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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: cedrat@cedrat.comWeb: 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
SYNCHRONOUS MOTOR PAGE 3
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
PAGE 4 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
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
Defining the problem FLUX 2D®9.20
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]
PAGE 6 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
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
SYNCHRONOUS MOTOR PAGE 7
Defining the problem FLUX 2D®9.20
- 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
L3 Segment P10 P11 STATOR
L4 Segment P11 P12 STATOR
L5 Segment P10 P13 STATOR
L6 Segment P13 P12 STATOR
L7 Segment P12 P16 STATOR
L8 Segment P15 P14 STATOR
L9 Segment P14 P13 STATOR
L10 Segment P14 P9 STATOR
L11 Segment P9 P10 STATOR
L12 Segment P9 P6 STATOR
L13 Segment P6 P7 STATOR
L14 Segment P6 P5 STATOR
L15 Segment P5 P4 STATOR
L16 Segment P4 P2 STATOR
L17 Arc_2pt_pt_center P2 P3 P1 STATOR
L18 Arc_2pt_pt_center P7 P8 P1 STATOR
L19 Arc_2pt_pt_center P15 P16 P1 STATOR
L20 Arc_2pt_radius P5 P4 3.15 STATOR
L21 Arc_2pt_pt_center P3 P50 P1 STATOR
L22 Arc_2pt_pt_center P8 P51 P1 STATOR
Fig 2.2.1.b : Overview of a stator slot with the lines designation
PAGE 8 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
• 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
SYNCHRONOUS MOTOR PAGE 9
Defining the problem FLUX 2D®9.20
• 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
PAGE 10 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
Fig 6 : Overvi a part or with the points designation
lines o f rotor
ew of of rot
- f eighth o
N° Type of line Starting point
End point Center point Radius Coordinate
system L23 Segment P1 P17 ROTOR
L24 Segment P17 P19 ROTOR
L25 Segment P19 P24 ROTOR
L26 Segment P20 P21 ROTOR
L27 Segment P22 P23 ROTOR
L28 Segment P23 P24 ROTOR
L29 Segment P24 P25 ROTOR
L30 Segment P25 P26 ROTOR
L31 Segment P25 P29 ROTOR
L32 Segment P29 P28 ROTOR
L33 Segment P26 P28 ROTOR
L34 Segment P26 P27 ROTOR
L35 Segment P22 P42 ROTOR
L36 Segment P22 P33 ROTOR
L37 Segment P33 P32 ROTOR
L38 Segment P33 P34 ROTOR
L39 Segment P32 P35 ROTOR
L40 Segment P32 P31 ROTOR
L41 Segment P36 P35 ROTOR
L42 Segment P35 P34 ROTOR
L43 Segment P34 P40 ROTOR
L44 Segment P35 P38 ROTOR
SYNCHRONOUS MOTOR PAGE 11
Defining the problem FLUX 2D®9.20
N° Type of line Starting point
End point Center point Radius Coordinate
system
L45 Segment P38 P37 ROTOR
L46 Segment P38 P39 ROTOR
L47 Segment P39 P40 ROTOR
L48 Segment P40 P41 ROTOR
L49 Segment P41 P42 ROTOR
L50 Segment P28 P30 ROTOR
L51 Arc_2pt_pt_center P17 P18 P1 ROTOR
L52 Arc_2pt_pt_center P19 P20 P1 ROTOR
L53 Arc_2pt_ray P29 P22 32.6 ROTOR
L54 Arc_2pt_ray P22 P21 32.6 ROTOR
L55 Arc_2pt_pt_center P27 P30 P1 ROTOR
L56 Arc_2pt_pt_center P30 P31 P1 ROTOR
L57 Arc_2pt_pt_center P31 P36 P1 ROTOR
L58 Arc_2pt_pt_center P36 P37 P1 ROTOR
L59 Arc_2pt_ray P41 P34 3.56 ROTOR
L93 Arc_2pt_pt_center P37 P58 P1 ROTOR
L156 Segment P1 P18 ROTOR
L157 Segment P18 P99 ROTOR
L1377 Segment P2 P27 ROTOR
L1378 Segment P277 P816 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
PAGE 12 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
• 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
SYNCHRONOUS MOTOR PAGE 13
Defining the problem FLUX 2D®9.20
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
FLUX 2D®9.20 Defining the problem
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
SYNCHRONOUS MOTOR PAGE 15
Defining the problem FLUX 2D®9.20
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
PAGE 16 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
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
SYNCHRONOUS MOTOR PAGE 17
Defining the problem FLUX 2D®9.20
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
PAGE 18 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
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
SYNCHRONOUS MOTOR PAGE 19
Defining the problem FLUX 2D®9.20
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
PAGE 20 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
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
SYNCHRONOUS MOTOR PAGE 21
Defining the problem FLUX 2D®9.20
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
PAGE 22 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
