Synchronous Motor
CAD Package for Electromagnetic and Thermal Analysis using Finite Elements FLUX 2D Application ® Synchronous motor tec
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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 FLUX2D technical papers
:
COPYRIGHT CEDRAT/INPG/CNRS/EDF : COPYRIGHT CEDRAT
FLUX2D's Quality Assessment: (Electricité de France standard, registered number AQM1L002)
This technical paper was edited on 18 April 2006 Ref.: K205-Q-920-EN-EN-04/06
CEDRAT 15 Chemin de Malacher - Inovallée 38246 Meylan Cedex FRANCE Phone: +33 (0)4 76 90 50 45 Fax: +33 (0)4 56 38 08 30 E-mail: [email protected] Web: 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 : AGENTA Select a surface or a menu item : 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 ↵
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 [ ] .
Bdg ↵ [q]uit ↵ ext in bold AGENTA
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.
P3
P3 P4
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.
- 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 2.2.2
2.3
The mesh and regions .................................................................................................. 15 2.3.1 2.3.2 2.3.3
2.4
Creation of coordinate systems, geometrical parameters .................................................6 Geometry and faces building and transformation creation................................................7 Creation of discretisations ...............................................................................................15 Assigning the mesh .........................................................................................................15 Regions............................................................................................................................19
Circuits models.............................................................................................................. 24 2.4.1 2.4.2 2.4.3 2.4.4
ME_CC ............................................................................................................................25 AC_SSFR_D_AXIS_POS................................................................................................26 AC_SSFR_Q_AXIS_POS................................................................................................27 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 3.2.2 3.2.3 3.2.4
3.3
Purpose ...........................................................................................................................31 Physical conditions ..........................................................................................................32 Solving conditions............................................................................................................33 Analysis ...........................................................................................................................34
Xd and Xq according to the stator current..................................................................... 35 3.3.1 3.3.2 3.3.3 3.3.4
Purpose ...........................................................................................................................35 Physical conditions ..........................................................................................................35 Solving conditions............................................................................................................37 Analysis ...........................................................................................................................37
4. Short-circuit tests....................................................................................................... 41 4.1
Unloaded operating....................................................................................................... 41 4.1.1 4.1.2 4.1.3 4.1.4
SYNCHRONOUS MOTOR
Purpose ...........................................................................................................................41 Physical conditions ..........................................................................................................41 Solving conditions............................................................................................................44 Analysis ...........................................................................................................................45
PAGE A
TABLE OF CONTENTS
4.2
Single phase short circuit...............................................................................................47 4.2.1 4.2.2 4.2.3 4.2.4
4.3
FLUX 2D®9.20
Purpose............................................................................................................................47 Physical conditions ..........................................................................................................47 Solving conditions ............................................................................................................50 Analysis............................................................................................................................51
Three phase short circuit ...............................................................................................53 4.3.1 4.3.2 4.3.3 4.3.4
Purpose............................................................................................................................53 Physical conditions ..........................................................................................................53 Solving conditions ............................................................................................................56 Analysis............................................................................................................................57
5. StandStill Frequency Reponse (SSFR) ..................................................................... 61 5.1
Direct and quadrature axis determination......................................................................61 5.1.1 5.1.2 5.1.3
5.2
Purpose............................................................................................................................61 Physical and solving conditions .......................................................................................62 Analysis............................................................................................................................69
Classical SSFR..............................................................................................................71 5.2.1 5.2.2 5.2.3 5.2.4
Purpose............................................................................................................................71 Physical conditions ..........................................................................................................71 Solving conditions ............................................................................................................74 Analysis............................................................................................................................75
6. Loaded on the network .............................................................................................. 79 6.1
Unloaded on the network...............................................................................................79 6.1.1 6.1.2 6.1.3 6.1.4
6.2
Loaded on the network without regulation .....................................................................86 6.2.1 6.2.2 6.2.3 6.2.4
6.3
Purpose............................................................................................................................91 Physical conditions ..........................................................................................................91 Solving parameters ..........................................................................................................94 Analysis............................................................................................................................94
Loaded on the network with appropriated field current and motor torque .....................97 6.4.1 6.4.2 6.4.3 6.4.4
PAGE B
Purpose............................................................................................................................86 Physical conditions ..........................................................................................................86 Solving parameters ..........................................................................................................89 Analysis............................................................................................................................90
Loaded on the network with appropriated motor torque ................................................91 6.3.1 6.3.2 6.3.3 6.3.4
6.4
Purpose............................................................................................................................79 Physical conditions ..........................................................................................................79 Solving parameters ..........................................................................................................82 Analysis............................................................................................................................83
Purpose............................................................................................................................97 Physical conditions ..........................................................................................................97 Solving parameters ........................................................................................................100 Analysis..........................................................................................................................101
SYNCHRONOUS MOTOR
FLUX 2D®9.20
1.
Overview of synchronous motor technical paper
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
PAGE 2
FLUX 2D®9.20
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 :
Armature
Field
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
Number of wires by slot
12
Number of turns per pole
215
D axis - slots by pole
4
D axis - wires by slot
74
Q axis - slots by pole
2
Q axis - wires by slot
74
Absorber
Fig 2.a : Synchronous machine
SYNCHRONOUS MOTOR
PAGE 3
FLUX 2D®9.20
Defining the problem
A cross section, given below, shows the overview of the machine : Field
Stator wires
2.1
Armature
Electrical absorber
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
2.2
Defining the problem
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
Armature wires 3 phases
The most part of the geometry construction will be created from geometrical parameters. Some dimensions are nevertheless given to close the construction.
SYNCHRONOUS MOTOR
PAGE 5
FLUX 2D®9.20
Defining the problem
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
XY1 STATOR ROTOR
Comments
Default system Stator system Rotor system
Origin Origin Origin X Y Z
Unit of length
Unit of angle
Definition
Type
2D_Global
Cartesian 2D
0
0
0
Millimeter Degree
2D_Global Polar 2D
0
0
0
Millimeter Degree
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 RIR RER AIR AER AOIR RAHA FSIR FSMR FOIR FOER ST SIR SER SSIR SSER SSHA AIRGAP MESH_AIRGAP NBSS
Comments Rotor internal radius Rotor external radius Absorber internal radius Absorber external radius Absorber opening internal radius Rotor slot half-angle Field slot internal radius Field slot medium radius Field opening internal radius Field opening external radius Skin thickness Stator internal radius Stator external radius Stator slot internal radius Stator slot external radius Stator slot half-angle Airgap Use for the mesh Number of stator slots
Values in [mm] or [°] 28.575 mm 113.2 mm 96.48 mm 111.05 mm 111.93 mm 4.5 ° 50.6 mm 82.9 mm 101.75 mm 109.35 mm 1 mm 114.34 mm 202.5 mm 127.04 mm 177.84 mm 3.33 ° (360/108) 1.14 mm 1.5*airgap 54
Note : To create geometrical parameter : [Geometry], [Geometric Parameter], [New]
PAGE 6
SYNCHRONOUS MOTOR
FLUX 2D®9.20
2.2.2
Defining the problem
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
Create with mirror_stator transformation
Fig 2.2.1.a : Overview of a stator slot with the points designation
SYNCHRONOUS MOTOR
PAGE 7
FLUX 2D®9.20
Defining the problem
-
lines of half stator slot
Segment
Starting point P3
Segment
P7
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
L21
Arc_2pt_pt_center
P3
P50
P1
STATOR
L22
Arc_2pt_pt_center
P8
P51
P1
STATOR
N° L1 L2
Type of line
End point
Center point
Angle
P8 P10
Coordinate system STATOR STATOR
2.2.2.1.1
3.15
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 halfstator. The lines 21 and 22 will be created before building half stator. Geometric transformation MIRROR_STATOR
Type Affine_line_2pt
First point P1
Second point P16
Ratio -1
Comment Create mirror image of a half slot of stator
Geometric Theta Coordinate Type R comp. Rot. Z Comment transformation comp. system STATOR_ROT Create all of Rot_coo_ang 0 0 360/NBSS STATOR 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
FLUX 2D®9.20
Defining the problem
•
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 : Overview of a part of rotor with the points designation
-
lines of eighth of rotor End point
Segment
Starting point 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
N°
Type of line
L23
SYNCHRONOUS MOTOR
Center point
Radius
Coordinate system
PAGE 11
FLUX 2D®9.20
Defining the problem
End point
Segment
Starting point 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
L93
Arc_2pt_pt_center
P37
P58
L156
Segment
P1
P18
ROTOR
L157
Segment
P18
P99
ROTOR
L1377
Segment
P2
P27
ROTOR
L1378
Segment
P277
P816
ROTOR
N°
Type of line
L45
Center point
Radius
3.56 P1
Coordinate system
ROTOR 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
MIRROR_ABSORBER
Affine_line_2pt
P1
P39
-1
MIRROR_ROTOR_1
Affine_line_2pt
P1
P18
-1
MIRROR_ROTOR_2
Affine_line_2pt
P1
P678
-1
Geometric transformation
Type
ABSORBER_ROT
Rot_coo_ang
SYNCHRONOUS MOTOR
R comp.
