TRANSIENT VOLTAGES COUPLING TO SHIELDED CABLES CONNECTED TO LARGE SUBSTATION EARTHING SYSTEMS DUE TO LIGHTNING L. GRCEV * UNIVERSITY OF SKOPJE

Transcription

1 CIGRÉ 996 : 36-2 O TRANSIENT OLTAGES COUPLING TO SHIELDED CABLES CONNECTED TO LARGE SUBSTATION EARTHING SYSTEMS DUE TO LIGHTNING by L. GRCE * UNIERSITY OF SKOPJE (Macedona) Suary: Paper presents a coputer analyss of transent voltages coupled to bured shelded control cables n hghvoltage substatons subjected to lghtnng. It s based on recent advances n antenna theory approach appled to large substaton earthng systes. oltages and currents n shelds are coputed by the rgorous antenna theory approach and then voltages coupled to the control crcuts are obtaned by usual crcut theory approach. Influence of paraeters, such as: lghtnng waveshape, sol conductvty, locaton of feed pont, cable routng, earthng syste sze, and conductor separaton, s nvestgated. Paraeters wth donant nfluence are dentfed and possbltes for reducton of nduced voltages are dscussed. Relaton between ground potental dfference and feld couplng coponents of the nduced voltages s also nvestgated. Keywords: Substaton Earthng Control Cable Sheldng Groundng Lghtnng Interference Transent Sulaton. INTRODUCTION The proble of protecton of the electronc systes n H substatons aganst electroagnetc nterference, n cases of power syste abnoral operaton or lghtnng, has been dealt wth by any researchers, for exaple, [] [6]. Ths paper concentrates on transent voltages coupled to shelded cables n case of lghtnng. Ths proble can be dvded n two parts: evaluaton of the transent voltages and currents n the earthng syste conductors, and evaluaton of the transent voltages coupled to shelded cables. The proble of couplng to shelded cables s well understood [7]. If the current or voltage n the sheld s known, than nduced voltages n the cable ay be deterned usng the concept of transfer pedance or reducton factors, respectvely [4], [8]. However, knowledge of the dstrbuton of transent currents and voltages n large earthng systes subjected to lghtnng stroke s consderably less coplete. Coplex earthng arrangeents are analyzed recently n [9] [3]. Whle, work n [9] s based on eprcal approach, other approaches are analytcal, based on: crcut theory [], transsson lne theory [], and antenna theory [2], [3]. The crcut and transsson lne odels are based on quas-statc approxaton and ther valdty s lted to lower frequences [4]. The antenna odels are based on an exact forulaton derved fro the coplete set of Maxwell s equatons and enable ore accurate analyss. Ther an advantage s n analyss of electroagnetc nteractons n structures of coplex geoetry. The frst purpose of the study n ths paper s evaluaton of currents and voltages along the sheld by applcaton of the rgorous antenna theory approach [3]. oltages coupled to the control cables ay be subsequently coputed by usual splfed crcut odelng [8]. Another purpose was to nvestgate the nfluence of dfferent paraeters to enable better understandng of the EMC probles n large substatons. 2. ANALYTICAL MODEL AND ITS ALIDATION The physcal stuaton s llustrated n Fg.. The earthng syste s consdered to be an arbtrary network of connected or dsconnected bured conductors. Arbtrary routed shelds are consdered grounded at both ends. The analytcal odel s based on the antenna theory approach and s descrbed n the recent publcaton [3]. The odel * Elektrotehnck fakultet, Karpos II bb, P. O. Box 574, 9 Skopje, Republc of Macedona

2 Ar Sol Current Source oltage () 8 u (x = ) 6 Current (A) 4 (x = ) 3 Cable Sheld 4 u (x = 3.5) 2 Earthng Syste Fg.. Physcal stuaton: lghtnng strkes above-ground structure connected to the earthng syste and double-end grounded cable sheld. s valdated by coparson wth feld easureents by EDF (Fg. 2) and wth other authors odels [3]. 2. Current dstrbuton n the network of bured conductors The transent proble s solved frst n the frequency doan. To evaluate voltages, t s necessary to deterne the current dstrbuton n the earthng conductors. The frst step n the analyss s to dvde the whole structure nto saller segents, accordng to the well known ethod of oents [7]. Segents ay be nsulated or bare cylndrcal conductors, etallc tubes or tubular shelds wth arbtrary orentaton. The ost portant part s odelng of the utual electroagnetc nteractons between the segents. Ths leads to a atrx equaton [3]: [ Z] [ I] = [ Z I s ] () where the eleents of the colun atrx [I] are unknown currents n segents. Eleents of [Z] express the utual electroagnetc nteractons between segents. Eleents of [ Z I s ] defne the energzaton of the structure by the njecton of currents I s at arbtrary ponts. Reader s referred to [3] for full detals on the odel and ts valdaton. The neglect of the non-lnearty of the sol due to onzaton s an nherent part of the frequency doan approach. For large enough currents, the earthng conductor surface electrc felds ay becoe greater than the onzaton threshold of approxately 3 k/ [8], and onzaton of the sol ay occur. Ths phenoenon s neglected n all exstng ethods for transent analyss of large earthng systes, but further research s requred to analyze ts effects on nduced voltages [9]. 2.2 Modelng of nterconnected earthng conductors and tubular shelds Antenna theory approach ay be drectly appled to sngle non-ferroagnetc tubular shelds wth or wthout delectrc coatng. Detals on the odelng of tubular shelds ay be found n [5]. The odel was valdated by coparson wth other authors odels n [6]. One ltaton s that the cables have to be thn,.e. ther outer daeters have to be about ten tes saller u (x = 7) 2 Measured Coputed Fg. 2. Coparson wth easureents by EDF. Measured and coputed transent GPR at three ponts along horzontal copper wre (5 length,.2 c radus,.6 depth, 7 Ω. sol s resstvty, 5 sol s relatve perttvty). than the length of sallest segent. Also lengths of the segents ust be about ten tes saller than the sallest edu wave length. 2.3 Coputaton of the transent response If transent voltage v(t) s requred, then correspondng transfer functon Z(jω) n frequency doan s frst obtaned: Z(jω) = (jω)/a (2) Here (jω) s voltage as a response to a te-haronc steady-state A current exctaton n a frequency range of nterest for the transent study. If Z(jω) s known, than v(t), as response to arbtrary exctaton (t), ay be straghtforwardly obtaned: ν(t)=f - {Z(jω) F[(t)]} (3) where F and F are Fourer and nverse Fourer transfors, respectvely. 3. DESCRIPTION OF THE CASES ADOPTED FOR ANALYSIS Fg. 3 llustrates the earthng grd adopted for analyss. Two types of hoogeneous sol are consdered: wth resstvty ρ = Ω. and relatve perttvty ε r = 9, correspondng to dry sol, and wth ρ = Ω. and ε r = 36, correspondng to wet sol []. Concernng the locaton of the feed pont, two scenaros are consdered: njecton n the corner pont, and, alternatvely, n the center pont of the grd. Two alternatve cable routngs are consdered between ponts and 3. Cables are bured at.3 depth and the sheld s bonded to the ground grd at both ends. The lghtnng current waveshapes adopted for coputatons are llustrated n Fg CURRENT DISTRIBUTION ALONG TUBULAR SHIELD As an exaple, longtudnal currents at three ponts along the sheld (, 2 and 3, Fg. 3), as response to T =.25/µs lghtnng current pulse wth axu I,

