Telephone interference caused by harmonics and

TELEPHONE INTERFERENCE CAUSED BY
HARMONICS AND UNBALANCE IN POWER LINES
by
MARIAM PAUL
submitted in partial fulfilment of the requirements for the degree of
MASTER IN ENGINEERING
in
ELECTRICAL AND ELECTRONIC ENGINEERING
in the
FACULTY OF ENGINEERING
of the
RAND AFRIKAANS UNIVERSITY
SUPERVISOR: PROF. J.A. FERREIRA
MARCH 1998
Abstract
Open-wire telecommunications were developed in the 19th and early 20th centuries
without any consideration of the deleterious effects of power lines; compatibility
problems were later caused by the proximity of power lines and telephone lines. The
coexistence of such systems requires careful planning in terms of energy coupled to the
telephone lines; this induction can cause interference, as well as dangerous
overvoltages in telephone circuits, and requires detailed studies of the effects of
coupling between high voltage lines and telephone systems to be done. In terms of
inductive co-ordination in South Africa, the minimum separation distances between
high voltage power lines and communication systems are calculated only for power
frequency and lower order harmonics (up to the 13th). The aim of the study was to
explore the agreement between theory and measurement for frequencies from 50 Hz to
the high order harmonic range of 4 kHz; this makes it possible to extend existing
methods for predicting compatible separations to cases where high order harmonics
(up to the 73rd) are present (balanced and unbalanced) on a 132 kV power line feeding
a large aluminium smelter plant.
Opsomming
Die ontwikkeling van oop-draad telekommunikasie netwerke gedurende die 19de en 20ste
eeu het plaasgevind sonder die nodige inagneming van potensiele kraglyn interaksies en
gevolglike steurings situasies het ontstaan onder sekere omstandigheede. Daar is besef dat
deeglike beplanning noodsaaklik is om aanpasbaarheid te verseker. Geinduseerde energie
kan steurings asook gevaarlike hoogspanningseffekte in telekommunikasie stelsels
veroorsaak wat gevorderde studie van elektromagnetiese koppeling tussen krag- en
telekommunikasie netwerk vereis. Om induksieverskynsels in Suid-Afrika te beheer, word
die minimum skeidingsafstande tussen hoogspannings- en kommunikasielyne bereken op
grond van drywingsfrekwensie en lae orde harmonieke (tot by die 13 de). Die doel van
hierdie studie was om die verwantskap tussen die teorie en praktyk te verken met
spesifieke verwysing na die 50 Hz tot 4 kHz harmoniekfrekwensie-band. Meer spesifiek,
die uitbreiding van voorspellingsmetodes vir minimum skeidingsafstande vir gevalle waar
hoe orde stroomharmonieke (tot die 73de), soos dit voorkom in 132kV kraglynvoer van
`n groot aluminium-verwerkingsaanleg.
LIST OF SYMBOLS AND ABBREVIATIONS
cp
Magnetic flux
?t,e
Sensitivity Coefficient for Electrostatic Coupling
Sensitivity coefficient for electromagnetic induction
permeability of free space
p
earth resistivity
conductivity of soil
co
angular velocity
B
Magnetic flux density
self capacitance
mutual (coupling) capacitance
Cn
Di;
C-message weighting factor for the n:th harmonic
distance between induced conductor and image of the inducing
conductor on the surface of the earth
di;
E
actual distance between inducing and induced conductor
-
power line service voltage
EAs
transverse electric field on the surface of the earth
EP
common mode longitudinal emf
ep
f
psophometric emf acting in a loop
H
magnetic intensity
If
harmonic r.m.s component of the line current at frequency f
In
line current of nth harmonic
IP
psophometrically - weighted current or Equivalent disturbing current
'peg
psophometric equivalent 800 Hz disturbing current
IO
earth current
Is
current in the shield wire
IR,Iw,IB -
phase currents
IRO
zero sequence current (red phase)
IR+
positive sequence current (red phase)
frequency
negative sequence current(red phase)
IRW
lo op currents
Iwg
IBR
k
screening factor
kf
kg„,
coupling function
ground wire shield factor
ksn
cable shield factor
kT
Telephone Harmonic Form Factor
inductance
M
mutual inductance between inducing line and induced line
M12
mutual inductance between the inducing line and induced line
n14
coupling function
4
mean value of the coupling function n14
Pf
psophometric weighting factor at frequency f
Pi;
self potential coefficient
mutual potential coefficient
Q
charge per unit length
R
DC
TIE
Telephone Influence Factor
Uf
harmonic r.m.s component of the line voltage at frequency f.
Up
Psophometrically weighted voltage
Upeq
Equivalent Disturbing Voltage
Vcn
common mode voltage
zu
Self impedance of a conductor
resistance
TABLE OF CONTENTS
Page
Chapter 1
INTRODUCTION
1
Chapter 2
ELECTROMAGNETIC COUPLING
6
2.1
Electromagnetic Coupling
7
2.1.1
7
9
2.2
General Theory
2.1.1.1 Loop Currents
2.1.2 General Description About Transmission Line
and Telephone Line
2.1.2.1 Telecommunication Network
2.1.2.1.1 Composition of Transmission Supports
10
11
12
2.1.3 Description of Scale Model
2.1.3.1 Transmission Line
2.1.3.2 Telephone line
12
12
13
2.1.4 Modelling of the System
2.1.4.1 Solution for a Multi-conductor System
2.1.4.2 Equations for Loop Inductance
14
17
18
2.1.5 Psophometer and Psophometrically WeightedCurrent
2.1.5.1 Psophometer
2.1.5.2 Psophometrically Weighted Current
18
18
19
Factors Influence the Induced Voltage in a Telephone
Line
2.2.1 Line Current
20
20
2.2.2 Separation Distance Between Power and
Telephone line
21
2.2.3 Frequency
22
2.2.4 Configuration of Power Line
23
2.2.5 Length of Exposure
2.2.5.1 Oblique Exposure and Crossing
23
24
2.2.6 Earth Resistivity
25
Page
2.2.7 Telephone Pair Spacing
Chapter 3
25
ELECTROSTATIC AND CONDUCTIVE COUPLING 26
3.1
Electrostatic Coupling
27
3.1.1
27
General Theory
3.1.2 Modelling of the System
3.1.2.1 Psophometrically Weighted Voltage
3.1.2.2 Sensitivity Coefficient for Electrostatic
Coupling
3.1.2.3 Telephone Harmonic Form Factor
29
32
32
33
33
3.1.3 Factors Influencing the Induced Voltage
33
3.1.3.1 Geometric Configuration of Installations
3.1.3.2 The Line Voltage and Operating Condition
33
of the Power Line
3.2
Conductive Coupling
34
3.2.1
34
General Theory
3.2.2 Ground Potential Rise Evaluation
3.2.2.1 Electrode GPR
3.2.2.2 Area of GPR
Chapter 4
35
35
36
EXPERIMENTAL MEASUREMENTS
39
4.1
Introduction
40
4.2
Electromagnetic Coupling
41
4.2.1 Balanced Three-phase Condition
4.2.1.1 Common Mode Voltage vs. Frequency
4.2.1.2 Differential Mode Voltage vs. Frequency
41
42
45
4.2.2 Unbalanced Three-phase Condition
4.2.2.1 Common Mode Voltage vs. Frequency
4.2.2.2 Differential Mode Voltage vs. Frequency
45
46
47
Electrostatic Coupling
48
4.3.1 Balanced Three-phase Condition
48
4.3
Page
4.3.1.1 Differential Mode Voltage
4.3
Chapter 5
Compatible Separations
48
49
DISCUSSION AND CONCLUSION
51
5.1
Discussion
52
5.2
Conclusion
54
REFERENCES
56
Appendix
A
Psophometric Weights
58
Appendix
B
Curves for Minimum Separation of Power Line
and Communication Line
62
Appendix
C
Soil Conductivity
68
Appendix
D
Tower Geometry
73
Appendix
E
Circuit Diagrams and Results
76
Appendix
F
Calculation Methods
86
Chapter 1
INT. ODUCTION
The techniques of telecommunication were free to develop without any
consideration of other transmission lines, because they are about five decades
older than those of power transmission. Problems were caused by the
introduction of coexistence of power lines and telephone lines. The coexistence
of power lines and telephone lines requires careful planning in terms of energy
induced into the telephone lines. This induction can cause interference as well
as danger on the telephone circuit, which compelled a detailed study of the
effect of the electromagnetic field produced by high voltage lines. The Comite
Consultatif International Telephonique (C.C.I.F) started research on
interference and protective measures, and published its findings and
recommendation in the form of Directives, in 1925, 1930, 1937/38 and 1952.
In 1957 C.C.I.F and the corresponding Comite Telegraphique (C.C.I.T)
amalgamated in the C.C.I.T.T and new Directives were subsequently produced
in 1963. A complete new set of Directives, comprise of nine volumes, were
published in 1989, incorporating the latest circuit theory and written especially
with computer implementation in mind.
1
Electromagnetic Compatibility (EMC) is a fast developing field. Studies in
Telephone noise interference caused by power line currents and voltages are
done under EMC in power systems environment. Few examples are
Mr.M.Kuussaani's studies about interference voltages in subscriber cables in
rural areas of Finland [12], Mr.Arne V. Johansson and Mr.Ake Ekstrom (both
from Sweden) studies in Telephone interference criteria for HVDC
transmission lines [7], WEE working group on power system harmonics [13]
etc. In all these studies people tried to find the methods to reduce the induced
voltage in the telephone line by improving the telephone circuit balance or by
reducing harmonic components of the voltage and currents in power line.
In South Africa the research work in the co-ordination of power and
communication systems was undertaken by the Power and Communication
Systems Co-ordinating Committee, appointed by the SAIEE, over the period
1938-1957. This committee comprised representatives from the Electricity
Supply Commission, the South African Railways and Harbours, the General
Post Office, the Victoria Falls and Transvaal Power Company, performed
extensive field tests and technical investigations for particular local conditions
[1]. Their conclusions were reflected in the "Code of Practice for Overhead
Power Lines" produced by SAIEE in 1966. In terms of legislation interference
limits are stipulated in the Postmaster General's Requirements, as gazetted [3].
Eskom is bound to this legislation and new power routes have to be approved
by Telkom before construction can start. Under normal circumstances, route
approval of a power line will be preceded by the calculation of the anticipated
induction levels in any nearby cabled or open wire telephone circuits, and these
levels are then compared to the limits stipulated. If the limits are exceeded,
certain remedial action must be taken, such as re-routing of the power line or
telephone line, improved screening on either or both systems, upgraded surge
protection or line isolation, or introduction of additional transpositions in the
case of open wire circuits. The final decision regarding remedial action depends
on the actual limit exceeded and a number of other factors, including cost, as
agreed upon by the respective authorities.
2
General procedure for controlling effects caused by power lines on
telecommunication lines are illustrated in the flowchart below.
START
V
Identify power and telecommunication
facilities involved
Determine electric and geometric parameters
required to estimate the effects
Calculate induced voltages and currents
Stipulate
protective measures
END
Figure 1
Flowchart to be followed when dealing with danger and disturbance
problems in practice.
For the calculation of the induction level, there are three distinct coupling
mechanisms to be considered, namely electrostatic, electromagnetic and
conductive coupling. For each of these there are two types of applicable limits.
The first one considers induced dangerous extraneous voltages and currents to
flow in the telecommunication installations due to abnormal conditions on the
power line (e.g. cable breaks, accidental short circuit, earth fault etc.). The
second one considers the level of interference which could result in degradation
of speech quality, or signal to noise ratio of the telephone circuit, and is
3
normally associated with normal (balanced) conditions on the power line.
Limits regarding danger are normally associated with longitudinal or common
mode voltages, and limits regarding interference with transverse or differential
mode voltage. Longitudinal e.m.f is the electromotive force arising from
induction by current in a power line into the circuit formed by the conductors
of the telecommunication line and earth. Metallic circuit component or
differential mode is the difference in longitudinal component at the two
conductors of the communication line due to system unbalance and the
separation distance between them. The Postmaster General's Requirements of
1978 stipulate the following limits for induction from power or railway lines:
Interference:
2mV maximum psophometrically weighted transverse emf on any wire
pair, which is equivalent to 1 mV potential difference measured with a
psophometer.
Danger:
60 V rms maximum longitudinal induced voltage during normal
operating conditions of the power line.
150 V rms maximum longitudinal voltage in "special cases" during
normal operating conditions.
650 V rms maximum longitudinal voltage during fault conditions on the
power supply system.
The 150 V limit applies to conditions of particular difficulty and is subject to
special precautions being taken such as
the marking of any part of the installation that could be raised to this
potential, and
the issue of special instructions to personnel likely to have access to
this exposed section.
It is generally found that the effect of electrostatic coupling is minimal and
interference levels are acceptable, if minimum stipulated separations between
the circuits can be maintained. The calculation of electromagnetic induction
during line faults as well as interference during normal operating condition are
very important. For the calculation of electromagnetic induction during fault
4
conditions Telkom currently uses a graphical procedure based loosely on the
1963 Directives as well as work produced by Pollaczek in 1926. This
procedure is outlined in their in-house Technical Instruction TI3009 [4]. There
are some limits for this method, especially the case for short exposures, for
which the "infinite line" approximations used in the TI3009 are invalid.
Another problem is that the damage to exchange equipment due to lightning.
For these reasons Eskom tried to establish a mutually (Eskom and Telkom)
accepted computer programme that could incorporate the latest theory and
numerical techniques available, as a general tool for interference problems [11].
Interference due to harmonic currents and voltages on the power line to the
open wire telephone line is a major issue for Eskom in the rural areas.
Harmonics up to 71st and 73rd are present on power lines which are injected
from smelter plant. The aim of this project is to find out the effect of higher
order harmonic voltages and currents on the induced voltage on the
telecommunication line and thus establish recommended guidelines and
techniques for ensuring power system/ telephone system compatibility. The
results will in particular show whether the present separation criteria
(Postmaster General's Directive on separation between power and telephone
lines) needs revision or not.
5
Chapter 2
ELECT °MAGNETIC COUPLING
The voltage induced on a communication circuit can be the result of currents
flowing in a power circuit. This induced voltage can cause interference with
service, damage to apparatus and hazard to persons using the former. The
magnitude of induced voltage increases at higher harmonics. In this chapter the
general theory, modelling of the system and factors influencing the induced
voltage in the case of electromagnetic coupling are discussed.
6
2.1 ELECTR I MAGNETIC COUPLING
2.1.1 GENERAL THEORY
Consider an infinitely long conductor(power line) carrying current of I A.
There will be a time varying magnetic field around the power line due to the
time varying current flowing through it. According to Biot-Savart law field
intensity H at a point P, produced by a differential current element IdL is
dH a
I dL sin
(2.1)
2
r
1 I dL sin 0
dH
(2.2)
r2
47r
where 9 is the angle between the current carrying conductor and a line
connecting the conductor to the point (p), "r" is the distance between the
conductor and the point (p) and
y4 7r is the constant of proportionality in
m.k.s units.
