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1 Electric Pwer Systems Research, 14 (1988) Harmnic Behavir during Arcing Faults n Pwer Distributin Feeders C. J. KIM and B. DON RUSSELL Department f Electrical Engineering, Texas A & M University, Cllege Statin, TX (U.S.A.) (Received January 3, 1988) SUMMARY The wavefrms f nrmal and arcing fault currents n pwer distributin feeders are investigated and cmpared in terms f the percentage amplitude with respect t the amplitude f the nrmal fundamental. The purpse f the study is t find better parameters t indicate arcing faults. The effect f capacitr banks n distributin feeder harmnics is discussed briefly. 1. INTRODUCTION The behavir f arcs has been studied by many scientists and, fr pwer systems, can be summarized as fllws. If tw cnductrs separated by a small gap have a small ptential difference between them, the air acts as an insulatr. As the ptential difference is increased, the resistance f the air gap decreases and current flws between the tw cnductrs. The rapid inizatin accunts fr the sudden ability f the air t cnduct current. Typically, a stable arc can be frmed after several strikes and restrikes ccur within a shrt perid f time. In general, fr the case f arcing in an AC system, stable arcs will frm and be extinguished every half-cycle [ 1 ]. Current harmnics have their rigin in the nnlinear vltage-current characteristics f the arc vltage. This effect results in typical wave shapes and thus in harmnics. The harmnic current characterized by an arc is variable and, althugh dd harmnic frequencies dminate, all harmnic frequencies are prduced at times and even harmnics can persist. Capacitr bank sizes and lcatins are imprtant factrs in determining the harmnics f a distributin system. Capacitr banks smetimes increase harmnic vltages with resnance and decrease sme harmnic vltages at ther times by acting as a shunt attenuatr. 2. BASIC ANALYSIS Here, the wavefrms f nrmal and arcing fault currents are investigated and cmpared in terms f the percentage amplitude with respect t the amplitude f the nrmal fundamental. The purpse f this study is t find better parameters t indicate arcing faults. The effect f capacitr banks n distributin feeder harmnics is discussed briefly. Firstly, Fig. l shws the current wavefrm f a 12 kv feeder system. The scale f the Figure is relative. This shws fundamental,$3,42 W,~2 i,21i ~. II ~,IN ~ -, 1 -,21 I.N 6,N 5,U 4.M! ~.u.~ -I,u -2,11 -I.IN -4.4{ -5,U A ~ A IS f ltarsmi,~ Fig. 1. Nrmal current wavefrm. Peridgram f the nrmal current wavefrm /88/$3.5 Elsevier Sequia/Printed in The Netherlands

2 22 6 Hz current wavefrms. Occasinally, deviatins ccur in the fundamental, but the amunt f deviatin is negligible {namely Hz). Figure l{b) shws the peridgram (i.e., squared amplitude f each frequency) f the nrmal current wavefrm. Here, the TIMESLAB sftware package was used t get the peridgram f each wavefrm [2]. Frm Figs. l and, it can be seen that a nrmal wavefrm has harmnic cntent. As expected, the dd harmnics, even thugh their abslute values are small, are predminant. Even harmnics are marginally present. Secndly, an arcing fault wavefrm is studied. As is explained in the abve sectin, arc current starts t flw at the quarter-pint f a cycle. This results in harmnics, as discussed earlier. Figure 2 shws a typical arcing fault current wavefrm. There are distrtins arund the peaks f every halfcycle+. Pssible phase shift is nt cnsidered here. As can be seen, the wavefrm is nt symmetric but variable and transient. Figure 2 shws a third wavefrm, called the differenced wavefrm, which is btained frm the fault current wavefrm after subtracting the nrmal wavefrm. Theretically, this differenced wavefrm starts at every quarterpint f a cycle and remains fr a quartercycle; it is zer at the ther prtins f the e.~ e,~,~,21.~,,1 O,(M ~ -,il -.21,21,11 O,(N ~[ -,11 -,21 T I.N 62,N 116,N l,~l,e$ 2(E,N 2~, S~ple d I I I J "~.. ~.'. m:. m:. 2.:. m:. Fig. 2. Arcing fault current wavefrm. Differenced wavefrm. 