Theta comp.
0
0
Rot. Z 9
Comment Create mirror image of a half slot of absorber Create a quarter of rotor Create an half of rotor
Coordinate Comment system 2 Times to create ROTOR the three first slot of absorber
PAGE 13
FLUX 2D®9.20
Defining the problem
Fig 7 and 8 : Different steps
Create with Mirror absorber
of creation of the rotor
Create with Absorber_rot
Create with Mirror rotor 1
Create with MIRROR_ROTOR_2
•
Creation of faces
The faces must be built before and after each transformation whether it is for the rotor or the stator. 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]
PAGE 14
SYNCHRONOUS MOTOR
FLUX 2D®9.20
2.3
Defining the problem
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 BIG LARGE MEDIUM SMALL AIRGAP
Value (in mm) 18 12 6 3 Mesh_airgap
Color Cyan Turquoise Yellow Red Magenta
Note : To create mesh point: [Mesh],[Mesh Point], [New] •
Mesh lines
Names A2 A3 A8
Type Arithmetic Arithmetic Arithmetic Geometric with imposed number of elements
GEO_1
2.3.2
Value
Ratio 2 3 8 2
1.3
Color Magenta Green Turquoise Yellow
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 BIG LARGE MEDIUM SMALL AIRGAP
SYNCHRONOUS MOTOR
Points P7,P10,P11,P12,P13,P43,P46,P48 P6,P9,P14,P15,P16,P22,P42,P44,P45,P47,P49 P4,P5,P21,P23,P26,P34,P35,P38,P39,P41,P52,P53 P8,P51 All points in relation with the airgap region
PAGE 15
FLUX 2D®9.20
Defining the problem
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 A2 A3 A8 GEO_1
Lines L8,L17,L19,L22,L28,L44,L52,L59,L60,L64,L74,L75 L20,L25,L26,L42,L43,L47,L72 L55 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 MAPPED
Faces 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]
L44 L60 L75 L59 L52
L64
L22
L17,L74
L28
L19
L8 Fig 2.3.2.a : A2 mesh lines
PAGE 16
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Defining the problem
L47 L43
L26
L42 L55
L72 L25 L20
Fig 2.3.2.c : A8 mesh lines
Fig 2.3.2.b : A3 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
FLUX 2D®9.20
Defining the problem
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
PAGE 18
Fig 2.3.2.j : small mesh points
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 AIR 1 AIR 2 AIR 3 AIRGAP AM 1 AM 2 AM 3 AM 4 AM 11 AM 22 AM 33 AM 44 AQ 1 AQ 2 AQ 11 AQ 22 COIL 1M COIL 1P COIL 2M COIL 2P COIL 3M COIL 3P Field 1M SYNCHRONOUS MOTOR
Comment Holes in the stator and horns in the rotor Opening slot of absorber Airgap between the stator teeth Airgap between stator and rotor Absorber Absorber Absorber Absorber Absorber Absorber Absorber Absorber Absorber Absorber Absorber Absorber Stator negative phase 1 Stator positive phase 1 Stator negative phase 2 Stator positive phase 2 Stator negative phase 3 Stator positive phase 3 Field negative phase 1
Color Magenta Magenta Magenta Yellow White White White White White White White White White White White White Yellow Red Yellow Red Yellow Red Turquoise PAGE 19
FLUX 2D®9.20
Defining the problem
Names Field 1P Field 2M Field 2P SHAFT ROTOR_CORE STATOR_CORE
Comment Field positive phase 1 Field negative phase 2 Field positive phase 2 Motor shaft Rotor magnetic core Stator magnetic core
Color Red Turquoise Red Turquoise Cyan 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.c Shaft region
PAGE 20
Fig 2.2.3.b Stator core region
Fig 2.2.3.d Airgap region
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
SYNCHRONOUS MOTOR
Fig 2.2.3.i Coil 1M region
PAGE 21
FLUX 2D®9.20
Defining the problem
Fig 2.2.3.j Coil 2P region
Fig 2.2.3.l Coil 3P region
PAGE 22
Fig 2.2.3.k Coil 2M 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
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Defining the problem
AM 11 AM 22 AQ 22
AM 33 AM 44 AQ 2
AQ 11
AQ 1
AM 2
AM 4
AM 1
AM 3
Fig 2.2.3.s All absorber regions Note : To assign regions to faces : [Physics],[Assign regions to geometric entities], [Assign regions to faces]
SYNCHRONOUS MOTOR
PAGE 23
FLUX 2D®9.20
Defining the problem
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
2.4.1
Defining the problem
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 shortcircuit will be modeled (single phase, three phase …) in modifying the value of resistors in which the stator is linked. Names B1,B2,B3 B_ROTOR L1, L2, L3
Type Coils Coils Inductances
R1, R2, R3,R6
Resistors
L4 RU1, RU2, RU3, AM1, AM2, AM3, AM4, AM11, AM22, AM33, AM44, AQ1, AQ2, AQ11, AQ22 R5,R7,R8, ……. …..R23, R24, R25 L5,L6,L7, …….. …..L22, L23, L24
Inductances
Values 181.2 mΩ 5.0136 Ω 1.104 mH According to test (106 or 10-6Ω) 8.8 mH
Resistors
106 Ω
Solid conductors
ρ = 2.7 10-8 Ω.m
Resistors
2.89 10-6 Ω
Inductances
10-9 H
Fig 10 : ME_CC
SYNCHRONOUS MOTOR
PAGE 25
FLUX 2D®9.20
Defining the problem
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 B1, B2, B3 B_ROTOR B5 B6 L1, L2, L3 L4 L5 L6 V1
Type Coils Coils Coils Coils Inductances Inductances Inductances Inductances Voltage source
Values 181.2 mΩ 5.0136 Ω 8.486 Ω 9.358 Ω 1.104 mH 8.8 mH 15.6 mH 11.2 mH According to the test
Fig 11 : AC_SSFR_D_AXIS_POS circuit
PAGE 26
SYNCHRONOUS MOTOR
FLUX 2D®9.20
2.4.3
Defining the problem
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 B1, B2, B3 B_ROTOR B5 B6 L1, L2, L3 L4 R1 R2,R3,R4, … …, R19, R20, R21 L5, L6, L7, … …, L22, L23, L24 V1
Type Coils Coils Coils Coils Inductances Inductances Resistance
Values 181.2 mΩ 5.0136 Ω 8.486 Ω 9.358 Ω 1.104 mH 8.8 mH
Resistors
2.89 10-6 Ω
Inductances
10-9 H
Voltage source
According to the test
4
10 Ω
Fig 12 : AC_SSFR_Q_AXIS_POS circuit
SYNCHRONOUS MOTOR
PAGE 27
FLUX 2D®9.20
Defining the problem
2.4.4
TM_NETWORK
This circuit will be used to know the behavior of machine when it is connected to the network. Names B1, B2, B3 B_ROTOR B5 B6 L1, L2, L3 L4 L5 L6 R1, R2, R3 L7, L8, L9 V1, V2, V3 I_rotor
Type Coils Coils Coils Coils Inductances Inductances Inductances Inductances Resistances Inductances Voltage source Current source
Values 181.2 mΩ 5.0136 Ω 8.486 Ω 9.358 Ω 1.104 mH 8.8 mH 15.6 mH 11.2 mH According to the test According to the test According to the test According to the test
Fig 13 :TM_NETWORK circuit
PAGE 28
SYNCHRONOUS MOTOR
FLUX 2D®9.20
2.5
Defining the problem
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 : Js = 1.6T and µr = 8000
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 : Js = 1.6T and µr = 8000 for B(H) curve. Iso_resistivity = 15. 10-8 Ω.m
SYNCHRONOUS MOTOR
PAGE 29
FLUX 2D®9.20
Defining the problem
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.
