1 Transmission line parametersTransmission line parameters · 1 Transmission line...

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Transmission line parametersTransmission line parameters

• Aim– Learn how to use ATP to obtain series

impedance parameters; • Contents• Contents

– Introducing the ground reference– Self and mutual impedances– Matrix descriptionp– Look into ATPDraw LCC module

Examples– ExamplesMTU-Houghton, 2010 Internett: www.elkraft.ntnu.no/

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Briefly about the speakerBriefly about the speaker• Professor at Norwegian Univ Science andProfessor at Norwegian Univ. Science and

Technology – Dept. Electrical Engineering– Power system transients and protectiony p– High voltage engineering, stress calculations– Recent focus on Power Transformers

• Honorary member of European EMTP user’s group– User of ATP for 20 years

• Developer of ATPDraw• Sabbatical at MTU

– Room 628, phone 487-2910– [email protected]

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Relevance of series impedance parameters

• Why do we have to understand the details? – The manufacturer provides only positiveThe manufacturer provides only positive

sequence 50/60 Hz data! – Zero sequence data important for ground fault

it ti !situations!– Mutual coupling between parallel transmission

lines is important for protection settings!lines is important for protection settings!– What is the influence of

• Transmission line height, h• Phase separation, D• Bundling, duplex/triplex• Ground resistivity • Ground resistivity,

MTU, Houghton, 2010 www.elkraft.ntnu.no/

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Ground planeGround plane

• The text book chapt. 4 handles only conductors in free space. Let us introduce pa ground plane:

ID D

Ia Ib Ia IbAir Air

Ia Ibh1 h2

h1 h2 Air

-Ia-Ib

EarthAirAir

I I

2

h1h2

2

h1h2

‘Air’-Ia

-Ib

Field lines perpendicular

Ideal case: Imaging concept

Real case: Penetration


perpendicular to earth surface

Imaging concept Penetration depth of earth

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Internal self impedanceInternal self impedance

• Self impedance is split in internal and external partp

I t l i d ( d lid d )s i eZ Z Z

• Internal impedance (round, solid cond.):

Z R j

Eq. 4.2 & 4.13 in text book.8i iZ R j

Depends on skin effect and

geometry. GMR available.

• The last part is often written on the form0 0 4ln

rrj j j e

Eq 4 23 in text book


ln8 2 4 2

j j j e Eq. 4.23 in text book.

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External self impedanceExternal self impedance

• A conductor over an ideal, lossless ground (Eq. 4.22 in text book): 2r( q )– Imaging:

0 2lj h / ]

h=0

h

• A conductor over a real earth surface0 2ln

2ej hZ

r

/m] image

– Penetration depth (or Carson’s formula)– For low frequencies (>>h): [m]

For low frequencies ( h):0 0 02ln ln

2 8 2j

e

Dj jhZr r

[Ωm]660 [m][Hz]jD

f

/m], with

0[m]

j


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Generalized self impedanceGeneralized self impedance

• The inductive part of the internal and external impedances can be mergedp g

0 0 ln js i e i

DjZ Z Z R j

0 0

8 8 2

ln8 2 '

s i e i

ji

jr

DjRr

[Ωm]660 [m][Hz]jD

f

/m], with

• Geometric mean radius:G l T bl i f A 3

8 2 r [Hz]f

– General . Tables exist, ref. A.3– For solid, circular, non-magnetic material

'r GMR


1/4' 0.7788r e r r

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Mutual impedanceMutual impedance• The conductor will link with both the otherThe conductor will link with both the other

conductor and its image: D’I

D’’

I

• According to Eq. 4.36 this givesD

2 2( )'' D h hj jD

-I

• Which for low frequencies becomes:

1 20 02 2

1 2

( )''ln ln2 ' 2 ( )

m

D h hj jDZD D h h

Which for low frequencies becomes:0 0 ln

8 2 'j

mD

Z jD


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Multiple conductors MatrixMultiple conductors - MatrixTh t f lf d t l i d• The concept of self and mutual impedances is easily expandable to multiple conductors

Conductors on the same potential can be handled– Conductors on the same potential can be handled with equivalent conductors, ref Chapt. 4.8 in text book, or by reduction of the full matrix