6,N 5,W I 3 ~ 7 9 II 13 Ig f llirvanies Fig. 3. Peridgram f the differenced wavefrm. cycle. This differenced wavefrm exhibits a peak amplitude at every quarter-pint f a cycle as high as that f a nrmal current wavefrm. In ther wrds, the amplitude f the arcing fault current wavefrm is abut twice as high as that f the nrmal current wavefrm. This, hwever, is nt enugh fr an vercurrent relay t detect and islate this type f arcing fault current. Nw, the frequency dmain is investigated. A peridgram is als used t see which harmnics are present and which ne r mre harmnics are predminant. Figure 3 shws the peridgram f a differenced wavefrm n a lgarithmic scale. Here, dd harmnics (3rd, 5th) are still predminant, but sme even harmnics (e.g. 2nd, 4th, 6th, 8th, and 1th) have significant amplitudes; the 8th harmnic is higher than the 7th harmnic, and the 1th harmnic is higher than the 9th harmnic. In additin, up t the 16th harmnic, each harmnic shws its frequency cmpnent, even thugh it is nt as high. Abve the 16th harmnic, all harmnics are present at the same r a similar level. It can be said that higher frequencies exhibit the characteristics f white nise. T use harmnics t discriminate arcing fault current frm nrmal current, several pssibilities exist. Three are used in this paper: (1) the relative amplitude increases f the dd harmnics {e.g. 3rd, 5th) with respect t the nrmal amplitude; (2) the relative amplitude increases f the even harmnics (e.g. 2nd, 4th, 6th, 8th, 1th); (3) cmparisn f the relative amplitude increases f the even harmnics with the relative increases f the dd harmnics. When a capacitr bank is present n a distributin feeder, sme harmnics are increased in sme cases and eliminated in ther cases. Mrever, the resnance is shifted t higher frequencies. All these are quite depen-

3 221 = TL E 8- --~ 4-._." 2- nln nl,nnn,nnn 1 Fig. 4. Frequency cmpnent f each harmnic f the nrmal current wavefrm with a capacitr bank. dent n the size and lcatin f the capacitr bank. A nrmal current wavefrm f a distributin feeder, when a capacitr bank is present, shws n significant change in phase current in the amplitude and wave shape. Figure 4 shws the frequency cmpnent f each harmnic f the nrmal current wavefrm when a 12 kvar capacitr bank is abut 3 miles away n a 12.5 kv feeder n wet sil. Odd harmnics, especially the 5th harmnic, shw big relative increases, and the 8th harmnic shws a significant relative increase. 3. STATISTICAL ANALYSIS A statistical study has been dne n tw different types f sil cnditin at tw different sites. Using recrded data at the tw sites, ver 8 different arcing fault wavefrms were sampled at the rate f 384 Hz, that is, 64 sample pints per cycle, and studied in the frequency dmain. The relative increases f in-between harmnics and the distributin f duratin and ff~luratin f arcing n different sft types has been presented in an earlier paper [3]. Here, three kinds f scenari are investigated: arcing fault withut capacitr banks, the effect f capacitr banks under nrmal cnditins, and arcing fault with capacitr banks. Arcing fault withut capacitr banks In this case, it is easy t see the harmnic distrtin f the nrmal current wave. The cntents f each harmnic at tw different sites are given in Table 1. Frm Table 1, the dd harmnics are predminant, as expected, at bth sites, but site 2 has mre harmnic cntent than site 1. Figure 5 shws the amplitude f each harmnic at site 1 (wet sil), and Fig. 5 shws the relative increase f each harmnic with respect t the fundamental at site 1 (wet sil). In Fig. 5, the dd harmnics are still predminant, but even harmnics can be seen t be present t sme extent. Thus, in Fig. 5, thugh the relative increase f the 6th harmnic is less than that f the 5th harmnic, up t the 16th harmnic the relative increases f the even harmnics are much higher than thse f the dd harmnics. Figures 6 and shw the same graphs as Figs. 5 and at site 2 (dry sil). In Fig. 6, the dd harmnics are still predminant, but the relative increases f the even harmnics are mre marked than befre. Based n the graphs f Figs. 5 and 6, it is TABLE 1 Relative increases f the dd and even harmnics (the unit is the percentage f the fundamental 6 Hz) during an arcing fault withut capacitr banks Odd harmnics Even harmnics Order Site 1 Site 2 Order Site 1 Site