H = I
4 7r
sit
(A/m)
dL
y e
(2.3)
.
Magnetic flux density B is defined as
B =
po H
(Wb/m2)
(2.4)
and magnetic flux (I) passing through any desired area is
0
=
JB .dS
(wb)
(2.5)
If there is another conductor (communication line) cutting this magnetic flux,
according to Faraday's law, time varying magnetic field produced by the power
line will produce an electromotive force (emf) on the communication line.
dcb
emf = – —
dt
(V)
(2.6)
The minus sign is an indication that the emf is in a direction as to produce a
current whose flux, if added to the original flux, would reduce the magnitude of
the emf (Lenz's law).
7
Consider a single phase power circuit, fig 2.1(a). G is the single phase power
are the go and return conductors. I is the current flowing
through the power circuit. C 1 and C2 are the communication conductors
source, P 1 and
P2
located in proximity and TE is the telephone terminal equipment. In fig 2.1(b) it
is shown that C 1 and
C2
lie in different equi-potential lines so that unequal
voltages are induced in these conductors.
F
G
Figure 2.1
I P2
(b)
Schematic diagram illustrating magnetic induction from a power
circuit on a communication circuit.
Elementary section
Equi-potential fields
8
2.1.1.1 Loop Currents
Consider a three phase system carrying currents of
IR, Iw
and IB. If the system
is balanced then:
=0
IR +4
(2.7.1)
(A)
For an unbalanced system:
(2.7.2)
(A)
IR +4 ±IB = IO
Where Ico is the return current.
Three phase currents that induce voltages in communication circuits can be
classified as (1) positive- and negative-sequence components and (2) the zerosequence component. The first type is normally confined to the line conductors
(balanced load) and for the second type the line conductors constitute one side
of the circuit and neutral or ground wires, or earth the return (unbalanced
load). Obviously the coefficients of induction from power-system currents are
different for these two cases.
Considering a 3- phase power line with phase conductors marked Red, White
and Blue, it is possible from knowledge of the respective current vectors (IR
Iw , IB) to determine the loop currents (IRw, IwB, IBR) as well as the earth
current 10 using the concept of sequence components. This reduces any
unbalanced 3 -phase system into balanced positive, negative and zero sequence
components. The sequence components of the red phase current, for example,
are given by the vector [2] :
-IRO
1
3
T
A R+
=
_ R-
with a = -0.5 + j 43/2 =
1 1
1
41
1
a a2
a
a2
(A)
(2.8)
(A)
(2.9)
a
ei2n5
we further have the relations:
=
Iw. = a
IR+
IB+ =
IR-
=
IWO = IRO
a
IR+
TR_
IBO = IRO
9
Introducing operator b = 43/2 + j/2 = ejni6 , the loop currents are easily shown
to be:
b
b-1 r
al b ab-14R+1
IR_
ab a2b-1
w
I
rBWB
I R_
(A)
(2.10)
The total earth current equals the sum of the zero sequence currents,
IRO
+ Iwo +
IBO
= 31R0
(A)
(2.11)
This return current will also produce some induced voltage in the telephone
conductors other than phase currents. In accordance to Lenz's law the flux
they create will be opposite to the flux due to phase currents. Therefore the
return current has a compensating effect on induced voltage and which enables
the neutral or ground wire to serve as electromagnetic screen.
2.1.2 GENERAL DESCRIPTION ABOUT TRANSMISSION LINE AND
TELEPHONE LINE
For the transmission of power in South Africa the commonly available nominal
voltages are 400kV, 275kV, 132kV, 88kV, 66kV, 44kV, 22kV, and 11 kV. For
a three phase over head power line mainly there are three types of
configurations available, horizontal, vertical and triangular. Number of
conductors per phase will be one or two. There will be one or two shield or
earth wires at the top of transmission line support. They are usually connected
galvanically. These wires have triple function:
to give protection against lighting ;
to interconnect the support earths;
to reduce fault currents circulating in the earth and thus reduce the induced
voltages and rise in potential of supports and station.
10
22kV
400 V
Auto transformer
Figure 2.2 Transformation of 275 kV Transmission Line to 400V
Distribution line
2.1.2.1 Telecommunication Network
A general picture showing the telecommunication line is given in the figure
(2.3) below:
Distribution cable
Transmission cable
Local
exchange
Transmission
subscriber
equipment
nn
Surge p otec ion devices
Figure 2.3 Telephone Line Network Between a Subscriber and an
Exchange
In two way telecommunication each end of the links comprise a transmitter and
a receiver, and bi-directional propagation is effected via the physical medium.
The temporary links between different telecommunications users are
established by means of switches. Each terminal installation is attached to a
local switching centre by one or more subscriber lines.
11
2.1.2.1.1 Composition of Transmission Supports
The different transmission supports are
open wire lines
Open wire lines are made of bare metal wires. They are arranged in groups and
fixed to supports by means of insulators. Open wire lines are about 6-10m
above the ground and their conductors vary in diameter between 3 and 5 mm.
The distance between associated conductors forming a circuit is between 20
and 40 cm.
symmetrical pairs cable lines
In this type telephone cables are capable of containing a large number of
conductors within an extremely small section. Each cable conductor consists of
an insulated metal wire. Different cabling methods are used for arranging these
conductors in pairs or quads.
coaxial pair cable lines
wave guides
radio relays
optical fibres
2.1.3 DESCRIPTION OF SCALE MODEL
2.1.3.1 Transmission Line
275kV horizontal configuration is used for the scale model of a transmission
line of practical purposes. The tower geometry for 433 A is given in Appendix
D. The scaling is done purely on the basis of area allocated for the
experimental purpose, i.e. the length of the line is chosen arbitrary as 100 m
and height of the power conductors from ground level is 3.5 m.
Transmission line configuration (Refer fig D.2 in Appendix D)
Height of phase conductors from ground level
19.3 m
Separation distance between the phase conductors
7.4 m
Number of earth or shield conductors
2
12
Height of shield conductors from ground level
26.6 m
Separation distance between the shield conductors
6.55 m
Scale model
1.Height of phase conductors from ground level
3.5 m
Scale constant
5.5
Separation distance between the phase conductors
1.35 m
2
Number of earth or shield conductors
Height of shield conductors from ground level
Separation distance between the shield conductors
4.4 m
Total length of the line
100 m
1.2 m
2.1.3.2 Telephone Line
Two wire open line is used for scale model. Scale constant is same as the one
used for transmission line.
Original config: Scale model
Height of conductors from ground level
Separation distance between conductors
6.5 m
15-20 cm
Total length of telephone line
1.2 m
5 cm
80 m
Photograph of Test Line at Rand Afrikaans University
13
2.1.4 MODELLING OF THE SYSTEM
A lot of research works were performed in the 1920's to establish formulae
suitable for the prediction of electromagnetic coupling between two circuits.
Numan's formula for the mutual magnetic energy of two circuits to linear
circuit, [2] gave completely wrong results when an earth return current path
was considered. In 1923, G.A. Campbell gave a solution for the mutual
impedance of earth-return circuits of finite length. Because of the imperfect
knowledge of the conductivity of deeper parts of soil, it was impossible to see
clearly which approximation are permitted in the calculation of the mutual
impedance between lines with earth return. Careful measurements on specially
erected lines, in regions of different conductivity of soil, proved that the later
theory, developed independently and nearly simultaneously by Pollaczek,
Carson, Haberland and Buchholz in 1926-1927, corresponds much better to
experiment than that formerly developed, [2]. This theory is still used in the
1989 Directives.
Carson's general formula is
CO
f[Vu 2 + j – u] e-bau
M = j
ecasf
cos(a au) du
(2.12)
0
Pollaczek general formula is
Mp =
./P0
27r a2
0
FT—
2 ja 2 [11 2
{j e u(ja+b)+c tJ
u +j a2 +u] du +
-CO
e ttCfa-b)+c 311-ja2
u2[
f
lug
j• a 2
u]du} (2.13)
o
Haberland's formula for a point in the air ( c>0 ) is
Mx,
-
Where a
2,r
ln—
D+
j[Vu 2 +i – ] e- ua(b+c) cos(a a u) du (2.14)
d
r 0
- horizontal distance between inducing conductor and
induced conductor, m
b
- height of the inducing conductor above surface of earth, m.
14
c
- height of induced conductor above surface of earth, m. (in the
buried conductor c<O)
D
-
distance between induced conductor and image of the
inducing conductor on the surface of the earth, m.
d
- actual distance between inducing and induced conductor, m.
a
- conductivity of soil, mho/m.
f
- frequency; w = 27r f
110
-
a,
-
4 it x 10 -7 permeability of free space, H/m.
a co
Figure 2.4 Mutual Inductance Between Conductors 1 and 4
Equation for the transverse electric field on the surface of the earth are of the
form,
co
E AS
2
Fj
) . 119- .1[ 1177-
= a
0
eb a u ec a PT cos(a a u) du (V/m)
(2.15)
where I is the inducing current. This simple equation is valid if both lines are
overhead. In the case of stratified soil, the conductivity of the different layers
can effectively be represented by homogeneous soil with an intermediate value
of a.
The mutual inductance
M14
=
M14
can be obtained from the relation:
EAs
27r f I
The solution to the integral relation for
(Wm)
EAs
as provided by Pollaczek yields the
following results for M14 a function of separation parameter aa. [2]
15
(2.16)
- if aa < 0.5 :
7r
2 15
[21n
+ 1 – j — + — (1+ j) a (b + c)] (H/m)
M14 = 42
gad
2
3
(2.17)
Where d
g
-actual distance between the conductors, = Va 2 + (b– c) 2
-1.7811.. is the complex of Euler's constant.
- if aa >= 0.5 :
4414
,u 0 kei aa – jker' aa
7ras
j
(aa)2 -I
(H/m)
(2.18)
where ker' and kei' are real and imaginary part of the first derivative of the
modified Bessel function (second kind, order zero)
- if as > 10 :
M14 =
Po
(Him)
7r (aa) 2
(2.19)
From these equations, it is observed that the mutual inductance is complex,
with phase angle always larger than 90 °, and tending towards 180 ° for larger
separations. The real component of
M14
is larger near the conductor, initially
decreases slowly (as the logarithm) with increasing distance, then decreases to
negligible values in an oscillatory manner with increasing distance. The
quadrature component of M14 is small near the inducing conductor, eventually
dominates with increasing distance, then decreases as 1/ a 2 .
Mutual impedance Z14 between the conductors 1 and 4 is:
Z 14 = - jcoMia(ohm/m)
(2.20)
Voltage induced on conductor 4 due to the current flowing through the
conductorl (I A)
is:
(V)
Where It is the length of exposure between 1 and 4.
V14 ZI4 I lt
16
(2.21)
2.1.4.1 Solution for a Multi-conductor System (Three-phase system)
B
O T2
b
Figure 2.5 Mutual Inductance Between Three-phase Conductors and
Telephone Conductors
In the above figure R,W and B represents three phase conductors and T1 and
T2
represents two telephone conductors. Mutual inductance(MRT1) between the
red phase conductor and the first conductor of the telephone line is:
4~47r [2 ln
MRT1
r
+ 2-5
2
+ 1 – j— — (1+ j)a(b+c)]
2
gadRn
3
(H/m)
(2.22)
Where diti= q[aRr1 2 + (b-c)2]
Similarly we can find Mwri and MBT1 .
Mutual impedance between the red phase conductor and the first conductor of
the telephone line,
ZRT1 is:
ZRT1
Similarly find Zwri and
(H/m)
-j(01\ARr1
(2.23)
Z$T1 •
Loop inductance ZRwri is:
ZRWT1 = ZRT1 ZWT1
(Him)
(2.24)
Similarly we can find ZWBT1 and ZBRT1
and IB be the current flowing through red, white and blue phase
conductors respectively. Now we can calculate the loop currents IRW , IwB and
IR, Iw
IBR (see section 2.1.1.1)
The induced voltage on the first conductor of the telephone line due three loop
currents and earth current (unbalanced load) is:
17
VT1
[ZR1PT1
ZWBTI
[ZRWTI
ZW73T1
ZBRT11
IRO
[Iwo
IBO _
4
(2.25)
(V)
For a balanced load the second part of the above equation will be zero.
Similarly we can calculate the induced voltage on the second conductor of the
telephone line (VT2). The differential mode voltage Vd is:
Vd =
VT1 - VT2
(2.26)
(V)
2.1.4.2 Equations for Loop Inductance - for small separations.
For small separations, loop induction becomes significant. Loop induction
occurs when the current returns via a second conductor, as is the case for
balanced conditions on a power line. The mutual inductance for a double wire
circuit and a circuit with earth return can be found by calculating the partial
derivative of M14 and forming the total differential, resulting in [2]:
M12/4
Po
[
2a
4n- d2
da +[
2 (b — c)
d2
+
ri
3
a (1+ j) ]db ] gym)
(2.27)
for a loop with horizontal projection da and vertical projection db.
2.1.5 PSOPHOMETER AND PSOPHOMETRICALLY WEIGHTED CURRENT
2.1.5.1 Psophometer
The psophometer is an instrument which has been introduced for measuring the
value of the parasitic voltages produced in telephone circuits by nearby power
lines, from the point of view of the interference which the noises due to these
voltages can cause to the normal use of the circuits[10]. It was developed with
a view to making measurements at the ends of long-distance circuits. It has a
very high input impedance, and can be used in the same circumstances as a
18
voltmeter; it consists essentially of an a.c. measuring instrument, associated
with a weighting network.
2.1.5.2 Psophometrically Weighted Current
In noise interference case, it may be necessary to measure the spectrum of
harmonics in the disturbing current.
The psophometrically - weighted current I„ is
1
(2.28)
(A)
p ilE 13; 1-;
800 if f
where Pf is the psophometric weighting factor at frequency f
If is the harmonic r.m.s component of the line current at frequency f.
Note:- Psophometric weighting coefficients for different frequencies are given
in Table A-1 in Appendix (A).
The psophometric equivalent 800 Hz disturbing current is:
/peq
P800
P 2 2 ELY
f If 800
(A)
(2.29)
To find the value of psophometrically induced voltage, the value of current
used in the above section(2.1.4.1) must be psophometrically weighted current.
Another assumption is that for a linear system, the effect of different harmonic
currents present in the line current (fundamental + different harmonics) will be
the same if we treat them separately and then find their combined effect. The
formula use in this case is:
2
VT = AAVTfiin) + (VT1)2 + (VT2 )2
Where
VITun, VT1, VT2
(VT02
(V/m) (2.30)
VT„ are the induced voltages at fundamental, first
second and nth harmonics respectively.
Vrfun = Zfun x 1 x ipueun
Pecliun
1
PS
= 800
( 50) 2
i502 800)
19
(2.31)
(V/m)
(A)
(2.32)
Zi X1Xl peg]
VT'
Vd = VT x A. m
(2.33)
IM)
(2.34)
(Wm)
is the sensitivity coefficient of electromagnetic coupling.
where
Sensitivity coefficient of electromagnetic coupling(t) is defined as the ratio
between the psophometric emf acting in a loop
ep
and the common mode
longitudinal emf Ep caused by magnetic induction.
