DIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS

CHAPTER 4 DIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS 4.1 INTRODUCTION Around the world, environmental and ost onsiousness are foring utilities to install more and more parallel lines to inrease the power transmission apabilities. In the transmission systems, it is very ommon to find parallel transmission towers transmitting power in narrow physial orridors. There are also plaes in the power systems where singleiruit towers run in parallel in wide orridors. These are the examples of parallel transmission lines. While transmitting power by the parallel transmission lines during normal or faulty onditions; the presene of mutual impedanes between the lines modify the voltage and urrent profile measured by the protetive relays proteting eah line. This is one of the most ritial problems of the distane relay used for the protetion of parallel transmission lines. The lose arrangement of the transmission lines leads to a higher fault rate and that influenes the results provided by the protetive relays. In power system design and operation, various types of fault analysis inluding shortiruit alulations are performed in order to obtain the symmetrial and phase omponents of bus voltages and branh urrents in all preditable fault situations. Among all the different types of fault analysis, one of the most troublesome problems is the solution of the faulted network involving two or more faults that an our simultaneously. Ourrene of suh simultaneous faults may be the result of some events, suh as a stroke of lightning or a atastrophi aident. These simultaneous faults may be any ombination of two different types of series and parallel faults ourring on the same phase or different phases, at the same point or at different points in the power system. The series faults are: one open phase and two open phases. The parallel faults are: single line-to-ground fault, double line fault, double lineto-ground fault, triple line fault and triple line-to-ground fault. Formally, beause of the limitations of the methods of analysis and omputational equipment, it was impossible to handle suh ompliated problems. Therefore, the fault analysis studies were limited to the simple (or simplified) ases of the power system faults, suh as a single-phase grounding or single-phase open iruit. Reently, there have been developed numerous power system fault analysis methods based on the appliations of digital 56

omputers and sophistiated mathematial tehniques. However, as soon as the mutual oupling effets are enountered in the zero-sequene network, the omputational proedures beome more omplex. Before few deades, some methods of inorporating the effet of mutual oupling have been developed for short-iruit studies. In this hapter, the disussion starts with determining the mutual impedanes between the parallel transmission lines and investigating the effet of mutual oupling between the parallel lines for a single line-to-ground fault. Afterwards, speifi features of the mutually oupled lines are examined and the same method is extended to analyze a typial type of simultaneous fault, namely an inter-iruit fault ourred on the mutually oupled transmission lines. The essential objet of the analysis is to perform the fault alulations using loal end voltages and urrents to design an appropriate protetion sheme to protet the parallel transmission line network. The ontents of this analysis should be of diret benefits to the engineers to study the behaviour of the protetion system during different types of simultaneous faults. 4.2 SELF AND MUTUAL IMPEDANCES OF TRANSMISSION LINES Figure 4.1 shows the iruit of a fully transposed transmission line situated at a speifi distane above the ground-return path. The ground-return path for I n is suffiiently away for the mutual effet to be ignored. The self and mutual impedanes are alled primitive impedanes. They are ombined to determine the total phase impedanes of the transmission line [59], [118]. Figure 4.1 Mutually oupled transmission line Referring to Figure 4.1, the KL equations an be written as follows: ' j I j I j I (4.1) a a aa a ab b a 57

' j I j I j I (4.2) b b ab a a a bb b b b b ' j I j I j I (4.3) The same equations an be written in matrix form as follows: a a ' b b ' ' j aa ab a ab bb b a b I I I a b (4.4) ' I (4.5) ab ab ab ab Multiplying both sides of equation (4.5) by T 1 yields equation (4.6), 1 1 1 T ab T ab ' T ab I ab where, (4.6) T 1 1 1 1 a 2 a 1 a 2 a Thus, equation (4.6) an be written as follows: 012 012 1 T ab T I 012 ' (4.7) ' I (4.8) 012 012 012 012 00 01 02 012 ab 10 11 12 (4.9) 20 21 22 1 where, T T For a fully transposed line, the self and mutual indutive reatanes are given by, aa ab (4.10) bb b a s (4.11) m Thus, equation (4.9) an be written as follows: 00 01 02 s 2 m 0 0 012 ab 10 11 12 0 s m 0 (4.12) 0 0 20 21 22 s m 1 T T 58

