46430035 Synchronous Motor

CAD Package for Electromagnetic and Thermal Analysis using Finite Elements

FLUX®2D Application

Synchronous motor technical paper

Copyright - April 2006

FLUX is a registered trademark.

FLUX software : COPYRIGHT CEDRAT/INPG/CNRS/EDF FLUX2D technical papers : COPYRIGHT CEDRAT FLUX2D's Quality Assessment: (Electricité de France standard, registered number AQM1L002)

This technical paper was edited on 18 April 2006

Ref.: K205-Q-920-EN-EN-04/06

CEDRAT 15 Chemin de Malacher - Inovallée

38246 Meylan Cedex FRANCE

Phone: +33 (0)4 76 90 50 45 Fax: +33 (0)4 56 38 08 30

E-mail: [email protected]: http://www.cedrat.com

mailto:[email protected]

http://www.cedrat.com/

CONVENTIONS USED

To make this tutorial easy to read, the following conventions have been used: • All the information and comments describing the current actions are written in the same

way as this sentence. • All dialogue text between the user and FLUX2D is written in courier font:

Name of the region to be created :

bdg ↵ Color of this region : <M>AGENTA Select a surface or a menu item :

<Q>uit

[q]uit ↵ The conventions used for the dialogue between the user and FLUX2D are presented below: Text in italic Message or question displayed on the screen by FLUX2D

Text in bold ↵

Bdg ↵

[q]uit ↵

User input to FLUX2D using the keyboard (name of a region, point coordinates, ...). This answer should be validated by the Return/Enter key, symbolised in this document by ↵. If there is no ambiguity, a keyboard answer can be shortened. In this case, you should press the characters indicated between square brackets [ ] .

<T>ext in bold <M>AGENTA <Coil>

A menu item of the graphical window can be selected using the mouse or, if there is no ambiguity, by entering the first character of the word displayed between angled brackets < >. If the menu must be necessarily selected using the mouse, it is enclosed by angled brackets < >.

Graphical input such as selection of a point, a line, a surface...

↵ The reply is by default. To enter a default response, simply press the Return/Enter key.

CREATE

Menu commands should be selected with the mouse.

Item that you should select from the graphics screen; (P3) point number 3 or (P3__P4) line connecting point number 3 and point number 4. P3 P3 P4

- REMARK -

The files corresponding to different cases studied in this technical paper are available in the folder:

…\DocExamples\Examples2D\SynchronousMotor\FluxFiles\ The corresponding applications are ready to be solved. This allows you to adapt this technical paper to your needs.

FLUX 2D®9.20 TABLE OF CONTENTS

TABLE OF CONTENTS

1. Overview of synchronous motor technical paper......................................................... 1

2. Defining the problem ................................................................................................... 3 2.1 Building method for the geometry and mesh .................................................................. 4 2.2 The Geometry ................................................................................................................. 5

2.2.1 Creation of coordinate systems, geometrical parameters .................................................6 2.2.2 Geometry and faces building and transformation creation................................................7

2.3 The mesh and regions .................................................................................................. 15 2.3.1 Creation of discretisations ...............................................................................................15 2.3.2 Assigning the mesh .........................................................................................................15 2.3.3 Regions............................................................................................................................19

2.4 Circuits models.............................................................................................................. 24 2.4.1 ME_CC ............................................................................................................................25 2.4.2 AC_SSFR_D_AXIS_POS................................................................................................26 2.4.3 AC_SSFR_Q_AXIS_POS................................................................................................27 2.4.4 TM_NETWORK ...............................................................................................................28

2.5 Materials data................................................................................................................ 29 2.6 Boundary conditions...................................................................................................... 30

3. Parameters Xd, Xq in magneto static ........................................................................ 31 3.1 Introduction ................................................................................................................... 31 3.2 Angles corresponding to Xd and Xq.............................................................................. 31

3.2.1 Purpose ...........................................................................................................................31 3.2.2 Physical conditions ..........................................................................................................32 3.2.3 Solving conditions............................................................................................................33 3.2.4 Analysis ...........................................................................................................................34

3.3 Xd and Xq according to the stator current..................................................................... 35 3.3.1 Purpose ...........................................................................................................................35 3.3.2 Physical conditions ..........................................................................................................35 3.3.3 Solving conditions............................................................................................................37 3.3.4 Analysis ...........................................................................................................................37

4. Short-circuit tests....................................................................................................... 41 4.1 Unloaded operating....................................................................................................... 41

4.1.1 Purpose ...........................................................................................................................41 4.1.2 Physical conditions ..........................................................................................................41 4.1.3 Solving conditions............................................................................................................44 4.1.4 Analysis ...........................................................................................................................45

SYNCHRONOUS MOTOR PAGE A

TABLE OF CONTENTS FLUX 2D®9.20

4.2 Single phase short circuit...............................................................................................47 4.2.1 Purpose............................................................................................................................47 4.2.2 Physical conditions ..........................................................................................................47 4.2.3 Solving conditions ............................................................................................................50 4.2.4 Analysis............................................................................................................................51

4.3 Three phase short circuit ...............................................................................................53 4.3.1 Purpose............................................................................................................................53 4.3.2 Physical conditions ..........................................................................................................53 4.3.3 Solving conditions ............................................................................................................56 4.3.4 Analysis............................................................................................................................57

5. StandStill Frequency Reponse (SSFR) ..................................................................... 61 5.1 Direct and quadrature axis determination......................................................................61

5.1.1 Purpose............................................................................................................................61 5.1.2 Physical and solving conditions .......................................................................................62 5.1.3 Analysis............................................................................................................................69

5.2 Classical SSFR..............................................................................................................71 5.2.1 Purpose............................................................................................................................71 5.2.2 Physical conditions ..........................................................................................................71 5.2.3 Solving conditions ............................................................................................................74 5.2.4 Analysis............................................................................................................................75

6. Loaded on the network .............................................................................................. 79 6.1 Unloaded on the network...............................................................................................79

6.1.1 Purpose............................................................................................................................79 6.1.2 Physical conditions ..........................................................................................................79 6.1.3 Solving parameters ..........................................................................................................82 6.1.4 Analysis............................................................................................................................83

6.2 Loaded on the network without regulation .....................................................................86 6.2.1 Purpose............................................................................................................................86 6.2.2 Physical conditions ..........................................................................................................86 6.2.3 Solving parameters ..........................................................................................................89 6.2.4 Analysis............................................................................................................................90

6.3 Loaded on the network with appropriated motor torque ................................................91 6.3.1 Purpose............................................................................................................................91 6.3.2 Physical conditions ..........................................................................................................91 6.3.3 Solving parameters ..........................................................................................................94 6.3.4 Analysis............................................................................................................................94

6.4 Loaded on the network with appropriated field current and motor torque .....................97 6.4.1 Purpose............................................................................................................................97 6.4.2 Physical conditions ..........................................................................................................97 6.4.3 Solving parameters ........................................................................................................100 6.4.4 Analysis..........................................................................................................................101

PAGE B SYNCHRONOUS MOTOR

FLUX 2D®9.20 Overview of synchronous motor technical paper

1. Overview of synchronous motor technical paper

This document presents some models for finite element based on analysis of synchronous motor. By post-processing the numerical results of the problems associated to these models, the main characteristics of the machine are evaluated. They correspond in fact to the longitudinal and transversal reactance. Several methods can be used to determine them. We shall present here some of them. Two configurations of the motor will be taken into account: with coil absorber or massive absorber. This paper contains two principal sections : • DEFINING THE PROBLEM (chapter 2) : Creation of geometry, mesh, circuit models

and materials data. This section describes the construction of geometry and mesh in using the functions, supplied by the software as transformations or geometrical parameters, in order to optimise the model. The regions, used to assign the physical proprieties to the machine, will be detailed. This part provides too the description of the circuits associated to different field cases (representing the electrical wiring diagram of machine with its supplying) as well as data on the materials. Finally, the study domain will be defined by the boundary conditions.

• DIFFERENT SIMULATIONS AND ANALYSIS (chapter 3 to 6) : This section is composed

of several simulation’s types that is to say the magneto-static, transient magnetic and magneto-dynamic. These simulations are used according to the characteristics studied and the operating of the machine. The magneto-static analysis corresponds to a machine without movement and a magnetic steady-state. The transient magnetic analysis corresponds to a machine in movement with a magnetic state in evolution. The last type, magneto-dynamic, corresponds to a magnetic state changing without movement of the machine.

Each test includes also the solving parameters and an analysis of simulation results. The simulation’s type, the initial conditions, the calculation’s resolution are defined. The first test, Parameters Xd, Xq, will allow to define the angles and the values of the direct and quadrature synchronous reactances. The two following tests, Short-circuit test and standstill frequency response, will allow to characterise the machine by these time constants and reactances. Finally, a connection to the network of the generator, Loaded on the network, with or without regulation, will be modelled.

SYNCHRONOUS MOTOR PAGE 1

Overview of synchronous motor technical paper FLUX 2D®9.20

PAGE 2 SYNCHRONOUS MOTOR

FLUX 2D®9.20 Defining the problem

2. Defining the problem

This numerical simulations refer to a 4 poles synchronous motor, three-phase, having the following characteristics :

CHARACTERISTICS DATA

Number of poles 4 Voltage 220 / 127 V

Frequency 50 Hz

Power 3 kVA

Slots number 54

Number of turns per phase 108 Armature

Number of wires by slot 12

Field Number of turns per pole 215

D axis - slots by pole 4

D axis - wires by slot 74

Q axis - slots by pole 2 Absorber

Q axis - wires by slot 74

Fig 2.a : Synchronous machine


Defining the problem FLUX 2D®9.20

A cross section, given below, shows the overview of the machine : Armature

Electrical absorber

Field

Stator wires

2.1 Building method for the geometry and mesh The model will be create in following each chapter until the 2.4.2. Nevertheless, the geometry and mesh are linked during the construction that’s why a method is presented to understand the sequences of construction. In this tutorial, the building method of stator is the following one :

- creation of points of half slot of stator - creation of lines of half slot of stator - creation of transformation necessary to obtain the complete stator slot - complement to the geometry with lines - creation of faces - creation of the stator mesh - creation of transformation necessary to obtain the half stator The building method of rotor is the following one : - creation of points of half slot absorber and one field of rotor - creation of lines of half slot absorber and field of rotor - creation of faces of half slot absorber - creation of half slot absorber mesh - creation of transformations necessary to obtain the six slots absorber - complement to the geometry of eighth of rotor with lines - creation of faces - creation of the eighth rotor mesh - creation of transformation necessary to obtain the half Ending of the building : - creation of lines to close the airgap - creation of airgap mesh



2.2 The Geometry The machine being build up of four poles and in a symmetric way, only an half machine will be described with two poles as it is shown below.

