Engineering, 2013, 5, 146-151
doi:10.4236/eng.2013.51b027 Published Online January 2013 (http://www.SciRP.org/journal/eng)
Copyright © 2013 SciRes. ENG
Live Line Mea surin g t h e P aramet ers of 220 kV
Transmission Lines with Mutual Inductance in Hainan
Power Gri d
Zhongzhu Xu1, Zhijian Hu2, Chuanqi Li2
1Hainan Power Technology Research Institute, Hainan Power Grid Corporation, Haikou, China
2Scho ol of Electri cal Engineering, Wuhan University, Wuhan, China
Email:zhijian_hu@163.com
Received 2013
Abstract
A live line measurement method for the zero sequence parameters of transmission lines with mutual inductance is in-
troduced. The mathematical models of the meas urement me thod are given. Global Positioning S ystem (GPS) is used as
the synchrono us signal for the meas urement carried out at differe nt substations simultaneousl y. The measurement sys-
tem and digital si mulation re sult s are give n. Fi nal ly, t he liv e line mea sure me nt re sults of t wo 220 kV t rans mis sio n line s
with mutual i nducta nce in Ha inan gri d are given. Re sults from both simulatio n and on-sit e measur ement s how tha t the
live line measurement method is feasible, and its measurement accuracy can satisfactorily meet the requirements of en-
gineer i n g mea sur e me nt .
Keywords: Trans mi s s i on lines; Zero sequence para meter; Mutual inductance ; Live line me a s ure me n t; GPS
1. Introduction
Accurate line parameters are the foundation of r ela y p ro-
tection setting calculation, fault location, fault analysis,
network loss and power flow calculation. With the in-
creasme n t of tra nsmission line s on the same towers, zero
sequence parameters will affect the fault states and zero
sequence currents of lines [1]-[4].
The traditional methods have the formulas calculation
met hod [5] and the o utage me asure ment methods [6]-[7].
The zero sequence impedances of lines are affected by
many factors, such as line alignment and ground resis-
tance. The calculated values are unable to meet the re-
quirement of relay protection setting calculation. For
example, if we use the calculated values in the setting
calculatio n, it will make t he pr otecti on refu sing act ion o r
mis-operation. So it is a great threat to the safe and stable
operation of power system. Acc ord ing to the r egulat ions,
the zero sequence impedances of the overhead lines and
cables shoul d be obtained by actual measuremen t [8].
The traditional measurement met hods can only be
used under the cases that all lines must be withdrawn
from normal operation. Because the transmission lines
are distributed components, the line length is over 1000
kilometers and the electromagnetic coupling between
lines which cause the measurement of line parameters
difficulty. To measure the zero sequence self inductance
of a new line, because the new line has electromagnetic
coupling with other live lines, the parameters of the new
line cannot be measured independently with the tradi-
tional methods. We should withdraw all the lines from
normal operation before measuring the zero sequence
parameters. Obviously, it is not acceptable for power
system. So the traditional measuremen t met h o ds cannot
satisfy the req ui rement of mode rn power system.
A new live line measur ement method based on Global
Positioning System (GPS) technology is introduced and
has been successfully applied in the live line measure-
ment of two 220 kV transmission lines with mutual in-
ductance in Hainan power grid. T he measurement results
of the live line measurement met h od prove that it can
meet the requirement of parameter measur ement of
transmission li nes.
2. The Theory of the Live Line
Measurement
Method
The algebra equation sets of n transmission lines with
mutual inductance can be described as follows,
Z. XU ET AL.
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147
11
11 1211
21 222222
12
12
in
in
i iiiinii
n nninnnn
IU
ZZZ Z
ZZZZI U
ZZZ ZIU
zzz zIU
 

 

 

 

 
=

 

 

 

 


 