The results of equation (4.12) obtained in the form of reatane an be extended in the form of impedane in equation (4.13) as follows: 00 01 02 s 2m 0 0 012 10 11 12 0 s m 0 (4.13) 0 0 20 21 22 s m 4.3 FORMULA FOR MUTUAL IMPEDANCE When the overhead transmission lines follow parallel paths, the effet of mutual oupling exists between the lines. For the distane protetion sheme, it is possible to ompensate the influene of mutual oupling between the parallel lines with the help of knowledge of the transmission line self and mutual impedanes. Magneti flux linkages between the parallel transmission lines depend on the total urrent flowing in one line and the magneti flux linkage of this line with the other line. Thus, positive- and negative-sequene urrents are indued between the two lines, whose magnitudes are related to the degree of asymmetry between the two lines. Pratially, the indued positive- and negative-sequene urrents are negligible beause of the symmetry between the two lines. During ground faults, the three-phase urrents do not add to zero, but rather a summation of all the urrents is orresponding to the urrent passing through the ground path. Hene, the zero-sequene urrents flowing in one of the lines are signifiantly high. As a result, the zero-sequene flux linking to the other line is also equally high. Analysis of transmission line impedane formulas an provide interesting data to the protetion engineer. To perform the analysis, the paralleled lines are modeled by two parallel single ondutors with an earth return path, for whih the mutual oupling impedane is required to be alulated. It is alulated using equations (4.14)-(4.16), given as follows [157], [186]: 0 ' 4 f j f M 0 l n D D e ab km (4.14) 4 s 0 4 10 km (4.15) De kd f (4.16) 59

where, D e = Depth of penetration in ground f = Frequeny in Hz ρ = Speifi resistane in Ω-m D ab = Spaing in meters between the two ondutors The onstant k D is approximately 2160 or 660 for units of length in feet or meters, respetively. The value of D e depends on ρ, the resistivity of soil. Table 4.1 gives a range of values. When atual earth resistivity data is unavailable, it is not unommon to assume the earth resistivity of 100 µ-m, whih orresponds to the values given in Table 4.1. Table 4.1 D e for various resistanes at 50 and 60 Hz Return Earth Resistivity ρ, Ω-m D e in ft @ 50 Hz D e in ft @ 60 Hz Condition Sea water 0.01 0.1 9.3 93.05 27.9 279 Swampy ground 10 100 294 930.5 882 2790 Average damp earth 100 931 2790 Dry earth 1000 2943 8820 Pure slate 10 7 294300 882000 Sandstone 10 9 2943000 8820000 4.4 ESTIMATION OF MUTUALLY COUPLED OLTAGES FOR PARALLEL TRANSMISSION LINES Figure 4.2 shows a three-phase iruit of mutually oupled parallel transmission lines. The three-phase parallel transmission lines have mutual oupling among all the ondutors in both the iruits. Figure 4.2 Three-phase iruit of mutually oupled parallel lines 60

The urrent I a flowing in transmission line 1 indues voltage in transmission line 2. Hene, the voltage b indued in line 2 is the produt of the urrent flowing in line 1 and the mutual impedane between the lines, and it is given by [157], b Iam 3Ia0 (4.17) m Therefore, the zero-sequene mutual impedane an be defined as follows: 3 (4.18) a0 m0 Ia0 m 4.5 ANALYSIS OF MUTUALLY COUPLED PARALLEL TRANSMISSION LINES Figure 4.3 shows a model of parallel transmission line. A single line-to-ground fault has ourred in phase A of transmission line x. To develop an algorithm for suh ondition, the iruit is required to be analyzed. Figure 4.3 Model of a single line-to-ground fault The voltage ( ) of the faulted phase A of line x is defined as follows [213]: I I I p I I I p (4.19) ss sm bx sm x where, ss = Self impedane of faulted phase sm = Mutual impedane between phases of the same iruit m = Mutual impedane between phases of the other iruit m ay m by m y 61