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]
SYNCHRONOUS MOTOR PAGE 23
Defining the problem FLUX 2D®9.20
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]
PAGE 24 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
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
SYNCHRONOUS MOTOR PAGE 25
Defining the problem FLUX 2D®9.20
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
PAGE 26 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
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
SYNCHRONOUS MOTOR PAGE 27
Defining the problem FLUX 2D®9.20
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
PAGE 28 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Defining the problem
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
SYNCHRONOUS MOTOR PAGE 29
Defining the problem FLUX 2D®9.20
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
PAGE 30 SYNCHRONOUS MOTOR
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.
SYNCHRONOUS MOTOR PAGE 31
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
PAGE 32 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Parameters Xd, Xq in magneto static
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
FIELD_2M 215 B_ROTOR negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR positive All conductors are in series
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
SYNCHRONOUS MOTOR PAGE 33
Parameters Xd, Xq in magneto static FLUX 2D®9.20
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
PAGE 34 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Parameters Xd, Xq in magneto static
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.
3.3.2 Physical conditions
Problem name XdXq_Is 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)
• 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.
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 COMPRESSIBLE - - - -
SYNCHRONOUS MOTOR PAGE 35
Parameters Xd, Xq in magneto static FLUX 2D®9.20
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)
Material Mechanical set
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
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
FIELD_2M 215 B_ROTOR negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 negative All conductors are in series
STATOR
Boundary condition automatically set by Flux 2D
PAGE 36 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Parameters Xd, Xq in magneto static
3.3.3 Solving conditions
• 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
SYNCHRONOUS MOTOR PAGE 37
Parameters Xd, Xq in magneto static FLUX 2D®9.20
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
PAGE 38 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Parameters Xd, Xq in magneto static
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.
SYNCHRONOUS MOTOR PAGE 39
Parameters Xd, Xq in magneto static FLUX 2D®9.20
PAGE 40 SYNCHRONOUS MOTOR
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
4.1.2 Physical conditions
Problem name bemf Problem type Transient_magnetic 2D 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)
SYNCHRONOUS MOTOR PAGE 41
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
Comment Type Coord. System
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
PAGE 42 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Short-circuit tests
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
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
FIELD_2M 215 B_ROTOR negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 negative All conductors are in series
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
SYNCHRONOUS MOTOR PAGE 43
Short-circuit tests FLUX 2D®9.20
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
Boundary condition automatically set by Flux 2D
• 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°).
4.1.3 Solving conditions
• Initialized by static computation • Time length : [0,20], step [5] • Time length : [20,20.04], step [0.001] • Initial position of rotor : 85 °
PAGE 44 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Short-circuit tests
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
SYNCHRONOUS MOTOR PAGE 45
Short-circuit tests FLUX 2D®9.20
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
PAGE 46 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Short-circuit tests
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.
