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 right-of-way, 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.
Double-circuit 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 single-circuit 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 right-of-way. Until now, the studies for induced voltage in distribution systems have been performed only on single-circuit lines, so it is necessary to consider the induced voltage from double-circuit lines [5, 6].
In this paper, the calculation method using four-terminal 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 four-terminal parameters.
2. Calculation of Induced Voltage on Telecommunication Line [4]
2.1 Calculation of induced voltage in single-circuit lines
To calculate an induced voltage on a telecommunication line, a system model of single-circuit 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 four-terminal parameters, the sending voltage and current (VS1, IS1), and the receiving voltage and current (VR1, IR1) are as follows [6]:
Fig. 1.System model of single-circuit lines
where
In (1), sub-matrices are defined as (2).
In (2), subscripts denote;
• G: overhead ground wire• a, b, and c: 3-phase 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 VSG and VRG can be assumed almost equal to zero. Accordingly, VRG is rewritten as follows:
where
ZGabcISabc = ZGaISa + ZGbISb + ZGcISc
The sending current of the overhead ground wire can be obtained from (4).
The sending neutral current is ISN, and VST is grounded. So the induced voltage on the telecommunication line (VRT) can be calculated using (5).
where
ZTabcISabc = ZTaISa + ZTbISb + ZTcISc
2.2 Calculation of induced voltage in double-circuit lines
Fig. 2 is a system model of double-circuit lines used to calculate an induced voltage on a telecommunication line.
In the double-circuit lines, voltages and currents on the sending and receiving ends are VS2, IS2 and VR2, IR2 respectively, so the relations between the sending and receiving are expressed by (6) [7].
In (6), sub-matrices are defined as follows (7):
Fig. 2.System model of double-circuit lines
In (7), Ua, Ub, and Uc indicate 3-phase lines in the upper side, and La, Lb, and Lc indicate 3-phase 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 double-circuit lines can be obtained using (9).
where
ZGUabcISUabc = ZGUaISUa + ZGUbISUb + ZGUcISUc
ZGLabcISLabc = ZGLaISLa + ZGLbISLb + ZGLcISLc
Because VSG and VRG can be also assumed to be almost zero in the double-circuit lines, the sending current of overhead ground wire can be expressed as follows:
In the double-circuit 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 (VRT) is represented by (12). Since the VST is grounded, it can be assumed to be almost zero. In shorthand form, VRT is expressed as follows:
where
ZTUabcISUabc = ZTUaISUa + ZTUbISUb + ZTUcISUc
ZTLabcISLabc = ZTLaISLa + ZTLbISLb + ZTLcISLc
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 single-circuit lines. Fig. 3 (b) is of double-circuit 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, VRT is a calculation value using four-terminal parameters, the EMTP simulation result is VEMTP, and the error is calculated on the basis of VEMTP. The unbalance ratio of the load is not more than 30%. To analyze the induced voltage in the single- and double-circuit lines, vector analysis is also applied.
Fig. 3.Configuration of distribution lines and telecommunication line
Table 1.Induced voltage results in single-circuit lines
4. Case Study in Single-Circuit 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 single-phase unbalanced load, and Case 3 has a 3-phase 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 single-circuit lines, vector analysis is applied. The VRT may be divided into two sides from (5), the inducing side (VP) and the shielding side (VGN). VRT in the single-circuit lines is expressed as follows:
where
VP = - (ZTabcISabc) , VGN = - (ZTGISG + ZTNISN)
Using the calculation method presented in (13), VP, VGN and VRT in partitioned from are displayed in Table 2.
Table 2.Vector analysis results in single-circuit lines
Fig. 4.Vector analysis in single-circuit lines (Case 1)
In Table 2, VP is caused by a 3-phase current and VGN 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 single-circuit lines.
5. Case Study in Double-Circuit 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 four-terminal parameters and the EMTP simulation, are compared below.
In Table 3, load conditions are as follows:
Case 4: 3-phase balanced load in both the upper and lower sidesCase 5: Single-phase (Uc, Lc-phase) unbalanced load in both the upper and lower sidesCase 6: 3-phase unbalanced load in both the upper and lower sidesCase 7A~7C: Single-phase unbalanced load in the upper side and balanced load in the lower sideCase 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 single-circuit lines, the VRT may be divided into an inducing side (VP) and a shielding side (VGN). Because of double-circuit lines, VP may be again divided into an upper (VUP) and lower side (VLP) using (13). VRT is expressed as follows:
Where
Table 3.Induced voltage results in double-circuit lines
Table 4.Vector analysis results in double-circuit lines
Fig. 5.Induced voltage(VP) is caused by a 3-phase current of the upper and lower sides in double-circuit lines (Case 4)
Fig. 6.Vector analysis in double-circuit lines (Case 4)
VUP = - (ZTUabcISUabc), VLP = - (ZTLabcISLabc)
VGN = - (ZTGISG + ZGNISN)
In (14), VUP, VLP, VGN, and VRT in partitioned form are displayed in Table 5.
In Table 4, VUP is caused by a 3-phase current in the upper side. VLP is caused by a 3-phase current in the lower side. For example, Fig. 5 shows t resultant vector of Case 4 in VP of the double-circuit lines.
The total induced voltage in the double-circuit lines is given as a vector sum (VRT = VUP + VLP + VGN). 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 double-circuit lines carry the same load type. The results indicate that the induced voltage in the double-circuit lines is larger than the induced voltage in the single-circuit lines.
Fig. 8 shows the induced voltage on a telecommunication line through which the single-circuit lines and the upper and lower sides of the double-circuit lines carry the same single-phase unbalanced load.
When comparing Case 2B in the single-circuit lines and Case 8B in the double-circuit 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 single-circuit lines. When comparing the upper and lower sides of the double-circuit 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 b-phase line and the lower sides of the double-circuit lines.
Fig. 7.Comparison of single and double-circuit lines
Fig. 8.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 four-terminal parameters to calculate the induced voltage in the double-circuit 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.
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