After simplifying equation (4.19), it an be written as, I I I p I I I p (4.20) ss sm bx x It is known that zero-sequene urrent is I 1/ 3I I I be written as follows: ssi sm 3I I 3pmI m ay by y 0 a b, so equation (4.20) an p (4.21) Referring to Figure 4.3, the relations between the self (s) and mutual (m) impedanes an be obtained from the zero- and positive-sequene data using the well known relations: 0 ss 2 sm, 1 ss sm (4.22) Substituting equation (4.22) in equation (4.21), is rewritten as, ss sm I sm 3I 3pmI p (4.23) sm an be determined by simplifying equation (4.22) and it is given by, sm 0 1 1/ 3 (4.24) Substituting equation (4.24) in equation (4.23), is rewritten as, 1I 0 1I 3pmI p (4.25) Using equation (4.18), is expressed as, 1I 0 1I p m0i p (4.26) Dividing equation (4.26) by p 1 and after manipulating it, p 1 is given by, p 1 I k0i km I (4.27) where, k 0 1 0 and 1 k M m0 1 4.6 INTER-CIRCUIT FAULTS ON PARALLEL TRANSMISSION LINES Figure 4.4 shows a ondition of an inter-iruit fault, involving/not-involving ground, present on an overhead parallel transmission line. Inter-iruit faults on parallel transmission lines usually our as a result of a lightning stroke to an earth-wire or tower, or due to a diret 62

lightning stroke to a phase ondutor. An inter-iruit fault on the parallel transmission line an give rise to operation of the phase and ground relays at loations J, K, L and M. Two types of inter-iruit faults onsidered are: phase a (line JK) to phase b (line LM) (referred to as phase-to-phase inter-iruit fault) and phase a (line JK) to phase b (line LM) to earth (referred to as phase-to-phase-to-earth inter-iruit fault). Figure 4.4 Inter-iruit fault It is demonstrated that in many ases the inter-iruit faults result in unusual urrent distributions between the parallel transmission lines. Therefore, the impedane measured by the digital distane relay is not proportional to the length of the transmission line [8]. Interiruit faults and lose-in earth faults are also known to result in a loss of phase seletivity for single-pole tripping shemes due to the addition of zero-sequene urrents [123]. This an be a serious problem for important iruits where system stability is of main onern. Further, when an inter-iruit fault without ground ours, eah transmission line has zero-sequene urrent, but no zero-sequene voltage at bus terminal. Hene, the traditional fault loation algorithm annot able to determine the orret fault distane and fault loation using just oneterminal data [229]. 4.7 TECHNIQUES USED IN COMMERCIAL RELAYS AND THEIR PROBLEMS In order to enhane the reliability and seurity of bulk power transmission and to share the same right of way, parallel transmission lines are ommonly used in modern high voltage transmission networks. The fault detetion/fault loation for parallel transmission lines thus beomes an important subjet in eletrial power industry. Conventionally, distane protetion is one of the ommonly used tehniques in the protetion of transmission lines. However, while using distane relay to protet parallel transmission lines, a number of problems aused by the presene of mutual oupling effet, ground fault resistane, pre-fault system onditions, shunt apaitane, et. ause performane degradation of the distane relay [5], [6], [130], [138], [150]. 63