Poles

Field coils

The most part of the geometry construction will be created from geometrical paramdimensions are nevertheless given to close the construction.

SYNCHRONOUS MOTOR

Armature wires 3 phases

eters. Some

PAGE 5


2.2.1 Creation of coordinate systems, geometrical parameters

• Coordinate system The armature and the field are created in two different systems in order to be able to simulate an eccentricity of the rotor. The different systems are:

Name Comments Definition Type Origin X

Origin Y

Origin Z

Unit of length

Unit of angle

XY1 Default system 2D_Global Cartesian

2D 0 0 0 Millimeter Degree

STATOR Stator system 2D_Global Polar 2D 0 0 0 Millimeter Degree

ROTOR Rotor system 2D_Global Polar 2D 0 0 0 Millimeter Degree

Note : To create coordinate systems : [Geometry], [Coord sys], [New] • Geometrical parameters The geometrical parameters used in geometry building are: Parameter names Comments Values in [mm] or [°] RIR Rotor internal radius 28.575 mm RER Rotor external radius 113.2 mm AIR Absorber internal radius 96.48 mm AER Absorber external radius 111.05 mm AOIR Absorber opening internal radius 111.93 mm RAHA Rotor slot half-angle 4.5 ° FSIR Field slot internal radius 50.6 mm FSMR Field slot medium radius 82.9 mm FOIR Field opening internal radius 101.75 mm FOER Field opening external radius 109.35 mm ST Skin thickness 1 mm SIR Stator internal radius 114.34 mm SER Stator external radius 202.5 mm SSIR Stator slot internal radius 127.04 mm SSER Stator slot external radius 177.84 mm SSHA Stator slot half-angle 3.33 ° (360/108) AIRGAP Airgap 1.14 mm MESH_AIRGAP Use for the mesh 1.5*airgap NBSS Number of stator slots 54

Note : To create geometrical parameter : [Geometry], [Geometric Parameter], [New]



2.2.2 Geometry and faces building and transformation creation

In order to simplify the geometry construction, the rotor and stator will be built from an half slot for the rotor and half slot for the stator. Some transformations will be used in order to propagate the original shape and to obtain the final geometry. • Creation of half stator slot

- points of half slot of stator

N° R coordinate θ coordinate Coordinate system

P1 0 0 STATOR

P2 SIR 0 STATOR

P3 SIR SSHA - 0,39 STATOR

P4 118.2 0 STATOR

P5 124.5 0 STATOR

P6 SSIR*COSD(0.87) 0 STATOR

P7 SSIR 0.87 STATOR

P8 SSIR 2.98 STATOR

P9 ((SSIR+SSER)/2) * cosd(1.28) 0 STATOR

P10 (SSIR+SSER) / 2 1.28 STATOR

P11 ((SSIR+SSER)/2) * cosd(2.053) SSHA STATOR

P12 SSER * cosd(1.76) SSHA STATOR

P13 SSER 1.57 STATOR

P14 SSER * cosd(1.57) 0 STATOR

P15 SER 0 STATOR

P16 SER SSHA STATOR

Fig 2.2.1.a : Overview of a stator slot with the points designation

Create with mirror_stator transformation



- lines of half stator slot

N° Type of line Starting point

End point

Center point Angle Coordinate system

L1 Segment P3 P8 STATOR

L2 Segment P7 P10 2.2.2.1.1 STATOR















L17 Arc_2pt_pt_center P2 P3 P1 STATOR



L20 Arc_2pt_radius P5 P4 3.15 STATOR



Fig 2.2.1.b : Overview of a stator slot with the lines designation



• Creation of transformation necessary for the stator construction Symmetry will be used to end the complete slot, and then a multiple rotation to create the half-stator. The lines 21 and 22 will be created before building half stator. Geometric transformation

Type First point

Second point

Ratio Comment

MIRROR_STATOR Affine_line_2pt P1 P16 -1 Create mirror image of a half slot of stator

Geometric transformation Type R comp. Theta

comp. Rot. Z Coordinate system Comment

STATOR_ROT Rot_coo_ang 0 0 360/NBSS STATOR Create all of stator slot

Note : To create geometric transformation : [Geometry], [Transformation], [New]

Fig 2.2.1.c Base shape of stator

Fig 2.2.1.d complete stator



• Creation of half rotor - points of eighth of rotor

N° Radius Angle Coordinate system

P17 RIR 0 ROTOR

P18 RIR 45 ROTOR

P19 FSIR 0 ROTOR

P20 FSIR 22.5 ROTOR

P21 FSMR 22.5 ROTOR

P22 ((AIR * COSD (2.109)) – 6.2) / COSD (4.5) 18 ROTOR

P23 91.312 14 ROTOR

P24 88.6 0 ROTOR

P25 FOIR * COSD (2.873) 0 ROTOR

P26 FOER * COSD (2.673) 0 ROTOR

P27 RER 0 ROTOR

P28 FOER 2.673 ROTOR

P29 FOIR 2.873 ROTOR

P30 RER 15 ROTOR

P31 RER 18 ROTOR

P32 AER 18 ROTOR

P33 AIR 18 ROTOR

P34 AIR 20.391 ROTOR

P35 AER 19.868 ROTOR

P36 RER 19.868 ROTOR

P37 RER 21.857 ROTOR

P38 AOIR 21.85 ROTOR

P39 AOIR * COSD (0.65) 22.5 ROTOR

P40 AIR * COSD (2.109) 22.5 ROTOR

P41 AIR * COSD (2.109) – 3.56 22.5 ROTOR

P42 AIR *COSD (2.109) – 6.2 22.5 ROTOR



Fig 6 : Overvi a part or with the points designation

lines o f rotor

ew of of rot

- f eighth o


End point Center point Radius Coordinate

system L23 Segment P1 P17 ROTOR

L24 Segment P17 P19 ROTOR
























End point Center point Radius Coordinate

system







L51 Arc_2pt_pt_center P17 P18 P1 ROTOR


L53 Arc_2pt_ray P29 P22 32.6 ROTOR












Note : the lines 93, 156, 157, 1377 and 1378 are created at the end of the construction in order to close the airgap region.

L55

Fig 7 : Overview of part of rotor with the lines designation



• Creation of transformation necessary for the rotor construction Symmetry will be used to end the absorber slot then a multiple rotation to create the two other ones. The line 92 will be created to end the first absorber slot and the lines 155 and 156 will be created before applying the first rotor symmetry. A first symmetry will be used to create the quarter of rotor then another one to finish the half rotor. Geometric transformation

Type First point Second point Ratio Comment

MIRROR_ABSORBER Affine_line_2pt P1 P39 -1 Create mirror image of a half slot of absorber

MIRROR_ROTOR_1 Affine_line_2pt P1 P18 -1 Create a quarter of rotor

MIRROR_ROTOR_2 Affine_line_2pt P1 P678 -1 Create an half of rotor

Geometric transformation Type R

comp. Theta comp. Rot. Z Coordinate

system Comment

ABSORBER_ROT Rot_coo_ang 0 0 9 ROTOR 2 Times to create the three first slot of absorber



Create with Mirror absorber

Fig 7 and 8 : Different steps

of creation of the rotor

Create with Absorber_rot

Create with Mirror rotor 1

• Ts

P

Create with MIRROR_ROTOR_2

Creation of faces

he faces must be built before and after each transformation whether it is for the rotor or the tator.

Warning: Before propagating faces, select the options [add faces and associated Linked Mesh Generator] in order to create faces automatically and to affect the mesh of the original shape to the whole geometry.

Note : To create faces : [Geometry],[Build]],[Build Faces]

AGE 14 SYNCHRONOUS MOTOR


2.3 The mesh and regions Further to an automatic meshing, some elements are not standard. Furthermore, the mesh applied to the airgap does not correspond to equilateral triangle. In order to improve the mesh, some discretisations will be assigned to points and lines.

2.3.1 Creation of discretisations

• Mesh points Names Value (in mm) Color BIG 18 Cyan LARGE 12 Turquoise MEDIUM 6 Yellow SMALL 3 Red AIRGAP Mesh_airgap Magenta

Note : To create mesh point: [Mesh],[Mesh Point], [New] • Mesh lines Names Type Value Ratio Color A2 Arithmetic 2 Magenta A3 Arithmetic 3 Green A8 Arithmetic 8 Turquoise

GEO_1 Geometric with imposed number of elements 2 1.3 Yellow

2.3.2 Assigning the mesh

In using the propagate function with the option “add faces and associated Linked Mesh Generator”, the mesh will be assigned only to the original shapes. With the automatic mesh, the discretisation will be carried out by Flux 2D but in order to optimize the number of nodes, the customized mesh point and mesh line will be applied. On some faces, knowing the circulating direction of flux density, the “mapped” option will be applied. • Mesh points Names Points BIG P7,P10,P11,P12,P13,P43,P46,P48 LARGE P6,P9,P14,P15,P16,P22,P42,P44,P45,P47,P49 MEDIUM P4,P5,P21,P23,P26,P34,P35,P38,P39,P41,P52,P53 SMALL P8,P51 AIRGAP All points in relation with the airgap region



Note : To assign mesh point : [Mesh],[Assign mesh information],[Assign mesh point to Points]

Note : To assign with a relation : [Mesh],[Assign mesh information],[Assign mesh point to Points], select the little arrow and then choose [Selection by surfacic region]

• Mesh lines Names Lines A2 L8,L17,L19,L22,L28,L44,L52,L59,L60,L64,L74,L75 A3 L20,L25,L26,L42,L43,L47,L72 A8 L55 GEO_1 L2,L12,L66,L67

Note : Please check that you have 563 faces created

Note : Please check that you have only 4 faces with bad quality elements corresponding to the edges of field horns.

• Mapped Mesh In order to simplify the mesh and reduce the number of node, the mapped mesh will be used. This mesh assigns a surface where the shape of mesh is quadrangular. This mesh is assigned to faces. Names Faces MAPPED 5, 7, 9, 10, 11, 12, 13, 14, 17, 24, 25

Note : To assign mapped mesh : [Mesh],[Assign mesh information],[Assign mesh generator to Faces], select the faces and assign [Mapped]

L52 L28

L59L17,L74

L75 L64L60

L22

L19

L8

L44

Fig 2.3.2.a : A2 mesh lines



L55

L26

L25

L47

L43

L42

L72

L20

Fig 2.3.2.b : A3 mesh lines Fig 2.3.2.c : A8 mesh lines

L6

L6

L2 L1

Fig 2.3.2.d : GEO_1 mesh lines

Fig 2.3.2. e : Mapped mesh



Fig 2.3.2.f : Big mesh points

Fig 2.3.2.g : Large mesh points

Fig 2.3.2.h : medium mesh points

Fig 2.3.2.i : airgap mesh points Fig 2.3.2.j : small mesh points



Fig 9 : Overview of complete mesh

About 7150 nodes will be created but it could be different according to the model.