3.1
Parameters Xd, Xq in magneto static
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
FLUX 2D®9.20
Parameters Xd, Xq in magneto static
3.2.2
Physical conditions
Problem name Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity Rotation about Z axis with number of repetitions
Angle_det Magneto static Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Offset angle with respect to the X line (ZOX plane) 0
Name of material
Type
STEEL_NLIN
Isotropic scalar analytic saturation (arctg, 2 coeff.)
Mechanical Comment Type Set name ROTOR Rotor Rotation around one axis STATOR AIRGAP
Stator Airgap
Coord. System ROTOR
FIXED COMPRES SIBLE
-
Initial relative permeability 8000
Rotation axis Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT AM_1, AM_2, AM_3, AM_4, AM_11, AM_22, AM_33, AM_44, AQ_1, AQ_2, AQ_11, AQ_22, COIL_1M, COIL_1P, COIL_2M, COIL_2P, COIL_3M, COIL_3P Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE
PAGE 32
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Saturation magnetization (T) 1.6
Pivot External Point characteristic (0,0,0) Multi-static
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR ROTOR STATOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Parameters Xd, Xq in magneto static
Stranded coil Name B_ROTOR
Stranded coil with imposed current 2
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and periodicities
Mechanical Set
215
B_ROTOR
negative
ROTOR
FIELD_1P
215
B_ROTOR
positive
FIELD_2M
215
B_ROTOR
negative
FIELD_2P
215
B_ROTOR
positive
All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Boundary condition
ROTOR ROTOR ROTOR
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
FLUX 2D®9.20
Parameters Xd, Xq in magneto static
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).
θ Xd = 55 ° θ Xq = 10 °
θd = 55 °
θq = 10 ° 6
3 4
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 : To jump to an other angle : [Parameter],[Manager] or click on (E-3) Weber
Cur 1
0
-1
-2
degres
-3
0
25
50
75
Fig 3.2.b : Flux in COIL_3P curve according the position of rotor
Note : To obtain the flux : [Computation],[2D curves manager] or click on chosse [parameter], [Inductance], [Flux by region] and a Coil.
then
Note : To obtain the cursor : [2D Curve], [New cursor]
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 Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation • •
XdXq_Is Magneto static Plane 132 mm 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 2
Offset angle with respect to the X line (ZOX plane) 0
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Name of material
Type
STEEL_NLIN
Isotropic scalar analytic saturation (arctg, 2 coeff.)
Initial relative permeability 8000
Saturation magnetization (T) 1.6
Rotation about Z axis with number of repetitions
Mechanical Comment Set name ROTOR Rotor
STATOR AIRGAP
Stator Airgap
SYNCHRONOUS MOTOR
Type Rotation around one axis
FIXED COMPRESSIBLE
Coord. System ROTOR
-
Rotation Pivot axis Point Rotation (0,0,0) around one axis parallel to Oz -
External characteristic Multi-static
PAGE 35
FLUX 2D®9.20
Parameters Xd, Xq in magneto static
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT AM_1, AM_2, AM_3, AM_4, AM_11, AM_22, AM_33, AM_44, AQ_1, AQ_2, AQ_11, AQ_22, Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR ROTOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
Stranded coil Name B_ROTOR B1 B2 B3
Stranded coil with imposed current 0 - 0.5 -0.5 1
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
negative
FIELD_1P
215
B_ROTOR
positive
FIELD_2M
215
B_ROTOR
negative
FIELD_2P
215
B_ROTOR
positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Boundary condition
PAGE 36
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
automatically set by Flux 2D
SYNCHRONOUS MOTOR
FLUX 2D®9.20
3.3.3 •
Parameters Xd, Xq in magneto static
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: X =
(4 × π × f × Φ ) ⎛ I AT ⎞ ⎜ ⎟ ⎝ 54 ⎠
with - f corresponding to the nominal frequency : 50 Hz - 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 computed for one phase then two coils. (E-3) Weber
400
300
200
100
(E3) Ampere 0,5
1
Fig 3.3.a : Flux curve in COIL_3 in direct position according to the stator current
SYNCHRONOUS MOTOR
PAGE 37
FLUX 2D®9.20
Parameters Xd, Xq in magneto static
Note : To create a group of two coils : [Supports], [Group manager] Warning : Do nott forget to give the turns number of each coil (54) in [Physics], [Coefficients], [Modify] All the flux values may be get back in order to be analyzed by a computer software like Excel. Each reactance will be computed for each value of current and a curve of the reactance evolution may be plotted. Note : To obtain the flux values : Right click on the flux curve, choose [Values], [Write all in review file] Is in At
Flux D in Wb
Flux 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-01
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 22.00
20.00
I nominal Reactances
18.00
Xd in ohm Xq in ohm
16.00
14.00
12.00
10.00 0
200
400
600
800
1000
1200
stator current in At
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
PAGE 40
FLUX 2D®9.20
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Short-circuit tests
4.
4.1
Unloaded operating
4.1.1
Purpose
Short-circuit tests
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 Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity Rotation about Z axis with number of repetitions
SYNCHRONOUS MOTOR
bemf Transient_magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Offset angle with respect to the X line (ZOX plane) 0
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
PAGE 41
FLUX 2D®9.20
Short-circuit tests
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
Isotropic Initial relative Saturation value permeability magnetization (T) 8000 1.6
1 2.7e-8 Ωm
Mechanical Comment Set name
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components V1 R1, R2, R3, R6 L1, L2, L3 L4 R5,R7,R8, ……. …..R23, R24, R25 L5,L6,L7, …….. …..L22, L23, L24
PAGE 42
-
Pivot Point
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
ME_CC Values 8.76 V 109 1.104 mH 8.8 mH 2.89 10-6 Ω 10-9 H
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Short-circuit tests
Name of Stranded coil component B_ROTOR B1 B2 B3
Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
negative
FIELD_1P
215
B_ROTOR
positive
FIELD_2M
215
B_ROTOR
negative
FIELD_2P
215
B_ROTOR
positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
PAGE 43
FLUX 2D®9.20
Short-circuit tests
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition • •
4.1.3 • • • •
PAGE 44
Symmetries and periodicities Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
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°).
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 °
SYNCHRONOUS MOTOR
FLUX 2D®9.20
4.1.4
Short-circuit tests
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.
49,999
49,999
0
0
-50
-50
(20,16+ x) 0
5
•
10
15
0,01
19,999E-3
0,03
39,999E-3
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
(20,16+ x) 0
0,01
19,999E-3
0,03
39,999E-
Fig 4.13.c : Current curve on the two last periods
SYNCHRONOUS MOTOR
PAGE 45
FLUX 2D®9.20
Short-circuit tests
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 Volt
SPECTRUMSpectr_Vs1
FromVs1 Fundamental 47,618
75
50
25
0
2,5
5
7,5
10
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 Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
SYNCHRONOUS MOTOR
SC_MONO Transient_magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account) Offset angle with respect to the X line (ZOX plane) 0
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Isotropic Initial relative Saturation value permeability magnetization (T) 8000 1.6
1 2.7e-8 Ωm
PAGE 47
FLUX 2D®9.20
Short-circuit tests
Mechanical Comment Set name
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components V1 R1, R6 R2, R3 L1, L2, L3 L4 R5,R7,R8, ……. …..R23, R24, R25 L5,L6,L7, …….. …..L22, L23, L24
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
ME_CC Values 8.76 V 10-6 Ω 10+6 Ω 1.104 mH 8.8 mH 2.89 10-6 Ω 10-9 H
Name of Stranded coil component B_ROTOR B1 B2 B3
PAGE 48
-
Pivot Point
Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Short-circuit tests
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
negative
FIELD_1P
215
B_ROTOR
positive
FIELD_2M
215
B_ROTOR
negative
FIELD_2P
215
B_ROTOR
positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
PAGE 49
FLUX 2D®9.20
Short-circuit tests
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition
Symmetries and periodicities Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
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
4.2.4
Short-circuit tests
Analysis •
Flux lines
The evolution of flux lines in the magnetic circuit can be displayed. 6
7 8 5 4
7
3
5
6
3
10 11 1
1 2
8
11
10
2 4
9
9
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
•
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. Ampere
150
99,999
50
0
s.