Many fault loation algorithms for parallel transmission lines have been developed [19], [82], [83], [103], [109], [115], [162], [189], [191], [217], [222]. These algorithms are based on either one-terminal [82], [103], [115], [162], [191], [217], [222] or two-terminal data [19], [83], [109], [189]. Although one-terminal algorithms are less preise than twoterminal algorithms, they appear more attrative sine they rely only on voltage and urrent measurements at one ommon terminal. Hene, one-terminal algorithms do not require ommuniation links to transmit the data between two terminals of the transmission line. Many researhers have developed different types of one-terminal data algorithms based on lumped parameter line model [103], [115], [162], [191], [217], [222]. These algorithms attempted to estimate the fault urrent ontribution from the other terminal by solving the Kirhhoff s voltage law (KL) equations around parallel lines loops. Sine they are based on lumped parameter line model, these algorithms do not fully onsider the shunt apaitane effet. This may lead to signifiant errors in fault loation estimation, espeially for long transmission lines where the magnitude of the apaitive harging urrent an be omparable to the fault urrent, partiularly under high impedane fault onditions. Moreover, none of these algorithms deals effetively with the inter-iruit faults, whih are more likely to our on parallel transmission lines loated on the same tower. Consequently, a one-terminal algorithm based on distributed parameter line model has been developed, having high fault loating auray and treating satisfatorily most of the asymmetrial fault types that an be enountered in parallel transmission lines [82]. However, it annot be used to loate asymmetrial faults between two lines, for example, a fault involving phases A and B of the two lines at the same instant. Contrary to one-terminal algorithms, there are few two terminal algorithms for parallel transmission lines developed by different researhers [19], [83], [109], [189]. The voltage and urrent measurements from all four measuring ends of a parallel transmission line are onsidered in [19]. Although this algorithm is based on distributed parameter line model and is apable of loating inter-iruit faults, it requires a great amount of data to be transferred from all line ends. There is also one two/multi-terminal algorithm based on lumped parameter line model [189] and two other algorithms based on distributed parameter line model [83], [109]. These last two algorithms utilize only urrent measurements from all four ends of the transmission line, whih adversely affets their auray due to the errors produed by the urrent transformers. 64

4.8 CURRENT STATE-OF-THE-ART Some methods have been proposed for improving the distane protetion performane of parallel transmission lines [5], [6], [150], [222]. These tehniques are very instrutive and ahieve some degree of improvement for the distane protetion of parallel lines. However, most of them possess some errors inherently due to the assumptions during the development proess of those algorithms. For example, Jongepier et al. [6] used artifiial neural networks to estimate the atual power system onditions and to alulate the appropriate tripping impedane. Hene, inauray in the distane protetion aused by the ontinuously hanging power system state is ompensated. However, the fault resistane effet has not been taken into aount in it, thus the auray of fault loation may be influened by the presene of fault resistane in the ground path. In order to inrease the auray of fault distane estimation for distane protetion, a new method that is independent of fault resistane, remote infeed and soure impedane is proposed by Liao et al. [222]. Nevertheless, the shunt apaitane is negleted, whih introdues errors for long transmission lines. Moreover, all studies mentioned above do not onsider the influene of line parameter unertainty, system frequeny flutuation and system noise on the auray of the proposed shemes. To ensure system stability, modern power systems require high speed protetive relaying. An inrease in power transfer of parallel transmission lines thus alls for faster protetive relaying shemes. With regard to this, traveling-wave-based or differential equation-based protetion shemes may be a way to derease the fault learing time and thus inrease reliability [7], [20], [124], [129]. However, in the traveling-wave algorithms, it is very diffiult to deide from the first arriving waves that whether the traveling-waves are generated by a fault or by any other disturbane [129]. IEEE has also made the standard synhrophasors for power systems [216]. Aiming suh a trend, some synhronization measurement tehniques have been proposed for transmission line protetion systems [91], [94], [95], [133]. These tehniques use synhronized data from the two terminals and the performane & auray of protetion systems have been partially improved over those algorithms whih use loal data. Based on the previous work [94], [95], researhers have developed an adaptive phasor measurement unit (PMU)-based tehnique for parallel transmission lines. This tehnique eliminates many of the assoiated problems typially enountered in this area. However, suh tehniques require ommuniation hannels to aquire the remote end data. 65

ery few papers have been published by researhers to analyze the problems of interiruit faults on parallel transmission lines using various fault analysis methods, suh as sequene-domain method and phase-domain method [33], [35], [102], [165], [199]. But none of the papers have presented the omplete solution to measure the orret value of fault impedane during inter-iruit faults between parallel transmission lines onsidering the effet of mutual oupling, remote infeed/outfeed and fault-resistane. 4.9 INTER-CIRCUIT FAULTS ON PARALLEL TRANSMISSION LINES In regions where large bloks of power are being transferred over parallel transmission lines, the ourrene of an inter-iruit fault beause of ondutor geometry, ould initiate serious system instability [48], [137], [138]. A brief introdution of two types of inter-iruit faults, namely, phase-to-phase inter-iruit fault and phase-to-phase-to-ground inter-iruit fault, present on a parallel transmission line is provided as follows: 4.9.1 Phase-to-Phase Inter-Ciruit Fault The shemati diagram of faulted tower with its equivalent three-phase iruit for a phase-to-phase inter-iruit fault is shown in Figure 4.5. For suh type of inter-iruit fault not involving ground, the onventional ground distane relays, loated at A and B, may maloperate unneessarily. Further, they are not in a position to measure the orret value of fault impedane [8]. (a) Shemati diagram of faulted tower, (b) Equivalent three-phase iruit Figure 4.5 Phase-to-phase inter-iruit fault 66

