1
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 Terms—Stray Voltage, Induction, Transmission Line,
Earth, Earth Current, Ground, Step Potential, Touch Potential
S
I. INTRODUCTION
tray voltage in power systems has been studied prior to
the 1970’s. 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@quantatechnology.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 conductor’s
configurations (arrangement), the distances between the
conductors, earth resistivity, the tower height, and the
conductor’s parameters.
For multiphase system the wave equations are written in the
matrix form:
d 2V
= Z 'Y 'V
2
dx
d 2I
= Z 'Y ' I
2
dx
(1)
(2)
Where:
[Z ] = [ R ] + s[L ] Series Impedance per unit length
And [Y ] = [G ] + s[C ] 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.
2
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
12
11
10
1.0 Ohms
9
Stray Voltage [Vrms]
Fig. 2 The Distributed Constant Parameters Line Model
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.
8
7
0.75 Ohms
6
0.5 Ohms
5
4
0.25 Ohms
3
2
0.1 Ohms
1
0
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 25
Pole number
Fig. 4 Impact of Substation Grounding on SV level
10
9
540 A
8
485 A
Stray Voltage [V]
7
Fig. 3 Generated Stray Voltage RMS at Each of the Transmission
Line Pole
375 A
5
4
3
215 A
III. SIMULATIONS AND RESULTS
2
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
1
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
430 A
6
260 A
325 A
0
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 25
Pole Number
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
3
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.
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).
10
9
8
Stray Voltage [Vrms]
8
100 Meters
7
120 Meters
Stray Voltage [Vrms]
6
5
4
7
20%
6
11%
5
6%
4%
4
3
Balanced load 0
2
1
3
80 Meters
0
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 25
Pole number
2
Fig. 8: Impact of the Current Unbalance on the Generated SV Level
1
0
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 25
Pole Number
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.
8
7
Stray Voltage [Vrms]
6
200 Ohm
5
5.0 Ohm
10.0 Ohm
20.0 Ohm
30.0 Ohm
50.0 Ohm
100 Ohm
200 Ohm
Fig. 9 Neutral-to-Earth Measurement without a 500Ω Resistor
4
IV. IMPACT OF TRANSMISSION LINE STRAY VOLTAGE ON
HUMANS
3
5.0 Ohm
2
1
0
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 25
Pole number
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
There are a number of references used in the industry that
discuss the resistance of the human body. It is common to use
1,000Ω from one hand to the other, hand to foot, etc... (See
IEEE Std. 80, which gives a range of 500 to 5,000Ω). Recent
published tests, performed by the authors, show human
resistance values for hand-to-hand as follows:
Dry skin
≈172kΩ
Wet skin
≈10kΩ
Wet (salt water)
≈5kΩ
Added to this is the contact resistance of the earth itself,
which can be very large. The earth is actually a pretty good
conductor—if 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 1,000Ω and a downed conductor typically
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measures from 100Ω 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.
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
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
10MΩ or even higher. With 4V driving the circuit, virtually
all the drop is across the meter and the reading is 4V.
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]
Fig. 10 Neutral-to-Earth Measurement with a 500Ω Resistor
TABLE I
ACTUAL FIELD MEASURED DATA
[2]
[3]
Example
Locations
Measured Voltage
Without Resistor
Measured Voltage
With 500 Ω
Resistor
A
B
C
5
0.6
0.4
0.01
0.003
0.08
When a 500Ω resistor is placed across the meter, the total
impedance of the circuit decreases significantly as shown in
Fig. 10. As shown below, the 500Ω 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 500Ω 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
[4]
[5]
[6]
[7]
J. Burke, “The Confusion Surrounding Stray Voltage”, 2007 IEEE Rural
Electric Power Conference, P. C1-C5.
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
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.
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.
J. Burke, Power Distribution Engineering: Fundamentals and
Applications, Marcel Dekker, INC., 1994.
A. Greenwood, Electrical Transients in Power Systems, WileyInterscience, 2 edition, 1991.
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