New Method of Measuring the Positive-sequence Capacitance of T-connection Transmission Lines

doi:10.4236/epe.2013.54B180

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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: [email protected]

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



/2z/2z

2



ygjb

Figure 1. The lumped parameter model of T-form equiva-

lent circuit.

Y. S. ZHANG ET AL.

942

(/)(/2)

UIz





 jb

(1)

where, 1 is the positive-sequence voltage vector at the

head of the line; 1



 is the positive-sequence current

vector at the head of the line.

Then, the capacitance can be written as follows,

cLw

 (2)

where, L is the length of the transmission lines; w equals

to 2



and

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

()()

()( )

ZYZY ZY

ZYZY

IZYZY ZY

ZYZY

ZYZY ZY

ZYZY

IZYZY ZY

ZYZY

ZYZ Y









 











 











 











 













22 3

112 233

112 2

()( )

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

ZZZZZZ YZZ YZZ YZZYYYYYYY

ZZ ZZZZYZ ZYYZZYYYYY

IZZZZZZ

  

  

 

 



1123132 23112231

331223133132 3231312 3

33122313112313223 1122313

)( )( )()

()()())

()()()()

YZZYZZ YZZ YYYYYYY

UZZZZZZY ZZYY ZZYYYYY

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

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;

U

 

, 22

 and 33

 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

Im( )

Cwl Y

















(5)

where , 2 and 3

l are the length of three branches;

w= 1

l l



and

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.

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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