2.3.3 Regions

29 regions will be created. Each coil of armature and field will be dissociated as well as all absorbers. • Creation of regions

Names Comment Color AIR 1 Holes in the stator and horns in the rotor Magenta AIR 2 Opening slot of absorber Magenta AIR 3 Airgap between the stator teeth Magenta AIRGAP Airgap between stator and rotor Yellow AM 1 Absorber White AM 2 Absorber White AM 3 Absorber White AM 4 Absorber White AM 11 Absorber White AM 22 Absorber White AM 33 Absorber White AM 44 Absorber White AQ 1 Absorber White AQ 2 Absorber White AQ 11 Absorber White AQ 22 Absorber White COIL 1M Stator negative phase 1 Yellow COIL 1P Stator positive phase 1 Red COIL 2M Stator negative phase 2 Yellow COIL 2P Stator positive phase 2 Red COIL 3M Stator negative phase 3 Yellow COIL 3P Stator positive phase 3 Red Field 1M Field negative phase 1 Turquoise



Names Comment Color

Field 1P Field positive phase 1 Red Field 2M Field negative phase 2 Turquoise Field 2P Field positive phase 2 Red SHAFT Motor shaft Turquoise ROTOR_CORE Rotor magnetic core Cyan STATOR_CORE Stator magnetic core Cyan

Note : To create region : [Physics],[Face Region],[New] • Assigning the surface region to faces

The region will be assigned to the faces according to the following pictures:

Fig 2.2.3.a Rotor core region Fig 2.2.3.b Stator core region

Fig 2.2.3.c Shaft region Fig 2.2.3.d Airgap region



Fig 2.2.3.e Air 1 region

Fig 2.2.3.f Air 2 region

Fig 2.2.3.g Air 3 region

Fig 2.2.3.h Coil 1P region Fig 2.2.3.i Coil 1M region



Fig 2.2.3.j Coil 2P region Fig 2.2.3.k Coil 2M region

Fig 2.2.3.l Coil 3P region Fig 2.2.3.m Coil 3M region

Fig 2.2.3.n Field 1P region Fig 2.2.3.p Field 1M region

Fig 2.2.3.q Field 2P region Fig 2.2.3.r Field 2M region



Fig 2.2.3.s All absorber regions

AM 1

AM 2

AQ 11

AM 11

AM 22

AQ 22

AM 33

AM 44

AQ 2

AQ 1

AM 4

AM 3

Note : To assign regions to faces : [Physics],[Assign regions to geometric entities], [Assign regions to faces]



2.4 Circuits models These circuits are used for dynamic and transient simulations. They will model:

• the three phases of the armature with or without the coil end winding • The field coils for the two poles. • The twelve absorbers which can be represented by two variants : some coil conductors or

solid conductors. • Some resistance with high value (106 or 104 Ω) in order to model the voltmeters. • The type of test, in which the circuit is used, and an abbreviation of test name compose

the name of each circuit.

Note : To create circuit : In the supervisor, choose [Circuit], [file], [New]



2.4.1 ME_CC

This circuit will be used: • to know the evolution of stator voltage in function of the supply in current of field. • to know the behavior of machine in case of sudden short-circuit. Different short-

circuit will be modeled (single phase, three phase …) in modifying the value of resistors in which the stator is linked.

Names Type Values

B1,B2,B3 Coils 181.2 mΩ B_ROTOR Coils 5.0136 Ω L1, L2, L3 Inductances 1.104 mH

R1, R2, R3,R6 Resistors According to test (106 or 10-6Ω)

L4 Inductances 8.8 mH

RU1, RU2, RU3, Resistors 106 Ω

AM1, AM2, AM3, AM4, AM11, AM22, AM33, AM44, AQ1, AQ2, AQ11, AQ22

Solid conductors ρ = 2.7 10-8 Ω.m

R5,R7,R8, ……. …..R23, R24, R25 Resistors 2.89 10-6 Ω

L5,L6,L7, …….. …..L22, L23, L24 Inductances 10-9 H

Fig 10 : ME_CC



2.4.2 AC_SSFR_D_AXIS_POS

This circuit will be used to determine the position of rotor in D axis for the SFFR test.

Names Type Values B1, B2, B3 Coils 181.2 mΩ B_ROTOR Coils 5.0136 Ω B5 Coils 8.486 Ω B6 Coils 9.358 Ω L1, L2, L3 Inductances 1.104 mH L4 Inductances 8.8 mH L5 Inductances 15.6 mH L6 Inductances 11.2 mH V1 Voltage source According to the test

Fig 11 : AC_SSFR_D_AXIS_POS circuit



2.4.3 AC_SSFR_Q_AXIS_POS

This circuit will be used to know the characteristics of machine with the StandStill Frequency Rotor or locked rotor.

Names Type Values B1, B2, B3 Coils 181.2 mΩ B_ROTOR Coils 5.0136 Ω B5 Coils 8.486 Ω B6 Coils 9.358 Ω L1, L2, L3 Inductances 1.104 mH L4 Inductances 8.8 mH R1 Resistance 104 Ω R2,R3,R4, … …, R19, R20, R21 Resistors 2.89 10-6 Ω

L5, L6, L7, … …, L22, L23, L24 Inductances 10-9 H

V1 Voltage source According to the test

Fig 12 : AC_SSFR_Q_AXIS_POS circuit



2.4.4 TM_NETWORK

This circuit will be used to know the behavior of machine when it is connected to the network.

Names Type Values B1, B2, B3 Coils 181.2 mΩ B_ROTOR Coils 5.0136 Ω B5 Coils 8.486 Ω B6 Coils 9.358 Ω L1, L2, L3 Inductances 1.104 mH L4 Inductances 8.8 mH L5 Inductances 15.6 mH L6 Inductances 11.2 mH R1, R2, R3 Resistances According to the test L7, L8, L9 Inductances According to the test V1, V2, V3 Voltage source According to the test I_rotor Current source According to the test

Fig 13 :TM_NETWORK circuit



2.5 Materials data Three types of materials will be used in the different simulations. They correspond to a magnetic core for the stator and rotor, to solid bars for the absorbers and to a resistive material for the rotor. Materials can be entered in a material database, or can be created directly in each FLUX project. • STEEL_NLIN This material is defined by the B(H) curve. The simple analytic saturation curve allows to characterise it by the saturation value Js and the slope of the origin of the curve. Characteristics : TJs 6.1= and 8000=µr

Fig 11 : B(H) curve of magnetic core

Note : To create material : In the supervisor, choose [Materials Database] : [Add],[Material] then [Property]

• ALU_BAR This material is defined by a resistivity corresponding to aluminium bars for the absorbers. This resistivity is given for 20° C temperature. Characteristics : iso_resistivity = 2.7 10-8 Ω.m • RESISTIV_ROTOR This material is defined by a B(H) curve, identical to the steel_nlin material, and a resistivity. This material will characterise the rotor property for some SSFR tests. Characteristics : TJs 6.1= 8000 and =µr for B(H) curve. Iso_resistivity = 15. 10-8 Ω.m



2.6 Boundary conditions The boundaries of computation domain are outer contour of stator magnetic core and the lines delimiting the section cut of the machine. The conditions will be:

- Dirichlet on the outer contour of stator magnetic core. Indeed, the magnetic flux through these boundaries is considered as null. Expressed in terms of magnetic vector potential, this condition means zero value of the magnetic vector potential along the two boundaries.

- Cyclic along of the section of machine. Indeed, the flux lines through these boundaries are considered as perpendicular to these boundaries and distributed symmetrically against the middle of machine.

Dirichlet

Cyclic

Fig 12 : Boundaries conditions

Note : All the boundary conditions are set automatically by Flux 2D


FLUX 2D®9.20 Parameters Xd, Xq in magneto static

3. Parameters Xd, Xq in magneto static

3.1 Introduction This section will supply the simulation conditions and the possible analysis for each type of test. In this section, the parameters of equivalent schema will be studied. The menu “Physical” in the supervisor will be used to describe the physical propriety of each region, the menu “Solve” to give the solving parameter and launch the computation and the menu “Result” to analyse the results supplied by Flux 2D.

3.2 Angles corresponding to Xd and Xq

3.2.1 Purpose

Reminder : equivalent schema : The machine is represented in generator convention. The value X = L.ω corresponding to the synchronous reactance. This reactance is decomposed in two reactances, longitudinal and transversal, corresponding to the representation in the Park transformation.

The longitudinal reactance is obtained when the north pole of rotor is lined up with a stator

phase. The transversal reactance is in quadrature with the longitudinal position. In order to determine the positions of the rotor corresponding exactly to these two reactances, the angle of rotor will be used as parameter in a magneto-static simulation. The evolution of flux, picture of stator voltage, will give the two corresponding angles.


Parameters Xd, Xq in magneto static FLUX 2D®9.20

3.2.2 Physical conditions

Problem name Angle_det Problem type Magneto static Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation

Automatic coefficient (Symmetry and periodicity taken into account)

Type of periodicity Repetition number

of the periodicity about Z

Offset angle with respect to the X line (ZOX plane)

Even or odd periodicity/number of modeled poles

Rotation about Z axis with number of repetitions

2 0 Even (cyclic boundary conditions)

Name of material Type Initial relative

permeability Saturation magnetization (T)

STEEL_NLIN Isotropic scalar analytic saturation (arctg, 2 coeff.)

8000 1.6

Mechanical Set name

Comment Type Coord. System

Rotation axis

Pivot Point

External characteristic

ROTOR Rotor Rotation around one axis

ROTOR Rotation around one axis parallel

to Oz

(0,0,0) Multi-static

STATOR Stator FIXED - - - - AIRGAP Airgap COMPRES

SIBLE - - - -

Name of face region (air or vacuum type) Mechanical set AIR_1 STATOR AIR_2 ROTOR AIR_3 STATOR AIRGAP AIRGAP SHAFT ROTOR AM_1, AM_2, AM_3, AM_4, AM_11, AM_22, AM_33, AM_44, AQ_1, AQ_2, AQ_11, AQ_22,

ROTOR

COIL_1M, COIL_1P, COIL_2M, COIL_2P, COIL_3M, COIL_3P STATOR Name of face region (magnetic non conducting region type)

Material Mechanical set

ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR



Stranded coil Name Stranded coil with imposed current B_ROTOR 2 Name of face region (coil conductor region type)

Turn number

Associated coil component

orientation Symmetries and periodicities

Mechanical Set

FIELD_1M 215 B_ROTOR negative All conductors are in series

ROTOR

FIELD_1P 215 B_ROTOR positive All conductors are in series

ROTOR


ROTOR


ROTOR

Boundary condition automatically set by Flux 2D

Note : To create physic properties : In the supervisor, choose Geometry and physics [New]

3.2.3 Solving conditions

Solving parameters : - Angle of rotor [-10; 80], step [5] - Initial position of rotor: 0°

Note : To enter solving parameters : In the supervisor, choose Solve [Direct],

[Parametrisation], [Parameter] or [Direct] and click on

Note : To create links between currents : [Direct], [Parametrisation], [Parameter], [Link]

Note : To launch the solving process : [Computation], [Solve] or click on



3.2.4 Analysis

As the flux is the picture of voltage, it may be used to know the positions of the rotor corresponding to two reactances. When the flux is maximum, we obtain the direct position (pole lined up with a phase), when flux is minimum, the quadrature position. The parameter of angular position is applied on the airgap region, then the computation will be carried out on this one. According to the result curve, the direct position (θd) is 55 degrees compared with the initial position (0°) and 10 degrees for the quadrature position (θq).

