Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
Comsol Conference 2008, Hannover, Germany
Presented at the COMSOL Conference 2008 Hannover
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
•Point of focus (transmission lines)
•Approach of estimating parameters using COMSOL Multiphysics
•Verification
•Conclusions
Calculation of Cable Parameters for Different Cable Shapes
•Motivation
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
•Motivation
•Point of focus (transmission lines)
•Approach of estimating parameters using Multiphysics
•Verification
•Conclusions
•3
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Established
•Conventional power flow analysis for the fundamental component
• Considering balanced load
• Single phase equivalent circuit diagram
Calculation of Cable Parameters for Different Cable Shapes
model and available parameters
•4
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
• Embedded generation, mainly based on wind-power, has achieved higher level of penetration scattered harmonic excitation
• Demand on Higher Harmonic Analysis Methods (scientific work):
Calculation of Cable Parameters for Different Cable Shapes
•Resonance mode analysis
•All-phase and full-state dynamic models
•For all Power System Components (generator,motor, lines, transformer, reactor, cap-banks) involved in Harmonic Resonance-Phenomena
•5
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Validation of Harmonic-Analysis Methodology in Laboratory-Scale
Calculation of Cable Parameters for Different Cable Shapes
1. Synchronous Generator
2. Generator Protection
3. Transformer
...
5. Line Segments and Busses
...
8. SCADA (Siemens WinCC)
9. Tap Changeable Transformer
14. Transient Grid Analyser
•6
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
Validation of Harmonic-Analysis Methodology in Laboratory-Scale
•7
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
• Embedded generation, mainly based on wind-power, has achieved higher level of penetration scattered harmonic excitation
• Demand on Higher Harmonic Analysis Methods (scientific work):
• Manufacturers also require such detailed knowledge for customer fulfillment
•8
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
•Motivation
•point of focus (transmission lines)
•Approach of estimating parameters using Multiphysics
•verification
•Conclusions
•9
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
•R‘ L‘ C‘ R‘(f) L‘(f) C‘(f)
Calculation of Cable Parameters for Different Cable Shapes
•10
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
•R‘ L‘ C‘ R‘(f) L‘(f) C‘(f)
Calculation of Cable Parameters for Different Cable Shapes
•11
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
•12
•skin and proximiti effect R‘(f) L‘(f)
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
++
++
00030201
30333231
40232221
20131211
''''''''''''''''
LRMMMMLRMMMMLRMMMMLR
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
•Motivation
•Point of focus (transmission lines)
•Approach of estimating parameters using Multiphysics
•Verification
•Conclusions
•13
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
R‘ L‘ C‘ R‘(f) L‘(f) C‘(f)
•14
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
R‘ L‘ C‘ R‘(f) L‘(f) C‘(f)
•15
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
r1r2
d
1
2 0
3
ra
calculation of the cable parameters with two separat steps
•Capacitances using „Electrostatic“ modul
•Resistances and Inductances using“AC-Electromagnetic” modul
•16
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
r1r2
d
1
2 0
3
ra
2
21 UCW •=
WU
C •= 2
2
•17
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
•
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡ 1
2
31
23
12
30
30
10
2
101001 eW
U
CCCCCC
•18
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
•
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
2
1
2
31
23
12
30
30
10
2110011101001
e
e
WW
U
CCCCCC
•19
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
•
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
6
5
4
3
2
1
2
31
23
12
30
30
10
2
011101101110110011110100011010101001
e
e
e
e
e
e
WWWWWW
U
CCCCCC
'10'20'30'12'23'31
14617.41461471477.24
CCC nF
kmCCC
⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟
=⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠
•20
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
'10'20'30'12'23'31
14617.41461471477.24
CCC nF
kmCCC
⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟
=⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠
•21
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
'10'20'30'12'23'31
14617.41461471477.24
CCC nF
kmCCC
⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟
=⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠
•22
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
r1r2
d
1
2 0
3
ra
LjRZ ω+=IUZ =
•23
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
side condition
3_2_ istIAdSistI −== ∫∫rr
•24
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
3_2_ istIAdSistI −== ∫∫rr
•25
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
( ) ∑≠=
++=3
0kl
llkkkkk IMILjRU ω ( ) ( ) ( ) ( ) ( )200233121222222 * MIjMIjMIjLIjRIU ωωωω −−−+=
−
( ) ( ) ( ) ( ) ( )300232131333333 * MIjMIjMIjLIjRIU ωωωω −−−+=−
case I1=I0=0
•26
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
( )2_2_
23222
2222
*
*istIerrUMLjR
IU
Z =−+== −−
ω
( )3_3_
23333
3333
*
*istIerrUMLjR
IU
Z =−+== −−
ωcase I1=I0=0
•27
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
++
++
00030201
30333231
40232221
20131211
LjRMjMjMjMjLjRMjMjMjMjLjRMjMjMjMjLjR
ωωωωωωωωωωωωωωωω
•28
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
+−+
−−+
−−−+
•
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
•
0
3
3
3
2
2
2
1
1
1
00
30
33
20
23
22
10
13
12
11
1000001000011000000000101000000010000100000101000000001100000000010010000000100100000001010000000011
UUUUUUUUUU
LjRMj
LjRMjMj
LjRMjMjMj
LjR
I
ωωω
ωωω
ωωωω
Postprocessing/
Global Variables
•29
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
Comsol Multiphysics program and the modules
„Electrostatic“
„AC Electromagnetic“
•30
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
•Motivation
•Point of focus (transmission lines)
•Approach of estimating parameters using Multiphysics
•Verification
•Conclusions
•31
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
.
-3
-3
2.150 10 Ws/m2.205 10 Ws/m
Kontr
FemLab
WW
⋅=
⋅
mmdmmd Kontr 2.07.5 =→=
•32
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
R’1
R’n
R’m
L’n
L’m
L’1
M’nmM’1m
M’1n
:::
:::::
:
[3] Jung-Hsiang Wang; Modeling of Frequency-Dependent Impedance of the Third Rail Used in Traction Power Systems, IEEE Trans. on Power Delivery, Vol. 15, No. 2, April 2000
[4] Alexander W. Barr; Calculation of Frequen-cy-Dependent Impedance for Conductors of Rec-tangular Cross Section, AMP Journal of Techno-logy Vol. 1 November, 1991
•33
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
R’1
R’n
R’m
L’n
L’m
L’1
M’nmM’1m
M’1n
:::
:::::
:
0/R R
0/L L
- Results Partial wire methodo Results Femlab
•34
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
•Motivation
•point of focus (transmission lines)
•Approach of estimating parameters using Multiphysics
•verification
•Conclusions
•35
Hannover, 05.Nov.2008
H. Lorenzen, J. TimmerbergUAS OOW Wilhelmshaven, Germany
S. MylvaganamTelemark University College, Porsgrunn, Norway
Calculation of Cable Parameters for Different Cable Shapes
•Comsol Multiphysics modules „Electrostatic“ and „AC Electromagnetic“•enable us to characterize the electrical parameters of cablesfor different frequencies
•Impedance values can be verified•using partial wire methods for inductances •simplified ideal models for capacitances
•helpfull for scientific and industrial work
•36