4.2.2 Physical conditions
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
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 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
SYNCHRONOUS MOTOR PAGE 47
Short-circuit tests FLUX 2D®9.20
Mechanical Set name
Comment Type Coord. System
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
PAGE 48 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Short-circuit tests
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
FIELD_2M 215 B_ROTOR negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 negative All conductors are in series
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
SYNCHRONOUS MOTOR PAGE 49
Short-circuit tests FLUX 2D®9.20
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
Boundary condition automatically set by Flux 2D
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.
4.2.3 Solving conditions
• 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]
PAGE 50 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Short-circuit tests
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
SYNCHRONOUS MOTOR PAGE 51
Short-circuit tests FLUX 2D®9.20
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
PAGE 52 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Short-circuit tests
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.
4.3.2 Physical conditions
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
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 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
SYNCHRONOUS MOTOR PAGE 53
Short-circuit tests FLUX 2D®9.20
Mechanical Set name
Comment Type Coord. System
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
PAGE 54 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Short-circuit tests
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
FIELD_2M 215 B_ROTOR negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 negative All conductors are in series
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
SYNCHRONOUS MOTOR PAGE 55
Short-circuit tests FLUX 2D®9.20
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
Boundary condition automatically set by Flux 2D
• 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.
4.3.3 Solving conditions
• 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 !
PAGE 56 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Short-circuit tests
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
SYNCHRONOUS MOTOR PAGE 57
Short-circuit tests FLUX 2D®9.20
-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
PAGE 58 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Short-circuit tests
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 =
SYNCHRONOUS MOTOR PAGE 59
Short-circuit tests FLUX 2D®9.20
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 ′′++
=′′
PAGE 60 SYNCHRONOUS MOTOR
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.
SYNCHRONOUS MOTOR PAGE 61
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
Type of equivalent B(H) curve
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6 Sine Wave flux density
ALU_BAR B(H) : Linear isotropic
1
ALU_BAR J(E) : isotropic resistivity
2.7e-8Ωm
PAGE 62 SYNCHRONOUS MOTOR
FLUX 2D®9.20 StandStill Frequency Reponse (SSFR)
Mechanical Set name
Comment Type Coord. System
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
SYNCHRONOUS MOTOR PAGE 63
StandStill Frequency Reponse (SSFR) FLUX 2D®9.20
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
PAGE 64 SYNCHRONOUS MOTOR
FLUX 2D®9.20 StandStill Frequency Reponse (SSFR)
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 Positive All conductors are in series
ROTOR
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 74 B5 Negative All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 74 B6 Positive All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
ROTOR
AQ_11 74 B5 Positive All conductors are in series
ROTOR
AQ_22 74 B5 Negative All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
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
Automatic coefficient (Symmetry and periodicity taken into account)
SYNCHRONOUS MOTOR PAGE 65
StandStill Frequency Reponse (SSFR) FLUX 2D®9.20
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
Type of equivalent B(H) curve
8000 1.6 Sine Wave flux density
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
ALU_BAR B(H) : Linear isotropic
1
ALU_BAR J(E) : isotropic resistivity
2.7e-8Ωm
Mechanical Set name
Comment Type Coord. System
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
PAGE 66 SYNCHRONOUS MOTOR
FLUX 2D®9.20 StandStill Frequency Reponse (SSFR)
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
SYNCHRONOUS MOTOR PAGE 67
StandStill Frequency Reponse (SSFR) FLUX 2D®9.20
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
Boundary condition automatically set by Flux 2D
Solving parameters : - Rotor positions : [-5°; 85°], step [2.5°]
PAGE 68 SYNCHRONOUS MOTOR
FLUX 2D®9.20 StandStill Frequency Reponse (SSFR)
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.
SYNCHRONOUS MOTOR PAGE 69
StandStill Frequency Reponse (SSFR) FLUX 2D®9.20
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.
PAGE 70 SYNCHRONOUS MOTOR
FLUX 2D®9.20 StandStill Frequency Reponse (SSFR)
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.