4.9.2 Phase-to-Phase-to-Ground Inter-Ciruit Fault Figure 4.6 shows the shemati diagram of faulted tower with its equivalent threephase iruit for a phase-to-phase-to-ground inter-iruit fault. For suh type of inter-iruit fault involving ground, the onventional phase distane relays, loated at A and B, may maloperate unneessarily and measure fault impedane with high perentage of error [8]. (a) Shemati diagram of faulted tower, (b) Equivalent three-phase iruit Figure 4.6 Phase-to-phase-to-ground inter-iruit fault 4.10 ANALYSIS OF INTER-CIRCUIT FAULTS ON PARALLEL TRANSMISSION LINES For all the analysis, positive- and negative-sequene impedanes ( and L2 ) of the transmission lines are assumed to be equal. Also, in the equations throughout the entire disussion subsripts 1, 2 and 0 represent positive-, negative- and zero-sequene omponents, respetively. It is to be noted that phase-to-phase inter-iruit fault (between A phase of line x and B phase of line y) has ourred between fault loations F and F at p perentage from bus S (Figure 4.5). Further, as shown in Figure 4.6, phase-to-phase-to-ground inter-iruit fault (between A phase of line x and B phase of line y to ground) has ourred between fault loations F and F to ground at p perentage from bus S. 67

4.10.1 Impedane Measured by the Conventional Ground Distane Relay For both types of inter-iruit faults, the value of apparent impedanes ( and by ) measured by the onventional ground distane relays, onsidering the effet of zero-sequene mutual oupling impedane ( LM0 ), is given by equation (4.28) as follows [32], [137], [139]: I k0i km I and by by Iby k0i km I (4.28) where, k L0 0, km LM 0 4.10.2 Impedane Measured by the Proposed Sheme In the proposed sheme, E f and E byf are the voltages produed at the fault points F and F on transmission lines x and y, respetively. I and I by are the fault urrents measured at the relaying points A and B, respetively. Symmetrial omponents of the voltage E f at the fault point F on line x an be expressed as follows: E E p I (4.29) xf 1 x1 x1 E E p I (4.30) xf 2 x2 x2 E E p I p I (4.31) xf 0 L0 LM 0 Adding equations (4.29), (4.30) and (4.31) yield, E f E E E (4.32) xf 1 xf 2 xf 0 Ex 1 Ex2 E p I x1 I x2 p L0I p LM 0I L0 I p LM 0I 0 E p I p (4.33) y Similarly, symmetrial omponents of voltage E byf at the fault point F on line y an be expressed as follows: E byf by L0 I p LM 0I 0 E p I p (4.34) by x It is to be noted with referene to Figures 4.5 and 4.6 that the value of ar resistane is very small during the early stage of an ar and hene, its value does not exeed 0.5 Ω for both 68