4 a 1 O ~ 8- '~ ,1n "t ") ~ 5 % 1 ~ c),,5,~ x$ ~5.~,,~5 ~% ``1,,~ x~,to rder f harmnlcs 4-2- N n [I n n ~ s i'l ~ 6- ~_,_" e L 4O- 2- \ I ~. I n ~. n n I'l n. n rl n n rder f harmnics Fig. 5. Amplitude f each harmnic f the arcing fault current wavefrm withut capacitr banks at site 1. Relative increase f each harmnic f the arcing fault current withut capacitr banks at site 1. u.c 2- % % % 1 ~ c) ~ ~ ~% ``% ~ ``% x% ~ \~b \% rd,r f hrmn~cs Fig. 6. Amplitude f each harmnic f the arcing fault current wavefrm withut capacitr banks at site 2. Relative increase f each harmnic f the arcing fault current withut capacitr banks at site 2. cncluded that, frm the 7th t the 14th harmnic, cmparisn f the relative increases f the even harmnics with thse f the dd harmnics, r simply the relative increases f the even harmnics, can be a gd candidate t discriminate an arcing fault cnditin frm the nrmal state. If nly ne r tw harmnics are chsen, the relative increase f the 8th and/r the 1th harmnic can be a gd indicatin f arcing fault at bth sites. This is cnfirmed in Fig. 3. A cmparisn f the relative increases f the even and dd harmnics at bth sites is shwn in Table 2. Here, site 2 shws a lwer rati f even t dd than site 1. The pssible reasns are: the sil type is different {wet) and the harmnic cntents f the nrmal wavefrm are much higher than thse f site 1. Therefre, a pssible strategy fr finding better parameters t indicate arcing faults is, frm the 7th t the 14th harmnic, either t cmpare the relative TABLE 2 Cmparisn f the relative increases f the even and dd harmnics during an arcing fault withut a capacitr bank Site 1 Site 2 Odd harmnics (7, 9, 11, 13th) Even harmnics (8, 1, 12, 14th) Even:dd 5.4:1 1.24:1 increases f the even and dd harmnics, r just t use the relative increases f the even harmnics. Capacitr bank n unfaulted feeder Figure 7 shws the cmparisn f frequency cmpnents f the nrmal current wavefrm with and withut a capacitr bank at site 1. Figure 7 shws the crrespnding plt at site 2. Frm the abve tw graphs, it is

5 223 c 2 u 4- = 2- E 12- O E~ nrmal withut cap bank Imm nrmal with cap bank nrmal withut cp bank nrrn1 with cap bank Fig. 7. Cmparisn f the frequency cmpnents f the nrmal current with and withut a capacitr bank at site 1. Cmparisn f the frequency cmpnents f the nrmal current with and withut a capacitr bank at site 2. cncluded that the dd harmnics (especially 3rd, 5th and/r 7th) dminate and the verall shapes f the frequency cmpnents are quite similar t the frequency cmpnent shape f the nrmal current wavefrm. The relative increases f the even and dd harmnics at the tw different sites are shwn in Table 3. At site 2, at higher frequencies the relative increases are higher, but dd harmnics are still predminant. At sites 1 and 2, the shapes f the relative increase f each harmnic are different. The pssible reasns are the different sizes and lcatins f the capacitr banks and the different harmnic cntents f the nrmal current wavefrms. Arcing fault with a capacitr bank Figures 8 and shw, respectively, the amplitude and relative increase f each harmnic at site 1. Figures 9 and shw, respectively, the amplitude and relative increase f each harmnic at site 2. Frm the graphs f Fig. 8, up t the 1th harmnic, all harmnics are increased except the 7th. The percentage f the fundamental shws that the dd harmnics are predminant, but the relative increases f the even harmnics are much higher than thse f the dd harmnics. In Figs. 9 and, the 3rd harmnic shws a big amplitude decrease. The 3rd harmnic generated by the arcing fault is prbably eliminated by the capacitr bank. Up t the 14th harmnic, all harmnics are increased and, up t the 8th harmnic, the even harmnics increase mre than the dd harmnics. Here it is cncluded that when a capacitr bank is present n the feeder, up t the 8th harmnic a cmparisn f the relative increases f the even harmnics with thse f the dd harmnics, r simply the relative increases f the even harmnics, can discriminate the arcing fault cnditin frm the nrmal state. TABLE 3 Relative increases f the even and dd harmnics during an arcing fault with a capacitr bank Odd harmnics Even harmnics Order Site 1 Site 2 Order Site 1 Site