°=°=

1055

Xq

Xd

θθ

θd = 55 ° θq = 10 °

3 4

6

Fig 3.2.a : Equiflux lines in the direct and quadrature axis positions

Note : To analyze the results : In the supervisor, choose Result

Note : To see flux lines : [Result],[Isovalue] or click on

Note : or click on To jump to an other angle : [Parameter],[Manager]

anager] or click on

Fig 3.2.b : Flux in COIL_3P curve according the position of rotor

Note : To obtain the flux : [Computation],[2D curves m then chosse [parameter], [Inductance], [Flux by region] and a Coil.

Note : To obtain the cursor : [2D Curve], [New cursor]

-3

-2

-1

0

1

0 25 50 75

degres

(E-3) Weber

Cur



3.3 Xd and Xq according to the stator current

3.3.1 Purpose

The values of synchronous reactance are determined for the nominal values of current, voltage and frequency of the machine. This simulation will allow then to determine the reactances but also to observe the influence of the saturation of the magnetic material for different values. The rotor is lined up with the stator coil corresponding to the third one.


Problem name XdXq_Is Problem type Magneto static Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation


• For this simulation, the current, supplying the stator phases, will be the parameter which

may be modified around the nominal value (7.84 Amperes). It will be given in total value. The field region will correspond to a source with a current equal to zero.

• The position of the rotor will be also considered as a parameter in order to see the influence of the saturation on the two reactances.










8000 1.6

Mechanical Set name


Rotation axis

Pivot Point



ROTOR Rotation around

one axis parallel to

Oz


STATOR Stator FIXED - - - - AIRGAP Airgap COMPRESSIBLE - - - -



Name of face region (air or vacuum type) Mechanical set AIR_1 STATOR AIR_2 ROTOR AIR_3 STATOR AIRGAP AIRGAP SHAFT ROTOR AM_1, AM_2, AM_3, AM_4, AM_11, AM_22, AM_33, AM_44, AQ_1, AQ_2, AQ_11, AQ_22,

ROTOR

Name of face region (magnetic non conducting region type)


ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR Stranded coil Name Stranded coil with imposed current B_ROTOR 0 B1 - 0.5 B2 -0.5 B3 1 Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR

COIL_1P 54 B1 Positive All conductors are in series

STATOR

COIL_1M 54 B1 negative All conductors are in series

STATOR


STATOR


STATOR


STATOR


STATOR





• Stator current : [100, 150, 200, 250, 270, 300, 350, 400, 450, 500, 550, 600, 650, 700,

750, 800, 1000, 1200] • Angle of rotor : [10 ; 55] • Initial position of rotor : 0°

Warning : Don’t forget to select multiparameter in the Solver or click on

3.3.4 Analysis

The reactances can not be obtained directly by Flux 2D. The flux values will be computed by Flux 2D for the different rotor positions and stator current. The two reactances will be computed from this flux by using the following expression:

( )

⎟⎠⎝⎞

⎜⎛

Φ×××=

4ATI

fX

54

π

Hz

puted for

one phase then two coils.

current

with - f corresponding to the nominal frequency : 50 - φ corresponding to the flux given by Flux 2D in Weber - 54 corresponding to the number of stator slots

The following curve gives the flux for different currents in direct position. It is com

100

200

300

400

0,5 1

(E3) Ampere

(E-3) Weber

Fig 3.3.a : Flux curve in COIL_3 in direct position according to the stator



Note : To create a group of two coils : [Supports], [Group manager]

s may be get back in order to be analyzed by a computer software like Excel. ach reactance will be computed for each value of current and a curve of the reactance evolution

Note : To obtain the flux values : Right click on the flux curve, choose [Values], [Write all in review file]

Warning : Do nott forget to give the turns number of each coil (54) in [Physics], [Coefficients], [Modify]

ll the flux valueA

Emay be plotted.

Is t in A F lux D in Wb F lux Q in Wb Xd in Ω Xq in Ω

100 3.42E-02 2.43E-02 21.48 15.24 150 6.33E-02 4.49E-02 21.47 15.24 200 9.48E-02 6.74E-02 21.45 15.24 250 1.26E-01 8.98E-02 21.43 15.23 270 1.58E-01 1.12E-01 21.40 15.22 300 1.70E-01 1.21E-01 21.38 15.21 350 1.89E-01 1.34E-01 21.35 15.20 400 2.20E-01 1.57E-01 21.30 15.18 450 2.50E-01 1.79E-01 21.22 15.15 500 2.80E-01 2.00E-01 21.12 15.09 550 3.09E-01 2.19E-01 20.98 14.85 600 3.36E-01 2.33E-01 20.74 14.36 650 3.60E-01 2.45E-01 20.35 13.87 700 3.80E-01 2.57E-01 19.83 13.44 750 3.96E-01 2.70E-01 19.19 13.07 800 4.09E-01 2.81E-01 18.51 12.73

1000 4.20E-01 2.93E- 1 0 17.82 12.44 1200 4.50E-01 3.38E-01 15.27 11.46

Fig 3.3.b : Reactances values computed from flux values computed by Flux 2D



REACTANCES / I Stator

10.00

12.00

14.00

16.00

18.00

20.00

22.00

0 200 400 600 800 1000 1200

stator current in At

Rea

ctan

ces

Xd in ohmXq in ohm

I nominal

Fig 3.3. c : Reactance in direct and quadrature axis according to stator current

A drop of reactance values can be noted above the nominal current. The machine is then designed at the limit of magnetic saturation.




FLUX 2D®9.20 Short-circuit tests

4. Short-circuit tests

4.1 Unloaded operating

4.1.1 Purpose

This simulation is necessary because of it is used as the initial condition for the different short circuit tests. As the magnetic circuit must not be saturated during the short circuit, the field voltage will correspond to 0.35 times the nominal voltage. In order to avoid the transient phenomena, the simulation will break down in two parts :

• a first part where the simulation duration will be long with some important time steps • a second part where the simulation duration will be short with little time steps


Problem name bemf Problem type Transient_magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation









Short-circuit tests FLUX 2D®9.20

Name of material Type Isotropic

value Initial relative permeability

Saturation magnetization (T)

STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)

8000 1.6

ALU_BAR B(H) : Linear isotropic

1

ALU_BAR J(E) : isotropic resistivity

2.7e-8 Ωm

Mechanical Set name


Rotation axis

Pivot Point

Imposed speed

ROTOR Rotor Rotation around

one axis ROTOR Rotation

around one axis

parallel to Oz

(0,0,0) 1500 rpm

STATOR Stator FIXED - - - - AIRGAP Airgap COMPRESSIBLE - - - - Name of face region (air or vacuum type) Mechanical set AIR_1 STATOR AIR_2 ROTOR AIR_3 STATOR AIRGAP AIRGAP SHAFT ROTOR Name of face region (magnetic non conducting region type)



Circuit ME_CC Components Values V1 8.76 V R1, R2, R3, R6 109

L1, L2, L3 1.104 mH L4 8.8 mH R5,R7,R8, ……. …..R23, R24, R25 2.89 10-6 Ω

L5,L6,L7, …….. …..L22, L23, L24 10-9 H



Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1 181.2 mΩ B2 181.2 mΩ B3 181.2 mΩ Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR

Name of face region (solid conductor

region type)

Material Associated solid conductor

Orientation Mechanical set

AM_1 Alu_bar M_AM1 positive ROTOR AM_2 Alu_bar M_AM2 Positive ROTOR AM_3 Alu_bar M_AM3 Positive ROTOR AM_4 Alu_bar M_AM4 Positive ROTOR AM_11 Alu_bar M_AM11 Positive ROTOR AM_22 Alu_bar M_AM22 Positive ROTOR AM_33 Alu_bar M_AM33 Positive ROTOR AM_44 Alu_bar M_AM44 Positive ROTOR AQ_1 Alu_bar M_AQ1 Positive ROTOR AQ_2 Alu_bar M_AQ2 Positive ROTOR AQ_11 Alu_bar M_AQ11 Positive ROTOR AQ_22 Alu_bar M_AQ22 Positive ROTOR



Name of solid conductor 2 terminals

Symmetries and periodicities Number of conductors in parallel

M_AM1 Number of conductors in parallel 1 M_AM2 Number of conductors in parallel 1 M_AM3 Number of conductors in parallel 1 M_AM4 Number of conductors in parallel 1 M_AM11 Number of conductors in parallel 1 M_AM22 Number of conductors in parallel 1 M_AM33 Number of conductors in parallel 1 M_AM44 Number of conductors in parallel 1 M_AQ1 Number of conductors in parallel 1 M_AQ2 Number of conductors in parallel 1 M_AQ11 Number of conductors in parallel 1 M_AQ22 Number of conductors in parallel 1


• To simulate an unloaded circuit at stator, some important values resistors will be used. • The rotor will be lined up with the coil 1 (85°).


• Initialized by static computation • Time length : [0,20], step [5] • Time length : [20,20.04], step [0.001] • Initial position of rotor : 85 °



4.1.4 Analysis

In the first part of simulation, each points of stator voltage and current must be close to zero because of it corresponds to a complete rotation of rotor (Fig 4.1.3.a). The transient phenomena will no exist before beginning the second part composed of short time steps.

-50

0

49,999

0 0,01 19,999E-3 0,03 39,999E-3

(20,16+ x) -50

0

49,999

5 10 15 20

• Voltage

Fig 4.1.3.a : Voltage curve between [5 , 20.2] s Fig 4.1.3.b : Voltage on two last period

In the second part, the unloaded steady state is reached in 2 periods and at the last step, the voltage of the phase 1 is equal to zero. The frequency is equal to 50 Hz.