-50
20,399
20,5
20,6
20,699
20,8
Fig 3.6.1.d : Current in the A phase with his d-c component
SYNCHRONOUS MOTOR
PAGE 51
FLUX 2D®9.20
Short-circuit tests
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. Ampere 15
10
5
s.
0
20,399
20,5
20,6
20,699
20,8
Fig 3.6.1.e : Field current with DC and AC components •
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. N.m 49,999
0
-50
s. 20,399
20,5
20,6
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 Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
SYNCHRONOUS MOTOR
SC_THREE Transient_magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account) Offset angle with respect to the X line (ZOX plane) 0
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Isotropic Initial relative Saturation value permeability magnetization (T) 8000 1.6
1 2.7e-8 Ωm
PAGE 53
FLUX 2D®9.20
Short-circuit tests
Mechanical Comment Set name
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components V1 R1, R2, R3, R6 L1, L2, L3 L4 R5,R7,R8, ……. …..R23, R24, R25 L5,L6,L7, …….. …..L22, L23, L24
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
ME_CC Values 8.76 V 10-6 Ω 1.104 mH 8.8 mH 2.89 10-6 Ω 10-9 H
Name of Stranded coil component B_ROTOR B1 B2 B3
PAGE 54
-
Pivot Point
Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Short-circuit tests
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
negative
FIELD_1P
215
B_ROTOR
positive
FIELD_2M
215
B_ROTOR
negative
FIELD_2P
215
B_ROTOR
positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
PAGE 55
FLUX 2D®9.20
Short-circuit tests
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition • •
Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
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 • •
Symmetries and periodicities
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
4.3.4
Short-circuit tests
Analysis
The current, flowing each phase of stator, is given as a function of time: −t
I ac = I s + I × e ' o
Td'
−t
+ I ×e '' o
Td''
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 : E X 'd = ( Is + I ' )
with : E unloaded maximum voltage before the short circuit. The time constant T’d is determined from the previous curve. 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 value of I’. The duration until the point on the straight line where the current is equal to 0.606 times I’ gives the half of T’d.
SYNCHRONOUS MOTOR
PAGE 57
FLUX 2D®9.20
Short-circuit tests
Ampere
0 -50 -100
s. 20,399
150
20,5
20,6
20,699
20,8
20,5
20,6
20,699
20,8
20,5
20,6
20,699
20,8
Ampere
100 49,999 0
s. 20,399 Ampere
0 -50 -100
s. 20,399
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
(Imax – Imin) / 2
(Imax - Imin) / 2
(Imax - Imin) / 2
76,609 54,846 43,425 35,712 29,951 25,506 22,077 19,426 17,374 15,792 14,561 13,602 12,845 12,238
79,807 55,814 42,878 35,233 29,579 25,216 21,845 19,227 17,191 15,615 14,397 13,448 12,697 12,094
72,416 53,005 42,149 34,904 29,420 15,885 21,917 19,379 17,389 15,827 14,601 13,641 12,882 12,273
PAGE 58
Periodic component average = I
I - Is Is = 8,97 A
76,278 54,555 42,817 35,283 29,650 22,203 21,946 19,344 17,318 15,745 14,520 13,563 12,808 12,202
67,308 45,585 33,847 26,313 20,680 13,233 12,976 10,374 8,348 6,775 5,550 4,593 3,838 3,232
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 11,340 11,002 10,719 10,480 10,277 10,103 9,954 9,825 9,715
11,604 11,201 10,866 10,585 10,348 10,146 9,975 9,829 9,704 9,596
11,779 11,372 11,033 10,748 10,508 10,303 10,127 9,977 9,848 9,735
11,710 11,304 10,967 10,684 10,445 10,242 10,068 9,920 9,792 9,682
2,740 2,334 1,997 1,714 1,475 1,272 1,098 0,950 0,822 0,712
Fig 4.3.2.b : Exemple of periodic components on 0.5 s
I - Is 100,0
Ampères
I’ = 26 A
0.606 x I’
10,0
1,0
0,1 0
0,1
0,2
0,3
0,4
0,5
0,6
Temps 0.5 x T’d
I - Is 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 : X d′ =
176 = (8.97 + 26) 5.03 Ω
SYNCHRONOUS MOTOR
and
0.5 × Td′ = 0.075 s
then T’d = 0.15 s
PAGE 59
FLUX 2D®9.20
Short-circuit tests
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 : X d′′ =
PAGE 60
E ( Is + I '+ I ′′)
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:
Voltage
100 Hz Fig 5.1.1.a Positionning of direct axis
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
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Voltag
100 Hz
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 Problem type Frequency Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
PAGE 62
AC_SSFR_DIRECT_POS Magnetic AC 2D 100 Hz Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Isotropic value
Offset angle with respect to the X line (ZOX plane) 0
Initial relative permeability
8000
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Saturation magnetization (T) 1.6
Type of equivalent B(H) curve Sine Wave flux density
1 2.7e-8Ωm
SYNCHRONOUS MOTOR
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Mechanical Comment Set name
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
-
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components V1 L1, L2, L3 L4 L5 L6
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
MH_SSFR_POS_DIRECT Values 1.5 V 1.104 mH 8.8 mH 15.6mH 11.2mH
Name of Stranded coil component B_ROTOR B1 B2 B3 B5 B6
SYNCHRONOUS MOTOR
Pivot Point
Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ 8.486 Ω 9.358 Ω
PAGE 63
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
PAGE 64
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Name of face Turn region (coil number conductor region type)
Associated coil component
AM_1
74
B5
AM_2
74
B5
AM_3
74
B6
AM_4
74
B6
AM_11
74
B5
AM_22
74
B5
AM_33
74
B6
AM_44
74
B6
AQ_1
74
B6
AQ_2
74
B6
AQ_11
74
B5
AQ_22
74
B5
Boundary condition
orientation
Positive Negative Negative Positive Negative Positive Positive Negative Positive Negative Positive Negative
Symmetries and periodicities All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Mechanical Set ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
automatically set by Flux 2D
Solving parameters : - Rotor positions : [-5°; 85°], step [2.5°] •
Quadrature simulation
Problem name Problem type Frequency Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation
SYNCHRONOUS MOTOR
AC_QUADRATURE_SSFR AC magnetic 2D 100 Hz Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
PAGE 65
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Type of periodicity Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
Offset angle with respect to the X line (ZOX plane) 0
Initial relative permeability
8000
Saturation magnetization (T) 1.6
2.7e-8Ωm
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
PAGE 66
Type of equivalent B(H) curve Sine Wave flux density
1
Mechanical Comment Set name
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
-
Pivot Point
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Circuit Components V1 R1 L1, L2, L3 L4 R2,R3,R4, ……. …..R19, R20, R21 L5,L6,L7, …….. …..L22, L23, L24 Name of Stranded coil component B_ROTOR B1, B2, B3
AC_SSFR_Q_AXIS Values 1.5 V 104 Ω 1.104 mH 8.8 mH 2.89 10-6 Ω 10-9 H Resistance 5.0136 Ω 181.2 mΩ
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
PAGE 67
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition
-
PAGE 68
Symmetries and periodicities Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
automatically set by Flux 2D
Solving parameters : Rotor positions : [-5°; 85°], step [2.5°]
SYNCHRONOUS MOTOR
FLUX 2D®9.20
5.1.3 • • •
StandStill Frequency Reponse (SSFR)
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
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Quadrature simulation
Fig 5.1.3.b Field voltage to determine quadrature axis
The quadrature axis position is close to 55 ° degree. •
PAGE 70
These two positions will be used as initial position for each SSFR test, direct or quadrature.
