1 Transmission line parametersTransmission line · PDF fileTransmission line...
Transcript of 1 Transmission line parametersTransmission line · PDF fileTransmission line...
1
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/
2
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]
3
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/
4
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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
perpendicular to earth surface
Imaging concept Penetration depth of earth
5
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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
ln8 2 4 2
j j j e Eq. 4.23 in text book.
6
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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
7
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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
1/4' 0.7788r e r r
8
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/
9
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
10
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!
11
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
12
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
13
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)
MTU, Houghton, 2010 www.elkraft.ntnu.no/
14
LCC model inputLCC model input• Choose PI model and Standard data• On Data page type in conductor data
MTU, Houghton, 2010 www.elkraft.ntnu.no/
15
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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
5.08928089E-01 1.57302035E+00 -1.58574976E-02 6.64863719E-01 4.79819218E+00 1.20191093E-01
16
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
10 5.657660E-02 5.667300E-02 5.670445E-02 5.657221E-02 5.653314E-02 5.653751E-02 5.667074E-02 5.663112E-02 5.663336E-022.445987E-01 2.981582E-01 5.498391E-01 2.432963E-01 2.433302E-01 2.446322E-01 2.955284E-01 2.955291E-01 2.981557E-01
1.163069E-018.404390E-01
11 5.653751E-02 5.663336E-02 5.666462E-02 5.653314E-02 5.649414E-02 5.649849E-02 5.663112E-02 5.659158E-02 5.659381E-022.446322E-01 2.981557E-01 5.237530E-01 2.433302E-01 2.433861E-01 2.446885E-01 2.955291E-01 2.956183E-01 2.982481E-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
MTU, Houghton, 2010 www.elkraft.ntnu.no/
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
13 5.582845E-02 5.581227E-02 5.573753E-02 5.582795E-02 5.578980E-02 5.579030E-02 5.581381E-02 5.577574E-02 5.577421E-023.131729E-01 2.901020E-01 2.469376E-01 3.121978E-01 3.153077E-01 3.163665E-01 2.917828E-01 2.935802E-01 2.918212E-01
17
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];
MTU, Houghton, 2010 www.elkraft.ntnu.no/
18
Check the result ICheck the result I
• User Verify in LCC module
MTU, Houghton, 2010 www.elkraft.ntnu.no/
19
Check the result IICheck the result II
• Line Check module– Select a line sections in the circuit
– Click ATP|Line Check
MTU, Houghton, 2010 www.elkraft.ntnu.no/
20
Line Check resultsLine Check results• Results differ somewhat from VerifyResults differ somewhat from Verify
because an improved method is used
MTU, Houghton, 2010 www.elkraft.ntnu.no/
21
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/
22
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
MTU, Houghton, 2010 www.elkraft.ntnu.no/