• Current

-50E-9

0

50E-9

0 0,01 19,999E-3 0,03 39,999E-

(20,16+ x)

Fig 4.13.c : Current curve on the two last periods



The current can be considered as sinusoidal and close to zero Ampere.

Note : To create multicurve picture : On the curve, click right and choose [Properties], select several curve in Selection Menu, choose Superimposed and the Range of Xaxis in Display Menu

• Spectral analysis

25

50

75

0 2,5 5 7,5 10

Volt

SPECTRUM Spectr_Vs1From Vs1Fundamental 47,618

The spectral analysis allows checking the quality of signal.

Fig 4.13.d : Spectrum of the phase A voltage

The preponderance of the fundamental harmonic shows that the harmonics of upper order are practically not present.

Note : To create spectrum : [Computation], [2D spectrum manager] or click on



4.2 Single phase short circuit

4.2.1 Purpose

The purpose of this simulation is to know the behavior of the generator further to a sudden short-circuit on a phase only (between one phase and neutral). This short-circuit will be activated from an unloaded operating of the alternator at the steady state speed. The different rotor and stator currents, the torque and the phenomena in the absorbers will be studied in particular, with a transient magnetic analysis.


The short circuit will be triggered from a unloaded operating in steady state speed. Exactly, at the end of the simulation unloaded_operating. The phase voltage on which the short circuit is triggered must be close to zero at this moment. Problem name SC_MONO Problem type Transient_magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation












8000 1.6


1


2.7e-8 Ωm



Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm




Circuit ME_CC Components Values V1 8.76 V R1, R6 10-6 Ω R2, R3 10+6 Ω L1, L2, L3 1.104 mH L4 8.8 mH R5,R7,R8, ……. …..R23, R24, R25 2.89 10-6 Ω

L5,L6,L7, …….. …..L22, L23, L24 10-9 H

Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1 181.2 mΩ B2 181.2 mΩ B3 181.2 mΩ



Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR


region type)










Warning : You must assign correctly each region to his corresponding component in the external circuit.

• The sudden short-circuit will be activated on the phase 1, the others will stay opened. • The field alimentation corresponds to 0.35 x the nominal voltage unloaded. • The phases in open circuit will be represented by important resistors and the phases in

short circuit will be represented by weak resistors.


• From the last step of the back emf simulation • Time length : [0.5], step [0.0005s]

Warning : The last step of the phase A voltage in the unloaded simulation must be close to zero !

Note : To prepare Transient startup : In the supervisor, choose Transient Startup

Note : To prepare batch computation : In the supervisor, choose Solve [Direct], [Computation], [Prepare batch computation]



4.2.4 Analysis

• Flux lines The evolution of flux lines in the magnetic circuit can be displayed.

Fig 3.6.1.b t =0.001 s after the short circuit Fig 3.6.1.c t =0.05 s after the short circuit

1

2

3

4

5

6

7

89

10

11

12

3

4

5

6

78

9

1011

• Currents

The short circuit being activated at armature on the phase 1, there is a current only in this phase. This current is sinusoidal and contains a d-c component which must cancel after a time corresponding to a time constant of exponential shape.

Fig 3.6.1.d : Current in the A phase with his d-c component

-50

0

50

99,999

150

20,399 20,5 20,6 20,699 20,8

s.

Ampere



The stator short circuit influences also the field current. This current consists of DC and AC components. The DC component must decrease with two time constants corresponding to the transient and sub-transient components. The AC component decays with time constant identical to that DC component of armature current.

Fig 3.6.1.e : Field current with DC and AC components

0

5

10

15

20,399 20,5 20,6 20,699 20,8

s.

Ampere

• Torque In this case, the torque allows displaying the imbalance of the system with a DC component on the phase in short circuit. This DC component corresponds to the rotor and stator losses. Oscillations on the curve correspond to a 2 order harmonic because of only the A phase is flowed by a current.

-50

0

49,999

20,399 20,5 20,6

s.

N.m

Fig 3.6.1.e : Torque curve with DC component and 2 order harmonic



4.3 Three phase short circuit

4.3.1 Purpose

The purpose of this simulation is to know the behavior of the generator further to a sudden three phase short circuit. This short circuit will be activated from an unloaded operating of the alternator at the steady state speed. The different rotor and stator currents, the torque and the phenomena in the absorbers will be studied in particular, with a transient magnetic analysis. This test allows also determining the different values of reactances and time constants. The sustained, transient and sub transient components will be then defined indirectly from the values of current computed by Flux 2D.


The short circuit will be triggered from an unloaded operating in steady state speed. Exactly, at the last step of the simulation unloaded operating. Problem name SC_THREE Problem type Transient_magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation












8000 1.6


1


2.7e-8 Ωm



Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm




Circuit ME_CC Components Values V1 8.76 V R1, R2, R3, R6 10-6 Ω L1, L2, L3 1.104 mH L4 8.8 mH R5,R7,R8, ……. …..R23, R24, R25 2.89 10-6 Ω

L5,L6,L7, …….. …..L22, L23, L24 10-9 H

Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1 181.2 mΩ B2 181.2 mΩ B3 181.2 mΩ




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR


region type)










• The sudden short-circuit will be activated on the three phases. • The field alimentation corresponds to 0.35 x the nominal voltage unloaded to avoid the

effects of magnetic saturation.


• From the last step of the back emf simulation • Time length : [1], step [0.0005s]

Warning : The last step of the phase 1 voltage in the unloaded simulation must be close to zero !



4.3.4 Analysis

The current, flowing each phase of stator, is given as a function of time:

''' ''' dd Tt

oT

t

osac eIeIII−−

×+×+=

With – Is : sustained current - I’o , T’d : transient current and time constant - I’’o , T’’d : subtransient current and time constant

• The method to define the different components is : - Get back all the values of current computed by Flux 2D in a computing software - Define the minimum and maximum envelopes of current for each phase - Compute the periodic armature current component in carrying out the half-difference of

the ordinates of upper and lower envelopes for each phase. - The periodic component is determined as a mean value of the periodic component in

three phases; - Determine the transient and sub-transient components, the value of the sustained short

circuit current is subtracted from the periodic component and the remainder is plotted on paper with a semi-log scale.

- The transient reactance is computed from the following formula :

)'('

IIsEX d +

=

with : E unloaded maximum voltage before the short circuit. The time constant T’d is determined from the previous curve.

lue int on the straight line where the current is equal to 0.606

mes I’ gives the half of T’d.

To determine I’ and T’d from the previous curve : The curve striving towards a straight line of which the extrapolation to t = 0 s gives the va

f I’. The duration until the pooti



-100

-50

0

20,399 20,5 20,6 20,699 20,8

s.

Ampere

0

49,999

100

150

20,399 20,5 20,6 20,699 20,8

s.

Ampere

-100

-50

0

20,399 20,5 20,6 20,699 20,8

s.

Ampere

Fig 4.3.2.a : Short circuit currents in the three phases on 0.4 s

Note : To create multicurve picture : On the curve, click right and choose [Properties], select several curve in Selection Menu, choose Side by side and the Range of X axis in Display Menu

- The sustained current, computed by Flux 2D, strives towards 8.97 Amperes.

Periodic

component Phase 1

Periodic component

Phase 2

Periodic component

Phase 3

Periodic component average = I

I - Is

(Imax – Imin) / 2 (Imax - Imin) / 2 (Imax - Imin) / 2 Is = 8,97 A 76,609 79,807 72,416 76,278 67,308 54,846 55,814 53,005 54,555 45,585 43,425 42,878 42,149 42,817 33,847 35,712 35,233 34,904 35,283 26,313 29,951 29,579 29,420 29,650 20,680 25,506 25,216 15,885 22,203 13,233 22,077 21,845 21,917 21,946 12,976 19,426 19,227 19,379 19,344 10,374 17,374 17,191 17,389 17,318 8,348 15,792 15,615 15,827 15,745 6,775 14,561 14,397 14,601 14,520 5,550 13,602 13,448 13,641 13,563 4,593 12,845 12,697 12,882 12,808 3,838 12,238 12,094 12,273 12,202 3,232



Periodic component

Phase 1

Periodic component

Phase 2

Periodic component

Phase 3

Periodic component average = I

I - Is

11,745 11,604 11,779 11,710 2,740 11,340 11,201 11,372 11,304 2,334 11,002 10,866 11,033 10,967 1,997 10,719 10,585 10,748 10,684 1,714 10,480 10,348 10,508 10,445 1,475 10,277 10,146 10,303 10,242 1,272 10,103 9,975 10,127 10,068 1,098 9,954 9,829 9,977 9,920 0,950 9,825 9,704 9,848 9,792 0,822 9,715 9,596 9,735 9,682 0,712

Fig 4.3.2.b : Exemple of periodic components on 0.5 s

I - Is

0,1

1,0

10,0

100,0

0 0,1 0,2 0,3 0,4 0,5 0,6

Temps

Am

père

s

I - Is

I’ = 26 A

0.5 x T’d

0.606 x I’

Fig 4.3.2.c : Graphic to find the transient components

With the results supplied by Flux 2D and found on the curve, the transient components are :

=+

=′)2697.8(

176dX

5.03 Ω . and 07505.0 =′× dT 0.15 s s then T’d =



To determine I’’ and T’’d : - Compute the difference between the curve of periodic component and the straight line of

I’ and plotted it on a semi–log paper. - Extrapolated the straight line obtained until t = 0 in order to define I’’. - The sub-transient reactance is computed from the following formula :

)'( IIIsEX d ′′++

=′′


FLUX 2D®9.20 StandStill Frequency Reponse (SSFR)

5. StandStill Frequency Reponse (SSFR)

5.1 Direct and quadrature axis determination

5.1.1 Purpose

Before launching the SSFR simulations, it is necessary to determine the positions of the rotor corresponding to the direct or quadrature axis. Each position is determined by a particular test even the supply voltage of armature is not identical in both case. The diagrams of these different tests are presented below:

Fig 5.1.1.a Positionning of direct axis

100 Hz

Voltage

The simulations will be carried out in AC steady state magnetic 2D application at low voltage with the rotor position as parameter. In both cases, the armature is supplied by a voltage source set up at 100 Hz, as describe in the IEEE standard, with a phase in open circuit or not. The direct and quadrature axis will correspond, in both case, at the position where the field voltage will be minor.


StandStill Frequency Reponse (SSFR) FLUX 2D®9.20

100 Hz

Voltag

Fig 5.1.1.b Positionning of quadrature axis

5.1.2 Physical and solving conditions

The voltage of the source will be 1.5 Volts. It corresponds to one percent of the nominal voltage in order to avoid exceed currents (V =0.1xVn). The rotor position will be used as a parameter and will change of 2.5 degrees at each step.