6 ! i 1 O ~" 6- c 3 4- t ~ I n rl nl~ rder f harmnics e 4-2-._~._," fl.lnn.nnnnnn. rder f harmnics Fig. 8. Amplitude f each harmnic f the arcing fault current wavefrm with a capacitr bank at site 1. Relative increase f each harmnic f the arcing fault current with a capacitr bank at site 1. "~ 2- ' N INlnnlnnN Fig. 9. Amplitude f each harmnic f the arcing fault current wavefrm with a capacitr bank at site 2. Relative increase f each harmnic f the arcing fault current with a capacitr bank at site 2. TABLE 4 Cmparisn f the relative increases f the even and dd harmnics during an arcing fault with a capacitr bank Site 1 Site 2 Odd harmnics (7, 9, 11, 13th) Even harmnics (8, 1, 12, 14th) Even :dd 5.21:1 3.79:1 In bth cases (arcing fault withut capacitr bank and arcing fault with capacitr bank), cmparisn f the relative increases f the 8th and 7th harmnics, r just the relative increase f the 8th harmnic, can be a gd indicatin f an arcing fault n the distributin feeder. This cnclusin is cnfirmed by the peridgram f the differenced wavefrm in Fig. 3. The relative increases f the even and dd harmnics up t the 8th harmnic are shwn in Table 4. Therefre, the strategy here is the same as that fr an arcing fault withut a capacitr bank. 4. CONCLUSION A nrmal current wavefrm and an arcing fault wavefrm are studied in bth the time and frequency dmains. When an arcing fault ccurs, the amplitudes f the dd harmnics are predminant but the relative increases f the even harmnics are much higher than thse f the dd harmnics. Here, care shuld be taken that almst all harmnic surces, including slid-state switching devices, generate dd harmnics. Then it wuld be better t use even harmnics than dd harmnics t indicate an arcing fault.

7 225 Faults withut capacitr banks, capacitr banks present withut fault, and faults with a capacitr bank were studied n tw different sites (wet and dry sil types). Withut a capacitr bank, at bth sites, frm the 7th t the 14th harmnic, a cmparisn f the relative amplitude increases f the even and dd harmnics, r the relative increases f the even harmnics, can be a gd indicatin f an arcing fault. When a capacitr bank is present n a distributin system, the dd harmnics predminate and the verall frequency cmpnent shape is very similar t that f the nrmal current wavefrm. With a capacitr bank, frm the fundamental t the 8th harmnic, a cmparisn f the relative amplitude increases f the even harmnics with thse f the dd harmnics, r just the relative increases f the even harmnics, can indicate the presence f an arcing fault. Fr bth arcing fault cases, cmparisn f the relative increase f the 8th harmnic with that f the 7th harmnic, r simply the relative increase f the 8th harmnic, can discriminate an arcing fault frm a nrmal state. The effect f the size and lcatin f the capacitr bank when arcing faults ccur remains t be studied. REFERENCES 1 W. L. Beasley, An investigatin f the radiated signals prduced by small sparks n pwer lines, Ph.D. Dissertatin, Texas A & M Univ., 197, pp H. J. Newtn, TIMESLAB: A Time Series Analysis Labratry, Preliminary Versin f Wadswrth & Brks/Cle, Pacific Grve, CA, B. D. Russell, R. P. Chinchali and C. J. Kim, Behavir f lw frequency spectra during arcing fault and switching events, IEEE PES Summer Meeting, San Francisc, CA, 1987, Paper N. 87 SM ADDITIONAL BIBLIOGRAPHY 1 B. D. Russell, K. Mehta and R. P. Chinchali, An arcing fault detectin technique using lw frequency current cmpnents- perfrmance evaluatin using recrded field data, IEEE PES Summer Meeting, San Francisc, CA, 1987, Paper N. 87 SM B. M. Aucin and B. D. Russell, Detectin f distributin high impedance faults using burst nise signals near 6 Hz, IEEE Trans., PWRD-2 (2) (1987) B. M. Aucin and B. D. Russell, Distributin high impedance fault detectin utilizing high frequency current cmpnents, IEEE Trans., PAS-11 (6) (1982)