– Conductors on ground potential has to be eliminated

Th i i d t i i t i l• The series impedance matrix is symmetrical on the form

sa mab mac magZ Z Z Z

sb mbc mbg

sc mcg

Z Z ZZ

Z Z


sgZ

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Positive and zero sequencePositive and zero sequence

• Let the series impedance matrix now be reduced to a 3x3 matrix on the form

s m m

s m

Z Z ZZ Z Z

For simplicity a perfectly transposed system is assumed

• Then the positive and zero seq. imps. aresZ

e t e pos t e a d e o seq ps a e0 0 0 0ln ln

8 2 ' 8 2 '

'

j js m i

D DZ Z Z R j j

r D

D

0 'ln

2 'iDR jr

0 032 3 l jDZ Z Z R j

Influence of ground disappears!

Strong groundMTU, Houghton, 2010 www.elkraft.ntnu.no/

0 00 3 2

2 3 ln8 2 ' '

js m iZ Z Z R j

D r

Strong ground influence!

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Coupling between transmission linesCoupling between transmission lines

• Consider two transmission lines:

S

• This gives a 6x6 series impedance matrix:11 12 12s m m m m mZ Z Z Z Z Z

A th di t b t11 12 12

22 23

22

s m m m m m

s m m m

s m

Z Z Z ZZ Z

Z

As the distance between the lines increases, the mutual impedances Z

s m m

s m

ZZ Z Z

Z ZZ

mutual impedances Zmijtends to become equal

0 0 jD


sZ 0 0 ln

8 2j

mijD

Z jS

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Coupling between transmission linesCoupling between transmission lines• Now consider a zero-sequence q

component (I02) in one line, what is the consequence on the other?consequence on the other?

11 12 12a s m m m m m aV Z Z Z Z Z Z IV Z Z Z Z I

22 23

22

b s m m m b

c s m c

V Z Z Z Z IV Z Z IV Z Z Z I

02 02

02 02

02 02

s m m

s m

s

V Z Z Z IV Z Z IV Z I

02 02s

11 12 13 02

012 02

( )( )

a s a m b m c m m mV Z I Z I Z I Z Z Z IZ Z I Z I

A zero sequence component is


012 02( )s m aZ Z I Z I A zero sequence component is coupled to the other line

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Using Line Constants in ATPUsing Line Constants in ATP

• LCC interface in ATPDraw– Get geometrical datag– Start ATPDraw, File New

Start LCC (right click in empty space)– Start LCC (right click in empty space)


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LCC model inputLCC model input• Choose PI model and Standard data• On Data page type in conductor data


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Creating an LCC modelCreating an LCC model

• Click on View to inspect• Click on Run ATP to create model (CancelClick on Run ATP to create model (Cancel

the plotting window that pops up)Wh i th lt ( t th f li )?• Where is the result (note the name of line)?– Check Tools|Options/Files&Folders (ATP)| p ( )– Lib file is final model, lis contains sub-results

1IN AOUT A 6 64863719E 01 4 79819218E+00 1 20191093E 011IN___AOUT__A 6.64863719E-01 4.79819218E+00 1.20191093E-01 2IN___BOUT__B 5.08928089E-01 1.57302035E+00 -1.58574976E-02

6.66163048E-01 4.72564369E+00 1.22277240E-01 3IN___COUT__C 4.86898502E-01 1.12911067E+00 -3.57568321E-03

5 08928089E 01 1 57302035E+00 1 58574976E 02


5.08928089E-01 1.57302035E+00 -1.58574976E-02 6.64863719E-01 4.79819218E+00 1.20191093E-01

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Inspecting the lis file

Impedance matrix, in units of [ohms/kmeter ] for the system of physical conductors.Rows and columns proceed in the same order as the sorted input.