• Direct simulation Problem name AC_SSFR_DIRECT_POS Problem type Magnetic AC 2D Frequency 100 Hz Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material

Type Isotropic value

Initial relative permeability


Type of equivalent B(H) curve


8000 1.6 Sine Wave flux density


1


2.7e-8Ωm



Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm




Circuit MH_SSFR_POS_DIRECT Components Values V1 1.5 V L1, L2, L3 1.104 mH L4 8.8 mH L5 15.6mH L6 11.2mH Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1 181.2 mΩ B2 181.2 mΩ B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω




Turn number



Mechanical Set

FIELD_1M 215 B_ROTOR Negative All conductors are in series

ROTOR

FIELD_1P 215 B_ROTOR Positive All conductors are in series

ROTOR


ROTOR


ROTOR


STATOR

COIL_1M 54 B1 Negative All conductors are in series

STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set

AM_1 74 B5 Positive All conductors are in series

ROTOR

AM_2 74 B5 Negative All conductors are in series

ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR

AQ_1 74 B6 Positive All conductors are in series

ROTOR

AQ_2 74 B6 Negative All conductors are in series

ROTOR


ROTOR


ROTOR


Solving parameters : - Rotor positions : [-5°; 85°], step [2.5°]

• Quadrature simulation Problem name AC_QUADRATURE_SSFR Problem type AC magnetic 2D Frequency 100 Hz Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation










Name of material








1


2.7e-8Ωm

Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm






Circuit AC_SSFR_Q_AXIS

Components Values V1 1.5 V R1 104 Ω L1, L2, L3 1.104 mH L4 8.8 mH R2,R3,R4, ……. …..R19, R20, R21 2.89 10-6 Ω L5,L6,L7, …….. …..L22, L23, L24 10-9 H Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




region type)



AM_1 Alu_bar M_AM1 Positive ROTOR AM_2 Alu_bar M_AM2 Positive ROTOR AM_3 Alu_bar M_AM3 Positive ROTOR AM_4 Alu_bar M_AM4 Positive ROTOR AM_11 Alu_bar M_AM11 Positive ROTOR AM_22 Alu_bar M_AM22 Positive ROTOR AM_33 Alu_bar M_AM33 Positive ROTOR AM_44 Alu_bar M_AM44 Positive ROTOR AQ_1 Alu_bar M_AQ1 Positive ROTOR AQ_2 Alu_bar M_AQ2 Positive ROTOR AQ_11 Alu_bar M_AQ11 Positive ROTOR AQ_22 Alu_bar M_AQ22 Positive ROTOR





Solving parameters : - Rotor positions : [-5°; 85°], step [2.5°]



5.1.3 Analysis

• The voltage will be taken at the field terminals. It is corresponding to B_ROTOR coil component.

• The found angle is given in comparison to the initial position. • The voltage amplitude will be chosen equal to the one of the classical SSFR. Direct simulation

Fig 5.1.3.a Field voltage to determine direct axis

The direct axis position is close to 10 ° degree.

Note : To create a group : [Supports], [Group] and click on the region concerned.



Quadrature simulation

Fig 5.1.3.b Field voltage to determine quadrature axis

The quadrature axis position is close to 55 ° degree. • These two positions will be used as initial position for each SSFR test, direct or

quadrature.



5.2 Classical SSFR

5.2.1 Purpose

This method is also used to determine the parameters of the machine. From the evolution of the inductance in function of electrical pulsation, the different time constants and reactances can be evaluated. In particular, the transient and sub-transient time constants in open circuit or short-circuit. The rotor is assumed at standstill and a weak voltage with a frequency varying from 1 mHz to 400 Hz is applied to the stator. The simulation will be carried out in AC steady state magnetic 2D application at low voltage with the frequency as parameter. The result will give the current and voltage values in complex. They will be analyzed in order to compute the reactances and time constants looked for.


Problem name AC_QUADRATURE_SSFR Problem type AC magnetic 2D Frequency 100 Hz Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material








1


2.7e-8Ωm



Mechanical Set name


Rotation axis

Pivot Point

Imposed speed

(0,0,0) ROTOR Rotor Rotation around


around one axis

parallel to Oz

1500 rpm




Circuit AC_SSFR_Q_AXIS Components Values V1 1.5 V R1 104 Ω L1, L2, L3 1.104 mH L4 8.8 mH R2,R3,R4, ……. …..R19, R20, R21 2.89 10-6 Ω

L5,L6,L7, …….. …..L22, L23, L24 10-9 H

Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR


region type)











• Stator frequency : [0.001, 0.005, 0.01, 0.02, 0.04, 0.08, 0.1, 0.2, 0.4, 0.8, 1, 2, 4, 5, 6, 8,

10, 20, 40, 50, 80, 100, 200, 400] • Initial position of rotor : 10°

Note : To enter parameters : In the supervisor, choose Solve [Direct], [Computation], [Prepare batch computation]



5.2.4 Analysis

• Theoric From the Bode diagram of inductance, different parameters of generator can be determined. Indeed, the poles and zeros of the inductance transfer function correspond to the different reactances and time constants. The expression of transfer function is:

( ) ( )( ) ( )pTpT

pTpTLpL

dodo

dccdccdd ′′+×′+

′′+×′+×=

1111

)(

With : - T’dcc = transient time constant in short circuit armature - T’’dcc = sub-transient time constant in short circuit armature - T’do = transient time constant in open circuit - T’’do = transient time constant in open circuit The corresponding curve is the following one:

Ld(jw

L’

Ld

L’’d

1 / T’do 1 / T’dcc 1 / T’’do 1 / T’’dccω

Fig 5.2.3.a Module of Ld(jw)

This curve shows that the transient and sub-transient reactances and time constants can be

determined thanks to the different steps. For an example, in extending the curve until pulsation = 0 for the synchronous reactance.

The inductance will be computed by:

ωω

ωj

rjZjL ad

d−

=)(

)(

with:

- 21)( xVarmj =ω with ½ for connection

IarmZd between phases



• Analysis

1

2

3

4

5

100 200 300 400

hertz

Ampere

CURVE I_modCircuit / Magnitude CurrentFrequencyB1 ; Phase (Deg): 0

100

125

150

175

100 200 300 400

hertz

Degree

CURVE I_phaseCircuit / Phase CurrentFrequencyB1 ; Phase (Deg): 0

Fig 5.2.3.b Module of armature current Fig 5.2.3.c Phase of armature current The voltage of armature is constant with a phase of 0°. The armature current is determined in module and phase for each frequency:

Note : To obtain phase and module in 2D curve manager : [Circuit], [module current] or [phase current] and choose the concerned component. The following method is used to obtain the Bode diagram of inductance and the value of

synchronous reactances and time constants:

For each frequency : • Computation of pulsation • Computation of impedance in module and phase from the voltage and current of armature • Computation of real and imaginary parts of complex inductance from :

ωφ

××

=2

)sin( zr

ZL

ωφ 1)

2)cos(

( ×−×

= armz

i rZ

L

• Computation of module and phase of complex inductance from :

²² LiLrL += πφ

180)( ×= i

r

lLLATAN

• Plotting of gain and phase diagram on semi-log paper



VOLTAGE CURRENT Vs/Is L(p) f w Vs (V) Ph (°) Is (A) Ph I (°) Module Phase Part_R Part_I Module Phase

0,001 0,01 2,12 0 5,85 179,86 0,36 359,86 0,070 -0,00008 0,070 0,07 0,005 0,03 2,12 0 5,85 179,30 0,36 359,30 0,070 0,00153 0,070 -1,25 0,01 0,06 2,12 0 5,85 178,61 0,36 358,61 0,070 0,00317 0,070 -2,60 0,02 0,13 2,12 0 5,82 177,26 0,36 357,26 0,069 0,00636 0,070 -5,24 0,04 0,25 2,12 0 5,73 174,75 0,37 354,75 0,067 0,01234 0,069 -10,38 0,08 0,50 2,12 0 5,45 170,96 0,39 350,96 0,061 0,02190 0,065 -19,82 0,1 0,63 2,12 0 5,30 169,74 0,40 349,74 0,057 0,02522 0,062 -23,97 0,2 1,26 2,12 0 4,72 167,75 0,45 347,75 0,038 0,03036 0,049 -38,70 0,4 2,51 2,12 0 4,32 167,89 0,49 347,89 0,021 0,02351 0,031 -48,91 0,8 5,03 2,12 0 4,09 165,81 0,52 345,81 0,013 0,01395 0,019 -47,82 1 6,28 2,12 0 4,02 164,18 0,53 344,18 0,011 0,01155 0,016 -45,26 2 12,57 2,12 0 3,70 155,44 0,57 335,44 0,009 0,00632 0,011 -33,70 4 25,13 2,12 0 3,08 140,60 0,69 320,60 0,009 0,00337 0,009 -21,21 5 31,42 2,12 0 2,80 134,80 0,76 314,80 0,009 0,00274 0,009 -17,73 6 37,70 2,12 0 2,54 129,95 0,83 309,95 0,008 0,00230 0,009 -15,18 8 50,27 2,12 0 2,12 122,49 1,00 302,49 0,008 0,00175 0,009 -11,75

10 62,83 2,12 0 1,80 117,17 1,18 297,17 0,008 0,00141 0,008 -9,57 20 125,66 2,12 0 0,98 104,63 2,16 284,63 0,008 0,00073 0,008 -5,00 40 251,33 2,12 0 0,51 97,66 4,20 277,66 0,008 0,00039 0,008 -2,71 50 314,16 2,12 0 0,41 96,25 5,23 276,25 0,008 0,00033 0,008 -2,28 80 502,65 2,12 0 0,26 94,14 8,31 274,14 0,008 0,00024 0,008 -1,64 100 628,32 2,12 0 0,20 93,43 10,37 273,43 0,008 0,00021 0,008 -1,43 200 1256,6

4 2,12 0

0,10 91,97 20,61 271,97 0,008 0,00014 0,008 -0,96 400 2513,2

7 2,12 0

0,05 91,20 41,06 271,20 0,008 0,00010 0,008 -0,69

Fig 5.2.3.d : Computation of impedance and inductance for each frequencies

Note : To obtain current values : Right click on the current curves, choose [Values], [Write all in review file] then copy and paste in the board

L(p) - Module

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

0.001 0.01 0.1 1 10 100 1000

Frequency (Hz)

L(p)

(H)

F2D results

Equivalent transferfunction

L(p) - Phase

-60.00

-50.00

-40.00

-30.00

-20.00

-10.00

0.00

10.000.001 0.01 0.1 1 10 100 1000

Frequency (Hz)

Phas

e (d

egre

s)

F2D results

Equivalent transfer function

Fig 5.2.3.e : Gain diagram Fig 5.2.3.f Phase diagram



- The synchronous reactance is obtained in extending the gain bode diagram to ω = 0 and in using :

ωω ×= =0LdXd then, in our case : Xd = 21.98 Ω

• For information

An approximation of the sub-transient reactance X’’d can be determined with the value of inductance at high frequency, always with the same computation formula used previously.