(1)
or
ZI U=

(2)
Where
ii iiii
zr jx= +
( )
1, 2,,in=
are the zero se-
quence self impedances.
ij ijij
zr jx= +
,
( )
,1, 2,,,i jnij= ≠
are the zero sequence mutual imped-
ances between line
and line
j
.
I
is the zero
sequence current vector.
U
is the zero sequence
vol ta ge ve cto r.
Suppose
pi
U
and
qi
U
are the zero sequence terminal
voltage vector s at the two ter minals of li ne
, and
qi
I
are the zero sequence terminal current vectors at the two
terminals of line
, Then
ipiqi
UU U= −
 
is the zero
sequence voltage drop vectors of line
,
( )2
ipiqi
III= +

is the average zero sequence current
vectors of line
i
. It is well known that t he zero sequence
voltages of lines are the difference of the zero sequence
voltage of bo th terminals. The equat ion o f any l ine
at
the k-th measurement can be described as follows,
112 2kiikikii kiin kn
UZIZ IZIZI=+++ ++
 

(3)
Fro m t he p pn(n+1)/2independence data groups
measured on line
( )
1, 2,,in=
, p independence equa-
tions will be obta ined. Fo r the co nveni e nc e o f calculation,
the p measurement equations is rewritten in a matrix,
such as
ii
U AZ=
. The unknown parameters are
[ ]
12
, ,,
T
ii iin
Z ZZZ=
.
( )( )( )
( )( )( )
( )( )( )
11 1
12
22 2
12
12
, ,,
, ,,
, ,,
n
n
pp p
n
II I
II I
A
II I



=




(4)
Where A is a
(1) 2p nn×+
order matrix. The su-
perscripts
1, 2,,p
of vectors
I
are the independent
measuring cases and the subscripts
1, 2,, n
of
vectors
I
are the serial number of n lines.
Set
( )()()
12
, ,,
T
p
ii n
U UUU

