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Impact of Transmission Lines on Stray Voltage Nagy Abed, Member, IEEE, Sasan Salem, Member, IEEE, and Jim Burke, Fellow, IEEE

Abstract-- The purpose of this paper is to study the effect of

transmission system parameters and operating conditions on stray voltage levels. This includes the transmission line conductor configurations, line loading levels, grounding system parameters, and unbalance loading. Excessive stray voltages levels may have a negative effect on dairy farm cows and endanger personnel safety. EMTP-RV was used to model the coupled electromagnetic- power circuit system. EMTP models of the poles and wires were built to represent the transmission line electromagnetic behavior and the stray voltage generation mechanism. The parameters of the proposed models were obtained from the technical literature. Different simulations were conducted by varying the system parameters and operating conditions. Calculations and field tests, which included the effect of earth contact resistance, indicated that most measured values of stray voltage may be incorrect and that the safety hazard to humans and animals may be greatly exaggerated. A discussion of these results is presented.

Index TermsStray Voltage, Induction, Transmission Line, Earth, Earth Current, Ground, Step Potential, Touch Potential

I. INTRODUCTION tray voltage in power systems has been studied prior to the 1970s. The term stray voltage typically means the

voltage between the neutral conductor and earth, which usually results from unbalanced loading. It was typically considered normal, with some issues arising from the dairy industry and pool owner. In the case of transmission lines, however, stray voltage is normally the result of induction.

The following factors contribute to induced stray voltages on transmission lines:

1- Unbalanced currents in the transmission line conductors

2- Transmission line conductors configuration (pole configuration and untransposed lines)

3- Additive phase angles between the induced and load related currents in neutral system

4- Soil resistivity along the transmission line This paper describes a case study involving induction

related stray voltage concerns, simulation, measurement, and mitigation.

II. SYSTEM MODELING This section deals with the modeling methodology utilized

Nagy Abed, Sasan Salem , and Jim Burke are with Quanta Technology, ,Raleigh, NC, USA (nabed@quanta-technology.com, ssalem@quanta-technology.com, jburke@quanta-technology.com )

to simulate and measure the stray voltage. Figure 1 shows the schematic diagram of the 115 kV transmission system used for the stray voltage study. This system was modeled using EMTP-RV to evaluate the stray voltage level and the impact of various system parameters on these generated voltages.

Fig. 1 Schematic Diagram of the Modeled 115 KV Transmission Line

System The transmission line model utilized in the study is a

distributed Constant Parameter (CP) model. The model is based on the Bergeron's traveling wave method [6]. In this model, the wave equation is solved to obtain the line operating characteristics (current, and voltage). Figure 2 shows the model circuit diagram. The transmission line parameters resistance, inductance, and capacitance per unit length were calculated using the transmission line conductors configurations (arrangement), the distances between the conductors, earth resistivity, the tower height, and the conductors parameters.

For multiphase system the wave equations are written in the matrix form:

VYZdx

Vd ''2

2

= (1)

IYZdx

Id ''2

2

= (2) Where: [ ] [ ]''' ][ LsRZ += Series Impedance per unit length And [ ] [ ]''' ][ CsGY += Shunt Branch per unit length

With eigenvalue theory, it becomes possible to transform the above two coupled equations from phase quantities to modal decoupled quantities. The multiphase line is transformed into a decoupled set of modal circuits. The equations are then solved to obtain the transmission line terminal response. In this study, a three wire untransposed transmission line with a static wire and grounded at each tower, is modeled.

S

2

Fig. 2 The Distributed Constant Parameters Line Model

A transmission system with 25 poles was modeled. Appropriate data was obtained to model poles, lines, shield wires, ground rods, and the substation grounding.

Unbalanced currents on transmission lines, caused by unbalanced load and/or un-transposed lines induce a voltage on parallel lines including static wires, communication lines, and other transmission or distribution wires. The study was conducted for balanced and unbalanced loading and with uniform pole configuration. The induced voltages are considered to be steady state and 60 Hz so; they manifest similar characteristics to stray voltage

Fig. 3 Generated Stray Voltage RMS at Each of the Transmission

Line Pole

III. SIMULATIONS AND RESULTS A transmission system with 25 poles was modeled to

determine the impact of various system parameters on the generated stray voltage level. For this purpose the following system parameters were studied:

Equivalent of substation grounding mat resistance Line loading Line Span length Pole ground rod resistance Unbalanced line loading

Figure 3 shows the stray voltage level on each pole of the 25 modeled transmission line poles. From the graph we can see that the minimum stray voltage in the middle (was zero), while its maximum value, of 7 volts, exists in the vicinity of the substation. a. Impact of Substation Grounding Resistance on the

Generated Stray Voltage In order to evaluate the effect of substation grounding on

the stray voltage, a series of cases were conducted in which the substation ground resistance was changed and stray voltage levels were recorded.

