A current flowing through a distribution conductor produces induced voltage, which is harmful to a telecommunication line. Previous research on induced voltage has been focused on singlecircuit lines in the distribution system. However, the doublecircuit lines, referred to as parallel distribution lines, are widely used in distribution systems because they have significant economic and environmental advantages over singlecircuit lines. Therefore, a study on the induced voltage in doublecircuit lines is needed. This paper presents a method of calculating the induced voltage in a parallel distribution system using fourterminal parameters and vector analysis. The calculation method is verified by the Electromagnetic Transient Program (EMTP) simulation.
1. Introduction
Overhead lines electrified with an alternating current (AC) can induce voltage into a telecommunication line. In general, the induced voltage on a telecommunication line has harmful effects; it may result in damage to telecommunication facilities, danger to maintenance workers, deterioration of telecommunication transmission quality, or disturbance of the signal
[1]
.
In a distribution system, the induced voltage on a telecommunication line is important to consider when designing a joint rightofway, as an unbalanced current can increase the induced voltage on the telecommunication line
[2

4]
. Therefore, the induced voltage should be calculated on the basis of agreements between the telecommunications company and electric power company. These calculations should be performed before an existing electric transmission facility is moved, expanded, or constructed. If the inducted voltage is above a certain limit, appropriate measures for the induced voltage should be taken.
Doublecircuit lines have recently become fairly common in distribution systems, and it is easy to find instances where distribution lines are physically parallel due to the significant economic and environmental advantage over singlecircuit lines. The parallel combination may require both distribution lines to be constructed on the same pole, or the two lines may run on separate, parallel poles on the same rightofway. Until now, the studies for induced voltage in distribution systems have been performed only on singlecircuit lines, so it is necessary to consider the induced voltage from doublecircuit lines
[5
,
6]
.
In this paper, the calculation method using fourterminal parameters is presented for determining induced voltage on a telecommunication line. Parallel overhead distribution lines and the telecommunication line are represented by series impedance and shunt admittance matrices. These matrices are applied for the calculation of the induced voltage on the telecommunication line and take into account the coupling with adjacent parallel distribution lines. Carson’s formula is used to calculate both the impedance and admittance. Effects on the induced voltage according to the load condition and pole type of the distribution lines are analyzed by using the calculation method based on fourterminal parameters.
2. Calculation of Induced Voltage on Telecommunication Line[4]
 2.1 Calculation of induced voltage in singlecircuit lines
To calculate an induced voltage on a telecommunication line, a system model of singlecircuit lines is shown in
Fig. 1
.
On the basis of
Fig. 1
, the telecommunication line laid parallel with overhead distribution lines can be expressed as the relation of voltage and current using an equivalent PI circuit. In this paper, the self and mutual impedance and admittance are obtained using Carson’s formula
[6]
. The system frequency is 60 [Hz] and the earth’s resistivity is 100 [Ω·m]. Using fourterminal parameters, the sending voltage and current (V
_{S1}
, I
_{S1}
), and the receiving voltage and current (V
_{R1}
, I
_{R1}
) are as follows
[6]
:
System model of singlecircuit lines
where
In (1), submatrices are defined as (2).
In (2), subscripts denote;

