1 Transmission line parameters Transmission line parameters • Aim – Learn how to use ATP to obtain series impedance parameters; • Contents • Contents – Introducing the ground reference – Self and mutual impedances – Matrix description – Look into ATPDraw LCC module Examples – Examples MTU-Houghton, 2010 Internett: www.elkraft.ntnu.no/
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1 Transmission line parametersTransmission line parameters · 1 Transmission line parametersTransmission line parameters •Aim – Learn how to use ATP to obtain series impedance
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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
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
• 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
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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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
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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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
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
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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
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
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.