=
,
Then
U AZ=
is an overdetermined algebraic equa-
tion, the least-square estimation algorithm is used to
solve the unknown parameters
LS
Z
,
( )
1
TT
iLS i
ZA AAU
=
( )
1, 2,,in=
(5)
Equation (5) uses the impedance method to measure
the zero sequence impedances of lines. It can calculate
both the zero sequence parameters of the new lines and
the zero sequence parameters of the origi nal lines.
The zero sequence self impedance
ii
Z
and the zero
sequence mutual impedance
ij
Z
can be calculated by
the computer.
3. Hardware Structure of the Live Line
Measurement System
The hardware structure of a live line measuring system
based on GPS technology is shown in Figure 1. The
measurement system consists of several sections, such as
the GPS receiver, input signal transformation channels,
embedded DSP (Digital Signal Processor) card,
double-port RAM (DRAM), Embedded PC card, control
signal output and other man-machine interfaces. The
central computer stores and processes the sampled data,
calculates line parameters and outputs measurement re-
sults.
CT
PT
filter A/D CPU
interface
GPS receiver
CT
PT
filter
A/D
CPU
interface
line
computer
PPS PPS
GPS antennaGPS antenna
GPS receiver
Figure 1 . The hardware structu re of the live line measure-
ment system
4. Digital Simulation Results
According to the above method, the zero sequence para-
meters of two transmission li nes with mutual inductance
are simulated under the measurement cases for sin-
gle-phase wire break, single-phase grounding, unba-
lanced load and external power source.
The parameters of two coupled 220 kV lines are
shown in table 1. Line I is 100 km and Line II is 50 km.
The voltage level of the lines source is 220 kV and the
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148
load is 100 MW. Put the measured voltage and current
data into the computer, the measurement results are
sho wn in t able 2. The simulation result s valid ate the live
line measurement method is correct.
Table 1. The Parameters of Two Lines wit h Mutual
Induc t ances
lin es
Zero se-
quence
resistance
(Ω/km)
Zero se-
quence
inductance
(mH/km)
Zero se-
quence
capacitance
(µF/km)
Zero
sequence
mutual
resistance
(Ω/km)
Zero se-
quence
mutual
inductance
(mH/km)
Line I
0.3864
4.1264
0.007751
0.1 1.0
Line II
0.3864
4.1264
0.007751
Table 2. The Digital Simulation Results
Measure-
ment cases
Zero sequence self
impedanc e of line I
Zero sequence self
impeda n ce of line
II
Zero sequence
mutua l im peda n ce
M
easuring
values(Ω)
Rela-
tive
error%
Measur-
ing values
(Ω)
Rela-
tive
error
(%)
Measur-
ing values
(Ω)
Rela-
tive
error
(%)
Unbalanced
load
39.2030
+j128.539
4 0.66 19.2531
+j64.1589
0.97 4.9 365
+j15.8589
0.76
Single-
phase
grounding
39.1287
+j130.596
0 0.78 19.6459
+j65.0125
0.41 4.8 998
+j15.9016
0.94
Single-
phase
wire break
38.3977
+j130.277
8 0.56 19.7547
+j64.3568
0.47 4.7 587
+j15.6541
0.75
Two-phase
grounding
38.4139
+j129.064
5 0.45 19.6545
+j65.0113
0.41 5.1 210
+j15.8146
0.81
5. An Example of Live Line Measurement
The schematic diagram of the two 220 kV transmission
lines with mutual inductance in Hainan power grid is
sho wn in F i gure 2.
Yangpu
power
plant
47.8 kmYangluo line I
Yangluo line II
Luoji
substation
Figure 2. The diagram of two lines with mutual inductance
in Haina n gri d
The length of two coupled 220 kV Yangluo I and
Yangluo II lines is 47.8 km.
According to practical situation, the external voltage
source is applie d at 220 kV Luoji substation. Live line
measurement equip ments are put at Luoji substation a nd
Yangpu power plant. The extern voltage source is ap-
plied to the outage line when 220 kV Yangluo I and II
lines rolling blackouts. The zero sequence currents are
taken from CT of lines. The zero sequence voltages are
taken from the open delta winding of PT of lines or bus-
es.
The measure me nt wire d iagra m with a n exte rn vol tage
source is shown in F ig ure 3.
I
U
CT
Live line
measurement
system
PT
Test
tranformer RegulatorSwitch Distribution
transformer
Control
signal
Figure 3. The measurement wire diagram with an ex t ern
voltag e sou r c e
The control signal is generated by the measurement
equipments, and it controls the air switch to supply zero
sequence voltage. The measurement wire of two coupled
lines is sho wn in Figure 4.
Live lien
Measure-
ment
system
B
Yangpu
power plant
Live line
Measure-
ment
system
A
PT
CT
Line II under normal
operation
CT
PT
3I0 3I0
3U0
3I0
3U0
Line I withdrawn from normal
operation and with an external
voltage source
L
u
o
j
i
s
u
b
s
t
a
t
i
o
n
CT CT
PT
Figure 4. T he wire diagram of live li ne mea s ur eme n t
The measurement cases of the lines are given in table
3.
Table 3. Live Line Measurement Cases
Case Li ne I Line II
1
Withdraw from normal opera-
tion, with an ext ernal voltage
source
Under normal operation
2 Under normal operation
Withdraw from norm al opera-
tion, with an ext ernal voltage
source
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149
The zero sequence voltages and currents recorded by
the measurement syste m are s hown i n Fig ure 5 to Figure
8.
Figure 5. The voltage wave recorded i n Yang luo I line
Figure 6. The current wave re corded in Ya ngluo I line
Figure 7. The voltage wave recorded i n Yang luo I I line
Figure 8. The current wave r ecorded in Yangluo II line
The measurement results of the zero sequence para-
meters of the two lines are given in table 4.
Table 4. The Measurement Results of Zero Sequence
Parameters
Cases
Zero sequence
self i mpedan ce
of line I
(Ω)
Zero sequence
self i mpedan ce
of line II
(Ω)
Zero sequence
mutual im-
pedance
(Ω)
1 8.891
+j56.614 8.591
+j57.634 6.624
+j35.420
2
7.921
+j56.732
7.289
+j57.720
5.630
+j35.512
3
8.008
+j56.305
7.08 2 +j57. 545
5.627
+j35.196
Average mea-
surem ent val-
ues
8.274
+j56.551 7.654
+j57.633 5.961
+j35.376
Traditional
method mea-
surem ent val-
ues
13.384
+j57.408 13.384
+j57.408 10.038
+j36.615
Average mea-
surem ent er ror
3.05% 1.37% 5.51%
6. The Analysis of Measurement Results
The trad itional meas ure ment met hod ca lculating
0
Z
can
be described by (6),
0
00
U
ZI
=
6
Where
0
I
is the zero sequence current vector.
0
U
is
the zero sequence voltage vector. The method can only
be use d under outage condit ion. Mutua l induct ance mu st
be taken into account if there are electromagnetic coupl-
ing between lines.
The results of traditional method are shown in table 5
and table 6.
Table 5. The measurement resul ts of Yanl uo I line
cases Current
input
(A)
Zero sequence
voltage
(V)
Zero sequence
current
(A)
Zero sequence
impedance
(Ω)
1
40
359.56-j419.732
-27.236-j31.404
5.883+j39.451
2
60
801.35-j100.84
0.749-j59.872
5.554+j40.084
3
80
-912.39-j568.36
-50.168+j61.135
5.289+j40.432
4
100
-1348.8-j199.18
-26.909+j96.174
5.156+j40.630
average
values 5.544+j39.998
Table 6. The measurement resul ts of Yanl uo II line
cases Current
input
(A)
Zero sequence
voltage
(V)
Zero sequence
current
(A)
Zero sequence
impedance
(Ω)
1 40 -298.62+j463.74 31.278+j27.311 5.785+j39.428
2
60
-33.479+j806.83
58.947+j10.635
5.525+j40.065
3
80
-1063.2+j152.39
0.942+j79.041
5.302+j40.417
4
100
-887.65+j1034.2
67.073+j 74.004
5.112+j40.617
500
550
600
650
700
750
-150
-100
-50
0
50
100
150
200
Curr ent
( A )
time (ms)
time (ms)
500
550
600
650
700
750
-2000
-1500
-1000
-500
0
500
1000
1500
2000
Volt a ge
( V )
time (ms)
500
550
600
650
700
750
-1000
-500
0
500
1000
Volt a ge
( V )
500
550
600
650
700
750
-80
-60
-40
-20
0
20
40
60
80
time (ms)
Current
( A )
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150
average
values
5.431+j40.132
The model of two lines with mutual inductance is
sho wn in F i gure 9.
U
10
I
10
Z
11
Z
22
Z
12
I
20
Line
1
Line
2
Figure 9. The model of two lines with mutual in ductance
The voltammetry characteristic can be written as fol-
lows,
10101020120
UIZ IZ=+
 
