Energy and Power Engineering, 2013, 5, 941-944
doi:10.4236/epe.2013.54B180 Published Online July 2013 (http://www.scirp.org/journal/epe)
New Method of Measuring the Positive-sequence
Capacitance of T-connection Transmission Lines
Yuansen Zhang1, Demin Cui1, Qingtao Cao1, Yongqiang Chai1, Peng Liu1, Xiaobo Li 1,
Zhijian Hu2, Chuanqi Li2, Chengxue Zhang2
1Dezhou Power Supply Company, Shandong Electric Power Group Co., Dezhou, China
2School of Electrical Engineering, Wuhan University, Wuhan, China
Email: zhijian_hu@163.com
Received February, 2013
ABSTRACT
A novel method of measuring the positive-sequence capacitance of T-connection transmission lines is proposed. The
mathematical model of the new method is explained in detail. In order to obtain enough independent equations, three
independent operation modes of T-connection transmission lines during the line measurement are introduced. The digi-
tal simulation results and field measurement results are show n. The simulation and measurement results hav e validated
that the new method can meet the needs of measuring the positive-sequence capacitance of T-connection transmission
lines. This method has been implemented in the newly developed measurement instrument.
Keywords: T-connection Transmission Lines; Line Parameter; Positive-sequence Capacitance; Measurement
1. Introduction
With the rapid development of power systems, line cor-
ridors become more and more crowed. In order to reduce
synthetic cost of the line construction and limited objec-
tive conditions, T-connection transmission lines are al-
ways applied in HV/EHV. The reliable operation of
power systems depends on the correct operation of re-
laying protection devices [1].
It is well known that the computation for parameters of
T-connection transmission lines is derived from Carson
formula [2]. It is influenced by many practical factors,
such as the resistance of earth, the equivalent depth of the
lines and, etc. So the parameters should be practically
measured rather than theoretically calculated.
There are many related literatures discussing about
measuring the impedance parameters of T-connection
transmission lines [3-5]. The capacitance parameters are
always ignored. But the capacitance is very important for
transmission line protection. When it exceeds certain
length, because the numerical value of capacity current is
big, the current flow on both sides of the lines and phase
relation will change according with the increase of ca-
pacity current value. Especially, when load current and
short-circuit current are small, it can lead to the malop-
eration of high frequency protection [6, 7]. If we use the
traditional method to measure the capacitance of T-con-
nection transmission lines, it can only calculate parallel
values of three branches. When the parameters of three
branches are different, the traditional method no longer
works. So, new measurement method needs to be found
out for the positive-sequence capacitance of T-connec-
tion transmission lines.
In this paper, a new method of measuring positive-
sequence capacitance of T-connection lines is proposed.
The method has been applied to the newly developed
measurement instrument.
2. The Theory of the Measurement Method
Usually, the length of T-connection transmission lines is
less than 50 km. So it can use the lumped parameter
model. Each branch can be equivalent to T-form circuit.
The lumped parameter model of T-form equivalent cir-
cuit is shown in Figure 1.
When the length and impedance of transmission lines
are known, the susceptance can be calculated. Three
phases end is opening circuit, , the susceptance y
is as follows, 20I
1
I
2
I
/2z/2z
1
U
2
U
ygjb
Figure 1. The lumped parameter model of T-form equiva-
lent circuit.
Copyright © 2013 SciRes. EPE
Y. S. ZHANG ET AL.
942
11
1
(/)(/2)
yg
UIz

 jb
(1)
where, 1 is the positive-sequence voltage vector at the
head of the line; 1
U
I
is the positive-sequence current
vector at the head of the line.
Then, the capacitance can be written as follows,
b
cLw
(2)
where, L is the length of the transmission lines; w equals
to 2
f
and
f
is power frequency.
Figure 1 can be applied to three branches of T-con-
nection transmission lines. The equivalent model is
shown in Figure 2.
The impedance parameters of three branches are
known. In order to obtain enough independent equations,
three independent operation modes of T-connection
transmission lines during the measurement are shown in
Table 1. In order to simplify the equations, substitute
half of the impedance parameters of three branches with
Z1, Z2 and Z3. Then, w e h ave,
2233 11
22 33
11 1
11 2233 11
22 33
113 322
113 3
22 2
22 113 322
113 3
112 2
11
33
33
()()
()()
()( )
()( )
()( )
ZYZY ZY
ZYZY
U
Z
IZYZY ZY
ZYZY
ZYZY ZY
ZYZY
U
Z
IZYZY ZY
ZYZY
ZYZ Y
ZY
U
I




 






 




 






 


33
22 3
112 233
112 2
()( )
ZY
ZY
Z
ZYZ YZY
ZYZY









 

