV Load characteristics Regulation characteristics Variation of x d and x q parameters

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

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

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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

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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

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

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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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40 Application – Two pole turbogenerator – no-load case Err max =2.41% Err max =1.03%Err max =16.46% Err max =7.11%

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

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42 Application – Two pole turbogenerator – load cases Regulation characteristics Variation of x d and x q parameters

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43 Application – Four pole turbogenerator

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

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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…

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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

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47 Application – Response surface study results K hB3 for T p1 minK hB3 for T p1 max

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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

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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

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Conclusion and perspectives General conclusion and perspectives

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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.

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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.

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Thank you for attention! Any questions?

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Chapter 1 MAGNETIC CIRCUIT.

Chapter 1 MAGNETIC CIRCUIT.

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