types of inter-iruit faults [130]. Moreover, the voltage drop produed by an ar resistane is negleted. Therefore, both the fault points F and F are assumed to be at the same potential, i.e. E f = E byf. Considering this assumption and after algebrai manipulation of equations (4.33) and (4.34), the ompensated value of impedane ( ) of the faulted portion of the transmission line using the proposed sheme is given by, L0 LM 0 I Iby I I E Eby p (4.35) The imaginary part of impedane mentioned on the right side of equation (4.35) indiates ompensated value of reatane ( ) of the faulted portion of the parallel transmission line provided by the proposed method. It is given by, E Eby imaginary (4.36) L0 LM 0 I Iby I I It is well known that the ratio of reatane () to resistane (R) of the transmission line remains onstant. Therefore, the ompensated value of resistane (R ) of faulted portion of parallel transmission line is determined by using the values of ( ) and is given by, R R (4.37) 4.11 RESULTS AND DISCUSSIONS In this setion, two types of inter-iruit faults on 400 k parallel transmission lines have been simulated. The system and line parameters are given in Appendix C. Throughout the entire disussion, by and represent the impedanes measured by the onventional ground distane relay at A, at B and by the proposed sheme, respetively. R, R by and R represent the resistive part of impedanes measured by the onventional ground distane relay at A, at B and by the proposed sheme, respetively., by, represent the reative part of impedanes measured by the onventional ground distane relay at A, at B and by the proposed sheme, respetively. R at and at represent atual values of the resistive part and the reative part of impedane of the faulted portion of the transmission line. %R E and % E indiate perentage error in the resistive part and reative part of the measured value of impedane. δ and R F represent power transfer angle between two buses (S and R) and fault 69

resistane present in the faulted path, respetively. R ar represents the resistane of ar that is present between the faulted phases of the transmission lines. The value of ar resistane is onsidered to be 0.5 Ω for both types of inter-iruit faults [132]. As the ground path is involved in the phase-to-phase-to-ground type of fault, the value of fault resistane plays a key role in the measurement of apparent impedane. Therefore, different values of fault resistane (25, 50 and 200 ) have been onsidered for this fault. 4.11.1 Phase-to-Phase Inter-Ciruit Fault Tables 4.2 and 4.3 show the values of apparent impedanes, by and measured by the onventional relays and the proposed sheme, respetively, at different fault loations (0% to 80% in steps of 10%) having different values of δ (30º and 15º) with R ar = 0.5. Table 4.2 Impedane measured by the onventional sheme and the proposed sheme at δ = 30º p at (at A) by (at B) (by proposed method) (%) R at at R %R E % E R by %R E by % E R %R E % E 0 0 0 4.2 0.31 3.42 0.35 0.002 0.02 10 0.3 3.33 6.73 2143 3.08 7.51 4.9 1733 3.64 9.31 0.302 0.500 3.35 0.601 20 0.6 6.66 9.36 1460 6.62 0.60 6.33 1155 6.85 2.85 0.601 0.200 6.68 0.300 30 0.9 9.99 12.09 1243 10.29 3.00 7.71 957 9.97 0.20 0.901 0.100 10.01 0.200 40 1.2 13.32 14.94 1145 14.17 6.38 9.08 857 13 2.40 1.203 0.275 13.37 0.375 50 1.5 16.65 17.95 1097 18.23 9.49 10.41 794 15.94 4.26 1.505 0.320 16.72 0.420 60 1.8 19.98 21.15 1075 22.54 12.81 11.74 752 18.8 5.91 1.808 0.450 20.09 0.551 70 2.1 23.31 24.63 1073 27.16 16.52 13.06 722 21.55 7.55 2.112 0.586 23.47 0.686 80 2.4 26.64 28.54 1089 32.23 20.98 14.5 704 24.18 9.23 2.420 0.838 26.89 0.938 Average % error 1291 7.63 959 2.17 0.409 0.509 Table 4.3 Impedane measured by the onventional sheme and the proposed sheme at δ = 15º p at (at A) by (at B) (by proposed method) (%) R at at R %R E % E R by %R E by % E R %R E % E 0 0 0 3.98 0.62 3.55 0.64 0 0 10 0.3 3.33 6.25 1983 2.34 29.73 5.22 1840 4.32 29.73 0.298 0.700 3.31 0.601 20 0.6 6.66 8.49 1315 5.26 21.02 6.91 1252 8.08 21.32 0.597 0.550 6.63 0.450 30 0.9 9.99 10.72 1091 8.11 18.82 8.63 1059 11.9 19.12 0.895 0.600 9.94 0.501 40 1.2 13.32 12.94 978 10.92 18.02 10.44 970 15.82 18.77 1.193 0.550 13.26 0.450 50 1.5 16.65 15.18 912 13.67 17.90 12.29 919 19.83 19.10 1.492 0.520 16.58 0.420 60 1.8 19.98 17.44 869 16.34 18.22 14.22 890 23.96 19.92 1.790 0.550 19.89 0.450 70 2.1 23.31 19.78 842 18.92 18.83 16.29 876 28.24 21.15 2.089 0.529 23.21 0.429 80 2.4 26.64 22.28 828 21.35 19.86 18.55 873 32.76 22.97 2.386 0.588 26.51 0.488 Average % error 1102 20.30 1085 21.51 0.573 0.474 70