1 1.163069E-018.404390E-01 Inspecting the lis file

Full system (14x14)2 5.667074E-02 1.163069E-01

2.955284E-01 8.404390E-01

3 5.657221E-02 5.667074E-02 1.163069E-012.432963E-01 2.955284E-01 8.404390E-01

4 5.670445E-02 5.666840E-02 5.656775E-02 1.163069E-015.498391E-01 2.929874E-01 2.420161E-01 8.404390E-01

5 5.666462E-02 5.662880E-02 5.652871E-02 5.666466E-02 1.162273E-015.237530E-01 2.929909E-01 2.420503E-01 5.498841E-01 8.405289E-01

6 5 666466E 02 5 663112E 02 5 653314E 02 5 666462E 02 5 662488E 02 1 162273E 016 5.666466E-02 5.663112E-02 5.653314E-02 5.666462E-02 5.662488E-02 1.162273E-015.498841E-01 2.955291E-01 2.433302E-01 5.237530E-01 5.499291E-01 8.405289E-01

7 5.667300E-02 5.670445E-02 5.666840E-02 5.667074E-02 5.663112E-02 5.663336E-02 1.163069E-012.981582E-01 5.498391E-01 2.929874E-01 2.955284E-01 2.955291E-01 2.981557E-01 8.404390E-01

8 5.663336E-02 5.666462E-02 5.662880E-02 5.663112E-02 5.659158E-02 5.659381E-02 5.666466E-02 1.162273E-018 5.663336E 02 5.666462E 02 5.662880E 02 5.663112E 02 5.659158E 02 5.659381E 02 5.666466E 02 1.162273E 012.981557E-01 5.237530E-01 2.929909E-01 2.955291E-01 2.956183E-01 2.982481E-01 5.498841E-01 8.405289E-01

9 5.663112E-02 5.666466E-02 5.663112E-02 5.662880E-02 5.658927E-02 5.659158E-02 5.666462E-02 5.662488E-02 1.162273E-012.955291E-01 5.498841E-01 2.955291E-01 2.929909E-01 2.930773E-01 2.956183E-01 5.237530E-01 5.499291E-01 8.405289E-01


1.163069E-018.404390E-01


5.666466E-02 1.162273E-015.498841E-01 8.405289E-01

12 5.653314E-02 5.663112E-02 5.666466E-02 5.652871E-02 5.648973E-02 5.649414E-02 5.662880E-02 5.658927E-02 5.659158E-022 433302E 01 2 955291E 01 5 498841E 01 2 420503E 01 2 421059E 01 2 433861E 01 2 929909E 01 2 930773E 01 2 956183E 01


2.433302E-01 2.955291E-01 5.498841E-01 2.420503E-01 2.421059E-01 2.433861E-01 2.929909E-01 2.930773E-01 2.956183E-01

5.666462E-02 5.662488E-02 1.162273E-015.237530E-01 5.499291E-01 8.405289E-01


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Reduced system (3x3)Reduced system (3x3)

Impedance matrix, in units of [ohms/kmeter ] for the system of equivalent phase conductors.Rows and columns proceed in the same order as the sorted inputRows and columns proceed in the same order as the sorted input.

1 6.648637E-024.798192E-01

2 5.089281E-02 6.661630E-021.573020E-01 4.725644E-01

3 4.868985E-02 5.089281E-02 6.648637E-021.129111E-01 1.573020E-01 4.798192E-01

Both "R" and "X" are in [ohms];


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Check the result ICheck the result I

• User Verify in LCC module


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Check the result IICheck the result II

• Line Check module– Select a line sections in the circuit

– Click ATP|Line Check


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Line Check resultsLine Check results• Results differ somewhat from VerifyResults differ somewhat from Verify

because an improved method is used


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Double circuit lineDouble circuit line

• Example

100 m17.5 m

18 0 m h=(2Vmid+Vtow)/3 m

• Verify (1 km line):

18.0 m =100 m

• Verify (1 km line):• Homework:

– Reproduce– Check with handCheck with hand

calculationsMTU, Houghton, 2010 www.elkraft.ntnu.no/

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SummarySummary• The concept of Self and MutualThe concept of Self and Mutual

impedances of a transmission line over lossy ground introducedlossy ground introduced

• Hand-calculation formulas presented and linked to text book chapt 4linked to text book chapt. 4

• Multi-conductor matrix systems introduced• Line Constants of ATP introduced via the

LCC module of ATPDraw– Verify– Inspection of lis-fileInspection of lis file


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