5.2.2 Physical conditions
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
Type of equivalent B(H) curve
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6 Sine Wave flux density
ALU_BAR B(H) : Linear isotropic
1
ALU_BAR J(E) : isotropic resistivity
2.7e-8Ωm
SYNCHRONOUS MOTOR PAGE 71
StandStill Frequency Reponse (SSFR) FLUX 2D®9.20
Mechanical Set name
Comment Type Coord. System
Rotation axis
Pivot Point
Imposed speed
(0,0,0) ROTOR Rotor Rotation around
one axis ROTOR Rotation
around one axis
parallel to Oz
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
PAGE 72 SYNCHRONOUS MOTOR
FLUX 2D®9.20 StandStill Frequency Reponse (SSFR)
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
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
SYNCHRONOUS MOTOR PAGE 73
StandStill Frequency Reponse (SSFR) FLUX 2D®9.20
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
Boundary condition automatically set by Flux 2D
5.2.3 Solving conditions
• 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]
PAGE 74 SYNCHRONOUS MOTOR
FLUX 2D®9.20 StandStill Frequency Reponse (SSFR)
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
SYNCHRONOUS MOTOR PAGE 75
StandStill Frequency Reponse (SSFR) FLUX 2D®9.20
• 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
PAGE 76 SYNCHRONOUS MOTOR
FLUX 2D®9.20 StandStill Frequency Reponse (SSFR)
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
SYNCHRONOUS MOTOR PAGE 77
StandStill Frequency Reponse (SSFR) FLUX 2D®9.20
- 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
PAGE 78 SYNCHRONOUS MOTOR
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.
6.1.2 Physical conditions
• 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
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)
SYNCHRONOUS MOTOR PAGE 79
Loaded on the network FLUX 2D®9.20
Name of material
Type Isotropic value
Initial relative permeability
Saturation magnetization (T)
Type of equivalent B(H) curve
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6 Sine Wave flux density
Mechanical Set name
Comment Type Coord. System
Rotation axis
Pivot Point
Coupled load
ROTOR Rotor Rotation around one axis
ROTOR Rotation around
one axis parallel to
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
PAGE 80 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
SYNCHRONOUS MOTOR PAGE 81
Loaded on the network FLUX 2D®9.20
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 Positive All conductors are in series
ROTOR
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 74 B5 Negative All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 74 B6 Positive All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
ROTOR
AQ_11 74 B5 Positive All conductors are in series
ROTOR
AQ_22 74 B5 Negative All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
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.
PAGE 82 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
SYNCHRONOUS MOTOR PAGE 83
1,475
1,5
1,524
1,55
0,05 99,999E-3 0,15 0,2
s.
(E3) rpm
Loaded on the network FLUX 2D®9.20
- 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
PAGE 84 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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).
SYNCHRONOUS MOTOR PAGE 85
Loaded on the network FLUX 2D®9.20
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.
6.2.2 Physical conditions
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6
Mechanical Set name
Comment Type Coord. System
Rotation axis
Pivot Point
Coupled load
ROTOR Rotor Rotation around one axis
ROTOR Rotation around
one axis parallel to
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°
STATOR Stator FIXED - - - - AIRGAP Airgap COMPRESS
IBLE - - - -
PAGE 86 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
SYNCHRONOUS MOTOR PAGE 87
Loaded on the network FLUX 2D®9.20
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
PAGE 88 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 Positive All conductors are in series
ROTOR
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 74 B5 Negative All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 74 B6 Positive All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
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 %
6.2.3 Solving parameters
• 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
SYNCHRONOUS MOTOR PAGE 89
Loaded on the network FLUX 2D®9.20
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.