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 shortcircuit. 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 Problem type Frequency Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
SYNCHRONOUS MOTOR
AC_QUADRATURE_SSFR AC magnetic 2D 100 Hz Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Isotropic value
Offset angle with respect to the X line (ZOX plane) 0
Initial relative permeability
8000
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Saturation magnetization (T) 1.6
Type of equivalent B(H) curve Sine Wave flux density
1 2.7e-8Ωm
PAGE 71
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Mechanical Comment Set name
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components V1 R1 L1, L2, L3 L4 R2,R3,R4, ……. …..R19, R20, R21 L5,L6,L7, …….. …..L22, L23, L24
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
AC_SSFR_Q_AXIS Values 1.5 V 104 Ω 1.104 mH 8.8 mH 2.89 10-6 Ω 10-9 H
Name of Stranded coil component B_ROTOR B1, B2, B3
PAGE 72
-
Pivot Point
Resistance 5.0136 Ω 181.2 mΩ
SYNCHRONOUS MOTOR
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
PAGE 73
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition
5.2.3 • •
Symmetries and periodicities Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
automatically set by Flux 2D
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
5.2.4 •
StandStill Frequency Reponse (SSFR)
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:
Ld ( p ) = Ld × With : -
(1 + Tdcc′ p ) × (1 + Tdcc′′ p ) (1 + Tdo′ p ) × (1 + Tdo′′ p )
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
Ld L’ L’’d
1 / T’do
1 / T’dcc
1 / T’’do
1 / T’’dcc
ω
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:
Ld ( jω ) =
Z d ( jω ) − ra jω
with: -
Z d ( jω ) =
SYNCHRONOUS MOTOR
Varm 1 x with ½ for connection between phases Iarm 2
PAGE 75
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
•
Analysis Ampere
Degree 175
CURVE I_phase
5
CURVE I_mod Circuit / Magnitude Current Frequency B1; Phase (Deg): 0
4
3
Circuit / Phase Current Frequency B1 ; Phase (Deg): 0
150
125
2
1 100
hertz
hertz 100
200
300
100
400
Fig 5.2.3.b Module of armature current
200
300
400
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 :
Lr = •
Z × sin(φ z )
Li = (
2 ×ω
L = Lr ² + Li ²
PAGE 76
2
− rarm ) ×
1
ω
Computation of module and phase of complex inductance from : ATAN (
•
Z × cos(φ z )
φl =
Lr ) × 180 Li
π
Plotting of gain and phase diagram on semi-log paper
SYNCHRONOUS MOTOR
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
VOLTAGE f
w
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
0,01 0,03 0,06 0,13 0,25 0,50 0,63 1,26 2,51 5,03 6,28 12,57 25,13 31,42 37,70 50,27 62,83 125,66 251,33 314,16 502,65 628,32 1256,6 4 400 2513,2 7
CURRENT Vs/Is
L(p)
Vs (V) Ph (°) Is (A) Ph I (°) Module Phase 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12 2,12
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2,12
0
5,85 5,85 5,85 5,82 5,73 5,45 5,30 4,72 4,32 4,09 4,02 3,70 3,08 2,80 2,54 2,12 1,80 0,98 0,51 0,41 0,26 0,20
179,86 0,36 179,30 0,36 178,61 0,36 177,26 0,36 174,75 0,37 170,96 0,39 169,74 0,40 167,75 0,45 167,89 0,49 165,81 0,52 164,18 0,53 155,44 0,57 140,60 0,69 134,80 0,76 129,95 0,83 122,49 1,00 117,17 1,18 104,63 2,16 97,66 4,20 96,25 5,23 94,14 8,31 93,43 10,37
Part_R
Part_I
Module
Phase
359,86 359,30 358,61 357,26 354,75 350,96 349,74 347,75 347,89 345,81 344,18 335,44 320,60 314,80 309,95 302,49 297,17 284,63 277,66 276,25 274,14 273,43
0,070 0,070 0,070 0,069 0,067 0,061 0,057 0,038 0,021 0,013 0,011 0,009 0,009 0,009 0,008 0,008 0,008 0,008 0,008 0,008 0,008 0,008
-0,00008 0,00153 0,00317 0,00636 0,01234 0,02190 0,02522 0,03036 0,02351 0,01395 0,01155 0,00632 0,00337 0,00274 0,00230 0,00175 0,00141 0,00073 0,00039 0,00033 0,00024 0,00021
0,070 0,070 0,070 0,070 0,069 0,065 0,062 0,049 0,031 0,019 0,016 0,011 0,009 0,009 0,009 0,009 0,008 0,008 0,008 0,008 0,008 0,008
0,07 -1,25 -2,60 -5,24 -10,38 -19,82 -23,97 -38,70 -48,91 -47,82 -45,26 -33,70 -21,21 -17,73 -15,18 -11,75 -9,57 -5,00 -2,71 -2,28 -1,64 -1,43
0,10 91,97
20,61
271,97
0,008
0,00014
0,008
-0,96
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
L(p) - Phase
0.080
0.001
0.01
0.1
1
10
100
1000
10.00
0.070
F2D results
0.060
Equivalent transfer function
0.00
-10.00
Phase (degres)
L(p) (H)
0.050
0.040
0.030
0.020
-20.00
-30.00
-40.00
0.010 -50.00
0.000 0.001
F2D results Equivalent transfer function
0.01
0.1
1
10
100
Frequency (Hz)
Fig 5.2.3.e : Gain diagram
SYNCHRONOUS MOTOR
1000
-60.00 Frequency (Hz)
Fig 5.2.3.f Phase diagram
PAGE 77
FLUX 2D®9.20
StandStill Frequency Reponse (SSFR)
-
The synchronous reactance is obtained in extending the gain bode diagram to ω = 0 and in using :
Xd = Ld ω =0 × ω 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: X ′′d = Ld ω →∞ × 2 × ω = 0.005 × 2 × 314.159
X’’d = 2.57 Ω
Warning : It is indicated only as a method but do not correspond to a standard.
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 Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
SYNCHRONOUS MOTOR
MT_SOLV_UNLOADED Transient Magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Offset angle with respect to the X line (ZOX plane) 0
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
PAGE 79
FLUX 2D®9.20
Loaded on the network
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
Mechanical Set name ROTOR
Comment
Type
Rotor
Rotation around one axis
STATOR AIRGAP
Stator Airgap
Initial relative permeability
8000
Coord. Rotation System axis ROTOR Rotation around one axis parallel to Oz
FIXED
-
COMPRESS IBLE
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components I_ROTOR V1 V2 V3 R1, R2, R3
L7, L8, L9
PAGE 80
-
Saturation magnetization (T) 1.6
Pivot Point (0,0,0)
-
Type of equivalent B(H) curve Sine Wave flux density
Coupled load
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° -
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
TM_NETWORK Values -5 A 127 V, 50 Hz, 0° 127 V, 50 Hz, -120° 127 V, 50 Hz, 120° 6
10 Ω -9
10 H
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of Stranded coil component B_ROTOR B1 B2 B3 B5 B6
Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ 8.486 Ω 9.358 Ω
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
PAGE 81
FLUX 2D®9.20
Loaded on the network
Name of face Turn region (coil number conductor region type)
Associated coil component
AM_1
74
B5
AM_2
74
B5
AM_3
74
B6
AM_4
74
B6
AM_11
74
B5
AM_22
74
B5
AM_33
74
B6
AM_44
74
B6
AQ_1
74
B6
AQ_2
74
B6
AQ_11
74
B5
AQ_22
74
B5
Boundary condition
6.1.3 • • •
orientation
Positive Negative Negative Positive Negative Positive Positive Negative Positive Negative Positive Negative
Symmetries and periodicities
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Mechanical Set
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
automatically set by Flux 2D
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
6.1.4 •
Loaded on the network
Analysis
First time step
6
9
11
4
1 5 3 2
10
8 7
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. 1,55
(E3) rpm
1,524
1,5
1,475
s. 0,05
99,999E-3
0,15
0,2
Fig 5.1.3.b : Rotor speed curve
SYNCHRONOUS MOTOR
PAGE 83
FLUX 2D®9.20
Loaded on the network
-
Voltage
The network voltage and generator voltage will be superimposed.
V_STATOR_1
200
Circuit / Voltage Time B1; 100
V_NETWORK_1
0
Circuit / Voltage Time V1 ;
-99,999
-199,999
0,05
99,999E-3
0,15
0,2
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
(E-6) Ampere
I_B1 Circuit / Current Time B1 ; 0
s.