It is to be noted that the average perentage error in the measurement of resistive part of the impedanes (R and R by ) by the onventional ground distane relays at A and B is 1196.5% and 1022%, respetively. This learly indiates that the onventional ground distane relays measure the resistive part of impedanes (R and R by ) with a very high perentage of error. Moreover, it has also been observed from Table 4.3 that the onventional ground distane relays measure the reative part of the impedanes ( and by ) with perentage error in the range of 30%. On the other hand, the average perentage error in the measurement of resistane (R ) and reatane ( ) of faulted portion of parallel transmission line by the proposed method is within 0.573%, whih learly indiates the effetiveness of the proposed sheme in terms of auray. Figure 4.7 represents the simulation results of apparent impedanes, by and measured by the onventional ground distane relays and the proposed sheme, respetively, for phase-to-phase inter-iruit fault with wide variations in system and fault parameters. Figure 4.7 Impedane measured by the onventional sheme and the proposed sheme at different values of δ (phase-to-phase inter-iruit fault) It is to be noted from Figure 4.7 that the onventional distane relay loated at A is able to sense only those phase-to-phase inter-iruit faults whih our approximately up to 30% of the omplete line setion from the relaying point. While, the onventional distane relay loated at B fails to sense suh inter-iruit faults as the operating point lies in the seond quadrant of R- plane (out of the zone of protetion for quadrilateral harateristi of 71

the onventional ground distane relay). On the other hand, the proposed digital distane relaying sheme measures the orret values of resistane and reatane of the faulted portion of the transmission line for all ases. 4.11.2 Phase-to-Phase-to-Ground Inter-Ciruit Fault Tables 4.4 and 4.5 show the values of apparent impedanes, by and measured by the onventional ground distane relays and the proposed sheme for different values of δ (30º and 15º) with R ar = 0.5 and R F = 50. Table 4.4 Impedane measured by onventional and proposed sheme at δ = 30º with R F = 50 Ω p at (at A) by (at B) (by proposed method) (%) R at at R %R E % E R by %R E by % E R %R E % E 0 0 0 3.76 0.47 3.69 0.72 0.002 0.02 10 0.3 3.33 5.77 1823 2.52 24.32 5.35 1883 4.7 41.14 0.302 0.500 3.35 0.601 20 0.6 6.66 7.75 1192 5.52 17.12 6.93 1255 8.74 31.23 0.601 0.200 6.68 0.300 30 0.9 9.99 9.79 988 8.57 14.21 8.44 1038 12.7 27.13 0.901 0.100 10.01 0.200 40 1.2 13.32 11.96 897 11.75 11.79 9.96 930 16.49 23.80 1.203 0.275 13.37 0.375 50 1.5 16.65 14.38 859 15.08 9.43 11.49 866 19.98 20.00 1.505 0.320 16.72 0.420 60 1.8 19.98 17.15 853 18.65 6.66 13.05 825 23.1 15.62 1.808 0.450 20.09 0.551 70 2.1 23.31 20.46 874 22.61 3.00 14.63 797 25.74 10.42 2.112 0.586 23.47 0.686 80 2.4 26.64 24.6 925 27.22 2.18 16.18 774 27.84 4.50 2.420 0.838 26.89 0.938 Average % error 1051 10.54 1046 21.73 0.409 0.509 Table 4.5 Impedane measured by onventional and proposed sheme at δ = 15º with R F = 50 Ω p at (at A) by (at B) (by proposed method) (%) R at at R %R E % E R by %R E by % E R %R E % E 0 0 0 3.57 0.72 3.81 1.09 0 0 10 0.3 3.33 5.36 1687 1.98 40.54 5.55 1950 5.64 69.37 0.298 0.700 3.31 0.601 20 0.6 6.66 7.03 1072 4.61 30.78 7.17 1295 10.52 57.96 0.597 0.550 6.63 0.450 30 0.9 9.99 8.66 862 7.18 28.13 8.64 1060 15.6 56.16 0.895 0.600 9.94 0.501 40 1.2 13.32 10.31 759 9.75 26.80 10.12 943 20.73 55.63 1.193 0.550 13.26 0.450 50 1.5 16.65 12.06 704 12.3 26.13 11.67 878 25.81 55.02 1.492 0.520 16.58 0.420 60 1.8 19.98 13.99 677 14.82 25.83 13.42 846 30.71 53.70 1.790 0.550 19.89 0.450 70 2.1 23.31 16.2 671 17.33 25.65 15.50 838 35.33 51.57 2.088 0.571 23.2 0.472 80 2.4 26.64 18.87 686 19.81 25.64 18.02 851 39.57 48.54 2.386 0.588 26.51 0.488 Average % error 890 28.69 1083 55.99 0.579 0.479 It is to be noted from Tables 4.4 and 4.5 that the average perentage errors in the measurement of resistane and reatane of the faulted portion of the transmission line 72