PAGE 90 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
6.3.2 Physical conditions
• 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
Automatic coefficient (Symmetry and periodicity taken into account)
SYNCHRONOUS MOTOR PAGE 91
Loaded on the network FLUX 2D®9.20
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6
Mechanical Set name
Comment Type Coord. System
Rotation axis
Pivot Point
Coupled load
ROTOR Rotor Rotation around one axis
ROTOR Rotation around
one axis parallel to
Oz
(0,0,0) Moment of inertia : 0.1215kg.m² Friction coefficient : 0.016N.m.S Drag Torque : -4.85 N.m Initial velocity : 1500 rpm Position at time t=0s : 90°
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
PAGE 92 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
SYNCHRONOUS MOTOR PAGE 93
Loaded on the network FLUX 2D®9.20
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 ROTOR Positive All conductors are in series
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 Negative 74 B5 All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 Positive 74 B6 All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
ROTOR
AQ_11 74 B5 Positive All conductors are in series
ROTOR
AQ_22 74 B5 Negative All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
6.3.3 Solving parameters
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.
PAGE 94 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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.
SYNCHRONOUS MOTOR PAGE 95
Loaded on the network FLUX 2D®9.20
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.
PAGE 96 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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.
6.4.2 Physical conditions
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
Automatic coefficient (Symmetry and periodicity taken into account)
- 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.
SYNCHRONOUS MOTOR PAGE 97
Loaded on the network FLUX 2D®9.20
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6
Mechanical Set name
Comment Type Coord. System
Rotation axis
Pivot Point
Coupled load
ROTOR Rotor Rotation around one axis
ROTOR Rotation around
one axis parallel to
Oz
(0,0,0) Moment of inertia : 0.1215kg.m² Friction coefficient : 0.016N.m.S Drag Torque : -4.85 N.m Initial velocity : 1500 rpm Position at time t=0s : 90°
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
PAGE 98 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
SYNCHRONOUS MOTOR PAGE 99
Loaded on the network FLUX 2D®9.20
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 Positive All conductors are in series
ROTOR
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 74 B5 Negative All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 74 B6 Positive All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
ROTOR
AQ_11 74 B5 Positive All conductors are in series
ROTOR
AQ_22 74 B5 Negative All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
6.4.3 Solving parameters
• Initial position of rotor : 90° • Time step [0.002s], study time limit [20], • Initialized by static computation
PAGE 100 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
SYNCHRONOUS MOTOR PAGE 101
Loaded on the network FLUX 2D®9.20
PAGE 102 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
SYNCHRONOUS MOTOR PAGE 103
Loaded on the network FLUX 2D®9.20
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
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 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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
PAGE 104 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
Solving parameters : • Angle of rotor [-10 ; 80], step [5] • Initial position of rotor: 0°
SYNCHRONOUS MOTOR PAGE 105
Loaded on the network FLUX 2D®9.20
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
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 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
PAGE 106 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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 0 B1 - 0.5 B2 -0.5 B3 1 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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
Boundary condition automatically set by Flux 2D
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°
SYNCHRONOUS MOTOR PAGE 107
Loaded on the network FLUX 2D®9.20
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
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 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
Comment Type Coord. System
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
PAGE 108 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
FIELD_1M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_1P 215 ROTOR B_ROTOR Positive All conductors are in series
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
SYNCHRONOUS MOTOR PAGE 109
Loaded on the network FLUX 2D®9.20
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
Boundary condition automatically set by Flux 2D
Solving parameters :
• First resolution : Time length : [20], step [5s] Initial position of rotor : 85 °
• Second resolution : Time length : [20,2], step [0.001s]
PAGE 110 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