7
So when we measure the zero sequence self imped-
ance of the line I, the zero sequence current of line II
which influences the zero sequence voltage of line I
should be taken into account. The traditional method
ignores the influence of line II, so there are theoretical
mistakes in (9) .
101010
U IZ=

8
Then,
10
10 10
U
ZI
=
9
From 7, we can get,
10101220
10 10 10
UUZI
ZII
= ≠
 

10
In fact, it indicates that when the current of line I
reaches 100 A and the current of line II reaches 47 A,
12 20
ZI
can’t be ignored. So the error of zero sequence
self impedance measured by traditional method is great.
In this measurement, the error has reached above 30%.
Measure the zero sequence voltages and zero sequence
currents of all transmission lines, then calculate (1) and
obtain zero sequence self impedance and zero sequence
mutual impedance. The live line measurement method
not only has high precision, but also is accurate and reli-
able. The measurement results of zero sequence parame-
ters are shown in table III, it shows that the average
measurement error of zero sequence mutual impedance is
about 5.5% and zero sequence self impedance is about
2%.
It shows that there are still certain difference between
theoretical values and measurement values. It is well
known that the computation formulate for zero sequence
parameters are derived from Carson formula. The tradi-
tional method needs the resistance of earth, the equiva-
lent depth of wires, the length of lines and the arrange-
ment of wires. But it is difficult to get the resistance of
earth and the equivalent depth of wires. So the theoreti-
cal values are only used as reference, they cannot be used
as accurate parameters.
In the case of disturbing, in order to obtain the accu-
rate parameters of zero sequence self impedance, the
zero sequence self impedance and the zero sequence
mutual impedance should be measured at the same time.
7. Conclusion
The field l ive l ine mea suri ng r esult s ha ve pr ove n tha t th e
live line measurement method is correct and the mea-
surement system can meet the requirement of measure-
ment. In addition, in order to eliminate the interference
of lines, using the live line measurement method to cal-
culate the zero sequence self impedance parameters and
the zero sequence mutual impedance parameters simul-
taneously can improve the accuracy of the measurement
results.
8. Acknowledgemen ts
This work was financially supported by the Ph.D. Pro-
grams Foundation of Ministry of Education of China
(20110141110032).
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