(R and ) by the onventional ground distane relay at loated A are 970.5% and 19.62%, respetively. Whereas, the onventional ground distane relay loated at B measures resistive part and reative part of the impedane (R by and by ) with an average perentage error of 1064.5% and 38.86%, respetively. On the other hand, the average perentage error in the measurement of resistane (R ) and reatane ( ) of the faulted portion of the transmission line using the proposed sheme is within 0.579%. Figure 4.8 represents the simulation results of apparent impedanes, by and measured by the onventional ground distane relays and the proposed sheme for phase-tophase-to-ground inter-iruit faults at different fault loations (0% to 80% in steps of 10%) having δ = 15º with R ar = 0.5 and varying fault-resistanes (25, 50 and 200 Ω). Figure 4.8 Impedane measured by the onventional sheme and the proposed sheme at different values of fault-resistane with δ = 15º (phase-to-phase-to-ground inter-iruit fault) It is lear from Figure 4.8 that the onventional ground distane relay loated at A is able to sense only those inter-iruit faults whih our approximately from 35% to 60% of the omplete line setion for different values of fault resistane. Whereas, the onventional distane relay loated at B ompletely fails to detet phase-to-phase-to-ground inter-iruit faults that our at any point on the line setion. On the other hand, the proposed digital distane relaying sheme is immune to the said problems and measures orret value of impedane of the faulted portion of the transmission line even against wide variations in system and fault parameters. 73

4.12 ADANTAGES OF THE PROPOSED SCHEME 1) In the proposed digital distane relaying sheme, there is no need to extend the boundary of the quadrilateral harateristi of digital distane relay against wide variations in the values of fault resistane. 2) The reah of the proposed sheme is not affeted by the zero-sequene mutual oupling impedane present between the parallel transmission lines. 3) The proposed sheme is not influened by the loading effets of the transmission lines, as it measures the orret value of impedane of the faulted portion of the transmission line even during presene of large disturbanes in power transfer angles (δ) between two buses. 4) The proposed tehnique is highly aurate and robust against large disturbane in system onditions and fault parameters, as it does its duty of fault impedane measurement with an average perentage error of 0.579%. 5) As the derivation of final equation of ompensated fault impedane is very simple, the omputational requirements are very less. 4.13 CONCLUSION In this hapter, a new digital distane relaying sheme has been proposed for parallel transmission lines, whih effetively ompensates the error present in the measurement of apparent impedane by the onventional ground distane relay during inter-iruit faults. The proposed sheme is based on digital omputation of the ompensated value of impedane using symmetrial omponents of voltages and urrents. The proposed sheme does not require data from remote end and hene, it is very simple ompared to the other tehniques whih require remote end data in order to hange relay harateristi in ase of variation in external system onditions. The proposed digital distane relaying sheme has been simulated using MATLAB/SIMULINK software. The proposed sheme is highly aurate as it measures orret values of resistane and reatane of the faulted portion of the transmission line having perentage error within 0.579%. Moreover, it remains stable during inter-iruit faults against wide variations in system and fault onditions. 74