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 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
Comment Type Coord. System
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)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
SYNCHRONOUS MOTOR PAGE 111
Loaded on the network FLUX 2D®9.20
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
PAGE 112 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
Boundary condition automatically set by Flux 2D
Solving parameters :
• From the last step of the back emf simulation • Time length : [0.5], step [0.0005s]
SYNCHRONOUS MOTOR PAGE 113
Loaded on the network FLUX 2D®9.20
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
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 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
Comment Type Coord. System
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
PAGE 114 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
Name of face region (magnetic non conducting region type)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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 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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
SYNCHRONOUS MOTOR PAGE 115
Loaded on the network FLUX 2D®9.20
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
Boundary condition automatically set by Flux 2D
Solving parameters :
• From the last step of the back emf simulation • Time length : [0.5], step [0.0005s]
PAGE 116 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
Type of equivalent B(H) curve
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6 Sine Wave flux density
ALU_BAR B(H) : Linear isotropic
1
ALU_BAR J(E) : isotropic resistivity
2.7e-8Ωm
Mechanical Set name
Comment Type Coord. System
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
SYNCHRONOUS MOTOR PAGE 117
Loaded on the network FLUX 2D®9.20
Name of face region (magnetic non conducting region type)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
PAGE 118 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 Positive All conductors are in series
ROTOR
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 74 B5 Negative All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 74 B6 Positive All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
ROTOR
AQ_11 74 B5 Positive All conductors are in series
ROTOR
AQ_22 74 B5 Negative All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
Solving parameters :
• Rotor positions : [-5°; 85°], step [2.5°]
SYNCHRONOUS MOTOR PAGE 119
Loaded on the network FLUX 2D®9.20
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
Type of equivalent B(H) curve
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6 Sine Wave flux density
ALU_BAR B(H) : Linear isotropic
1
ALU_BAR J(E) : isotropic resistivity
2.7e-8Ωm
Mechanical Set name
Comment Type Coord. System
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
PAGE 120 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
Name of face region (magnetic non conducting region type)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
SYNCHRONOUS MOTOR PAGE 121
Loaded on the network FLUX 2D®9.20
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
Boundary condition automatically set by Flux 2D
Solving parameters :
• Rotor positions : [-5°; 85°], step [2.5°]
PAGE 122 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
Type of equivalent B(H) curve
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6 Sine Wave flux density
ALU_BAR B(H) : Linear isotropic
1
ALU_BAR J(E) : isotropic resistivity
2.7e-8Ωm
Mechanical Set name
Comment Type Coord. System
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
SYNCHRONOUS MOTOR PAGE 123
Loaded on the network FLUX 2D®9.20
Name of face region (magnetic non conducting region type)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
PAGE 124 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
Boundary condition automatically set by Flux 2D
Solving parameters :
• 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°
SYNCHRONOUS MOTOR PAGE 125
Loaded on the network FLUX 2D®9.20
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6
Mechanical Set name
Comment Type Coord. System
Rotation axis
Pivot Point
Coupled load
ROTOR Rotor Rotation around one axis
ROTOR Rotation around
one axis parallel to
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
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
PAGE 126 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
Name of face region (magnetic non conducting region type)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
SYNCHRONOUS MOTOR PAGE 127
Loaded on the network FLUX 2D®9.20
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
PAGE 128 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 Positive All conductors are in series
ROTOR
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 74 B5 Negative All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 74 B6 Positive All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
ROTOR
AQ_11 74 B5 Positive All conductors are in series
ROTOR
AQ_22 74 B5 Negative All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
Solving parameters :
• Time step [0.0005s], study time limit [0.2s],
• Initial position of rotor : 90°
• Initialized by static computation