Figure 4 shows the generated stray voltage for different substation grounding values. By increasing the substation resistance from 0.1 ohms to 1.0 Ohm the stray voltage will increase significantly. Most substation grounds are generally assumed to be on the order of 1 ohm (or higher in distribution substations). The stray voltage rises particularly on the poles in the vicinity of the substation, which is consistent with the results of other papers on this topic.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2525

0

1

2

3

4

5

6

7

8

9

10

11

12

Pole number

Stra

y Vo

ltage

[Vrm

s]

0.5 Ohms

0.25 Ohms

0.1 Ohms

0.75 Ohms

1.0 Ohms

Fig. 4 Impact of Substation Grounding on SV level

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2525

0

1

2

3

4

5

6

7

8

9

10

Pole Number

Stra

y Vo

ltage

[V]

485 A

430 A

375 A

260 A

215 A

325 A

540 A

Fig. 5 Impact of Line Loading on the Generated SV Level

b. Impact of Line Loading on the Generated Stray Voltage

In order to evaluate the effect of transmission line current loading on the generated stray voltage levels, different loading cases were simulated and the generated stray voltage levels were measured.

Figure 5 shows the stray voltage levels for various line currents. As was expected, higher line currents induce higher voltages in the shield wire and consequently stray voltages will increase.

c. Impact of Line Span on the generated Stray Voltage

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In order to evaluate the line span effect on the generated stray voltage, a series of simulations was conducted in which the line span was changed. Figure 6 shows the impact of the line span length on the stray voltage. The line spans were increased and then reduced by 20% in order to evaluate the impact on the stray voltage level. The simulation results demonstrated the line span length has a little impact on the stray voltage level.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2525

0

1

2

3

4

5

6

7

8

Pole Number

Stra

y Vo

ltage

[Vrm

s]

100 Meters

120 Meters

80 Meters

Fig. 6 Impact of Line Span on the Generated SV Level

d. Impact of Pole Grounding Resistance on the Generated Stray Voltage

In this part of the study, the pole grounding resistance is varied between 5-200 ohms to study the relationship between the stray voltage and the pole grounding.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2525

0

1

2

3

4

5

6

7

8

Pole number

Stra

y Vo

ltage

[Vrm

s]

5.0 Ohm10.0 Ohm20.0 Ohm30.0 Ohm50.0 Ohm100 Ohm200 Ohm

200 Ohm

5.0 Ohm

Fig. 7 Impact of Pole Grounding Resistance on the SV Level

The impact of pole ground rod resistance on stray voltage

is shown in Figure 7. The simulation results demonstrate that ground rod resistances above 50 Ohm have a slight impact on the stray voltage. In many areas, it is very difficult to drive ground rods to attain values less than 50 ohms, so the impact of grounding, to reduce stray voltage, might be considered minimal for most transmission lines. e. Impact of load unbalanced on the Stray Voltage

To evaluate the impact of unbalanced loading on the stray voltage the transmission line loading was changed to create

currents unbalance one of the phases. The loading unbalance was varied from 4% to 20%.

Figure 8 shows the stray voltage levels results for different unbalance loading. The results show that stray voltage increases with the increase in the unbalance (the zero sequence current).

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 250

1

2

3

4

5

6

7

8

9

10

Pole number

Stra

y Vo

ltage

[Vrm

s]

20%

11%

6%4%

Balanced load 0

Fig. 8: Impact of the Current Unbalance on the Generated SV Level

Fig. 9 Neutral-to-Earth Measurement without a 500 Resistor

IV. IMPACT OF TRANSMISSION LINE STRAY VOLTAGE ON HUMANS

There are a number of references used in the industry that discuss the resistance of the human body. It is common to use 1,000 from one hand to the other, hand to foot, etc... (See IEEE Std. 80, which gives a range of 500 to 5,000). Recent published tests, performed by the authors, show human resistance values for hand-to-hand as follows:

Dry skin 172k Wet skin 10k

Wet (salt water) 5k Added to this is the contact resistance of the earth itself,

which can be very large. The earth is actually a pretty good conductorif you can make good contact with it. It is the problem of making contact with the earth that negates the impact of grounding. When the fact is considered that an 8 foot copper ground rod driven into the earth typically measures 100 to 1,000 and a downed conductor typically

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measures from 100 to many thousands of ohms even in wet soil, the impact of this contact resistance can be appreciated. For the purposes of this study a contact resistance of 10,000 ohms was assumed. This is not particularly large but illustrates the technical point, shown below.