• G: overhead ground wire

• a, b, and c: 3phase lines

• N: neutral wire

• T: telecommunication line
Overhead ground wires laid on the top of the distribution lines are installed for the purpose of preventing lightning and are grounded, so V
_{SG}
and V
_{RG}
can be assumed almost equal to zero. Accordingly, V
_{RG}
is rewritten as follows:
where
Z
_{Gabc}
I
_{Sabc}
= Z
_{Ga}
I
_{Sa}
+ Z
_{Gb}
I
_{Sb}
+ Z
_{Gc}
I
_{Sc}
The sending current of the overhead ground wire can be obtained from (4).
The sending neutral current is I
_{SN}
, and V
_{ST}
is grounded. So the induced voltage on the telecommunication line (V
_{RT}
) can be calculated using (5).
where
Z
_{Tabc}
I
_{Sabc}
= Z
_{Ta}
I
_{Sa}
+ Z
_{Tb}
I
_{Sb}
+ Z
_{Tc}
I
_{Sc}
 2.2 Calculation of induced voltage in doublecircuit lines
Fig. 2
is a system model of doublecircuit lines used to calculate an induced voltage on a telecommunication line.
In the doublecircuit lines, voltages and currents on the sending and receiving ends are V
_{S2}
, I
_{S2}
and V
_{R2}
, I
_{R2}
respectively, so the relations between the sending and receiving are expressed by (6)
[7]
.
In (6), submatrices are defined as follows (7):
System model of doublecircuit lines
In (7), Ua, Ub, and Uc indicate 3phase lines in the upper side, and La, Lb, and Lc indicate 3phase lines in the lower side. The relation between the receiving voltage and current is as follows:
The receiving voltage of the overhead ground wire in the doublecircuit lines can be obtained using (9).
where
Z
_{GUabc}
I
_{SUabc}
= Z
_{GUa}
I
_{SUa}
+ Z
_{GUb}
I
_{SUb}
+ Z
_{GUc}
I
_{SUc}
Z
_{GLabc}
I
_{SLabc}
= Z
_{GLa}
I
_{SLa}
+ Z
_{GLb}
I
_{SLb}
+ Z
_{GLc}
I
_{SLc}
Because V
_{SG}
and V
_{RG}
can be also assumed to be almost zero in the doublecircuit lines, the sending current of overhead ground wire can be expressed as follows:
In the doublecircuit lines, the sending neutral current can be calculated assuming that the upper and lower sides share the ground point of the neutral line and the neutral current is equal to the total current of the upper and lower side using the principle of superposition. If these things are true, then the neutral current is the same as (11)
[8]
.
In conclusion, the induced voltage on the telecommunication line (V
_{RT}
) is represented by (12). Since the V
_{ST}
is grounded, it can be assumed to be almost zero. In shorthand form, V
_{RT}
is expressed as follows:
where
Z
_{TUabc}
I
_{SUabc}
= Z
_{TUa}
I
_{SUa}
+ Z
_{TUb}
I
_{SUb}
+ Z
_{TUc}
I
_{SUc}
Z
_{TLabc}
I
_{SLabc}
= Z
_{TLa}
I
_{SLa}
+ Z
_{TLb}
I
_{SLb}
+ Z
_{TLc}
I
_{SLc}
3. System Modeling[4]
To verify the calculation method,
Fig. 3
illustrates the configuration of the overhead distribution lines and the telecommunication line.
The induced voltage on the telecommunication line is analyzed according to the pole type in case studies;
Fig. 3 (a)
is of singlecircuit lines.
Fig. 3 (b)
is of doublecircuit lines.
For this case study, the induced voltage with respect to load condition and pole type is measured by EMTP. All results of the case study are measured and calculated on the basis of 1 km parallel distance. In case studies, V
_{RT}
is a calculation value using fourterminal parameters, the EMTP simulation result is V
_{EMTP}
, and the error is calculated on the basis of V
_{EMTP}
. The unbalance ratio of the load is not more than 30%. To analyze the induced voltage in the single and doublecircuit lines, vector analysis is also applied.
Configuration of distribution lines and telecommunication line
Induced voltage results in singlecircuit lines
Induced voltage results in singlecircuit lines
4. Case Study in SingleCircuit Lines
 4.1 Simulation results
Table 1
shows the calculated induced voltages and the EMTP simulation results. For the case study of the singlecircuit lines, as shown in
Table 1
, Case 1 has a balanced load, Case 2A ~ 2C have a singlephase unbalanced load, and Case 3 has a 3phase unbalanced load. The numerical error in the difference between the EMTP simulation results and the calculated value of (5) is less than 1.14 [%].
 4.2 Vector analysis
To analyze the induced voltage in the singlecircuit lines, vector analysis is applied. The V
_{RT}
may be divided into two sides from (5), the inducing side (V
_{P}
) and the shielding side (V
_{GN}
). V
_{RT}
in the singlecircuit lines is expressed as follows:
where
V
_{P}
=  (Z
_{Tabc}
I
_{Sabc}
) , V
_{GN}
=  (Z
_{TG}
I
_{SG}
+ Z
_{TN}
I
_{SN}
)
Using the calculation method presented in (13), V
_{P}
, V
_{GN}
and V
_{RT}
in partitioned from are displayed in
Table 2
.
Vector analysis results in singlecircuit lines
Vector analysis results in singlecircuit lines
Vector analysis in singlecircuit lines (Case 1)
In
Table 2
, V
_{P}
is caused by a 3phase current and V
_{GN}
is caused by the current of an overhead ground wire and a neutral wire. For example,
Fig. 4
shows the resultant vector of Case 1 in the singlecircuit lines.
5. Case Study in DoubleCircuit Lines
 5.1 Simulation results
Table 3
shows the calculated induced voltages and the EMTP simulation results. In
Table 3
, the upper and lower side loads were changed. The calculation results of (12), using the fourterminal parameters and the EMTP simulation, are compared below.
In
Table 3
, load conditions are as follows:

