Download Three-phase cable: Computation of the dielectric losses

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Example
Creation
date
Three-phase cable: Computation of the dielectric losses
2009
Author : Pascal Ferran - Université Claude Bernard Lyon
Ref. FLU2_EH_REL_01
Program
Dimension
Version
Physics
Application
Work area
Flux
2D
10.3
Electric
Steady AC
Electric
networks
FRAMEWORK
Presentation
General remarks
Study of the dielectric losses in a three-phase insulating cable according to the loss
factor and the insulator permittivity.
This example explains how to evaluate the sensitivity of the losses results according
to the properties of the electric cable material.
Objective
Computation of the dielectric losses value in the insulator according to different
parameters.
The parameters the user can change are :
Global insulator’s relative permittivity (RP)
Global insulator’s loss factor (LF)
Theoretical
reminders
There is no theoretical formula to easily calculate the dielectric losses in our device
but we can rely on theoretical notions related to dielectric losses to obtain
approximate results.
Properties
- Rated conductor diameter D = 10 mm
- PVC insulating sheath with thickness ID = 4 mm
- Rated properties of the insulating sheath are :
r = 8 and tg ()= 0.1
- Global insulating cable :
r = 8 and tg ()= 0.1
- Ext. Radius of the cable REXT = 50 mm
- Rated radius of the circle where the conductors
circles are located : R = 15 mm
- Voltage applied to each of the conductors :
Efficient value V = 15000 V and frequency f = 50
Hz.
Illustration
Main characteristics
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FRAMEWORK
Flux
Some results …
Power density distribution at a rated working point
Equipotential lines distribution at the initial moment for the specified characteristics
PAGE 2
Three-phase cable: Computation of the dielectric losses
Flux
FRAMEWORK
Dielectric losses = f (loss factor of the global insulator)
(other parameters are rated)
Dielectric losses = f (permittivity of the global insulator)
(other parameters are rated)
To go further …
-
Coupling between the conductors (Computation of corresponding impedance matrix)
…
Three-phase cable: Computation of the dielectric losses
PAGE 3
MODEL IN FLUX
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MODEL IN FLUX
Domain
Dimension
2D
Depth
10000
Infinite Box
Length unit.
mm
Angle unit.
degrees
Size
Periodicity
In. radius :
Symmetry
Characteristics
Out. Radius :
none
Repetition number :
Offset angle :
Even/odd periodicity
Application
Steady AC electric
Properties
Electric potential stiff at 0V in
periphery
Geometry / Mesh
Full model in the FLUX environment
Mesh
2nd order type
Mesh
Number of nodes
3369
Input Parameters
Name
Type
RP
Physical
LF
Physical
V
Physical
PAGE 4
Description
Relative permittivity of
the global insulator
Loss factor of the global
insulator
Voltage source
Rated value
8
0.1
15000 V
Three-phase cable: Computation of the dielectric losses
Flux
MODEL IN FLUX
Material Base
NAME
B(H) model
Magnetic property
J(H) model
Electrical property
D(E) model
Dielectric property
PVC
Linear isotropic with losses
GIP
Linear isotropic with losses
r = 8
tg (
r = RP
tg (LF
K(T) model
K(T) characteristics
RCP(T) model
RCP(T) characteristics
-
-
NAME
Nature
CONDUCTORS
Surface region
Type
Inactive region
Material
Mechanical Set
Corresponding circuit
component
-
CI
Surface region
Dielectric and conductive
region
PVC
-
GI
Surface region
Dielectric and
conductive region
GIP
-
-
-
-
Electrical characteristics
-
-
-
Current source
-
-
-
Thermal characteristics
-
-
-
Possible thermal source
-
-
-
NAME
Nature
Type
Material
Mechanical Set
Corresponding circuit
component
L1
Line region
Stiff electric potential
-
L2
Line region
Stiff electric potential
-
L3
Line region
Stiff electric potential
-
-
-
-
Electrical characteristics
V volts
= 0°
Current source
-
V volts
= - 120°
-
V volts
= - 240°
-
Thermal characteristics
-
-
-
Possible thermal source
-
-
-
Regions
Three-phase cable: Computation of the dielectric losses
PAGE 5
MODEL IN FLUX
Flux
Mechanical Set
Fixed part :
Compressible part :
Type
Characteristics
Miscellaneous
Mobile part :
Type of kinematics
Internal characteristics:
External characteristics :
Mechanical stops
Electrical circuit
Component
Type
Characteristics
Associated Region
Electric scheme
Solving process options
Type of linear system solver
Type of non-linear system
solver
Automatically
chosen
Parameters
Precision
Newton Raphson
Automatically defined
0.0001
Method for computing the
relaxation factor
Nb iterations
100
Automatically defined
Thermal coupling
Advanced characteristics
Solving
Scenario
Name of
parameter
Controllable
parameter
Variation
method
Interval definition
Step selection
SCENARIO_1
SCENARIO_2
RP
LF
Physical
Physical
Step value
Steps list
1 to 10
0.001 to 1000
Step of 1
Factor 10 between
each step
Duration of the solving
PAGE 6
SCENARIO_1 : 8 seconds
SCENARIO_2 : 6 seconds
Operating System
Windows XP 32 bits
Three-phase cable: Computation of the dielectric losses
Flux
ANNEX
ANNEX
Theoretical reminders
Dielectric properties of a few materials
Typical values
The below table reviews the typical values of the relative permittivity and loss factor
for high voltage cables insulators.
Insulating material
Fluid oil low pressure
Fluid oil high pressure
Relative permittivity:r
3.3
3.5
PVC
8
PE
Impregnated paper
Loss factor: tan ()
0.004
0.0045
0.1
2.3
0.001
4
0.1
The below table reviews the voltage value (between phases) from which the dielectric
losses have to be taken into account.
Insulating material
Fluid oil
PVC
PE
Impregnated paper
Voltage (kV)
110
10
225
66
Three-phase cable: Computation of the dielectric losses
PAGE 7