Figure 9 shown above, illustrates testing performed without a resistor. The circuit is basically between the neutral conductor (assumed at 4 volts) and true earth (assumed at 0 volts). The circuit of importance is that which involves the meter impedance and the earth contact resistance in series. As shown, a typical digital meter has an input impedance of about 10M or even higher. With 4V driving the circuit, virtually all the drop is across the meter and the reading is 4V.

Fig. 10 Neutral-to-Earth Measurement with a 500 Resistor

TABLE I

ACTUAL FIELD MEASURED DATA

Example Locations

Measured Voltage Without Resistor

Measured Voltage With 500

Resistor A 5 0.01 B 0.6 0.003 C 0.4 0.08

When a 500 resistor is placed across the meter, the total

impedance of the circuit decreases significantly as shown in Fig. 10. As shown below, the 500 resistor is small when compared to the contact resistance of the earth (assumed to be 10K ohms); therefore, most of the 4V drop now occurs in the earth itself. The voltage shown by the meter probes now measure less than 0.2V (for the assumptions given). The voltage collapses across the resistor but there is still 4V on the neutral. This is what would actually happen to a 500 human being standing on the earth and touching the tower or neutral down lead. Also, it can be expected that this phenomena will occur at all locations, similar to the actual field results (and computer simulations) shown in the table above. Digital simulations were run to confirm these field results. The conclusion being (based on actual field measurements and digital simulations) that while a digital voltmeter measurement may read values of stray voltages of 10 volts or even higher

without a 500 ohms resistor, as soon as a human being is placed in series with this circuit, the voltage across the human will collapse to a very low level (not necessarily imperceptible) due to the contact resistance of the circuit.

V. CONCLUSIONS Transmission lines induce stray voltage levels for virtually all voltages and configurations. Also, transmission lines will usually cause stray voltage that, measured with a voltmeter, may exceed the threshold limits of regulatory bodies.

These voltages, however, when applied to humans and animals will collapse due to the contact resistance of the earth.

Finally, there are several conclusions to this analysis which the authors wish to share with others in the industry:

Highest SV is found near the substations Substation grounding has a significant impact on SV

levels Line loading plays a significant role in SV levels Span length does not have much impact on SV Tower ground rod resistance does not have a major

impact on SV levels Unbalanced transmission line current loading

increases the stray voltage levels. SV levels collapse when a human is in contact with

the tower (down lead) due to the contact impedance of the earth.

VI. REFERENCES [1] J. Burke, The Confusion Surrounding Stray Voltage, 2007 IEEE Rural

Electric Power Conference, P. C1-C5. [2] D. J. Ward, J. F. Buch, T.M. Kulas, and W. J. Ros, An Analysis of the

Five-Wire distribution system IEEE Transaction on power delivery, Vol. 18, No.1 Jan 2003

[3] T. C. Surbrook, N. D. Reese, A. M. Kehrle, Stray Voltage: Sources and Solutions, IEEE Transactions on Industry Applications, Vol. IA-22, No. 2, March 1983.

[4] M. E. Galey, Benefits of performing unbalanced voltage calculations, IEEE Transactions on Industry Applications, Vol. IA-24, No. 1, Jan-Feb 1988, pp. 15-24.

[5] J. Burke, Power Distribution Engineering: Fundamentals and Applications, Marcel Dekker, INC., 1994.

[6] A. Greenwood, Electrical Transients in Power Systems, Wiley-Interscience, 2 edition, 1991.

[7] J. Burke, C. Untiedt, Stray Voltage: Two Different Perspectives IEEE REPC 2008

Nagy Abed is with Quanta Technology. He received his B.Sc. (The first Rank

on the class) and M.Sc. from Mansoura University, Egypt, and his PhD from Florida International university, Miami. His research interests include power system modeling, fault diagnosis, power quality, FACTS devices, Application of Finite Element in power system and real time control with HIL.

Sasan Salem is a Principal Engineer with Quanta Technology. He received

his BS in Electrical Power Engineering form Iran university of Science and Technology and his M.Sc. from Concordia University in Montreal. His main research interests include power system analysis and control and FACTS applications in power systems.

Jim Burke is an Executive Advisor with Quanta Technology. He has been in

the industry over 43 years. He is the former chair of the IEEE Distribution Subcommittee as well as the Working Group on Distribution Neutral Grounding. He is a Fellow of the IEEE

I. IntroductionII. System ModelingIII. Simulations and ResultsIV. Impact of Transmission Line Stray Voltage on HumansV. CONCLUSIONSVI. References