=
ep
(2.35)
Ep
Measurement can be done using exiting induction, or for a more systematic
approach, artificial induction can be used. These techniques are
comprehensively detailed in the Directives [10]. Measured values for 2 m
typically range from 0.001 to 0.05 for open wire circuits, while for cables
values are normally much lower.
2.2. FACTORS INFLUENCE THE INDUCED VOLTAGE IN A
TELEPHONE LINE
From equations 2.22, 2.23 and 2.25 it is clear that the factors influencing the
induced voltage in a telephone line are: line current, separation distance
between the power and telephone line, frequency of the inducing current,
configuration of the power line, earth resistivity (soil conductivity) and
telephone pair spacing.
2.2.1 LINE CURRENT
From equation 2.21 it is clear that voltage induced on a conductor is directly
proportional to the magnitude of current flowing through the inducing line. To
verify this mathematically induced voltage is calculated for two different
inducing currents(10 A and 5 A) in the case of test line configuration (section
2.1.3). The separation distance between the two lines is 1.57 m (from the red
phase conductor to the telephone conductor), the exposure length is 80 m and
soil resistivity is 260 ohm-m. In the graph given below (from 50 Hz- 5 kHz) it
is shown that when magnitude of current doubles the magnitude of induced
20
voltage will also double if there is no change in the other parameters of the
lines.
In duceddiff:mode vo ltage (my)
45
40 —
35 —
30 —
Diff:mode induced
voltage 1=10 A
(my)
Diff:mode induced
voltage 1=5 A (my)
25 —
20 —
15 —
10—
5—
"0
0
1000
2000
3000
4000
Frequency (Hz)
Figure 2.6 Effect of Line Current on Induced Voltage
2.2.2 SEPARATION DISTANCE BETWEEN POWER AND TELEPHONE LINES
The separation distance between power and telephone routes is the
fundamental factor which determines the value of induced voltage. Even if the
currents are balanced, because of the difference in separation distance between
each phase conductor and the telephone conductor the magnitude of the
induced voltage is different due to each phase current. This causes a differential
voltage in the telephone loop. To minimise the magnitude of this differential
voltage, transposition of power line or telephone line can be done. In the graph
below induced differential mode voltage in the telephone line is calculated for
the test line configuration (section 2.1.3) for two different separation distances
(1,57m and 3,14m) for frequencies 50 Hz- 5 kHz. The magnitude of inducing
current is 10 A, exposure length is 80 m and soil resistivity is 260 ohm-m.
From the curves it is clear that induced voltage decreases the separation
distance between the power and telephone line increases.
21
Induced diff:mode voltage (mV)
45
40 —
35 —
30 —
for 1.57m
separation
for 3.14 m
separation
25 —
20 —
151050
0
1000
2000
3000
4000
Frequency (Hz)
Figure 2.7
Effect of separation distance on induced voltage
In Postmaster General's Requirements curves to determine minimum
separation distance between power lines and communication routes for
different exposure lengths are given [ Appendix B].
2.2.3 FREQUENCY
The magnitude of induced voltage varies approximately directly with
frequency. Note that the mutual inductance is also a function of frequency.
Thus, the higher the frequency (higher order harmonics), the higher the value
of the induced voltage. Induction at harmonic frequencies, particularly at 180
Hz and 3000 Hz occurs most frequently during normal operation and may
result in significant audible disturbance which affects transmission and
reception of telephone conversations. In the graph below induced differential
mode voltage (calculated) is shown for frequencies 50 Hz to 4 kHz for the test
line configuration (section 2.1.3) for inducing current of 10 A, exposure length
of 80 m and soil resistivity of 260 ohm-m.
22
Induceddiff:mode voltage (mV)
45
40 —
35 —
30 —
25 —
20 —
151050
0
1000
2000
3000
4000
Frequency (Hz)
Figure 2.8
Effect of Frequency on Induced Voltage
2.2.4 CONFIGURATION OF THE POWER LINE
The configuration of the power route conductors, i.e. whether they are
arranged in vertical, horizontal or triangular formation, is of importance in that
it determines the relative phase of the induced voltage in the phone line from
each of the phase conductors and consequently, the net longitudinal voltage in
each wire of the telephone line.
2.2.5 LENGTH OF EXPOSURE
The induced longitudinal voltage is a function of the length of exposure
(directly proportional). In normal case, length of exposure indicates the length
over which the separation between telephone and power lines remains sensibly
constant (parallelism). The graph below shows the effect of exposure length
(80 m and 40m) on induced voltage. The test configuration (section 2.1.3) is
used for calculation with inducing current of 10 A, separation distance of 1.57
m and soil resistivity of 260 ohm-m.
23
Induced diff:mode voltage (mV)
45
40 —
35 —
Diff:mode induced
voltage, 80 m
exposure(mV)
Diff:mode induced
voltage (mV), 40 m
exposure
30 —
25 —
20 —
15 —
10 —
•
5—
0
1000
2000
3000
4000
Frequency (Hz)
Figure 2.9
Effect of length of exposure on induced voltage
2.2.5.1 Oblique Exposure and Crossing
An exposure section between the limits of which there is an almost linear
increase or decrease of the distance between the lines is called an oblique
exposure. The passage of a telecommunication line from one side of the electric
line to the other is termed a crossing.
dl
V
Inducing line
Figure 2.10 Geometric layout of oblique exposure and crossing
1= exposure length
A crossing is considered as a parallel section having a separation distance,
(2.36)
d= 6m
24
where d =Ic11.712 and length "I" equal to the projection of the segment
contained in the zone of 10 meters around the power line. Outside the 10 m
boundary the exposure is treated as a normal oblique exposure.
2.2.6 EARTH RESISTIVITY (p)
The mutual inductance increases with increased values of earth resistivity since
the earth currents will flow at greater depths ( 659 frri), thus increasing the
magnetic effect of the current. Soil conductivity (a = f ) can vary from 0.1
to 0.0001 mho/m, depending on the type and age of the formation. Wenner 4electrode method for finding earth resistivity is explained in Appendix C. If the
local composition of the soil is known, a fair estimate for a may be obtained
from table C-1 in Appendix C. In the absence of measured values or adequate
knowledge of the soil composition, fig.C-1 in Appendix C can be used.
2.2.7 TELEPHONE PAIR SPACING
The spacing of the wires of the telephone pair will affect the relative distance of
the two wires from the power route. This difference in distance will produce a
different longitudinal voltage in each conductor and will, therefore, influence
the value of the transverse voltage.
25
Chapter 3
ELECT °STATIC AND CONDUCTIVE COUPLING
The voltage induced on a communication circuit can be the result of its position
in the electric field or electrostatic field produced by the line voltages of the
power line. Electrostatic or capacitive coupling expresses the relation between
the potential of the inducing electric line and the induced charging current, per
unit length occurring on the telecommunication circuit. Conductive coupling is
the phenomena where part of the earth potential (due to power line earth
currents) will transfer to the telecommunication circuit through its earth
electrodes. In this chapter general theory of electrostatic and conductive
coupling, modelling of system for these and factors influencing them are
discussed.
26
3.1 ELECTROSTATIC COUPLING
3.1.1 GENERAL THEORY
An important source of extraneous voltage on communication circuits under
normal operating conditions, may be electric induction from a neighbouring
power circuit. By this is meant the voltage impressed on a communication
circuit because of its position in the electric field, or electrostatic field produced
by the circuit voltages of the power system.
Consider a section of line with power conductor P energised from a singlephase grounded source (G) and with communication conductor Cl and C2
figure(3.1.a). There are capacitances between conductors and between
conductors and ground. In fig (3.1.b) we can see that even if the
communication conductors are separated for a short distance they lie in
different electric potential lines produced by the power line, and different
potentials are induced on them.
(a)
27
180160140-12010080 _
60 40 20
M
20-
N
.................................................
.......
..•
........
..... - . . ....
'•.
60 •.
.
80 100 120 -
„.•
*-- ... ..
140 -
.
. • ''
... ...
......... ••"..
160 _
......... ..•
180 -
(b)
Figure 3.1
Schematic Diagram Illustrating Electric Induction From a Single
phase Ground-return Power Circuit on a Communication
Circuit Conductor.
Elementary section.
Equi-potential fields.
The effect of electrostatic coupling is important only if induction from an open
power line to open wire telephone line or suspended cables without a metal
sheath are considered.
When calculating the effect of a poly-phase line the phase-to-earth voltages are
replaced by their symmetrical components. The expressions for the induction
effects due to zero-phase sequence voltage U o of an balanced system and to the
balanced voltage U1 , i.e. positive-phase sequence, differ greatly and will be
studied separately. In the case of a three-phase line the service voltage U is the
28
line-to-line voltage. For a balanced three-phase system the modulus of the
positive sequence component Ui is equal to U/'13 and Uo is zero. If one of the
phase conductors of a three-phase system with insulated neutral is accidentally
earthed then the modulus of the zero sequence voltage Uo is equal to U/43.
3.1.2 MODELLING OF THE SYSTEM
For the calculation of capacitive coupling, we are confined to systems of lines
which are long in relation to all dimensions perpendicular to length and we
suppose also that the lines are parallel with the surface of earth and with each
other, so that a two-dimensional problem results. The effect of earth is taken
into account by means of Kelvin's method of electrostatic images. This method
would be absolutely correct if the soil were a perfect conductor; even if this
condition is not fulfilled the correction may be neglected up to 1 MHz. [2]
1
D1
Figure 3.2 Electrostatic Coupling Between Two Conductors 1 and 4
Consider two thin infinite conductors 1 and 4, of radius r 11 and r44 , with charge
per unit length Q 1 and Q4 parallel to each other and placed horizontally above
the earth, the line potentials can be written as
= Pn
U4
=
P41
+
P4 Q4
Q1 + P44 Q4
29
(V)
(V)
(3.1)
(3.2)
Where
=
ln r:11 = ko
P
14 = k0 1n R4
d
, 2b
(m/F)
a2 1-(1).+c) 2
a2 + 0-02
= ko In
14
Coupling function
14
= In D14
(3.5)
(3.6)
P41 = P14
P44 =
, D44
K 0 in
r44
,
2c
= K0 in—
r44
(m/F)
(3.7)
1
(3.8)
18x109
(mIF)
27rso
Similarly for a system of 'n' parallel conductors we have a system of 'n'
k0
=
equations:
=
1
ko[a 1 1 -F Q2 P2i
+....------ -F Q.P.i ]
(V)
(3.9)
The factor Pi; is termed as mutual potential coefficient and if i = j it is termed as
self potential coefficient. Multiple conductor bundles are often used no power
lines. In this case the conductor radius rii is replaced by the effective
electrostatic radius.
= VrN A N-1
Where r
N
(3.10)
(m)
= radius of each conductor
= number of conductors, arranged on circle of radius A
To solve this system of equations the classical (analytical) approach involves
solving for the self and mutual capacitances of the system of conductors.
Mutual (coupling) capacitance
C14 = C41
P14
111 1'44
30
(F/m)
(3.11)
Self capacitance
1
CI I
1
P44
C44
(F/m)
(3.12)
(F/m)
(3.13)
Let 1/4 be the electrostatic potential at conductor 4 due to conductor 1:
174 =
P14
1
(3.14)
(V)
P1 1
Under normal conditions the telephone lines are closely spaced, and potentials
therefore almost equal. The open circuit voltage of one line is not affected by
others. It is therefore normally only necessary to consider a single induced line,
for calculation of the potentials and for the open circuit voltage of the complete
exposure.
To calculate the discharge current to earth where a person come into contact
with one or two of the telephone line(s), we can treat those line(s) as earth
wire(s) [U4 = 0] and compute the charge present on the line(s). The current is
then obtained by differentiation of this charge for frequency f.
From equation (3.1) (neglecting the second term)
Q i = 1 Ul
(coulomb)
(3.15)
P11
substituting (3.15) in (3.2)
1
Q4 =
P44
UA„
(coulomb)
pi 1 4' U,•
P44
(3.16)
The current flowing through the telephone conductor:
1
i4 = jcp—U 4 /CO
44
41U1
P1 1 P44
(Aim)
(3.17)
when U4 = 0
ja =
j w Poi rT
u1
P„ P
P44
44
31
(A/m)
(3.18)
3.1.2.1 Psophometrically Weighted Voltage (Up)
The psophometricaly weighted voltage can be defined similarly as the current
(refer section 2.1.2.1).
Up = 1 ilEP; U;
P800
(3.19)
(V)
where Pf - psophometric weighting factor
Ur - harmonic r.m.s component of the line voltage at frequency f.
Equivalent Disturbing Voltage
81
Upeq
(U peq)
VEQ
P800
f
Pf
)
2
(V)
(3.20)
where k, — f
— and it represents the increased influence of higher frequency
—80 0
term due to the capacitive coupling effect.
3.1.2.2 Sensitivity Coefficient for Electrostatic Coupling (.1, e)
'l e is defined, for a specific telephone pair, as twice the ratio of the differential
voltage uf (line-to line) to the common-mode voltage U r (line-to-ground)
appearing on the wires when the line is subject to electrostatic induction. For a
mixture of frequencies, this coefficient is described as twice the ratio of the
psophometric voltage up to the psophometric voltage Up of the lines with
respect to earth.
=
2uP
(3.21)
Up
The sensitivity coefficient applied to a telephone line is normally taken as the
average of all the pairs on the line, and adequate description of its measurement
is provided in the Directives. Its value depends largely on geometric
considerations and the unbalance of the pair. This unbalance has three
components, namely, the unbalance of the coupling parameters with respect to
the power line, the unbalance with respect to earth and the unbalance with
32
respect to nearby wires. The usual means of improving balance and hence the
sensitivity coefficient is regular transpositions of the telephone line, which also
has the benefit of reducing cross-talk. For twisted pairs, the unbalance is
practically zero.
3.1.2.3 Telephone Harmonic Form Factor kr
Also simply termed the Telephone Form Factor, kr is defined as the ratio
between Up and the power line service voltage E. For calculation purpose, the
measured value of kr has to be increased by 50 % to allow for the most
unfavourable :working conditions. In the absence of measurements, the
Directive suggest the following values [10]:
Loads with
All other
Table 3.1
E < 80 kV E
>= 80 kV
static converters
10
5
loads
4
2
Suggested Working Values for the Telephone Form Factor
3.1.3 FACTORS INFLUENCING THE INDUCED VOLTAGE
3.1.3.1 Geometric Configuration of Installations.
The induced voltage due to electrostatic coupling depends on the capacitance
between conductors as well as capacitance between conductors and earth. The
value of these capacitance's depend on the height of conductors above ground
level, separation distance between them etc. The longitudinal voltage varies
inversely with the separating distance.
3.1.3.2 The Line Voltage and Operating Conditions of the Power Line.
Like power system currents, power system voltages which produce induction
effects in communication circuits can be classified as (1) positive- and negativesequence components (balanced load) (2) zero-sequence component
33
(unbalanced load). Balanced conditions will produce significantly less effects
than unbalanced condition. The induced voltage depends on the magnitude of
the line voltage.