Case 4: 3phase balanced load in both the upper and lower sides

Case 5: Singlephase (Uc, Lcphase) unbalanced load in both the upper and lower sides

Case 6: 3phase unbalanced load in both the upper and lower sides

Case 7A~7C: Singlephase unbalanced load in the upper side and balanced load in the lower side

Case 8A~8C: Balanced load in the upper side and single phase unbalanced load in the lower side
The results of the case studies listed in
Table 3
show that the numerical error in the difference between the EMTP simulation results and the calculated value of (12) is less than 3.38 [%], so it can be regarded as an exact method.
 5.2 Vector analysis
Similar to the vector analysis of the singlecircuit lines, the V
_{RT}
may be divided into an inducing side (V
_{P}
) and a shielding side (V
_{GN}
). Because of doublecircuit lines, V
_{P}
may be again divided into an upper (V
_{UP}
) and lower side (V
_{LP}
) using (13). V
_{RT}
is expressed as follows:
Where
Induced voltage results in doublecircuit lines
Induced voltage results in doublecircuit lines
Vector analysis results in doublecircuit lines
Vector analysis results in doublecircuit lines
Induced voltage(V_{P}) is caused by a 3phase current of the upper and lower sides in doublecircuit lines (Case 4)
Vector analysis in doublecircuit lines (Case 4)
V
_{UP}
=  (Z
_{TUabc}
I
_{SUabc}
), V
_{LP}
=  (Z
_{TLabc}
I
_{SLabc}
)
V
_{GN}
=  (Z
_{TG}
I
_{SG}
+ Z
_{GN}
I
_{SN}
)
In (14), V
_{UP}
, V
_{LP}
, V
_{GN}
, and V
_{RT}
in partitioned form are displayed in Table 5.
In
Table 4
, V
_{UP}
is caused by a 3phase current in the upper side. V
_{LP}
is caused by a 3phase current in the lower side. For example,
Fig. 5
shows t resultant vector of Case 4 in V
_{P}
of the doublecircuit lines.
The total induced voltage in the doublecircuit lines is given as a vector sum (V
_{RT }
= V
_{UP}
+ V
_{LP}
+ V
_{GN}
). The resultant vector is shown in
Fig. 6
, and the above results agree with the vector analysis.
6. Comparison of Case Study
Fig. 7
shows the induced voltage on a telecommunication line over which the single and doublecircuit lines carry the same load type. The results indicate that the induced voltage in the doublecircuit lines is larger than the induced voltage in the singlecircuit lines.
Fig. 8
shows the induced voltage on a telecommunication line through which the singlecircuit lines and the upper and lower sides of the doublecircuit lines carry the same singlephase unbalanced load.
When comparing Case 2B in the singlecircuit lines and Case 8B in the doublecircuit lines, regardless of the pole type listed in
Fig. 8
, the induced voltage of the doublecircuit lines is smaller than the induced voltage in the singlecircuit lines. When comparing the upper and lower sides of the doublecircuit lines, the induced voltage of the lower side is smaller than the upper side. This is because of the screening effect of neutral current, which is closely arranged to the bphase line and the lower sides of the doublecircuit lines.
Comparison of single and doublecircuit lines
Comparison of induced voltage results
7. Conclusion
This paper presented a method to calculate the induced voltage on a telecommunication line in a parallel distribution system. For more actual analysis on the induced voltage from a practical point, parallel overhead distribution lines and the telecommunication line were represented by series impedance and shunt admittance matrices. These matrices were applied to calculate the induced voltage on the telecommunication line. The advantage of this method was that it uses the actual neutral current value and fourterminal parameters to calculate the induced voltage in the doublecircuit lines. The calculation method was verified by both the EMTP and vector analysis. Also, various case studies were compared and analyzed according to the load condition and pole type of the distribution system. From the results which did not generate very much of an error when calculating the induced voltage, it is expected that the proposed method be useful to a real system.
BIO