-500
0,05
99,999E-3
0,15
0,2
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
FLUX 2D®9.20
Loaded on the network
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 Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions Name of material STEEL_NLIN
Repetition number of the periodicity about Z 2
Offset angle with respect to the X line (ZOX plane) 0
Isotropic value
Type
Comment
Type
Rotor
Rotation around one axis
STATOR AIRGAP
Stator Airgap
FIXED COMPRESS IBLE
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Initial relative permeability
8000
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
Mechanical Set name ROTOR
PAGE 86
MT_SOLV_LOADED Transient Magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Coord. Rotation System axis ROTOR Rotation around one axis parallel to Oz
-
-
Pivot Point (0,0,0)
-
Saturation magnetization (T) 1.6
Coupled load
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° -
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components I_ROTOR L1, L2, L3 L4 L5 L6 V1 V2 V3 R1, R2, R3 L7, L8, L9
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
TM_NETWORK Values -5 A 1.104e-3 8.8mH 15.6mH 11.2mH 254 V, 50 Hz, 0° 254 V, 50 Hz, -120° 254 V, 50 Hz, 120° 72.14 Ω 0.1717 H
Name of Stranded coil component B_ROTOR B1, B2, B3 B5 B6
SYNCHRONOUS MOTOR
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
Resistance 5.0136 Ω 181.2 mΩ 8.486 Ω 9.358 Ω
PAGE 87
FLUX 2D®9.20
Loaded on the network
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
PAGE 88
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face Turn region (coil number conductor region type)
Associated coil component
AM_1
74
B5
AM_2
74
B5
AM_3
74
B6
AM_4
74
B6
AM_11
74
B5
AM_22
74
B5
AM_33
74
B6
AM_44
74
B6
AQ_1
74
B6
AQ_2
74
B6
AQ_11
74
B5
AQ_22
74
B5
Boundary condition
•
orientation
Positive Negative Negative Positive Negative Positive Positive Negative Positive Negative Positive Negative
Symmetries and periodicities
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Mechanical Set
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
automatically set by Flux 2D
Load conditions at 30 %
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
6.2.3 • • •
Solving parameters Initial position of rotor : 90° Time step [0.0005s], study time limit [0.2], Initialized by static computation
SYNCHRONOUS MOTOR
PAGE 89
Loaded on the network
6.2.4 -
FLUX 2D®9.20
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 :
New point with adapted torque
Constant active power
Old point
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 Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation
SYNCHRONOUS MOTOR
MT_SOLV_LOADED_T Transient Magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
PAGE 91
FLUX 2D®9.20
Loaded on the network
Type of periodicity
Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Offset angle with respect to the X line (ZOX plane) 0
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
Mechanical Set name ROTOR
Comment
Type
Rotor
Rotation around one axis
STATOR AIRGAP
Stator Airgap
FIXED
Initial relative permeability
8000
Coord. Rotation System axis ROTOR Rotation around one axis parallel to Oz
COMPRESS IBLE
-
-
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE
PAGE 92
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Saturation magnetization (T) 1.6
Pivot Point (0,0,0)
-
Coupled load
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° -
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Circuit Components I_ROTOR L1, L2, L3 L4 L5 L6 V1 V2 V3 R1, R2, R3 L7, L8, L9
TM_NETWORK Values -5 A 1.104e-3 8.8mH 15.6mH 11.2mH 254 V, 50 Hz, 0° 254 V, 50 Hz, -120° 254 V, 50 Hz, 120° 72.14 Ω 0.1717 H
Name of Stranded coil component B_ROTOR B1, B2, B3 B5 B6
Resistance 5.0136 Ω 181.2 mΩ 8.486 Ω 9.358 Ω
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
PAGE 93
FLUX 2D®9.20
Loaded on the network
Name of face Turn region (coil number conductor region type)
Associated coil component
AM_1
74
B5
AM_2
74
B5
AM_3
74
B6
AM_4
74
B6
AM_11
74
B5
AM_22
74
B5
AM_33
74
B6
AM_44
74
B6
AQ_1
74
B6
AQ_2
74
B6
AQ_11
74
B5
AQ_22
74
B5
Boundary condition
6.3.3 • • •
6.3.4
orientation
Positive Negative Negative Positive Negative Positive Positive Negative Positive Negative Positive Negative
Symmetries and periodicities
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Mechanical Set
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
automatically set by Flux 2D
Solving parameters
Initial position of rotor : 90° -3 Time step [2E ], study time limit [7], Initialized by static computation
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
1,8
(E3) t/mn
Vitesse rotor Mecanique/ Vitesserotation Temps 1,7
1,6
1,5
s. 1
2
3
4
5
6
Fig 6.3.3.a : Rotor speed evolution
This divergence can be explained by the equation of electromagnetic torque: p × 3× E ×V C em = × sin δ ω × Xd 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. C ×ω × X d δ = arcsin( em ) p × 3 × E ×V 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: 0,066
(E6) Deg.
65,75E-3
65,5E-3
65,25E-3
s. 6,969
6,979
6,989
7
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
FLUX 2D®9.20
Loaded on the network
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 Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation
-
MT_SOLV_LOADED_F_T Transient Magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Computation of the field current :
It is computed from the Behn-Eshenburg diagram : Q coefficient for coils flux computation Type of periodicity
Angle_det Magneto static Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Offset angle with respect to the X line (ZOX plane) 0
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Name of material
Type
STEEL_NLIN
Isotropic scalar analytic saturation (arctg, 2 coeff.)
Initial relative permeability 8000
Saturation magnetization (T) 1.6
Rotation about Z axis with number of repetitions
Mechanical Comment Set name ROTOR Rotor
STATOR AIRGAP
Stator Airgap
Type
Rotation around one axis
FIXED COMPRESSIBLE
Coord. System ROTOR
-
Rotation Pivot axis Point Rotation (0,0,0) around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT AM_1, AM_2, AM_3, AM_4, AM_11, AM_22, AM_33, AM_44, AQ_1, AQ_2, AQ_11, AQ_22, COIL_1M, COIL_1P, COIL_2M, COIL_2P, COIL_3M, COIL_3P Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE
PAGE 104
External characteristic Multi-static
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR ROTOR
STATOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Stranded coil Name B_ROTOR
Stranded coil with imposed current 2
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and periodicities
Mechanical Set
215
B_ROTOR
Negative
ROTOR
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Boundary condition
ROTOR ROTOR ROTOR
automatically set by Flux 2D
Solving parameters : • Angle of rotor [-10 ; 80], step [5] • Initial position of rotor: 0°
SYNCHRONOUS MOTOR
PAGE 105
FLUX 2D®9.20
Loaded on the network
CASE 2: Xd and Xq Problem name Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
XdXq_Is Magneto static Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Offset angle with respect to the X line (ZOX plane) 0
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Name of material
Type
STEEL_NLIN
Isotropic scalar analytic saturation (arctg, 2 coeff.)