3.2 CONDUCTIVE COUPLING
3.2.1 GENERAL THEORY
Alk
1s7i
iii
NAM
Figure 3.3
Current Distribution in the Event of a Phase-earth Fault
Occurring Inside a Substation.
When a phase to earth fault occurs the fault current will have two paths to
choose, earth or shield. Most of the fault current will flow through earth and
that will cause a potential rise at the earthmat or electrode closer to the point
where fault happens. Currents flowing in the ground in the case of a shortcircuit to earth in an electric system will cause a potential difference between
the electrode and remote earth. This happens in the regions where current
enters or leaves the ground. The potential difference is referred to as electrode
ground potential rise (GPR). The area surrounding a high voltage earth
electrode that is raised in potential is referred to as zone of GPR.
If a telecommunication electrode is located in the zone of GPR a part of
potential transfers to this electrode. This may enter the telecommunication
circuit through over voltage protection which are connected to these
34
electrodes. The phenomenon described above is, the effect of conductive
coupling.
When there is an unbalance in the three-phase power line (normal operating
condition) part of the return current flows through earth. This happens in the
single wire earth return line as well. Thus there will a zone of GPR around the
electrode which allows the return current to enters or leaves the ground.
3.2.2 GROUND POTENTIAL RISE (GPR) EVALUATION
3.2.2.1 Electrode GPR
The magnitude of conductive coupling between the electrode e and the point p
can, in a general manner, be expressed by the transfer resistance which is
defined as
Re(p) =
v(p)
Ie
(ohm)
(3.22)
where R. (p) is the transfer resistance between the electrode e and the point
I);
V(p) is the potential to remote earth of the point p due to current
injected in the ground by electrode e;
1e
is the total current injected in the ground by electrode e.
The idea of transfer resistance can be used to obtain the potential at a given
point in the zone of GPR due to an earth electrode and can be expressed as
(V)
V(p) = R e (p).
(3.23)
The GPR voltage of an earth electrode, e.g. tower footing is:
Ve = Re I.
Where Ve
Ie
(3.24)
(V)
is the electrode GPR;
is the current flowing through the electrode; it is
= Ics I
I
is the earth-fault current (in three-phase network I = 310, where
10 is the zero-sequence current component);
35
ks
is a factor expressing the reduction in the current; due to tower
footing resistance and earth wires;
Re
is the earth resistance of the electrode.
3.2.2.2 Area of GPR
One of the simplest form of electrode is the driven rod. Suppose this rod is a
part of an infinite conductor of uniform resistivity and a unit current enters to
it. This current will flow away radially from the point of entry and at a distance
`r.' from the point of entry the current density will be 1/4 it ?. This follows
from the fact that at a radius r, the current will be uniformly distributed over a
sphere of radius r and hence of area 4
it
r2. From these assumptions we can
prove that the earth electrode resistance of that is,(the resistance of a
hemisphere on the surface of homogeneous soil) [10]:
2 ,r re
Where p
(n)
(3.25)
is the resistivity of soil;
re
is the radius of the hemisphere
2 7i. re
Electrode
Potential rise
Zone of Influence
!<1
Figure 3.4
Resistance and Potential Rise of Equivalent Hemisphere
36
x
Netural Zone
When a current I is injected into the ground, then potential of electrode is:
V =
P I
2n-re
(volt)
(3.26)
and GPR Vx around the electrode is:
V =
Where I
x
27rX/
(volt)
(3.27)
is the injected current;
is the distance from the axis of hemisphere (x bigger than r e);
If we combine the formulas (3.24) and (3.25) then the GPR:
Vz = V re
(volt)
(3.28)
The equivalent hemisphere of a real electrode is defined in such a way that the
resistance of the hemisphere electrode and the real ones should be equal to
each other:
Re
= P
2 7r re
(CI)
(3.29)
From this, the radius of the equivalent hemisphere is given by:
re =
22rRe
(m)
(3.30)
The formulas of resistance R e and equivalent radius re are given in the table
below for three common electrode shapes [10]
37
Earth resistance
Electrode
Type
Re
Shape and size
1
Driven
P 11n81 — 11
27z-li_ d
j
d
Radius of equivalent
hemisphere
re
/
8/
ln- —1
d
rod
Ring of
C=Z5
r
wire
O
Earth
Area of the plate
plate
Table 3.2
4D
In ,—
7r2D Vd h
p
h
p
4A
7rD
21n 4D
frrh
2
'—
,M =0.35921171
71-.11 7r
A
Formulae for the Earth Resistance R e and Radius re of
Equivalent Hemisphere
38
Chapter 4
EXPERIMENTAL MEASUREMENTS
In this chapter the results of experimental work done on the practical (scale
model) set-up is compared with the calculated/ predicted values.
Psophometrically weighted induced voltage is calculated for different harmonic
components of the inducing current. Curve showing the minimum separation
distance vs. exposure length is done for an original 132 kV line.
39
4.1
INTRODUCTION
The aim of the experimental work was to explore the agreement between
theory and measurement of induced voltage for frequencies from 50 Hz to the
high order harmonic range of 4 kHz. This makes it possible to extend the
existing methods for predicting compatible separations to cases where high
order harmonics are present on power lines.
For experimental purposes, a scale model of a three phase power line and an
open wire telephone line was constructed at the Rand Afrikaans University
campus. Scaling was done purely on the basis of area available; the total length
of the power line is 100 m length and the attachment height of the phase
conductors was arbitrarily chosen as 3.5 m. A 275 kV horizontal configuration
light suspension tower was used for the basic scaling of the transmission line.
The open-wire telephone was scaled from standard Telkom designs.
An ELGAR (132 V / 22 A, 50 Hz-5 kHz, power amplifier) was used as the
three phase power source and load (resistors) was connected in the star
formation. For the telephone line both ends were terminated at 600 ohm. A
selective voltmeter (HP 3581 A, 0-50 kHz, 20 V-0.1 ptV) was used to measure
the induced voltage. To measure the magnitude and phase shift of phase
currents by using an oscilloscope three LEM 101 were connected in the circuit.
To get more accurate values for phase currents shunts were connected in series
(at each phase) and voltage was measured across them. Common mode and
differential mode induced voltages were measured on the telephone conductors
for frequencies 50 Hz- 4 kHz. Special attention was given to make sure that the
measured values are the real components of the specified frequency.
The cases discussed are;
Electromagnetic Coupling:
1. Balanced three phase condition (three phase currents are equal in magnitude,
10A)
Common mode induced voltage
Differential mode induced voltage
40
2. Unbalanced three phase condition, ground return (the magnitude of three
phase currents are not equal and the return current flows through true earth)
Common mode induced voltage
Differential mode induced voltage
3. Single Wire Earth Return
Electrostatic Coupling:
1. Balanced three phase condition (three phase voltages are equal in magnitude,
65V)
For all these conditions the induced voltage is calculated using the equations
from C.C.I.T.T. Directives [5] and HRJ Klewe's book [2]. The calculation
procedure is given in Appendix F. Experimental work proved that these
equations are valid even at high order harmonic frequencies (4 kHz). To find
the effect of these high order harmonic frequencies on induced voltage (limit of
1 mV) psophometrically weighted induced voltage is calculated for different
harmonic components of the inducing current. The maximum exposure length
for different separation distances are then calculated. This is done for a 132 kV
transmission line (not for test line).
4.2 ELECTROMAGNETIC COUPLING
For balanced three phase condition the three phase currents were equal in
magnitude, 10A and induced voltage is measured from 50 Hz- 4 kHz. The
magnitude of three phase currents were kept as a constant value by adjusting
the load and the line voltage at each frequency. Common and differential mode
induced voltages were measured and compared with the calculated values.
4.2.1 BALANCED THREE-PHASE CONDITION
IR = Iw = IB = 1 0 A at 120° phase shift
41
- - - - SHUNT
LEM 101
Source
132 V/ 22 A
Figure 4.1
Circuit Diagram for Balanced Three-phase Condition
Like as showed in the circuit diagram the star point of the load is not connected
to earth or shield wires to make sure that there were no return current.
Common Mode Voltage vs.
Frequency
2
1.8 —
Common mode voltage (V)
4.2.1.1
1.6 —
1.4 —
0
1.2 —
—o—Calculated value (V)
o Measured value (V)
10.8 —
0.6 —
0.4 —
0.2 —
0
0
Figure
1000
2000
3000
Frequency (Hz)
4000
4.2 Common mode Voltage versus Frequency
42
Common mode voltage
Frequency
(kHz)
Calculated
(V)
0.06
0.028
0.0256
8.5
Corrected
Calculated
Voltage (V)
0.0264
0.15
0.072
0.07
2.7
0.068
-3.1
0.25
0.12
0.116
3.3
0.1132
-2.5
0.35
0.168
0.18
-7.1
0.1585
-13.6
0.5
0.242
0.26
-7.4
0.228
-13.9
0.65
0.316
0.293
7.3
0.2981
1.7
1.0
0.483
0.454
6.0
0.4557
0.36
1.5
0.725
0.658
9.2
0.684
3.8
2.0
0.966
0.858
11.2
0.9113
5.9
2.5
1.208
1.04
13.9
1.14
8.7
3.0
1.45
1.226
15.5
1.368
10.4
3.5
1.691
1.421
16
1.595
11
4.0
1.933
1.653
14.5
1.824
9.4
Table 4.1
Measured
(V)
Error (%)
Error after
correction
(%)
3.1
Result : Balanced Three-phase, Common Mode Voltage
This is the voltage induced on each conductor of the telephone line and which
is measured with respect to earth. Narrow band measurement was performed
to make sure that the values measured were accurate. The reasons for the
deviation between the measured and the calculated values could be the
following:
The equation used to find the mutual impedance between the inducing loop
and the induced loop is a partial derivative equation. This itself can cause an
error in the calculation.
The equation is more accurate if the separation distance between the
inducing loop and the induced loop is much bigger than the separation distance
43
between the conductors of the inducing loop. For the scale model these two
separation distances are almost same. This also influence the calculated value.
3. The input impedance of the selective voltmeter, which was used to measure
the common mode voltage has relatively low input impedance (in the order of
10 kn).
Rt/2
Re
Re
eas
Figure 4.3
Thevenin Equivalent Circuit for Measurement
In the above figure Veal is the calculated common mode voltage and V.I. is the
measured common mode voltage. Rt /2 =300 n which is half of the terminating
resistance of the telephone line. R e=150 n which is the earth electrode
resistance and Rin=10 ica which is the input impedance of the selective
voltmeter. Using \I'm,as at each frequency V ea l is found by circuit analysis and
given in Table 4.1 as corrected calculated voltage. At higher frequencies (from
650 Hz) error drops down significantly if this corrected voltage is used. But at
the same time it has a negative impact on the lower frequency range. The
reason for this can be the variation of the input impedance of the selective
voltmeter with frequency.
4. The magnitude of current at each phase at each frequency was taken as 10 A
for calculation. But in the experimental measurement there could be a slight
variation in this value and that makes a small error.
44
4.2.1.2 Differential Mode Voltage vs. Frequency
Differe ntial mo de voltage (mV)
45
40
35
30
25
—x—Calculated value (mV)
o Measured value (mV)
20
15
10
5
0
0
Figure 4.4
1000
2000
3000
Frequency (Hz)
4000
Differential mode voltage versus Frequency
The differential mode induced voltage was measured between the two
conductors of the telephone line (the other end of the telephone line was
earthed). Measurement was performed by tuning the frequency (the required
value) to get accurate readings especially at lower frequencies. Result of this
measurement is given in Table E.1 of Appendix E. From the result it is quite
clear that there is a good agreement between the predicted and measured
values (max. error is 9%). The reason for this small deviation can be the
following:
1. The experimental set-up and the ideal set-up for calculation will have
variations in the physical modelling. This will influence the differential mode
voltage. Moreover the errors at the common mode voltage will also have an
influence on the differential mode voltage.
4.2.2 Unbalanced Three-phase Condition (Return current through earth)
IR = 8.21 A Iw = 8.35 A
Ig = 7.03 A
45
Circuit Diagram for Unbalanced Three-phase Condition
Figure 4.5
(Return current through true earth)
The star point of the load is connected to earth to allow the return current to
flow through true earth.
4.2.2.1 Common Mode Voltage vs. Frequency
Common mode voltage (my)
300
250 —
200 —
Calculated (mV)
A Measured (mV)
150 —
100 —
50 —
0
1
2
3
4
Frequency (kHz)
Figure 4.6 Common mode versus Frequency
The' common mode induced voltage on each conductor of the telephone line
was measured between the conductor and true earth. Voltage induced on the
earth electrodes of the telephone line due to conductive coupling influenced the
46
measured common mode voltage. Detailed study was done on this matter
(measurement of earth electrode potential with respect to remote earth). More
details are given under discussion section. Result of this measurement is given
in Table E.2 of Appendix E.
Differential mode voltage (mV)
4.2.2.2 Differential Mode vs. Frequency
—x--Calculated value (mV)
Measured value (mV)
❑
1000
Figure 4.7
3000
2000
Frequency (Hz)
4000
Differential mode versus Frequency
The differential mode induced voltage was measured between the two
conductors of the telephone line (the other end of the telephone line was
earthed). Readings were taken by tuning the frequency (the required value) to
get accurate values especially at lower frequencies. Result of this measurement
is given in Table E.2 of Appendix E. The reason for the small deviation can be
the following:
1. The experimental set-up and the ideal set-up for calculation will have
variations in the physical modelling. This will influence the differential mode
voltage. Moreover the errors at the common mode voltage will also have an
influence on the differential mode voltage.
47
Unbalanced three phase (return current through shield wires) and Single Wire
Earth Return (SWER) conditions were also performed. Results of these
measurements are given in Table E.3 and Table E.4 in Appendix E.
4.3 ELECTROSTATIC COUPLING
For electrostatic coupling experimental work is done only for balanced three
phase condition (V R = Vw = VB = 65 V). Differential mode induced voltage is
measured and *compared with the calculated value. The reason for not
measuring common mode voltage is due to the unavailability of high impedance
measuring equipment.
4.3.1 BALANCED THREE-PHASE CONDITION
VR
Vw -= VB -= 65 V
V
B
100 m
0
Source
132V/ 22A
1.2m
80 m
Wept 600Ohm
Figure 4.8
600 ohm
Circuit Diagram for Balanced Three-phase
(Electrostatic)
4.3.1.1 Differential mode versus Frequency
Result of this measurement is given in Table E.5 of Appendix E.
48
Differential mode voltage (micro volt)
160
140
120
100
—x— Calculated value
(micro volt)
❑ Measured value
(micro volt)
80
60
40
20
3000
2000
1000
4000
Frequency (Hz)
Figure 4.9
Differential mode versus Frequency
The deviation between measured and calculated value can be due to the
resolution of the measuring instrument at these very low values (in the micro
volt range). The physical set-up of the experimental line will also have an
influence on the deviation.
