Comsol Conference 2008, Hannover, Germany · Hannover, 05.Nov.2008 H. Lorenzen, J. Timmerberg UAS OOW Wilhelmshaven, Germany S. Mylvaganam Telemark University College, Porsgrunn,

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




•Point of focus (transmission lines)

•Approach of estimating parameters using COMSOL Multiphysics

•Verification

•Conclusions


•Motivation





•Motivation


•Approach of estimating parameters using Multiphysics

•Verification

•Conclusions

•3




Established

•Conventional power flow analysis for the fundamental component

• Considering balanced load

• Single phase equivalent circuit diagram


model and available parameters

•4




• Embedded generation, mainly based on wind-power, has achieved higher level of penetration scattered harmonic excitation

• Demand on Higher Harmonic Analysis Methods (scientific work):


•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




Validation of Harmonic-Analysis Methodology in Laboratory-Scale


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





Validation of Harmonic-Analysis Methodology in Laboratory-Scale

•7





• 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





•Motivation

•point of focus (transmission lines)


•verification

•Conclusions

•9




•R‘ L‘ C‘ R‘(f) L‘(f) C‘(f)


•10




•R‘ L‘ C‘ R‘(f) L‘(f) C‘(f)


•11





•12

•skin and proximiti effect R‘(f) L‘(f)

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

++

++

00030201

30333231

40232221

20131211

''''''''''''''''

LRMMMMLRMMMMLRMMMMLR





•Motivation



•Verification

•Conclusions

•13





R‘ L‘ C‘ R‘(f) L‘(f) C‘(f)

•14





R‘ L‘ C‘ R‘(f) L‘(f) C‘(f)

•15





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





r1r2

d

1

2 0

3

ra

2

21 UCW •=

WU

C •= 2

2

•17





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=

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⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

•

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⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡ 1

2

31

23

12

30

30

10

2

101001 eW

U

CCCCCC

•18





⎥⎥⎥⎥⎥⎥⎥⎥

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⎤

⎢⎢⎢⎢⎢⎢⎢⎢

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⎡

=

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⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

•

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

2

1

2

31

23

12

30

30

10

2110011101001

e

e

WW

U

CCCCCC

•19





⎥⎥⎥⎥⎥⎥⎥⎥

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⎤

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⎡

=

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⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

•

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⎦

⎤

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⎡

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





'10'20'30'12'23'31

14617.41461471477.24

CCC nF

kmCCC

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟

=⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

•21





'10'20'30'12'23'31

14617.41461471477.24

CCC nF

kmCCC

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟

=⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

•22





r1r2

d

1

2 0

3

ra

LjRZ ω+=IUZ =

•23





side condition

3_2_ istIAdSistI −== ∫∫rr

•24





3_2_ istIAdSistI −== ∫∫rr

•25





( ) ∑≠=

++=3

0kl

llkkkkk IMILjRU ω ( ) ( ) ( ) ( ) ( )200233121222222 * MIjMIjMIjLIjRIU ωωωω −−−+=

−

( ) ( ) ( ) ( ) ( )300232131333333 * MIjMIjMIjLIjRIU ωωωω −−−+=−

case I1=I0=0

•26





( )2_2_

23222

2222

*

*istIerrUMLjR

IU

Z =−+== −−

ω

( )3_3_

23333

3333

*

*istIerrUMLjR

IU

Z =−+== −−

ωcase I1=I0=0

•27





⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

++

++

00030201

30333231

40232221

20131211

LjRMjMjMjMjLjRMjMjMjMjLjRMjMjMjMjLjR

ωωωωωωωωωωωωωωωω

•28





⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

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⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

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⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

+−+

−−+

−−−+

•

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⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

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•

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





Comsol Multiphysics program and the modules

„Electrostatic“

„AC Electromagnetic“

•30





•Motivation



•Verification

•Conclusions

•31





.

-3

-3

2.150 10 Ws/m2.205 10 Ws/m

Kontr

FemLab

WW

⋅=

⋅

mmdmmd Kontr 2.07.5 =→=

•32





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





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





•Motivation

•point of focus (transmission lines)


•verification

•Conclusions

•35





•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

Comsol Conference 2008, Hannover, Germany · Hannover, 05.Nov.2008 H. Lorenzen, J. Timmerberg UAS OOW Wilhelmshaven, Germany S. Mylvaganam Telemark University College, Porsgrunn,

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