HyunSoo Kim He received the B.S degree from Youngdong University, Korea, in 2004, and the M.S. degree from Sungkyunkwan University in 2009. Since 2010, he joined Electricity Control Technology Team, Device Solutions, Samsung Electronics, Korea. His current research interests include power system transients, modeling and simulation for power system protection using EMTP.
SangBong Rhee He received the B.S., M.S., and Ph.D. degrees form Hanyang University, Korea in 1994, 1999, and 2004, respectively. He serves as a Research Professor at the College of Electrical and Computer Engineering, Sungkyunkwan University, Korea. Currently, he is an assistant professor with the dept. of electrical engineering at Yeungnam University, Korea. His research interests include a distribution system control and operation, and artificial intelligence applications to power system protection
SoonJeong Lee He received his B.S. degree in Department of Electrical and Electronics Engineering from Kangwon National University, 2010 and M.S. dgree in College of Information and Communication from Sungkyunkwan University, South Korea, 2012 respectively. At present, he is working for his Ph. D. course in Sungkyunkwan University. His research interests are power quality, power system transient analysis and electric vehicle.
ChulHwan Kim He received his B.S. and M.S. degrees in Electrical Engineering from Sungkyunkwan University, South Korea, 1982 and 1984, respecttively. He received a Ph.D. degree in Electrical Engineering from Sungkyunkwan University in 1990. In 1990 he joined Cheju National University, Cheju, South Korea, as a fulltime Lecturer. He has been a visiting academic at the University of BATH, UK, in 1996, 1998, and 1999. Since March 1992, he has been a professor in the College of Information and Communication, Sungkyunkwan University, South Korea. His research interests include power system protection, artificial intelligence application for protection and control, the modelling/protection of underground cable and EMTP software.
Yoon Sang Kim He received B.S., M.S., and Ph.D. degrees in Electrical Engineering from Sungkyunkwan University, Seoul, Korea, in 1993, 1995, and 1999, respectively. He was a member of the Postdoctoral Research Staff of Korea Institute of Science and Technology (KIST), Seoul, Korea. He was a Faculty Research Associate in the Department of Electrical Engineering, University of Washington, Seattle. He was a Member of the Senior Research Staff, Samsung Advanced Institute of Technology (SAIT), Suwon, Korea. Since March 2005, he has been an Associate Professor at the School of Computer and Science Engineering, Korea University of Technology Education (KOREATECH), Cheonan, Korea. His current research interests include Virtual simulation, PowerIT technology, and devicebased interactive application. Dr. Kim was awarded the Korea Science and Engineering Foundation (KOSEF) Overseas Postdoctoral Fellow in 2000. He is a member of IEEE, IEICE, ICASE, KIPS, and KIEE.
Sharafi S.
2008
“Longitudinal induction voltage measurement on communication cables running parallel to overhead lines”
T&D. IEEE/PES
Transmission and Distribution Conference and Exposition
2124 Apr., 2008
Dugan Roger C.
,
McGranaghan Mark F.
,
Santoso Surya
,
Beaty H. Wayne
2002
“Electrical Power Systems Quality”
second edition
McGrawHill
Oka K.
,
Koizumi S.
,
Oishi K.
,
Yokota T.
,
Uemura S.
2002
“Analysis of a neutral grounding method for a threephase fourwire 11.4 kV distribution system”
Transmission and Distribution Conference and Exhibition 2002: Asia Pacific. IEEE/PES
2
(610)
998 
1003
Kim H. S.
,
Rhee S. B.
,
Yeo S. M.
,
Kim C. H.
,
Lyn S. H.
,
Kim S. A.
,
Weon B. J.
2008
“Calculation of an Induced Voltage on Telecommunication Lines in Parallel Distribution Lines”
Trans. KIEE
57
(10)
1688 
1695
Park K. W.
,
Rhee S. B.
,
Seo H. C.
,
Kim C. H.
2007
“A Calculation Method of Neutral Current of Two Step Type Pole in Distribution Line”
IPST
Kersting William H.
2006
“Distribution System Modeling and Analysis”
CRC Press
Kersting William H.
2006
“The Modeling and Analysis of Parallel Distribution Lines”
IEEE Transactions on Industry Applications
42
(5)
Park K. W.
,
Seo H. C.
,
Kim C. H.
,
Jung C. S.
,
Yoo Y. P.
,
Lim Y. H.
,
Lee W. J.
2007
“A Study on the Effects of Neutral Current by Unbalanced Load in Two Step Type Pole Using KEPCO’s Distribution System”
Trans. KIEE
56
(3)