4.4 COMPATIBLE SEPARATIONS
The power line (6.6 kV to 765 kV) separation distance versus exposure to
parallel communication lines are given in NRS 041 of 1995. But these curves
were done by considering only upto 11th harmonics. Very high order, 71st and
73rd, harmonic components are now present on certain 132 kV power lines
supplying a large smelter plant.. So it is necessary to find the compatible
separations between power and telephone lines for this type of situation.
Experimental work on test line revealed that the method described in C.C.I.T.T
Directives and HRJ. Klewe's book could be used for calculating induced
voltage even at high frequencies (4 kHz). To calculate compatible separation
between a 132 kV line and an open wire telephone line the following
informations of both lines are used.
49
132 kV power line
Rating : 800 MVA (three lines)
Line voltage : 132 kV
Phase current : 50 A
Percentage of different harmonic currents (split busbar at hill side)
5th - 13.5%
23rd - 9.6%
7th - 11.4%
25th - 9.8%
11th - 17.3%
29th - 8.9%
13th - 12.0%
31st - 8.3%
17th - 11.1%
71st - 2.9%
19th - 9.9%
73rd - 3.05%
This data is provided by Eskom.
A 275 kV horizontal configuration light suspension tower geometry is used for
calculation purpose.
Separation (m)
For open wire telephone line standard Telkom line geometry is used.
100
90
80
70
60
50
40
30
20
10
0
0
20
40
60
80
100
Exposure (m)
Figure 4.10
Power Line Separation Distance versus Exposure to
Parallel Communication Lines (132 kV, horizontal
configuration, I= 50 A, p = 1000
50
n m)
Chapter 5
DISCUSSION AND CONCLUSION
In this chapter accuracy in modelling and measurement is discussed.
Measurement problems faced due to conductive coupling effect is mentioned.
Recommendation for the revision for Postmaster General's Requirement for
minimum separation distance is also given under conclusion.
51
5.1 DISCUSSION
The main objective of this project was to explore the agreement between
theory and measurement for frequencies from 50 Hz to the higher order
harmonic range of 4 kHz. This make it possible to extend the existing methods
for predicting compatible separations to cases where high order harmonics (up
to the 73rd) are present. During the experimental work more importance was
given to electromagnetic coupling compared to electrostatic coupling. This is
due to the fact that current harmonics are more common and severe than
voltage harmonics. Another fact is if the telephone lines are properly balanced
the effect of electrostatic coupling can be eliminated.
In the case of electromagnetic coupling the two main cases studied are induced
voltage on the telephone line during balanced and unbalanced operating
conditions of the power line from 50 Hz to 4 kHz. From the results it is clear
that for balanced condition the agreement between the predicted and measured
value (common mode induced voltage) is in the limit of <15%. Deviation is
higher at higher frequencies. The reasons for this are:
The three-phase power source used couldn't give properly balanced output
at higher frequencies. Therefore the assumption of balanced current on three
phases is not accurate at higher frequencies (±2%).
At higher frequencies the reactance of the power line and the load increases
and to get 10 A at these higher frequencies the line voltage has to be increased
in step. This also causes an error in keeping phase current at exactly 10 A.
The magnitude of the induced voltage measured was in the range of 0 to 30
mV. The accuracy of the selective voltmeter used to measure the induced
voltage also got an influence on the reading.
The geometry of the test line will also have an effect on measured value.
When we are looking at small separations like this (less than 3m), the height of
the conductors (power and telephone) will also have an effect. The real test line
geometry (experimental set-up) is not that accurate if we compare the values
with the scale model. Line sag (power and telephone conductors) will also have
an effect on induced voltage.
52
For an unbalanced three-phase condition all the above reasons are valid. But
the most important reason for the variation in induced common mode voltage is
conductive coupling. During unbalanced condition the return current was
allowed to flow through true earth. This causes a ground potential rise at the
earth electrodes of the power line. For the test line (the experimental set-up)
the earth electrodes of the telephone line are also very close to the earth
electrodes of the power line and they are in the zone of area of GPR. The
magnitude of induced voltage measured was higher than predicted values.
Potential on the earth electrode of the telephone line was measured and it is
found that this voltage is adding in quadrature to the induced common mode
voltage due to the power line current. To reduce this effect measurement is
done with respect to a remote earth. The problem faced at that point is the
induced voltage on the voltmeter leads. That means accuracy of the
measurement is under question.
In the case of SWER condition lot of time was spent on finding out the reason
for very high induced common mode voltage compared to the predicted value.
This leads to the fact that the induced voltage sitting at the earth electrodes of
the telephone line due to conductive coupling is adding in quadrature to the
real common mode induced voltage due to the current flowing through the
SWER line.
At 500 Hz: the voltage at the earth electrode of the telephone line due to
conductive coupling (measured profile), V3 = 0.905 V
Common mode induced voltage measured, V2 = 1.004 V
Common mode induced voltage calculated, V1 = 0.058 V
From this we can conclude that,
V(Vi2 + V32 ) =
V22
(V)
(5.1)
In the case of capacitive coupling measurement was done only for differential
mode induced voltage. This is due to the unavailability of proper measuring
instrument.
53
Calculation of compatible separation between the power and the
telecommunication line is done for a 132 kV, horizontal configuration with I =
50 A and earth resistivity of 1000 ohm-m. Harmonics up to 73 rd were
considered. Comparison of this criteria with compatible separations specified in
"Code of Practice for Overhead Power Lines for Conditions Prevailing in
South Africa" NRS 041 shows that the exposure length for a specific
separation distance is only 1/280 th. This means for a 100 m separation,
according to NRS 041, the exposure length can be 28 km. But this new criteria
will give only 100 m of exposure length for 100 m of separation. Due to this
very high difference in these two values calculation was done for the same
power line configuration considering only harmonics up to the 11th.
Comparison between this result and NRS 041 showed that for a 100 m
separation instead of 28 km (NRS 041) the new calculated value was 9 km.
The reasons for this can be the following:
The curves for power line separation distance versus exposure to parallel
communication lines were considered the effect of frequencies in the band of
800-1400 Hz other than the power frequency. This makes a big difference.
Instead of considering the effect of each harmonic frequency in that band the
spectrum was considered as a whole and form factor was used. Value of this
form factor was given by Eskom and it is not specified any where.
The conditions used for this curves are also not specified clearly. For
example the magnitude of current in the 132 kV line. This factor has got a big
influence on exposure length.
Moreover all these calculations were done 30 years ago and it is too difficult
to get hold of more details required to verify these curves against the new
criteria.
5.2 CONCLUSION
It is proven that the existing methods for predicting compatible separations
between power and telephone lines are valid even at higher order harmonic
frequencies. The calculation for minimum separation distance versus exposure
length is done for the worst case. Comparing the result with the existing
54
requirement for minimum separation and exposure length it is obvious that it
needs revision to accommodate the effect of higher order harmonic
frequencies.
Detailed study must be done on different types of power line configurations to
make recommendations on the separation criteria. Research work in the field of
modelling of earth is required. It is recommended that new techniques should
be developed to predict electromagnetically induced voltages on the telephone
line when considering conductive coupling effects as well.
55
REFERENCES
"Inductive Interference in South Africa, " The Power and Communication
Systems Co-ordinating Committee, SAME, 1959.
Klewe HRJ, "Interference between Power Systems and Telecommunication
Lines", E Arnold Ltd, London, 1958.
"Postmaster General's Requirements for Electrical Works," Issue 1, August
1978.
"Low Frequency Induction in Telecommunication Lines due to Faults on
Paralleling Power Lines," SAPO Technical Instructions, Protection, Power A
3009, June 1982.
C.C.I.T.T. "Directives concerning the protection of telecommunication lines
against harmful effects from electric power and electrified railway lines, volume
II," International Telecommunication Union, Geneva, 1989.
Reference Guide, "Eskom Quality of Supply Group", 1995.
Arne V Johansson and Ake Ekstrom, "Telephone Interference Criteria for
HVDC Transmission Lines," IEEE Trans. on Power Delivery, Vol. 4, No. 2, pp.
1408-1421, April 1989.
C.C.I.T.T "Directives concerning the protection of telecommunication lines
against harmful effects from electric power and electrified railway lines, volume
VI," International Telecommunication Union, Geneva, 1989.
William H. Hayt, JR "Engineering Electromagnetics," Fifth Edition, Mc GrawHill International 1989.
56
C.C.I.T.T "Directives concerning the protection of telecommunication lines
against harmful effects from electric power and electrified railway lines",
International Telecommunication Union, Geneva, 1963.
Bart Druif, " The Theory and Calculations of Coupling Parameters Between
High Voltage AC Power Systems and Metallic Telephone Circuits," thesis
presented for degree of Master of Engineering Science at the University of
Stellenbosch, September 1994.
M.Kuussaari, " Statistical Evaluation of Telephone Noise Interference Caused
by AC Power Line Harmonic Currents," IEEE Trans. on Power Delivery, Vol.8,
No.2, pp. 524-530, April 1993.
IEEE Working Group on Power System Harmonics, " Power Line Harmonic
Effects on Communication Line Interference," IEEE Trans. on Power
Apparatus and Systems, Vol. PAS- 104, No. 9, pp. 2578-2587 September 1985.
Tagg G.F, "Earth Resistances", George Newnes Ltd, London, 1964.
"Electricity Transmission and Distribution- Code of Practice for Overhead
Power Lines for Conditions Prevailing in South Africa" NRS 041: 1995
57
Appendix A
JD
SOPHOMETRIC WEIGHTS
58
A.1 PSOPHOMETER
The psophometer is an instrument which has been introduced for measuring the
value of the parasitic voltages produced in telephone circuits by nearby
interferance sources eg. power lines. It was developed with a view to make
measurements at the end of long-distance circuits. It has a very high input
impedance, and thus can be used as a voltmeter without disturbing the circuit.
The psophometer consists essentially of an a.c. measuring instrument,
associated with a weighting network. It has got the ability to determine an
average sensitivity curve for various single frequencies for the combination
made up of a telephone receiver and the ear. When the voltage applied to a
psophometer is a combination of frequencies, the reading obtained on the
indicating instrument gives the square root of the sum of the squares of the
readings which would be obtained if each component were considered
separately.
Table A.1 indicates the psophometric weights attributed to by various
frequencies. Only the values corresponding to the underlined frequencies need
be regarded as specifying the weighting network of the psophometer and only
these need be taken into consideration for verification tests of the apparatus.
The other values, obtained by interpolation, are given to facilitate calculations.
59
Weights
Frequenc'y
c/s
16.66..
50
100
150
200
250
300
350
400
450
500
550
600
650
700
750
800
Numerical
values
0.056
0.71
8.91
35.5
89.1
178
295
376
434
The square of
the numerical
values
0.003136
0.5041
79.3881
1 260.25
7 933.81
3! 684
87 025
141 376
234 256
Values
in decibels
Values
in nencra
85.0
- 63.0
-41.0
- 29.0
- 21.0
- 15.0
- 10.6
- 8.5
- 6.3
- 9.79
- 7.25
- 4.72
- 3.34
-2.42
- 1.73
- 1.22
- 0.98
- 0.73
582
661
733 •
794
851
902
955
1 000
338 724
436 921
537 239
630 436
724 201
813 604
912 025
1 000 000
- 4.7
- 3.6
- 2.7
- 2.0
- 1.4
- 0.9
- 0.4
0.0
- 0.54
- 0.41
- 0.31
- 0.23
- 0.16
- 0.10
- 0.046
0.000
850
900
950
1 000
1 050
1 100
1 150
1 200
1 035
1 072
1 109
1 1 77
1 109
1 072
1 035
1 000
1 071 225
1 149 184
1 229 831
1 253 884
1 229 831
1 149 184
1 071 225
1 000 000
0.3
± 0.6
± 09
÷ 1.0
± 0.9
± 0.6
± 0.3
0.0
÷ 0.034
+ 0.069
± 0.103
± 0.115
± 0.103 •
± 0.069
± 0.034
0.000
1 250
1 300
1 350
1 400
1 450
1 500
1 550
1 600
977
955
923
905
831
861
84 7
824
954 529
912 025
861 184
819 025
776 161
741 321
708 964
678 976
--
0.20
0.40
0.65
0.87
1.10
1.30
1.49
1.68
- 0.023
- 0.046
- 0.075
- 0.100
- 0.126
- 0.150
- 0.172
- 0.193
1 650
1 700
1 750
1 800
1 850
1 900
1 950
2 000
807
791
77)
760
745
732
720
708
651 249
625 681
600 625
577 600
555 025
535 824
518 400
501 264
-
1.86
2.04
2.22
2.39
2.56
2.71
2.86
3.00
- 0.214
- 0.234
- 0.255
- 0.275
- 0.295
- 0.311
- 0.329
- 0.345
2 050
2 100
2 150
2 200
2 250
2 300
2 350
2 400
693
689
679
670
661
652
643
634
487 204
474 721
461 041
448 900
436 921
425 104
413 449
401 956
-
3.12
3.24
3.36
3.43
3.60
3.72
3.84
3.96
- 0.359
- 0.373
- 0.386
- 0.400
--0.414
- 0.428
- 0.442
- 0.456
Table A.1
Psophometric Weights for Commercial Telephone Circuits
60
Weights
Frequency
cis
Values
in decibels
•
Values
in nepers
2 450
2 500
2 550
2 600
2 650
2 700
2 750
2 800
625
617
607
598
590
580
571
562
390 625
380 689
368 449
357 604
348 100
336 400
326 041
315 844
- 4.08
- 4.20
- 4.33
- 4.46
- 4.59
- 4.73
- 4.87
- 5.01
- 0.470
- 0.484
- 0.499
-0.513
- 0.528
- 0.544
- 0.560
- 0.576
850
900
950
000
100
200
300
400
553
543
534
525
501
473
444
305 809
294 849
285 156
275 625
251 001
223 729
197 136
169 744
-
- 0.593
- 0.610
- 0.627
- 0.645
- 0.691
- 0.748
- 0.812
-0.886
141 376
112 225
85 26•
63 001
45 796
31 684
20 880.25
13 456
- 8.5
- 9.5
- 10.7
- 12.0
- 13.4
- 15 0
- 16.8
- 18.7
8 519.29
5 241.76
3 158 44
1 909.69
1 149.21
691 69
416.16
252.81
<252.81
- 20 7
- 22.8
- 25.0
- 17 . 2
- 29.4
- 31.6
- 33.8
- 36.0
< - 36.0
2
2
2
3
3
3
3
3
'
The square of
the numerical
values
Numerical
values
3 500
3 600
3 700
3 800
3 900
4 000
4 100
4 200
4 300
4 400
4 500
4 600
4 700
4 800
4 900
5 000 '
> 5 000
Table A.1
412
376
'335
297
251
214
178
• 144.5
116.0
92.3
72.4
56.2
43.7
33.9
26.3
20.4
15.9
< 15.9
'
5.15
5.30
5.45
5.60
6.00
6.50
7.05
7.70
- 0.979
- 1.09
- 1.23
- 1.38
- 1.54
*-- 1.73
- 1.93
- 2.15
- 2.38
- 2.62
- 2.88
- 3.13
- 3.38
- 3.64
- 3.89
- 4.14
< - 4.14
Psophometric Weights for Commercial Telephone Circuits
(contd.)