SYNCHRONOUS MOTOR PAGE 129
Loaded on the network FLUX 2D®9.20
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6
Mechanical Set name
Comment Type Coord. System
Rotation axis
Pivot Point
Coupled load
ROTOR Rotor Rotation around one axis
ROTOR Rotation around
one axis parallel to
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°
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
PAGE 130 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
Name of face region (magnetic non conducting region type)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
SYNCHRONOUS MOTOR PAGE 131
Loaded on the network FLUX 2D®9.20
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 Positive All conductors are in series
ROTOR
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 74 B5 Negative All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 74 B6 Positive All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
ROTOR
AQ_11 74 B5 Positive All conductors are in series
ROTOR
AQ_22 74 B5 Negative All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
Solving parameters :
• Initial position of rotor : 90° • Time step [0.0005s], study time limit [1s], • Initialized by static computation
PAGE 132 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6
Mechanical Set name
Comment Type Coord. System
Rotation axis
Pivot Point
Coupled load
ROTOR Rotor Rotation around one axis
ROTOR Rotation around
one axis parallel to
Oz
(0,0,0) Moment of inertia : 0.1215kg.m² Friction coefficient : 0.016N.m.S Drag Torque : -4.85 N.m Initial velocity : 1500 rpm Position at time t=0s : 90°
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
SYNCHRONOUS MOTOR PAGE 133
Loaded on the network FLUX 2D®9.20
Name of face region (magnetic non conducting region type)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
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
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
PAGE 134 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 Positive All conductors are in series
ROTOR
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 74 B5 Negative All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 74 B6 Positive All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
ROTOR
AQ_11 74 B5 Positive All conductors are in series
ROTOR
AQ_22 74 B5 Negative All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
Solving parameters :
• Initial position of rotor : 90° • Time step [0.002s], study time limit [7s], • Initialized by static computation
SYNCHRONOUS MOTOR PAGE 135
Loaded on the network FLUX 2D®9.20
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
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 Isotropic value
Initial relative permeability
Saturation magnetization (T)
STEEL_NLIN B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
8000 1.6
Mechanical Set name
Comment Type Coord. System
Rotation axis
Pivot Point
Coupled load
ROTOR Rotor Rotation around one axis
ROTOR Rotation around
one axis parallel to
Oz
(0,0,0) Moment of inertia : 0.1215kg.m² Friction coefficient : 0.016N.m.S Drag Torque : -4.85 N.m Initial velocity : 1500 rpm Position at time t=0s : 90°
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
PAGE 136 SYNCHRONOUS MOTOR
FLUX 2D®9.20 Loaded on the network
Name of face region (magnetic non conducting region type)
Material Mechanical set
ROTOR_CORE STEEL_NLIN ROTOR STATOR_CORE STEEL_NLIN STATOR
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
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
FIELD_1M 215 All conductors are in series
B_ROTOR Negative ROTOR
FIELD_1P 215 B_ROTOR Positive All conductors are in series
ROTOR
FIELD_2M 215 B_ROTOR Negative All conductors are in series
ROTOR
FIELD_2P 215 B_ROTOR Positive All conductors are in series
ROTOR
COIL_1P 54 B1 Positive All conductors are in series
STATOR
COIL_1M 54 B1 Negative All conductors are in series
STATOR
COIL_2P 54 B2 Positive All conductors are in series
STATOR
COIL_2M 54 B2 Negative All conductors are in series
STATOR
COIL_2P 54 B3 Positive All conductors are in series
STATOR
COIL_2M 54 B3 Negative All conductors are in series
STATOR
SYNCHRONOUS MOTOR PAGE 137
Loaded on the network FLUX 2D®9.20
Name of face region (coil conductor region type)
Turn number
Associated coil component
orientation Symmetries and periodicities
Mechanical Set
AM_1 74 B5 Positive All conductors are in series
ROTOR
AM_2 74 B5 Negative All conductors are in series
ROTOR
AM_3 74 B6 Negative All conductors are in series
ROTOR
AM_4 74 B6 Positive All conductors are in series
ROTOR
AM_11 74 B5 Negative All conductors are in series
ROTOR
AM_22 74 B5 Positive All conductors are in series
ROTOR
AM_33 74 B6 Positive All conductors are in series
ROTOR
AM_44 74 B6 Negative All conductors are in series
ROTOR
AQ_1 74 B6 Positive All conductors are in series
ROTOR
AQ_2 74 B6 Negative All conductors are in series
ROTOR
AQ_11 74 B5 Positive All conductors are in series
ROTOR
AQ_22 74 B5 Negative All conductors are in series
ROTOR
Boundary condition automatically set by Flux 2D
Solving parameters :
• Initial position of rotor : 90° • Time step [0.002s], study time limit [20s], • Initialized by static computation
PAGE 138 SYNCHRONOUS MOTOR
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