Initial relative permeability 8000
Saturation magnetization (T) 1.6
Rotation about Z axis with number of repetitions
Mechanical Comment Set name ROTOR Rotor
STATOR AIRGAP
Stator Airgap
Type
Rotation around one axis
FIXED COMPRESSIBLE
Coord. System ROTOR
-
Rotation Pivot axis Point Rotation (0,0,0) around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT AM_1, AM_2, AM_3, AM_4, AM_11, AM_22, AM_33, AM_44, AQ_1, AQ_2, AQ_11, AQ_22,
PAGE 106
External characteristic Multi-static
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR ROTOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
Stranded coil Name B_ROTOR B1 B2 B3
Stranded coil with imposed current 0 - 0.5 -0.5 1
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Boundary condition
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
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
FLUX 2D®9.20
Loaded on the network
CASE 3: back emf computation Problem name Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions Name of material STEEL_NLIN
ALU_BAR ALU_BAR
bemf Transient_magnetic Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Type
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
Offset angle with respect to the X line (ZOX plane) 0
Isotropic Initial relative value permeability 8000
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
PAGE 108
Saturation magnetization (T) 1.6
1 2.7e-8 Ωm
Mechanical Comment Set name
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
-
Pivot Point
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Circuit Components V1 R1, R2, R3, R6 L1, L2, L3 L4 R5,R7,R8, ……. …..R23, R24, R25 L5,L6,L7, …….. …..L22, L23, L24
ME_CC Values 8.76 V 109 1.104 mH 8.8 mH
2.89 10-6 Ω 10-9 H
Name of Stranded coil component B_ROTOR B1 B2 B3
Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
PAGE 109
FLUX 2D®9.20
Loaded on the network
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition
Symmetries and periodicities
Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
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 Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
SC_mono Transient_magnetic Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account) Offset angle with respect to the X line (ZOX plane) 0
Isotropic value
Initial relative permeability 8000
Saturation magnetization (T) 1.6
1 2.7e-8 Ωm
Mechanical Comment Set name
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
-
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE
SYNCHRONOUS MOTOR
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Pivot Point
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
PAGE 111
FLUX 2D®9.20
Loaded on the network
Circuit Components V1 R1, R6 R2, R3 L1, L2, L3 L4 R5,R7,R8, ……. …..R23, R24, R25 L5,L6,L7, …….. …..L22, L23, L24
ME_CC Values 8.76 V 10-6 Ω 10+6 Ω 1.104 mH 8.8 mH
2.89 10-6 Ω 10-9 H
Name of Stranded coil component B_ROTOR B1 B2 B3
Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
PAGE 112
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
Loaded on the network
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition
Symmetries and periodicities
Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
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
FLUX 2D®9.20
Loaded on the network
Case 5: three phase short circuit Problem name Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
SC_THREE Transient_magnetic Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account) Offset angle with respect to the X line (ZOX plane) 0
Isotropic value
Initial relative permeability
8000
2.7e-8 Ωm
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
PAGE 114
Saturation magnetization (T) 1.6
1
Mechanical Comment Set name
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
-
Pivot Point
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components V1 R1, R2, R3, R6 L1, L2, L3 L4 R5,R7,R8, ……. …..R23, R24, R25 L5,L6,L7, …….. …..L22, L23, L24
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
ME_CC Values 8.76 V 10-6 Ω 1.104 mH 8.8 mH
2.89 10-6 Ω 10-9 H
Name of Stranded coil component B_ROTOR B1 B2 B3
Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
PAGE 115
FLUX 2D®9.20
Loaded on the network
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition
Symmetries and periodicities
Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
automatically set by Flux 2D
Solving parameters :
• •
PAGE 116
From the last step of the back emf simulation Time length : [0.5], step [0.0005s]
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Case 6: direct axis determination for SSFR test Problem name Problem type Frequency Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
AC_SSFR_DIRECT_POS Magnetic AC 2D 100 Hz Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account) Offset angle with respect to the X line (ZOX plane) 0
Initial relative permeability
8000
Saturation magnetization (T) 1.6
Type of equivalent B(H) curve Sine Wave flux density
1 2.7e-8Ωm
Mechanical Comment Set name
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
SYNCHRONOUS MOTOR
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
-
Pivot Point
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
PAGE 117
FLUX 2D®9.20
Loaded on the network
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components V1 L1, L2, L3 L4 L5 L6
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
MH_SSFR_POS_DIRECT Values 1.5 V 1.104 mH 8.8 mH 15.6mH 11.2mH
Name of Stranded coil component B_ROTOR B1 B2 B3 B5 B6
Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ 8.486 Ω 9.358 Ω
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
PAGE 118
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face Turn region (coil number conductor region type)
Associated coil component
AM_1
74
B5
AM_2
74
B5
AM_3
74
B6
AM_4
74
B6
AM_11
74
B5
AM_22
74
B5
AM_33
74
B6
AM_44
74
B6
AQ_1
74
B6
AQ_2
74
B6
AQ_11
74
B5
AQ_22
74
B5
Boundary condition
orientation
Positive Negative Negative Positive Negative Positive Positive Negative Positive Negative Positive Negative
Symmetries and periodicities
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Mechanical Set
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
automatically set by Flux 2D
Solving parameters :
•
Rotor positions : [-5°; 85°], step [2.5°]
SYNCHRONOUS MOTOR
PAGE 119
FLUX 2D®9.20
Loaded on the network
Case 7: quadrature position for SSFR test Problem name Problem type Frequency Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
AC_QUADRATURE_SSFR AC magnetic 2D 100 Hz Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account) Offset angle with respect to the X line (ZOX plane) 0
Initial relative permeability
8000
Saturation magnetization (T) 1.6
Type of equivalent B(H) curve Sine Wave flux density
1 2.7e-8Ωm
Mechanical Comment Set name
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
PAGE 120
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
-
Pivot Point
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components V1 R1 L1, L2, L3 L4 R2,R3,R4, ……. …..R19, R20, R21 L5,L6,L7, …….. …..L22, L23, L24
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
AC_SSFR_Q_AXIS Values 1.5 V 104 Ω 1.104 mH 8.8 mH
2.89 10-6 Ω 10-9 H
Name of Stranded coil component B_ROTOR B1, B2, B3
Resistance 5.0136 Ω 181.2 mΩ
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
PAGE 121
FLUX 2D®9.20
Loaded on the network
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition
Symmetries and periodicities
Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
automatically set by Flux 2D
Solving parameters :
•
PAGE 122
Rotor positions : [-5°; 85°], step [2.5°]
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Case 8: SSFR test Problem name Problem type Frequency Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
Repetition number of the periodicity about Z 2
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.) B(H) : Linear isotropic J(E) : isotropic resistivity
ALU_BAR ALU_BAR
AC_QUADRATURE_SSFR AC magnetic 2D 100 Hz Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account) Offset angle with respect to the X line (ZOX plane) 0
Initial relative permeability
8000
Saturation magnetization (T) 1.6
Type of equivalent B(H) curve Sine Wave flux density
1 2.7e-8Ωm
Mechanical Comment Set name
Type
Coord. System
Rotation axis
ROTOR
Rotor
Rotation around one axis
ROTOR
STATOR AIRGAP
Stator Airgap
FIXED COMPRESSIBLE
Rotation around one axis parallel to Oz -
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
SYNCHRONOUS MOTOR
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
-
Pivot Point
Imposed speed
(0,0,0)
1500 rpm
-
-
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
PAGE 123
FLUX 2D®9.20
Loaded on the network
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components V1 R1 L1, L2, L3 L4 R2,R3,R4, ……. …..R19, R20, R21 L5,L6,L7, …….. …..L22, L23, L24
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
AC_SSFR_Q_AXIS Values 1.5 V 104 Ω 1.104 mH 8.8 mH
2.89 10-6 Ω 10-9 H
Name of Stranded coil component B_ROTOR B1, B2, B3
Resistance 5.0136 Ω 181.2 mΩ
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
PAGE 124
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Name of face region (solid conductor region type) AM_1 AM_2 AM_3 AM_4 AM_11 AM_22 AM_33 AM_44 AQ_1 AQ_2 AQ_11 AQ_22
Loaded on the network
Material
Associated solid conductor
Orientation
Mechanical set
Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar Alu_bar
M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22
Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive Positive
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