61
Appendix
CURVES FOR MINIMUM SEFA
N OF
OWER LINE AND COMMUNICATIoN LINE
62
In South Africa the research work in the co-ordination of power and communication
systems was undertaken by the Power and Communication Systems Co-ordinating
Committee, appointed by the SAIEE, in the period 1938-1957. Their conclusions were
reflected in the "Code of Practice for Overhead Power Lines" produced by SAIEE in
1966. In terms of legislation, interference limits are stipulated in Electricity
Transmission and Distribution- Code of Practice for Overhead Power Lines for
Conditions Prevailing in South Africa (NRS 042:1995) [15]. Eskom is bound to this
legislation for the new power routes have to be approved by Telkom before
construction can start.
Under normal circumstances, route approval of a power line will be preceded by the
calculation by Telkom for the anticipated induction levels (fault and steady state) in
any nearby cabled or open wire telephone circuits, and these levels are then compared
to the CCITT limits stipulated. The horizontal separation between the power line and
the telephone line should be in accordance with figures B.1, B.2, B.3 and B.4. This
separation distance shall grant the level of immunity required in the "Postmaster
General Requirements", for communication systems without reference to the powerfrequency carrier operator. These limits require that induced power-frequency voltages
shall not exceed:
50 V r.m.s. in steady state;
430 V r.m.s. on power lines where an earth fault is cleared in more than 0.5 s;
1000 V r.m.s. on power lines where an earth fault is cleared in 0.35 s to 0.5 s; or
1200 V r.m.s. on power lines where an earth fault is cleared in less than 0.35 s.
The curves are based on the recommendations of the CCITT, viz. that the noise
induced in a communication circuit should not exceed 2 mV e.m.f when measured
with a psophometer fitted with the CCITT telephone weighting network. The 2 mV
e.m.f is equivalent to 1 mV potential difference, as measured on the psophometer. For
power line voltages up to and including 33 kV, a TIF (Telephone Influence Factor) of
10 % has been used. For lines of higher voltage, a TIF of 5 % has been adopted, since
it is likely that interfering factors (such as phase balance, wave form etc.) are more
closely controlled on such routes.
63
34
32
30
28
26
24
22
65"
20
18
E
C
.O
CJ
a)
16 cn
14
12
AAK
10
8
6
211pP91111111/-
4
2
Exposure (km)
10
15
20
25
30
35
40
45
Figure B.1 Power Line Separation Distance versus Exposure to Parallel
Communication Lines (up to 33 kV) [15]
64
130
A
4b1
120
id
li
110
100
90
80
70
60
50
40
30
20
10
Exposure (km)
10
15
20
25
30
35
40
45
Figure B.2 Power Line Separation Distance versus Exposure to Parallel
Communication Lines (from 44 kV to 132 kV) [15]
65
1 400
1 300
1 200
1 100
1 000
900
'&7
800 fa..
C)
E
C
700
-2
C3
D.
600 u)
500
400
300
200
100
III I
5
10
Exposure (km)
15
20
25
30
35
40
45
Figure B.3 Power Line Separation Distance versus Exposure to Parallel
Communication Lines (from 275 kV to 400 kV) [15]
66
3 600
3 400
'1c3 ‘41
3 200
3 000
2 900
—sepa rat ion (me tres}—{
2 500
2 400
2 200
2 000
1 800
1 600
1 400
1 200
1 000
800
600
400
200 i
I
Exposure (km)
0
0
5
10
15
20
25
30
35
40
Figure B.4 Power Line Separation Distance versus Exposure to Parallel
Communication Lines (for 765 kV) [15]
• 67
45
50
Appendix C
SOIL C#Nti UCTIVITY
68
C.1 SOIL. CONDUCTIVITY
Soil conductivities can vary from 0.1 to 0.0001 1/S/ m, depending on the type
and age of the formation. For the calculation of electromagnetic induction
effects, measurement methods are required that penetrate into the deep layers
of the soil, such as Wenner (4-electrode) method [14]. If the local composition
of the soil is known, a fair estimate for a may be obtained from Table C.1. In
the absence of measured values or adequate knowledge of the soil composition,
Figure C.2 can be used.
C.1.1 Wenner 4-electrode Method
For a homogerieous soil, conductivity can be measured by conducting Wenner
4 - electrode method. The arrangement of four electrodes in a straight line at
equal intervals is shown in Figure C.1. C1 &
P2
C2
are current electrodes and P1 &
are potential electrodes.
a
a
C1
P1
a
P2
C2
Figure C.1 Wenner 4 - electrode configuration
In homogeneous soil the soil resistivity is given by the formula;
p=27caR
Where a
R
(e
(C.1)
- actual spacing between two adjacent electrodes
- resistance calculated from the potential readings and the value
of current injected into the soil
Result of soil resistivitiy measurement done at the RAU campus by Wenner 4electrode method is given in Table C.1. The soil resistivity at that site is 260
ohm-m. For more details, practical set-up and theoretical background, refer
[14].
69
Separation distanceadjacent electodes, a (m)
1
49.8
Soil resistivity
p = 2iraR (ohm- m)
312.9
2
9.64
121.14
4
5.36
134.71
6
5.16
194.53
8
4.85
243.79
10
4.03
253.21
12
3.49
263.14
14
3.16
277.96
16
2.72
273.44
18
2.22
251.08
Table C.1
Meggar reading, R (0)
Result of soil Resistivity Measurement
70
Condition relating to the climate _ Rainfall readings
normal or high
- i.e. more than 500 millimeters
per year
Nature
of
earth
Probable
value
Possible
variation
low and desert
conditions - i.e.
lower than 250
millimetres per
year
Saline
subterranean
water
Possible
variation
Possible
variation
4
5
1
2
3
Alluvial and light
clay soil
0.2
0.5 to 0.1
according to the
level of water in
area concerned
0.2 to 0.001
according to the
level of water in
area concerned
Clay (without
alluvium)
0.1
0.2 to 0.05
0.1 to 0.01
Marl (e.g. Keuper
marl)
0.05
0.1 to 0.03
Porous calcium
(e.g. chalk)
0.02
0.03 to 0.01
Porous sandstone
(e.g. Keuper
sandstone and
clayey slate)
0.01
0.03 to 0.003
0.02 to 0.003
1 to 0.2
0.3 to 0.1
0.1 to 0.03
Quartz, hard
crystalline
limestone (e.g.
marble,
carboniferous
chalk
0.003
0.01 to 0.001
Clayey slate and
slaty shale
0.001
0.003 to 0.0003
Granite
0.001
Slate, fossils,
schists, gneiss,
igneous rocks
0.0005
5 0.001
0.03 to 0.01
0.001 to 0
.
Table C.2
Earth Conductivities (mhos per meter) for Different Soil
Compositions [10]
71
•
o p t i on
°
•
ilk 44ar.s.ttisr.
0
mr fun 1...“
I II 61.1.A
if It 4.4) A.11' LAIIIIC
•
A ILE A
) (1108tV11
Cut‘'(
PP4 IC 4511.
A
II/ATA
r1d.V1111 A ;.;••
■
1,Its-;••• •I
C
•
1.1 1
.0!it
.•
I WA Lt:: I
:.--- •
•
SI. rims
AA
,....-PI•orkT nit-
air)
LA
lulvil
I • l' 4 4
1)
AREA A : a < 0.0003
mho/m
AREA B : 0.003 < a < 0.0003
mho/m
AREA C : 0.01 < a < 0.003
mho/m
AREA D :
Figure C.2
a > 0.01
mho/m
Soil Conductivities Applicable in south Africa [1]
72
Ap endix D
T WE GEOMETRY
73
,•
n
-
C
ci
•
/
\
•
G•L
TYP E
7. SS
q.
Figure D.1 'Type - 433A' Tower Geometry
74
A
The "433 A" Light Suspension Tower Type is mainly used for 275 kV power lines.
Conductors are arranged in flat horizontal configuration. This "433 A" tower is used
for the Athene- Smelter 132 kV lines as well. The phase conductors of these 132 kV
lines are of 'ZEBRA' ACSR (Aluminium Conductor Steel Reinforced) type.
2.4 m
14
es2
1.35 m
1.57 m
T2
GL
Figure D.2 Transmission and Telephone Line Configuration (experimental
set up)
S1 and
S2
are shield wires
R, W and B are phase conductors
T1 and T2 are telephone conductors
75
Appendix E
CIRCUIT IAGRAMS AND RESULTS
76
E.1 CIRCUIT DIAGRAMS
E.1.1 Electromagnetic Coupling
E.1.1.1Balanced three-phase
IR =Iw =IB = 10 A
- - - - SHUNT
LEM 101
Source
132 V/ 22 A
Figure E.1 Circuit Diagram - Balanced Three-phase
E.1.1.2 Unbalanced three-phase (return current through true earth)
IR = 8.21 A
IB = 7.03 A
Iw =8.35 A
Source
132V/ 22A
V
80 m
600ohm
600 ohm
Vcm
Figure E.2 Circuit Diagram - Unbalanced Three-phase (return current
through true earth)
E.1.1.3Unbalanced Three-phase (return current through shield wire)
:= 8.21 A
Iw =8.35 A
L = 7.03 A
77
shield wire
1k
- - - SHUNT
LEM 101
Source
132 V/ 22 A
1.2m
80 m
1.74 600ohm
h
600 ohm
Figure E.3 Unbalanced Three-phase (return current through shield
wire)
E.1.1.4 Single Wire Earth Return System
I = 0.22 A
Figure E.4 Circuit Diagram - Single Wire Earth Return
E.1.2 Electrostatic Coupling
E.1.2.1Balanced Three-phase
VR Vw VB = 65 V
78
100 m
0
Source
132V/ 22A
1.2m
80 m
WI) 600ohm
600 ohm
Figure E.5 Circuit Diagram - Balanced Three-phase (electrostatic)
E.2 RESULTS
E.2.1 Electromagnetic Coupling
E.2.1.1Balanced Three-phase
IR = Iw =IB = 10 A
79
Common mode voltage
Frequency
(kHz)
Differential mode voltage
0.06
Induced
voltage:
Calculated
(V)
0.028
0.15
0.072
0.07
1.2
0.8
0.25
0.12
0.116
2.6
2.24
0.35
0.168
0.18
3.64
3.2
0.5
0.242
0.26
5.2
3.54
0.65
0.316
0.293
6.76
1.0
0.483
0.454
10.4
8.6
1.5
0.725
0.658
15.6
13.2
2.0
0.966
0.858
20.8
18.4
2.5
1.208
1.04
26.1
24.2
3.0
1.45
1.226
31.3
30
3.5
1.691
1.421
36.5
34
4.0
1.933
1.653
41.7
37.9
Table E.1
Induced
voltage:
Measured (V)
0.0256
Induced
voltage:
Calculated
(mV)
0.624
Result : Balanced Three-phase
E.2.1.2 Unbalanced Three phase (return current through true earth)
-
IR = 8.21 A
Iw =8.35 A
TB =
80
7.03 A
Induced
voltage:
Measured
(mV)
0.72
-
5.4
Common mode voltage
Frequency
(kHz)
0.06
Induced
voltage:
Calculated
(mV)
7
Differential mode voltage
Induced
voltage:
Measured
(mV1
7.25
Induced
voltage:
Calculated
(mV1
0.103
Induced
voltage:
Measured
(mV)
0.3
0.15
16
27.5
0.259
0.4
0.25
25
32.9
0.431
0.62
0.35
33
37.5
0.603
0.7
0.5
45
42.3
0.862
0.76
0.65
56
61
1.12
0.84
1.0
79
81.8
1.72
1.4
1.5
111
121.9
2.59
2.9
2.0
140
161.25
3.45
3.8
2.5
168
207.12
4.31
5.6
3.0
194
218.2
5.2
5.85
3.5
220
307.41
6.03
6.8
4.0
244
360.5
6.9
8
Table E.2
Result : Unbalanced Three-phase (return current through true
earth)
81
E.2.1.3Unbalanced Three-phase (return current through shield wire)
IR = 8.21 A
Iw =8.35 A.
LEI -= 7.03 A
Differential mode voltage
Common mode voltage
Frequency
(kHz)
Induced
voltage:
Calculated
(mV)
Induced
voltage:
Measured
(mV)
Induced
voltage:
Calculated
(mV)
Induced
voltage:
Measured
(mV)
0.05
5
8
0.0175
0.03
1.5
137
143
0.525
0.2
3.0
, 274
1
0.5
Table E.3
275.6
Result : Unbalanced Three-phase (return current through shield
wire)
E.2.1.4Single Wire Earth Return
Common mode induced voltage (V)
Frequency
(kHz)
I = 0.44 A
I = 0.22 A
Calculated
value (V1)
Measured
value (V2)
Calculated
value (V1)
Measured
value (V2)
0.5
0.058
1.004
0.166
2.04
1.0
0.11
1.033
0.217
2.074
Table E.4
Result : Single Wire Earth Return
At 500 Hz:
Voltage sitting at the earth electrode of the telephone line (conductive
coupling) V3 = 0.905V
4(1712 ± v3 2) = V2
82
E.2.2 Electrostatic Coupling
E.2. 2.1 Balanced Three-phase
VR = Vw VB 65 V
Differential mode voltage (micro volt)
Frequency (kHz)
Calculated value
Measured value
0.05
1.824
2.0
0.07
2.553
2.4
0.15
5.4
5.5
0.25
9.12
10
0.5
18
14
1.0
36.5
40
1.5
55
60
3.0
109
100
4.0
146
132
Table E.5
Result : Electrostatic Coupling (balanced three-phase)
83
E.1.3 Earth Potential Distribution
14
Earth potential (V)
12 —
10 —
8—
—
a-- Earth pot:
measured(V)
• Earth pot:
calculated(V)
6—
4—
2—
0
0
5
10
15
20
25
Earth electrode distance (m)
Figure E.6
Earth Potential Distribution (Measured with respect to remote
earth; I= 0.43 A)
E.2.4 Compatible Separations
Experimental work done on the scale model agreed well with the modelling.
Scaling was done for a 132 kV horizontal configuration. Final calculation for
minimum separation for different exposure lengths are done for a 132 kV line.
Information about different harmonic current contents were provided by
Eskom and calculation is done for the worst case. After calculating the
common mode voltage differential mode voltage is calculated for a balance
factor of 200. This information is provided by Telkom.
For the 132kV line ; I= 50 A
84
Frequency (Hz)
Differential mode voltage
(mV)
0.00195
50
Common mode voltage
(my)
0.939
250
4.69
0.0099
350
6.57
0.014
550
10.3
0.022
650
12.21
0.026
850
16
0.034
950
17.83
0.038
1150
21.6
0.046
1250
23.5
0.05
1450
27.2
0.058
1550
29.11
0.062
3550
66.7
0.141
3650
69.5
0.145
Table E.6
Calculated induced voltage for 132 kV horizontal configuration
(separation distance 100m and soil resistivity is 1000 n
Exposure length (m)
Separation distance (m)
26
10
28
25
43
50
69
75
90
100
Table E.7 Exposure Length for Different Separation Distances (132 kV,
Horizontal configuration, p = moon m)
85
Appendix F
CALCULATION METHODS
86
All the calculations were done by using Mathcad PLUS 6.0, Professional
Edition.