(3)
Equation (3) can be simplified as,
122313 112 1313 12123
11 1
11122313 112313223 1122313
122313223 121223123
22 2
221 2231 3
()()()
()()()()
()()()
(
ZZZZZZ YZZYYZZ YYYYY
UZ
ZZZZZZ YZZ YZZ YZZYYYYYYY
ZZ ZZZZYZ ZYYZZYYYYY
UZ
IZZZZZZ
  
  
 
 
1123132 23112231
331223133132 3231312 3
3
33122313112313223 1122313
)( )( )()
()()())
()()()()
YZZYZZ YZZ YYYYYYY
UZZZZZZY ZZYY ZZYYYYY
Z
3
ZZZZZZ YZZ YZZ YZZ YYYYYYY
 

  
(4)
Figure 2. The equivalent model of T-connect transmission lines.
Table 1. The Measurement Modes of Three Braches.
Cases Branch 1 Branch 2 Branch 3
1 Applied with an external positive-sequence
voltage source Open circuit Open circuit
2 Open circuit Applied with an external positive-sequence
voltage source Open circuit
3 Open circuit Open circuit Applied with an external positive-sequence
voltage source
Copyright © 2013 SciRes. EPE
Y. S. ZHANG ET AL. 943
Where Z1, Z2 and Z3 are half of the positive-sequence
impedance parameters of three branches; Y1, Y2 and Y3
are the reciprocal of the positive-sequence susceptance
parameters of three branches; 11
U, 22 and 33
U are
the positive-sequence voltage vectors of three branches;
11
U
 
I
, 22
I
and 33
I
are the positive-sequence current
vectors of three branches; Subscripts 11, 22 and 33 mean
that th e first number represen ts one of the three br anches
and the second number represents one of the measure-
ment modes.
Then, the positive-sequence capacitance of three
branches can be written as follows,
111
222
333
11
Im( )
11
Im( )
11
Im( )
Cwl Y
Cwl Y
Cwl Y
(5)
where , 2 and 3
l are the length of three branches;
w= 1
l l
2
f
and
f
is power f requency.
3. Digital Simulation Results
According to the above method, the positive-sequence
capacitance of T-connection transmission lines is simu-
lated under the three cases. Each branch is applied with
an external positive-sequence voltage source in turn and
the other two branches are opening circuit.
The simulation results of three different cases are
shown in Tables 2-4 respectively.
Table 2. The Simulation Results of Three Branches with the
Same Length.
The length of
three branches
(km)
Capacitance
Setting Values
(Unit: nF/km)
Capacitance
Measurement Values
(Unit: nF/km)
Relative
Error
(%)
30 9.15 9.1501 0.0011
50 12.74 12.734 0.0471
Table 3. The Simulation Results of Three Branches with
Different Length.
Length
(km)
Capacitance
Setting Values
(Unit: nF/km)
Capacitance
Measurement Values
(Unit: nF/km)
Relative
Error
(%)
Branch 1: 10 12. 74 12.830 0.71
Branch 2: 20 9.15 9.3793 2.51
Branch 3: 30 14. 0 0 13.816 -1.31
Table 4. The Simulation Results of Three Branches with
Different Length.
Length
(km)
Capacitance
Setting values
(Unit: nF/km)
Capacitance
Measurement values
(Unit: nF/km)
Relative
Error
(%)
Branch 1: 5012.74 12.739 0.0078493
Branch 2: 309.15 9.1438 0. 067760
Branch 3: 4014.00 13.992 0. 057143
Tongyi
Substation Haizhou
Substation
Yongnin
Substation
Branch 1
6.35km
Branch 2
4.25km
Branch 3
5.08km
Figure 3. Diagram of the T-connection transmission lines.
Table 5. The Positive-Sequence Capacitance Measurement
Results of Three Branches.
Length
(km)
Capacitance
Calculation Values
(Unit: nF)
Capacitance
Measurement Values
(Unit: nF)
Relative
Error
(%)
Branch 1: 6.35 km58.075
Branch 2: 4.25 km38.869
Branch 3: 5.08 km46.459
4. An Example of Field Test
The new measurement method has been successfully
used in measuring the positive-sequence capacitance
parameters of 110kV T-connection transmission lines in
a power grid as shown in Figure 3.
The independent measuring cases of the T-connection
line are shown in Table 1.
The positive-sequence capacitance measurement re-
sults with the new method are shown in Table 5.
5. Conclusions
The new measurement method of the positive-sequence
capacitance parameters of T-connection transmission
lines is introduced. The theoretical analysis, digital si-
mulation results and the field measurement results have
proven that the new measurement method is correct and
can be used for measuring the positive-sequence capaci-
tance parameters of T-connection transmission lines.
Copyright © 2013 SciRes. EPE
Y. S. ZHANG ET AL.
944
6. Acknowledgements
This work was financially supported by the Ph.D. Pro-
grams Foundation of Ministry of Education of China
(20110141110032).
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