Name of solid conductor 2 terminals M_AM1 M_AM2 M_AM3 M_AM4 M_AM11 M_AM22 M_AM33 M_AM44 M_AQ1 M_AQ2 M_AQ11 M_AQ22 Boundary condition
Symmetries and periodicities
Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel Number of conductors in parallel
Number of conductors in parallel 1 1 1 1 1 1 1 1 1 1 1 1
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
FLUX 2D®9.20
Loaded on the network
Case 9: Loaded on the network (unload) Problem name Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
MT_SOLV_UNLOADED Transient Magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
Mechanical Set name ROTOR
Comment
Type
Rotor
Rotation around one axis
STATOR AIRGAP
Stator Airgap
FIXED
Initial relative permeability
8000
Coord. Rotation System axis ROTOR Rotation around one axis parallel to Oz
COMPRESS IBLE
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
PAGE 126
Offset angle with respect to the X line (ZOX plane) 0
-
-
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Saturation magnetization (T) 1.6
Pivot Point (0,0,0)
-
Coupled load
Moment of inertia : 0.1215kg.m² Friction coefficient : 0.016N.m.S Drag Torque : 2.51 N.m Initial velocity : 1500 rpm -
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components I_ROTOR L1, L2, L3 L4 L5 L6 V1 V2 V3 R1, R2, R3
Loaded on the network
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
TM_NETWORK Values -5 A 1.104e-3 8.8mH 15.6mH 11.2mH 254 V, 50 Hz, 0° 254 V, 50 Hz, -120° 254 V, 50 Hz, 120°
L7, L8, L9 Name of Stranded coil component B_ROTOR B1 B2 B3 B5 B6
SYNCHRONOUS MOTOR
6
10 Ω -9
10 H Resistance 5.0136 Ω 181.2 mΩ 181.2 mΩ 181.2 mΩ 8.486 Ω 9.358 Ω
PAGE 127
FLUX 2D®9.20
Loaded on the network
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
PAGE 128
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face Turn region (coil number conductor region type)
Associated coil component
AM_1
74
B5
AM_2
74
B5
AM_3
74
B6
AM_4
74
B6
AM_11
74
B5
AM_22
74
B5
AM_33
74
B6
AM_44
74
B6
AQ_1
74
B6
AQ_2
74
B6
AQ_11
74
B5
AQ_22
74
B5
Boundary condition
orientation
Positive Negative Negative Positive Negative Positive Positive Negative Positive Negative Positive Negative
Symmetries and periodicities
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Mechanical Set
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
automatically set by Flux 2D
Solving parameters :
• • •
Initial position of rotor : 90° Time step [0.0005s], study time limit [0.2s], Initialized by static computation
SYNCHRONOUS MOTOR
PAGE 129
FLUX 2D®9.20
Loaded on the network
Case 10: Loaded on the network (30% load) without regulation Problem name Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
MT_SOLV_LOADED Transient Magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
Mechanical Set name ROTOR
Comment
Type
Rotor
Rotation around one axis
STATOR AIRGAP
Stator Airgap
Initial relative permeability
8000
Coord. Rotation System axis ROTOR Rotation around one axis parallel to Oz
FIXED COMPRESS IBLE
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
PAGE 130
Offset angle with respect to the X line (ZOX plane) 0
-
-
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Saturation magnetization (T) 1.6
Pivot Point (0,0,0)
-
Coupled load
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° -
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components I_ROTOR L1, L2, L3 L4 L5 L6 V1 V2 V3 R1, R2, R3 L7, L8, L9
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
TM_NETWORK Values -5 A 1.104e-3 8.8mH 15.6mH 11.2mH 254 V, 50 Hz, 0° 254 V, 50 Hz, -120° 254 V, 50 Hz, 120° 72.14 Ω 0.1717 H
Name of Stranded coil component B_ROTOR B1, B2, B3 B5 B6
Resistance 5.0136 Ω 181.2 mΩ 8.486 Ω 9.358 Ω
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
PAGE 131
FLUX 2D®9.20
Loaded on the network
Name of face Turn region (coil number conductor region type)
Associated coil component
AM_1
74
B5
AM_2
74
B5
AM_3
74
B6
AM_4
74
B6
AM_11
74
B5
AM_22
74
B5
AM_33
74
B6
AM_44
74
B6
AQ_1
74
B6
AQ_2
74
B6
AQ_11
74
B5
AQ_22
74
B5
Boundary condition
orientation
Positive Negative Negative Positive Negative Positive Positive Negative Positive Negative Positive Negative
Symmetries and periodicities
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Mechanical Set
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
automatically set by Flux 2D
Solving parameters :
• • •
PAGE 132
Initial position of rotor : 90° Time step [0.0005s], study time limit [1s], Initialized by static computation
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Case 11: Loaded on the network (30% load) with appropriated motor torque Problem name Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
MT_SOLV_LOADED_T Transient Magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
Mechanical Set name ROTOR
Comment
Type
Rotor
Rotation around one axis
STATOR AIRGAP
Stator Airgap
Initial relative permeability
8000
Coord. Rotation System axis ROTOR Rotation around one axis parallel to Oz
FIXED COMPRESS IBLE
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
SYNCHRONOUS MOTOR
Offset angle with respect to the X line (ZOX plane) 0
-
-
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Saturation magnetization (T) 1.6
Pivot Point (0,0,0)
-
Coupled load
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° -
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
PAGE 133
FLUX 2D®9.20
Loaded on the network
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components I_ROTOR L1, L2, L3 L4 L5 L6 V1 V2 V3 R1, R2, R3 L7, L8, L9
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
TM_NETWORK Values -5 A 1.104e-3 8.8mH 15.6mH 11.2mH 254 V, 50 Hz, 0° 254 V, 50 Hz, -120° 254 V, 50 Hz, 120° 72.14 Ω 0.1717 H
Name of Stranded coil component B_ROTOR B1, B2, B3 B5 B6
Resistance 5.0136 Ω 181.2 mΩ 8.486 Ω 9.358 Ω
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
PAGE 134
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face Turn region (coil number conductor region type)
Associated coil component
AM_1
74
B5
AM_2
74
B5
AM_3
74
B6
AM_4
74
B6
AM_11
74
B5
AM_22
74
B5
AM_33
74
B6
AM_44
74
B6
AQ_1
74
B6
AQ_2
74
B6
AQ_11
74
B5
AQ_22
74
B5
Boundary condition
orientation
Positive Negative Negative Positive Negative Positive Positive Negative Positive Negative Positive Negative
Symmetries and periodicities
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Mechanical Set
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
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
FLUX 2D®9.20
Loaded on the network
Case 12: Loaded on the network (30% load) with appropriated field current and motor torque Problem name Problem type Type of domain Depth Symmetry and periodicity => coefficient for coils flux computation Type of periodicity
Rotation about Z axis with number of repetitions
MT_SOLV_LOADED_F_T Transient Magnetic 2D Plane 132 mm Automatic coefficient (Symmetry and periodicity taken into account)
Repetition number of the periodicity about Z 2
Isotropic value
Name of material
Type
STEEL_NLIN
B(H) : Isotropic scalar analytic saturation (arctg, 2 coeff.)
Mechanical Set name ROTOR
Comment
Type
Rotor
Rotation around one axis
STATOR AIRGAP
Stator Airgap
Initial relative permeability
8000
Coord. Rotation System axis ROTOR Rotation around one axis parallel to Oz
FIXED COMPRESS IBLE
Name of face region (air or vacuum type) AIR_1 AIR_2 AIR_3 AIRGAP SHAFT
PAGE 136
Offset angle with respect to the X line (ZOX plane) 0
-
-
Even or odd periodicity/number of modeled poles Even (cyclic boundary conditions)
Saturation magnetization (T) 1.6
Pivot Point (0,0,0)
-
Coupled load
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° -
Mechanical set STATOR ROTOR STATOR AIRGAP ROTOR
SYNCHRONOUS MOTOR
FLUX 2D®9.20
Loaded on the network
Name of face region (magnetic non conducting region type) ROTOR_CORE STATOR_CORE Circuit Components I_ROTOR L1, L2, L3 L4 L5 L6 V1 V2 V3 R1, R2, R3 L7, L8, L9
Material
Mechanical set
STEEL_NLIN STEEL_NLIN
ROTOR STATOR
TM_NETWORK Values -6.85 A 1.104e-3 8.8mH 15.6mH 11.2mH 254 V, 50 Hz, 0° 254 V, 50 Hz, -120° 254 V, 50 Hz, 120° 72.14 Ω 0.1717 H
Name of Stranded coil component B_ROTOR B1, B2, B3 B5 B6
Resistance 5.0136 Ω 181.2 mΩ 8.486 Ω 9.358 Ω
Name of face region (coil conductor region type) FIELD_1M
Turn number
Associated coil component
orientation
Symmetries and Mechanical periodicities Set
215
B_ROTOR
Negative
FIELD_1P
215
B_ROTOR
Positive
FIELD_2M
215
B_ROTOR
Negative
FIELD_2P
215
B_ROTOR
Positive
COIL_1P
54
B1
Positive
COIL_1M
54
B1
Negative
COIL_2P
54
B2
Positive
COIL_2M
54
B2
Negative
COIL_2P
54
B3
Positive
COIL_2M
54
B3
Negative
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
SYNCHRONOUS MOTOR
ROTOR ROTOR ROTOR ROTOR STATOR STATOR STATOR STATOR STATOR STATOR
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FLUX 2D®9.20
Loaded on the network
Name of face Turn region (coil number conductor region type)
Associated coil component
AM_1
74
B5
AM_2
74
B5
AM_3
74
B6
AM_4
74
B6
AM_11
74
B5
AM_22
74
B5
AM_33
74
B6
AM_44
74
B6
AQ_1
74
B6
AQ_2
74
B6
AQ_11
74
B5
AQ_22
74
B5
Boundary condition
orientation
Positive Negative Negative Positive Negative Positive Positive Negative Positive Negative Positive Negative
Symmetries and periodicities
All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series All conductors are in series
Mechanical Set
ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR ROTOR
automatically set by Flux 2D
Solving parameters :
• • •
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Initial position of rotor : 90° Time step [0.002s], study time limit [20s], Initialized by static computation
SYNCHRONOUS MOTOR