In our case, we find:

159.3142005.02 ××=××=′′ ∞→ ωωLddX X’’d = 2.57 Ω

arning : It is indicated only as a method but do not correspond to a standard. W


FLUX 2D®9.20 Loaded on the network

6. Loaded on the network

6.1 Unloaded on the network

6.1.1 Purpose

The purpose is to simulate the generator unloaded before connecting it at the network. Indeed, the three phases of the generator, operating unloaded, must be in phase with those of the network before to link both. Phases of network and generator will be compared in amplitude and angle. In order to avoid the transient phenomena, the [initialised by a static computation] option will be used. The first time step will give the initial magnetic state in the entire machine.


• These conditions correspond to the transient magnetic static simulation. - The network will be represented by a voltage supply, an inductance and a resistor. - The generator will be adjusted for an unloaded operating at the nominal voltage.

Problem name MT_SOLV_UNLOADED Problem type Transient Magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation









Loaded on the network FLUX 2D®9.20

Name of material







Mechanical Set name


Rotation axis

Pivot Point

Coupled load




Oz

(0,0,0) Moment of inertia : 0.1215kg.m² Friction coefficient : 0.016N.m.S Drag Torque : -2.51 N.m Initial velocity : 1500 rpm Position at time t=0s:0°

STATOR Stator FIXED - - - - AIRGAP Airgap COMPRESS

IBLE - - - -

Name of face region (air or vacuum type) Mechanical set AIR_1 STATOR AIR_2 ROTOR AIR_3 STATOR AIRGAP AIRGAP SHAFT ROTOR Name of face region (magnetic non conducting region type)



Circuit TM_NETWORK Components Values I_ROTOR -5 A V1 127 V, 50 Hz, 0° V2 127 V, 50 Hz, -120° V3 127 V, 50 Hz, 120° R1, R2, R3 106 Ω L7, L8, L9 10-9H



Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1 181.2 mΩ B2 181.2 mΩ B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


6.1.3 Solving parameters

• Initial position of rotor : 90° • Time step [0.0005s], study time limit [0.2], • Initialized by static computation

Note : This angle corresponds to the rotor position in the axis of the phase 1 which will be taken as reference in the transient simulation.

• The drag torque corresponds only to torque generate by the mechanical friction • The field will be supplied by a continuous current alimentation. • The phase 1 will be chosen as the reference phase for the network, that’s why the rotor is

positioned in the axis of this phase.

Note : The supply voltage used to represent the network is a sinusoidal shape.



6.1.4 Analysis

• First time step

1

23

4

5

6

7

8

9

10

11

Only the flux lines will be checked.

Fig 5.1.3.a : Flux lines with the rotor at 90 °

• Transient magnetic simulation

- Speed The rotor speed must little change during the 0.2 seconds.

Fig 5.1.3.b : Rotor speed curve


1,475

1,5

1,524

1,55

0,05 99,999E-3 0,15 0,2

s.

(E3) rpm


- Voltage The network voltage and generator voltage will be superimposed.

-199,999

-99,999

0

100

200

0,05 99,999E-3 0,15 0,2

V_STATOR_1Circuit / VoltageTimeB1 ;

V_NETWORK_1Circuit / VoltageTimeV1 ;

Fig 5.1.3.c : Network voltage and stator voltage comparison

The voltages are opposite, which is normal.

Fig 5.1.3.d : Zoom between 0.15 and 0.2 seconds



Both voltages are well identical and have a period of 0.02 s.

Note : To obtain the period : create two cursors with [2D curves], [new cursor], and check the time on the second cursor with the difference on X axis.

- Current

-500

0

500

0,05 99,999E-3 0,15 0,2

s.

(E-6) Ampere

I_B1Circuit / CurrentTimeB1 ;

Fig 5.1.3.e : Curve of current supplied by the generator

The generator is well unloaded since the current is close to zero (10-6).



6.2 Loaded on the network without regulation

6.2.1 Purpose

In this simulation, the generator will be loaded at 30 % of his nominal power. Therefore, neither the field current nor the drag torque will be fitted to this operating point. This test corresponds in reality to the pulling out of synchronism of the generator without regulator.


Problem name MT_SOLV_LOADED Problem type Transient Magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material





8000 1.6

Mechanical Set name


Rotation axis

Pivot Point

Coupled load




Oz

(0,0,0) Moment of inertia : 0.1215kg.m² Friction coefficient : 0.016N.m.S Drag Torque : -2.51 N.m Initial velocity : 1500 rpm Position at time t=0s : 90°


IBLE - - - -






Circuit TM_NETWORK Components Values I_ROTOR -5 A L1, L2, L3 1.104e-3 L4 8.8mH L5 15.6mH L6 11.2mH V1 254 V, 50 Hz, 0° V2 254 V, 50 Hz, -120° V3 254 V, 50 Hz, 120° R1, R2, R3 72.14 Ω L7, L8, L9 0.1717 H Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR

AQ_11 74 B5 All conductors are in series

Positive ROTOR

AQ_22 74 ROTOR B5 Negative All conductors are in series

Boundary condition automatically set by Flux 2D • Load conditions at 30 %


• Initial position of rotor : 90°

The power will be equal to 0.3 x 2400 = 720 Watts In imposing a different phase equal to a cosinus of 0.8, the resulting current will be of

2.42 Amperes

• Time step [0.0005s], study time limit [0.2], • Initialized by static computation



6.2.4 Analysis

- speed

On the curve, the speed falls rapidly. It corresponds to the pulling out of synchronism of the generator.

Fig 6.2.3.a : rotor speed curve

- Voltage

There is a different phase between the generator voltage and the network voltage. The amplitudes of voltages are not the same too.



6.3 Loaded on the network with appropriated motor torque

6.3.1 Purpose

With the previous result, we can see that the generator has not the necessary absorbed power in order to provide the load need by the network. In this simulation, the generator is always loaded at 30% of his nominal power but the torque setting to the rotor is adapted to the output power. The excitation current is the same. The operating point is then changed but the internal generated voltage stays constant. It corresponds to the following diagram :

Old point

New point with adapted torque Constant

active power

Fig 6.3.1.a : Power diagram with modification of torque


• The torque setting to the rotor is the addition of torque corresponding to the output power and torque corresponding to the Joules losses. In our case, this supplementary torque corresponds approximately to 2.3 N.m.

• The Joules losses are computed with the current corresponding to 30% of the nominal power that is to say 2.42 Amperes.

Problem name MT_SOLV_LOADED_T Problem type Transient Magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation










Name of material





8000 1.6

Mechanical Set name


Rotation axis

Pivot Point

Coupled load




Oz



IBLE - - - -






Circuit TM_NETWORK

Components Values I_ROTOR -5 A L1, L2, L3 1.104e-3 L4 8.8mH L5 15.6mH L6 11.2mH V1 254 V, 50 Hz, 0° V2 254 V, 50 Hz, -120° V3 254 V, 50 Hz, 120° R1, R2, R3 72.14 Ω L7, L8, L9 0.1717 H Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set

AM_1 74 B5 ROTOR Positive All conductors are in series


ROTOR


ROTOR


ROTOR

AM_11 Negative 74 B5 All conductors are in series

ROTOR


ROTOR


ROTOR


ROTOR

AQ_1 Positive 74 B6 All conductors are in series

ROTOR


ROTOR


ROTOR


ROTOR



Initial position of rotor : 90° •

• Time step [2E-3], study time limit [7], • Initialized by static computation

6.3.4 Analysis

The speed of the rotor will give a picture of the stabilisation or not of generator. In our case, after two oscillation periods, the speed increases rapidly. The generator will never reach a stabilized point.



1,5

1,6

1,7

1,8

1 2 3 4 5 6

s.

(E3) t/mn

Vitesse rotorMecanique / Vitesse rotationTemps

Fig 6.3.3.a : Rotor speed evolution

This divergence can be explained by the equation of electromagnetic torque:

δω

sin3×

××××

=d

em XVEpC

At no-load, E is lined up with V then the angle δ is equal to zero. If the field current has not changed, the fem voltage stays equal at V then 63.5 V.

)3

arcsin(VEp

XC dem

×××××

=ωδ

In order to stabilize the speed, the electromagnetic torque must be identical to the mechanical torque setting to the rotor. As the torque applied to the shaft is 2.3 Nm, the internal angle should be:

65,25E-3

65,5E-3

65,75E-3

0,066

6,969 6,979 6,989 7

s.

(E6) Deg.

Fig 6.3.3.b : Evolution of rotor position on the last period

At 30% of nominal power, it would correspond to an angle of 38.8 °. The internal angle can be computed from the position of the rotor on the last period.



On this period, the rotor has turned of 210 °. As the machine has 2 pairs of poles, one electrical period should correspond to 180°, then the internal angle has moved from zero to 30°. This angle does not correspond to the nominal angle and the generator may not reach the nominal point. The supplementary torque associated to the initial speed creates an inertia too high for the electromagnetic torque which can not block the acceleration of rotor.

Note : To obtain the position : [Computation], [2D spectrum manager] and choose [mechanical], [Position]

Note : To obtain the angle : Create two [New cursor] and read on the second the difference on the Y axis.



6.4 Loaded on the network with appropriated field current and motor torque

6.4.1 Purpose

In this simulation, the generator is always loaded at 30% of his nominal power but now, both adjustment parameters are modified. As there is always no regulation, the field current and the torque setting to the rotor will correspond to the nominal point. Even if they are right, there will be however, a response time enough important before reaching the equilibrate point.


Problem name MT_SOLV_LOADED_F_T Problem type Transient Magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation


- Computation of the field current : It is computed from the Behn-Eshenburg diagram :

With :

Generator

Synchronous Motor

Absorbed

Q < 0 Supplied

δ

• the single voltage V = 63.5 V • the armature nominal current I = 2.42 A • the synchronous reactance X = 15.8 Ω • the dephasing angle ϕ = 36 ° (cos ϕ = 0.8) • and in negligecting the resistance. Graphically, the fem voltage found is about 167 V. If we consider the same ratio for the field current as for the fem voltage, the new current corresponding to this operate point is about 6.85 Amperes.









