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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