F.1
Calculation of electromagnetic coupling (balanced three phase,
no return current)
a - conductivity of the soil
f - frequency
pto - permeability of free space
a :=0.0038•
rad
sec
f
(ohm .m)
a :=411.0.a.2.711
It 0 :=4.71.10_ 7 henry
a =1.225-10 •M 1
g - Euler's constant'
aRT is the horizontal distance between the red phase conductor and the first conductor of the
telephone line
b is the height of the red phase conductor from thr ground level
c is the height of the telephone conductor from the ground level
g:=1.7811
a RT :=
c := 1.3.m
b := 3.6.m
d
1 :=jaRT2+ (13- c ) 2
d 1 =2.785•m
RT =1.923.10
Mu _ Mutual impedance between the red phase and the first conductor of the telephone line
AO
MRT:=—. 2.1n
2
+1-i
4•7t
(g•a•d
2 .42
(1+i )•a•(b+c)
henry
MRT =1.259909.10 6 - 1.565138.10-7 i
a wT := 2.92.m d 2 := Jawr2+(b-c)2
M WT
AO
2 )
+1 i • +
2.11
2
g.a.d 2
4-a
3
11
M BT
0 2171
.
(1+1 ) • a.(b+c)
henry
m
M WT =1.202156.10 6 - 1.565138.10-7 i
a BT := 4.27.m
d 2 =3.717.m
d 3 =4.85.m
d 3 := ja BT2 + (1)- c
2
ga. d 3
)
+1.
2
+
2.12.
MBT =1.148944.10 6 - 1.565138.10-7 i
3
.
•(1 +1 ).a.(b + c
. henry
87
ZRT
-
mutual inductance between the red phase and the first conductor of the telephone line
ZRT
' 2' 1111‘11 RT
ZRT =4.917026.10 5 +3.958121.10i
Z WT := i •2•71•f•M WT Z WT = 4.917026-10 5 +3.776684-10 4 i
ZBT =4.917026.10 5 +3.609515-10-4 1
Z BT I ' 2*ThfI MBT
IR - red phase current
h
om
m
ohm
m
ohm
m
IR := (10 + .0)-ampI w := (- 5 + 8.664 )•amp IB := (- 5 - 8.664 )•amp
a :=- 0.5 i . 5
2
IRO is the zero sequence of the red phase current
iRi is the positive sequence of the red phase current
IR2 is the negative sequence of the red phase current
1
I RO
IR1
:= 1
3
IR2
1
1
1 a a2
1 a2 a
IR
IRO
1w
[0
R1 = 1.467-10 I .amp
IB
IR2
10
i
2 2
IRw is the loop current between the red phase and the white phase
I RW
b
I RW
b-1
:= -. a2.13 a.b- 1
4-3
a•b a2.13-1
I BR
(1 R1
(5 - 2.886667i
I wB = 5.773333i
IWB
R2
I BR
•amp
-5 - 2.886667i
It - tota length of the telephone line
t := 40.m
ZRW is the loop impedance between the red phase and the white phase
ZRW:=ZRT-ZWT
Z wB :=Z wr -ZBT
Z BR :=Z BT
Z RT
Z Rw = 1.814368.10
5. •hm
o
m
5.
ohm
ZwB =1.671698.10
•
m
lun
o
5.
•
Z BR =-3.486•10
m
VTI is the voltage induced on the first conductor of the telephone conductor
88
I RW
V T1 =-5.791.10-7 +0.011i •voliV T1 I = 0.012 .volt
V T1 := (Z Rw Z wB Z BR). I wg • 1 t
I BR
b :=3.6•m
a RT2 := 1.62.m
2
d RT2 := Ja RT22 +
0
2.1n
•
M RT2
c := 1.3.m
c
d RT2 =2.813•m
2
+
.7t +
2
3
2
ga.dRT2
"" n
M RT2 = 1.258.10
a WT2 := 2- 97•m
6
(1+i )•a•(b+c)
.henry
— 1.565.10-7i
m
d•
WT2 = 3 .756•m
d WT2 := Va WT2 2 ÷ (b c ) 2
2
ft 0 [ „, (
7c i.. 2.42 (1
+ - i
M WT2 '=• ‘. -111
3
2
4.7c
g- d WT2
M WT2 = 1.200047-10 6 - 1.565138.10-7 i
( + )1
i ).a. 13
c
.henry
m
:=110
M BT2
4.7c
c)2
d BT2 := BT2 2 +
a BT2 := 4. 32'm
2
.4'1"
)
g.a.dBT2
+1i
2
+ 5 .(1 + i )•ct•(b+c)1
2
3
M BT2 1.147135.10 6 - 1.565138.10-7 1
Z
i•
Z WT2 i
— RT2
d BT2 = 4.894.m
•henry
Z RT2 = 4.917026.10 5 +3.951725.10 4 i
WT2 Z WT2 =4.917026.10-5 +3.770058.10 4 i
Z BT2 = 4.917026.10 5 +3.609515.10 4 i
5
Z
-WT2
Z
Z R2w2 = 1.816669.10 i -° hm
z :=RT2
m
Z BT2 := i .2.71-f*M BT
Z
•
Z W2B2 WT2 - Z BT2
ZW2B2 =1.605438.10-5 i - cam
Z B2R2 :=Z BT2 Z RT2
ZB2R2 =-
89
5 i - thm
ohm
m
•
•
ohm
m
ohm
VT2 IS the voltage induced on the second conductor of the telephone line
I RW
V T2 := (z R2W2 Z W2B2 Z B2R2 )* I WB ' 1 t .
I BR
V T2 = -5.561.10 +0.01i 'volt
IV T21 =0.012.volt
VTd is the differential voltage induced on the telephone line
VTd :=V T1 - VT2
V Td = -2.295.10 4 +1.233.10 4 i
90
-voll V Tdi =2.605555.10 4 'volt
F.2
Calculation of induced voltage due to magnetic coupling
(unbalanced three phase condition,return current through true earth)
G
:= 0.0038•(ohinl
rad
f '= 50-sec
a :=,ig 0.a-2.711
g o :=4•m104 henry
m
g := 1.7811
a= 1.225.10
aRT is the horizontal distance between the red phase conductor and the first conductor of the
telephone line
b is the height of the red phase conductor from thr ground level
c is the height of the telephone conductor from the ground level
a RT := 1.57.m b 3.6•m
c := 1.3-m
d 1 :=,ja RT2 + (13- c )2d 1 =2.785•m
•aRT =1.923.10-3
MRT is the mutual inductance between the red phase connductor and the telephone conductor
wi RT :=
0 „ ( 2 )
+1
4.111
g.a. d
.
•+
2
242. (1+1. )-a-(b+c)
3
.henry
m
MRT =1.259909.10 6 - 1.565138.10-7 i
a WT := 2.92•m d 2 := ja wT2 + (b - c ) 2 d 2 =3.717-m
m wi• := P-O • 2•In ( 2 ) 1_ 1 i • a ÷
2
4•1
g.ad 2
242 (1+i )•ct• (3 ÷ e )
3
. henry
m
M WT =1.202156.10 6 - 1.565138.10-7 i
a BT :=4.27.m
P- 0
M BT
(
2111
d 3 =4.85.m
d 3 := Ja BT2 + 03- c
2
gad 3
)
+1 .
2
+
3
(1 4-1 )••(b+c)
.henry
m
ZR-r is the mutual impedance between the red phase conductor and the telephone conductor
MBT =1.148944.10 6 - 1.565138.10-7i
Z RT
' 2.7141M RT
ZRT =4.917026.10 5 +3.9581.21°10i
91
ohm
Z WT := .2.711M WT
Z WT = 4.917026.10 5 +3.776684-10 4 i
Z BT
ZBT =4.917026.10 5 +3.609515-10 4 i
ohm
m
ohm
•
•
IR Is the red phase current
I R := (8.21 + i •0)•amp I w := (- 4.175 ÷ 7.234 )•amp
IB :=(- 3.515 - 6.0884 )•amp
2
IRO Is the zero sequence of the red phase current
I RI is the positive sequence of the red phase current
IR2 is the negative sequence of the red phase current
1
IRO
IR1
:= 1 1 a
IR
IRO
[0.173 + 0.381i
2
a • 1w
IR1
= 0.174 - 0.381i
B
1R2
1
—
3
1 a2 a
1 R2
b :=
1
amp
7.863 + 1.923.10 i
II Rol =0.418 •amp
43
2 2
IRw is the loop current between the red phase and the white phase
I RW
1
I wB
b
b-1
1
2•b
a•ba
I Rw
(I RI
a2•b-1
'BR
(4.128333 - 2.41i
I wB = -0.22 + 4.439331
R2
'BR
-3.908333 - 2.029333i
l is the total length of the telephone line
1 t :=20•m
ZRW is the loop impedance between the red phase and the white phase
ZWT
Z RW
ZwB:=Z wT-ZBT
Z BR :=Z BT
/ WO :7-- I RO
Z RT
Z Rw = 1.814368.10 5 i • °hm
m
ohm
Z wB =1.671698.10 5 •
m
Z=3.486.10 5 i •thni
B
/ BO :7- I RO
VT1 is the voltage induced on the first conductor of the telephone conductor
I RW
V T1 :=
I RO
Rw Z wE3 Z BR ). IWB 1 t - RT ZWT Z BT )• I WO I t
I BR
'BO
92
) •amp
I V Ti I =6.168.1V •volt
•volt
V Ti =6.101.10 - 9.063.10 4 i
aRT2 is the horizontal distance between the white phase conductor and the second conductor of the
telephone line
b :=3.6•m
a RT2 := 1.62.m
d RT2
c ) 2 d RT2 = 2.813.m
RT22 +
110 •
+ 2.42
+ 1 i
, ,
M RT2
c := 1.3.m
4 .1"
2
g'cc'dRT2
'P•11
)..
ct
3
7
i•+
2
2
[1 0
A •
M BT2 —
4.n
BT22 ÷
)
4.1"
÷I
i•
d WT2 = 3 •756 •m
2 ,12- (1+i )•cqb+c)
3
henry
M wr2 = 1.200047.10 6 - 1.565138.10-7 i
d BT2
)1
m
a WT2 := 2 • 97•m d wn := ja WT22+ (b - c )2
a BT2 :=4.27•m
c
henry
M RT2 =1.258.10 6 - 1.565.10-7 i
I+1
A2
M WT2 := 11
---o ' 2411
4.a
(g' a. - WT)
b
m
d BT2
)2
2
-I-
2-.13
=4 . 85 •m
(1+i )•cv(b+c)
BT2
M BT2 = 1.148944.10 6 - 1.565138.10-7 i
• henry
Z RT2 :=i • 2 •71.1 MRT2
Z RT2 = 4.917026.10-'5 +3.951725.10 4 i
Z WT2 := . 2. 7t. CM WT2
Z wT2 = 4.917026.10 5 +3.770058.10-4 i
Z BT2 :=i • 2 •71•fMBT
V +3.609515.10 4 1
Z BT2 =4.917026-1
Z RW2 Z RT2 Z WT2
ZRW2 = 1.816669.10-5 i .°11m
Z WB2 Z WT2 - Z BT2
Z wB2 = 1.605438-10 5 i. •ohm
Z BR2 Z BT2 Z RT2
Z BR2 = -3.422-10 5 i
m
m
VT2 is the voltage induced on the second conductor of the telephone line
93
• ohm
m
• ohm
m
• ohm
m
I RW
V T2 :z (Z RW2 Z WD2 Z BR2 )•
[ IRO
WB ' 1 t - (Z RT2 Z WT2 Z BT2 )* I WO .1 t
I BR
V T2 =6.177.10 3 - 9.47.10 4 i
-
'BO
IV TII =6.168.10 3 •volt
•vo4V T21 =6.249.10-3 •volt
V-rd is the differential voltage induced on the telephone line
V Td := V T1
V T2
V Td =-7.598.10 5 +4.067-10 5 i
94
• volt
IV Tdi = 8.618173.10 5 •volt
F.3
Calculation of induced voltage due to magnetic coupling (Single
Wire Earth Return, SWER)
:=0.004•(
f :.