Name of material





8000 1.6

Mechanical Set name


Rotation axis

Pivot Point

Coupled load




Oz



IBLE - - - -






Circuit TM_NETWORK

Components Values I_ROTOR -6.85 A L1, L2, L3 1.104e-3 L4 8.8mH L5 15.6mH L6 11.2mH V1 254 V, 50 Hz, 0° V2 254 V, 50 Hz, -120° V3 254 V, 50 Hz, 120° R1, R2, R3 72.14 Ω L7, L8, L9 0.1717 H Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR



• Initial position of rotor : 90° • Time step [0.002s], study time limit [20], • Initialized by static computation



6.4.4 Analysis

In this various results, the speed of the rotor, the current supplied by the armature and the active power will be analyzed more particularly in order to verify if the nominal point is reached.

• speed The speed seems to stabilize close to 1500 rpm. But on the zoom, we can conclude that 20 seconds are not sufficient to reach the steady state speed.

• Current

The oscillations on the current are due to the variation of speed during the stabilization phase. The value of current is not exactly identical to the nominal point. The approximations on the computation of nominal point, the simplification on the Behn-Eshenburg diagram and the Joule losses can justify this deviation





Case 1: Xd Xq position Case 2: Xd and Xq Case 3: back emf computation Case 4: single phase short circuit Case 5: three phase short circuit Case 6: direct axis determination for SSFR test Case 7: quadrature position for SSFR test Case 8: SSFR test Case 9: Loaded on the network (unload) Case 10: Loaded on the network (30% load) without regulation

Case 11: Loaded on the network (30% load) with appropriated motor torque

Case 12: Loaded on the network (30% load) with appropriated field current and motor torque

APPENDIX



CASE 1: Xd Xq position Problem name Angle_det Problem type Magneto static Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation











8000 1.6

Mechanical Set name


Rotation axis

Pivot Point





Oz


STATOR Stator FIXED - - - - AIRGAP Airgap COMPRESSIBLE - - - - Name of face region (air or vacuum type) Mechanical set AIR_1 STATOR AIR_2 ROTOR AIR_3 STATOR AIRGAP AIRGAP SHAFT ROTOR AM_1, AM_2, AM_3, AM_4, AM_11, AM_22, AM_33, AM_44, AQ_1, AQ_2, AQ_11, AQ_22,

ROTOR

COIL_1M, COIL_1P, COIL_2M, COIL_2P, COIL_3M, COIL_3P STATOR Name of face region (magnetic non conducting region type)





Stranded coil Name Stranded coil with imposed current B_ROTOR 2 Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


Solving parameters : • Angle of rotor [-10 ; 80], step [5] • Initial position of rotor: 0°



CASE 2: Xd and Xq

Problem name XdXq_Is Problem type Magneto static Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation











8000 1.6

Mechanical Set name


Rotation axis

Pivot Point





Oz


STATOR Stator FIXED - - - - AIRGAP Airgap COMPRESSIBLE - - - - Name of face region (air or vacuum type) Mechanical set AIR_1 STATOR AIR_2 ROTOR AIR_3 STATOR AIRGAP AIRGAP SHAFT ROTOR AM_1, AM_2, AM_3, AM_4, AM_11, AM_22, AM_33, AM_44, AQ_1, AQ_2, AQ_11, AQ_22,

ROTOR





ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR Stranded coil Name Stranded coil with imposed current B_ROTOR 0 B1 - 0.5 B2 -0.5 B3 1 Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR


Solving parameters :

• Stator current : [100, 150, 200, 250, 270, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 1000, 1200]

• Angle of rotor : [10 ; 56] • Initial position of rotor : 0°



CASE 3: back emf computation Problem name bemf Problem type Transient_magnetic Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material





8000 1.6

ALU_BAR B(H) : Linear isotropic 1 ALU_BAR J(E) : isotropic resistivity 2.7e-8

Ωm

Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm






Circuit ME_CC

Components Values V1 8.76 V R1, R2, R3, R6 109

L1, L2, L3 1.104 mH L4 8.8 mH R5,R7,R8, ……. …..R23, R24, R25 2.89 10-6 Ω

L5,L6,L7, …….. …..L22, L23, L24 10-9 H


Turn number



Mechanical Set


ROTOR

FIELD_1P 215 ROTOR B_ROTOR Positive All conductors are in series


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




region type)









• First resolution : Time length : [20], step [5s] Initial position of rotor : 85 °

• Second resolution : Time length : [20,2], step [0.001s]



Case 4: single phase short circuit Problem name SC_mono Problem type Transient_magnetic Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation












8000 1.6


1


2.7e-8 Ωm

Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm






Circuit ME_CC

Components Values V1 8.76 V R1, R6 10-6 Ω R2, R3 10+6 Ω L1, L2, L3 1.104 mH L4 8.8 mH R5,R7,R8, ……. …..R23, R24, R25 2.89 10-6 Ω

L5,L6,L7, …….. …..L22, L23, L24 10-9 H


Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




region type)












Case 5: three phase short circuit Problem name SC_THREE Problem type Transient_magnetic Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation












8000 1.6


1


2.7e-8 Ωm

Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm

STATOR Stator FIXED - - - - AIRGAP Airgap COMPRESSIBLE - - - - Name of face region (air or vacuum type) Mechanical set AIR_1 STATOR AIR_2 ROTOR AIR_3 STATOR AIRGAP AIRGAP SHAFT ROTOR






Circuit ME_CC Components Values V1 8.76 V R1, R2, R3, R6 10-6 Ω L1, L2, L3 1.104 mH L4 8.8 mH R5,R7,R8, ……. …..R23, R24, R25 2.89 10-6 Ω

L5,L6,L7, …….. …..L22, L23, L24 10-9 H


Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




region type)












Case 6: direct axis determination for SSFR test Problem name AC_SSFR_DIRECT_POS Problem type Magnetic AC 2D Frequency 100 Hz Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material








1


2.7e-8Ωm

Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm







Circuit MH_SSFR_POS_DIRECT Components Values V1 1.5 V L1, L2, L3 1.104 mH L4 8.8 mH L5 15.6mH L6 11.2mH Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1 181.2 mΩ B2 181.2 mΩ B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR



• Rotor positions : [-5°; 85°], step [2.5°]



Case 7: quadrature position for SSFR test Problem name AC_QUADRATURE_SSFR Problem type AC magnetic 2D Frequency 100 Hz Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material








1


2.7e-8Ωm

Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm








L5,L6,L7, …….. …..L22, L23, L24 10-9 H

Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




region type)









• Rotor positions : [-5°; 85°], step [2.5°]



Case 8: SSFR test Problem name AC_QUADRATURE_SSFR Problem type AC magnetic 2D Frequency 100 Hz Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material








1


2.7e-8Ωm

Mechanical Set name


Rotation axis

Pivot Point

Imposed speed



around one axis

parallel to Oz

(0,0,0) 1500 rpm








L5,L6,L7, …….. …..L22, L23, L24 10-9 H

Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




region type)









• Stator frequency : [0.001, 0.005, 0.01, 0.02, 0.04, 0.08, 0.1, 0.2, 0.4, 0.8, 1, 2, 4, 5, 6, 8, 10, 20, 40, 50, 80, 100, 200, 400]




Case 9: Loaded on the network (unload) Problem name MT_SOLV_UNLOADED Problem type Transient Magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material





8000 1.6

Mechanical Set name


Rotation axis

Pivot Point

Coupled load




Oz

(0,0,0) Moment of inertia : 0.1215kg.m² Friction coefficient : 0.016N.m.S Drag Torque : -2.51 N.m Initial velocity : 1500 rpm


IBLE - - - -

Name of face region (air or vacuum type) Mechanical set AIR_1 STATOR AIR_2 ROTOR AIR_3 STATOR AIRGAP AIRGAP SHAFT ROTOR






Circuit TM_NETWORK Components Values I_ROTOR -5 A L1, L2, L3 1.104e-3 L4 8.8mH L5 15.6mH L6 11.2mH V1 254 V, 50 Hz, 0° V2 254 V, 50 Hz, -120° V3 254 V, 50 Hz, 120° R1, R2, R3 106 Ω L7, L8, L9 10-9H Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1 181.2 mΩ B2 181.2 mΩ B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR



• Time step [0.0005s], study time limit [0.2s],


• Initialized by static computation



Case 10: Loaded on the network (30% load) without regulation

Problem name MT_SOLV_LOADED Problem type Transient Magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material





8000 1.6

Mechanical Set name


Rotation axis

Pivot Point

Coupled load




Oz



IBLE - - - -







Circuit TM_NETWORK Components Values I_ROTOR -5 A L1, L2, L3 1.104e-3 L4 8.8mH L5 15.6mH L6 11.2mH V1 254 V, 50 Hz, 0° V2 254 V, 50 Hz, -120° V3 254 V, 50 Hz, 120° R1, R2, R3 72.14 Ω L7, L8, L9 0.1717 H Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR



• Initial position of rotor : 90° • Time step [0.0005s], study time limit [1s], • Initialized by static computation



Case 11: Loaded on the network (30% load) with appropriated motor torque

Problem name MT_SOLV_LOADED_T Problem type Transient Magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material





8000 1.6

Mechanical Set name


Rotation axis

Pivot Point

Coupled load




Oz



IBLE - - - -







Circuit TM_NETWORK Components Values I_ROTOR -5 A L1, L2, L3 1.104e-3 L4 8.8mH L5 15.6mH L6 11.2mH V1 254 V, 50 Hz, 0° V2 254 V, 50 Hz, -120° V3 254 V, 50 Hz, 120° R1, R2, R3 72.14 Ω L7, L8, L9 0.1717 H Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω Name of face region (coil conductor region type)

Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR






Case 12: Loaded on the network (30% load) with appropriated field current and motor torque

Problem name MT_SOLV_LOADED_F_T Problem type Transient Magnetic 2D Type of domain Plane Depth 132 mm Symmetry and periodicity => coefficient for coils flux computation








Name of material





8000 1.6

Mechanical Set name


Rotation axis

Pivot Point

Coupled load




Oz



IBLE - - - -







Circuit TM_NETWORK Components Values I_ROTOR -6.85 A L1, L2, L3 1.104e-3 L4 8.8mH L5 15.6mH L6 11.2mH V1 254 V, 50 Hz, 0° V2 254 V, 50 Hz, -120° V3 254 V, 50 Hz, 120° R1, R2, R3 72.14 Ω L7, L8, L9 0.1717 H Name of Stranded coil component Resistance B_ROTOR 5.0136 Ω B1, B2, B3 181.2 mΩ B5 8.486 Ω B6 9.358 Ω Name of face region (coil conductor region type)

Turn number



Mechanical Set

FIELD_1M 215 All conductors are in series

B_ROTOR Negative ROTOR


ROTOR


ROTOR


ROTOR


STATOR


STATOR


STATOR


STATOR


STATOR


STATOR




Turn number



Mechanical Set


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR


ROTOR





Documents

46430035 Synchronous Motor