1 )
om.m
li
a :=4110.0.2.711
500
sec
IL 0 :=4.71.10 7 henry
a=3.974.10 •m 1
aRT is the horizontal distance between the red phase conductor and the first conductor of the
telephone line
b is the height of the red phase conductor from the ground level
c is the height of the telephone conductor from the ground level
g := 1.7811
c := 1.3.m
a RTi := 1.57.m b := 3.6.m
d 1 =2.785•m
d 1 :=,ja RT12 (1) c )2;
a. a RT1 =6.239.10
MRT1 Mutual impedance between the red phase and the first conductor of the telephone line
2
M RT1
4•n
nn
÷ 1
÷ 243,
i
2
(g•c•:1 1
M RT1 = 1.025791.10 6 - 1.552438.10-7i
ZRT1
+1 •
3
)
.henry
mutual inductance between the red phase and the first conductor of the telephone line
ZRT1 -4.877.10 +3.223.10-3 i
•
Z RT1 :=i .2. n• f:M RT1
IR - red phase current
It - total length of the telephone line
VTR - voltage induced on the first conductor of the telephone line
IR := 0.22•amp
ohm
1 t :=80.m
VT1 = 8.584.10 ÷0.057i •volt IV T1 I =0.057364•volt
V T1 := IRlf Z RT1
aRT2 is the horizontal distance between the red phase conductor and the second conductor of the
telephone line
a RT2 := 1.62.m
b := 3.6.m
c
d RT2 := ja RT22 + (b -
)
2
d- RT2
c := 1.3.m
=2.813.m
).a.(b÷c)
"
) + 1- i .-11 i.-2-±(1+i
11°
A [
• (2-111 (
,21
M RT2 :::3
2
'''n
g a. " RT2
95
M RT2 1.024.10 6 — 1.552.10-7i
Z RT2 :=i 2 nfMRT2
•henry
elm
m
•volt IV T21 =0.057253 •volt
+3.216.10-3i
Z RT2 =4.877.10 4
V T2 :=IRl t Z RT2
V T2 =8.584.10 +0.057i
V Td :=V T1 — V T2
V Td = 1.126.10 4 i welt
96
1 V Td1
1.126.10 4 ••volt
F.4
Calculation of capacitive coupling for three phase balance
condition
Inducing line (power line)
Induced line (tele: line)
aRT1 is the horizontal distance between the red phase conductor and the first conductor of the
telephone line
b is the height of the red phase conductor from thr ground level
c is the height of the telephone conductor from the ground level
b := 3.5.m
a RT1 := 1.57'm
d RT1
RT1 2+ (b - c)2
D RT1 4RT12-1- (b
0 := 8.854.10-12. farad
c)2
d RT1 =2.703•m
D RT1 =5.05•m
1( 0 :-
1
2-m2 0
r1 is radius of the power line conductor
r2 is radius of the telephone line conductor
r 1 := 0.892.10-3 .m
pRR :=k
PT1T1
21)
(r )
2c
r2
c := 1.3.m
r 2 := 0.691.10-3•m
P RR =1.612.1011 . m
farad
PT1T1 =1.48.10 11 • m
farad
97
1( 0 =1.798.10 10
m
farad
P RTI • = k0.1n
D RT1
PRTI =1.124.10
d RT I
10 • m
farad
P TIR :=P RT1
UR
C RTI
P RT I
TIT1
P
1
C T1T1 •–• t,
C RT I – 4.711.10 –
13
•
12
C6.757.10
T1T1 =
T1T1
farad
m
. farad
m
U R := (65 + •0)•volt
U w := (- 32.5+ 56.29•i ).volt
a WTI := 2.92.m
b := 3.5•m
d WTI
D WTI
wr1 2 ÷ (b._ 0 2
2
WTI +" (b÷
p ww 0.111 (2.1
r
•
P TIT1 :=1( 0.111 (—
2r 2c
P
:=k0 In
WTI
dwr
UB := (-32.5 -- 56.29•i )•volt
d wri =3.656•m
D wn =5.618•m
P ww = 1.612.10 11 •
P TITI
1.48.1011
m
farad
m
farad
P WT I =7.724-109 • m
farad
98
P TIW -1° WT1
CWrlP WT1
CWT1 =3.238.1013 farad
P WW P TIT1
C T1T1
C TITI
T1T1
4 . / ci. 1012
1 -11
1.3.m
a BTI :=4 .27 •m
b :=3.5•m
dBT1 : ' ,.sia BT1 2 + ( 1) - c)2
dBT1 =4.803•m
D BTI := Ja BT1 2 ÷ (b + 02
D BTI =6.424•m
2.13
r1
,.. 2.c
P TITI := k 0 .1" (—
r2
P BB =1.612-1011
P BB :="k 0411 (-
D BT1)
PBTI -5.227.109
''BT1
P BT I
1
U RT1 '=
C T1TI = 6.757.1012 farad
m
TI T1
C RTI
c
T1T1
C RTI
UR
IURT11 =4.236 .volt
U RT1 =4.235909.volt
C WT1
U WT1
. farad
farm
CBTI - 2.191.1013 farad
m
I BB' T1T1
C T1T1 •-•
m
• farad
P TIT1 = 1.48.10 11 • m
farad
P BT1 ::'0 .111 A
C
CBT1
m
farad
m
Uw
T1T1 1-C WT1
U WT1 = -1.485952 +2.573669i °volt
C BT1
UBT1' r,
`-' T1T1
IU WT 1 =2.972 -volt
UB
C BT1
UBT1 = -1.020674 - 1.767808i •volt
IU
=2.041 •volt
99
P T1B :=PBT1
UT1 := URT1+ U WT1+ U BT1
IUT11 =1.908 •volt
U Ti = 1.729 +0.806i •volt
aRT2 is the horizontal distance between the white phase conductor and the second conductor of the
telephone line
2
D RT2 Ala RT22÷ (b + c) 2
P WW
D RT2 =5.066.m
:=k0.1n(2.1
P ww =1.612.1011 • m
farad
r1
P T2T2
2•c)
r2
,
P T2T2 =1.48.10 11 • m
farad
„( D RT2)
P RT2 :=1` V" A
uRT2
m
P RT2 =1.11.10 1° • farad
P RT2
C RT2
C T2T2
a WT2
2.732• m
dRT2
RT22 + (b -
dRT2
c := 1.3.m
b := 3.5•m
aRT2 := 1.62.m
C RT2
T2T2
1
= 4.653.10-13 •farad
m
CT2T2 6.757
. 10 12 .farad
m
T2T2
b := 3.5.m
2.97'm
2
d WT2 :-7'ja WT22 + (b
d WT2 = 3.696•m
2
D WT2 := Ja WT22+ (b + c)
D WT2 =5.645•m
2 11
,
P ww :=K 0.m(—
r1
Pww=1.612•10 11 ° m
farad
•
„ 2•c)
P T2T2
P T2R := P RT2
P
r2
WT2
P WT2 :=k0.1nr
d wr2
c := 1.3.m
T2T2 = 1.48'1011 • m
farad
)
PwT2 =7.611'109 • m
farad
100
P T2W
WT2
P WT2
C WT2 ' „
WW-s. T2T2
1
C T2T2 •
C T2T2 = 6.757.10
T2T2
b :=3.5.m
d BT2
d BT2 = 4.848•m
BT22 + (b -c)2
p
k
0'
r1
P T2T2
(D BT2)
P BT2. ••=k 0.111 d
BT2
P BT2 =5.154-10
P BT2
1
farad
9
°
In
farad
farad
m
C T2T2 = 6.757.1012 •farad
P T2T2
U RT2 • 0
M
farad
1.48• 10 11 • in
C BT2 2.16.1013
BB'- T2T2
C T2T2
m
P BB =1.612.10 11 •
111 (21
2•c)
P T2T2 := '0'"±(---r2
C BT2 • 1,
• farad
D BT2 =6.458.1n
BT221- (b C)2
BB
12
c := 1.3•m
a BT2 :=4.32•m
D BT2
. farad
m
C WT2 = 3.19.10-13
C RT2
UR
T2T2 C RT2
U RT2I = 4.187 •volt
U RT2 = 4.187206 wok
C w-r2
U'
WT2 ' -
C T2T2 C WT2 U w
U WT2 =-1.4653 +2.537899i •volt
U BT2 •'-
C BT2
T2T2
I U wa.2 1 = 2.931 •volt
UB
C BT2
U BT2 =-1.006913 - 1.743974i •volt
U BT21 = 2.014 *volt
101
P T2B :=P BT2
U
"-*U RT2 U WT2 + U BT2
U T2 =1.715 +0.794i 'volt
I U T21 =1.89.volt
U Td :=U T1 - U T2
U Td = 0.014 +0.012i •volt
R tel := 1.84. ohm
f := 150.Hz
6
L tel :=1.713.80.10 .henry
X Ltel := 'cu'L tel
C tel := 6.496.80.10- 12. farad
1 t := 80•m
co := 2•71.f
X Ctel .
1 *6).•- • tel
Z T := 600•ohm
Z :=R tel
.
U Td
1
z
X Ltell- X.Ctel÷
T
U Tdl :=Z T
U Tdl = -3.505.106 +4.201.10 6 i
-voltIU Tdi = 5.471 - 10- -volt
102
I U TdI = 0.019 •volt
F.5
Calculation of electromagnetic coupling (balanced three
phase, no return current) for a 132kV line at the smelter plant
a - conductivity of the soil
f - frequency
116- permeability of free space
a :=0.001.( ohml .m)
f := 50. --
a :=410.0.2.n.f
a = 6.283.10 4
ra d
see
p. :=4•a.10 -7 henry
g - Euler's constant
aRT is the horizontal distance between the red phase conductor and the first conductor of the
telephone line
b is the height of the red phase conductor from thr ground level
c is the height of thetelephone conductor from the ground level
aRT :=42.6.m
g := 1.7811
d 1 := Ja RT2 +
b := 19.3.m
c :=6.5•m
d 1 =44.481•m
(13- c
a.a RT =0.027
M RT _ Mutual impedance between the red phase and the first conductor of the telephone line
11 0 In
MRT
ill.
2 )
+1
g•a•d
. n + 2 •(1+1.
3
2
.
M RT =8.401897.10-7 - 1.555513.10-7 i
).a.(b+c)
henry
I M RTI =8.545.10-7 •kg•m•coul-2
m
d 2 =51.612.m
a wr := 50.m
d 2 :=
wT2 + -
11 0
M wT :=2.1n
2 )
7(
2
•(1+1 ).a.(b÷c)
+
3
g.a.d2 +1 . 2
•
M WT =8.104518.10-7 - 1.555513.10-7i
a BT
57.4 • m
11 0
M BT :=
.
.henry
m
d 3 =58.81•m
d 3 :=,.ja BT2 ÷ (b- c
2.4-2 (1+i )•a•(b+c)
,„( 2 )
+11•+
3
2
g•a•d3
L.L"
MBT =7.843423.10-1 - 1.555513.10-7i
, henry
ZRT - mutual inductance between the red phase and the first conductor of the telephone line
103
ZRT :=i •2•11•MRT
.ohm
ZRT =4.886788.10 5 +2.639534.104i
ohm
Z WT :=i • 2.n.f.M WT Z WT =4.886788.10 5 +2.546109.10 4 i
m
.olun
Z BT =4.886788.10 5 +2.464084.104i
ZBT :7- '2.71.11\11BT
IR - red phase current
I R :=(50-1-i .0).ampIw:=(-25-h 43.301.i )•amPB :=(- 25- 43.301•i )•amp
a :=- 0.5 +
2
IRO is the zero sequence of the red phase current
IRi is the positive sequence of the red phase current
IR2 is the negative sequence of the red phase current
1
1. 1
I RO
RI
R2
1
IR
I RO
a a2
Iw
IRI
3 [1 a2 a
IB
1
[0
= 1.56-10
50
I R2
-amp
2 2
IRw is the loop current between the red phase and the white phase
b
2
a •b
I RW
1)-1
I RI
•b-1
25 - 14.433667i
I wB = (28.867333i
(I R2
a2•b-1
amp
-25 - 14.433667i
I BR
It tota length of the telephone line
-
l t :=1•m
ZRW
is the loop impedance between the red phase and the white phase
6•
ohm
Z RW :=Z RT Z WT
Z Rw =9.342442.10
ZWB :=Z WT ZBT
Z wB =8.202547.10 6 i • ohni
m
m
-5. ohm
Z BR —1.754.10 1 •
Vri is the voltage induced on the first conductor of the telephone conductor
I RW
Z BR :=Z BT - Z RT
V T1 (Z RW ZWB Z BR)•
I W13
.I t
4
V TI =-3.552 -10 +6.722.10-
'BR
104
TI[ve1?.603•10
4
•VOlt
a RT2
42.75•m
b := 19.3 .m
c := 6.5 •m
d RT2 := ja RT22+ (1) - c )2 d RT2 = 44.625 .m
) 242+1-1 72 + 3- (1+1 )a. (b+c)
2
M RT2 := 2 • [ (2.1n
g C'u RT2
A"1
•henry
M RT2 = 8.395- 10-7 - 1.556.10-7i
m
wr22
a wT2 := 50.15 • m d wT2
c
d wT2 = 51.758• m
2
2 4-2
(1 +i ). •(b+c)I
+ 1 - i—
7+
M WT2 := --(212.1n (
3
2
4.7
g•c•d WT2
henry
M wT2 = 8.098895. 10-7 - 1.555513 . 10-7 1
m
a BT2 := 57.55'm d BT2 := Ja BT22÷ (b
M BT2 *=
)
2
It 0 { ,
4.1"
1- 1
.
2
g••BT2
)2
242( 1+ i) a•(b+c )
3
M BT2 = 7.83845 . 10-7 - 1.555513.10-71
Z RT2 :=5 .2.11.f"M RT2
•henry
m
Z RT2 = 4.886788. 10 5 +2.637508. 10 4 i
ohm
m
ohm
wT2 Z wT2 = 4.886788 . 10 5 +2.544343 . 10 4 i
Z WT2
m
Z BT2 :=5 .2.711M BT
Z R2W2 := Z RT2
Z W2B2
d BT2 = 58.956'm
Z BT2 = 4.886788. 10 5 +2.464084. 10 4 i
Z WT2
Z WT2 - Z BT2
Z B2R2 := Z BT2
Z RT2
•
ohm
m
Z R2W2 = 9.31649 . 10 6 i -Ohm
Z W2B2 = 8.025878 . 10 6 i
• thni
m
Z B2R2= -1.734. 10-5 i
VT2 is the voltage induced on the second conductor of the telephone line
I Rw
V T2 := R2W2 Z W2B2 Z B2R2 ).
I wB .1 t
' BR
105
4
V T2 —3.475.10 +6.665.10
4•
•volt
IVT21
=7.516384.10 4 •volt
IVT1I =7.602536.10 4 .volt
VTd
is the differential voltage induced on the telephone line
Balance factor is 200
V Td
I V T1 1
200
V Td =3.801°103
106
e.
F.6
Calculation of psophometrically weighted induced differential
mode voltage (fundamental + harmonics) for 132kV line at the
smelter plant
Psophometric weighting factor for 50 Hz (k) = 0.0007079
for 250 Hz (f5)= 0.178
f fun := 7.079.10-4
f 23 := 0.966
f5 :=0.178
f 25 := 0.977
f 7 := 0.376
f 29
:= 0.881
f 11 :=0.733
f 31 := 0.842
f 13 :=0.851
f 71 :=0.355
f 17 := 0.966
1 73 := 0.313
f 1 9 :=0.902
Percentage of different harmonic currents (split busbar at hill side)
Percentage of 5th harmonic: i5 = 13.5%
1 5 :=0.135
i 23 := 0.096
i7 :=0.114
i 25 :=0.098
i 11 :=0.173
i 29 := 0.089
i 13 :=0.12
i 31 :=0.083
i 1 7 :=0.111
i 71 :=0.029
i 19 := 0.099
i 73 := 0.0305
Calculateddifferential mode voltage (mV/m)
For a separation of 100m and earth resistivity
of 1000 ohm m
V fun := 0.00195
V 17 := 0.034
V 31 := 0.062
V 5 := 0.009923
V 1 9 :=0.038
V 71 :=0.141
V 7 := 0.014
V 23 := 0.046
V 73 :=0.145
V 11 :=0.022
V 25 :=0.05
V 13 := 0.026
V 29 := 0.058
107
Psophometrically weighted induced differential mode voltage Vpd
P800' 1
Psophometrically weighted signal at fundamental frequency
U 23 :=V 234' 234 23
U fun := (NT fun.f fun)
U 5 :=V 5 • 5 • 5
U 25 := V 254. 254 25
U 7 := V 7 •f•i 7
U 11 :=V 11 4 11 .i 11
U 13 :=V 13•f 13•i 13
V pd
U 29 :=
291 294 29
U 31 :=
3 14' 3 0 31
U 71 :=V 71170 71
U 1 7 := V 1 7117.1 17
U 19 :=
Ufun
U 73 := V 73.f 73.i73
194' 1 0 1 9
TT
I Al
P 800
,
2
2
2
TT
fun2-r
5 +
V + +U
LI 11 -I+U
V 132 1-U
+U
172 + u 192 ÷u 232 ±u 252 +u 292" 312" 712 +1
V pd = 0.011165
Psophometrically weighted induced voltage is 0.011 mV/m
Limit for interference is 1mV (psophometrically weighted)
Calculation of exposure length (lexp)
l exp v
1 exp = 89.568
pd
For a separation of 100m the exposure length will be 90m
108
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