3 Alternate Lghtnng Current Feed Ponts.2.25/ sµ.3 2 Alternate Cable Routes Between and Fg x 6 2 earthng grd wth 6 x 6 square eshes at.8 depth, constructed or copper conductor wth.4 c daeter. Cable sheld s double-end grounded at ponts and 3, and s bured at.3 depth. Two alternatve cable routes (-2-3 and -3) and two alternatve lghtnng current feed ponts (at the corner and at the center of the grd) are shown Fg. 5. Lghtnng current njected at the corner of the 6 x 6 2 grd n sol wth ρ = Ω. and ε r = 9, and longtudnal currents at three ponts (, 2 and 3) along bare etallc tubular sheld (Fg. 3). Currents are noralzed for I (the axu of the lghtnng current pulse)..2.25/ µ s /35 µ s R O R I U DM.8.6 I S UCM Fg. 4. Two lghtnng current waveshapes defned n IEC Standard [2] adopted for analyss. (Frst stroke: T = /35 µs; subsequent stroke: T =.25/ µs). are shown n Fg. 5. The sheld s a bare copper tube wth daeter 3 c and wall. Approxately 25% of the partal lghtnng current n the earthng conductor at pont s captured by the sheld. The behavor of the current s dfferent along the sheld, and f crcut odelng s appled, the sheld should be segented to saller segents. 5. COMMON AND DIFFERENTIAL MODE OLTAGES E S Fg. 6. One exaple of crcut representaton of sngle double-end grounded sheld [8]. R O and R I output and nput resstances, I S longtudnal current n the sheld, E S voltage between sheld s end ponts, U CM coon ode voltage, U DM dfferental ode voltage. Fg. 6 llustrates one exaple of crcut odelng of double-end grounded sheld [8]. When the current n the sheld I S s known then the coon ode voltage coupled to the shelded cables U CM ay be coputed usng known transfer pedance Z T [4], [7], [8]: U CM = ZT I (4) S Drect applcaton of the antenna theory approach s lted to sple tubular non-ferroagnetc shelds. Snce n practce cables ay be screened by ultple shelds, conduts, trays or wres wth dfferent fors, t s advantageous to cobne the antenna theory approach wth the usual crcut odelng. For exaple, f the voltage along sheld s known than coon and dfferental ode voltages ay be deterned by known reducton factors [8]. Therefore the nfluence of dfferent paraeters on the voltages nduced n the shelded cables ay be studed by studyng the voltage along the sheld. 6. OLTAGE BETWEEN SHIELD S END POINTS Total voltage between the sheld s end ponts and 3 along the sheld (Fg. 3) ay be expressed as su of two ters [2]: = + T ( Φ Φ ) A d t = + (5) 3 where = Φ Φ 3 s dfference between ground potental rse (GPR) at ponts and 3, and s feld couplng ter due to te-varyng currents n earthng syste conductors. The frst ter s unquely defned, but the second ter s path dependent. In ths analyss, feld couplng due to above ground sources s neglected.

4 v/i (k/ka) 4 v/i (k/ka) Fg. 7. oltage along the sheld (cable route: -2-3). total voltage along sheld; scalar potental dfference; feld coupled coponent; lghtnng current njected at the corner of the grd. It can be seen fro Fg. 7 that and are opposte, and the total voltage s saller than these two ters. has donant nfluence on the total voltage, but s consderably saller than due to the effect of. Fg. 8 llustrates the nfluence of the cable routng on the total voltage. Snce n route -3, the cable s not lad near earthng conductors, such as n case of -2-3 routng, s saller and total voltage s nearer to the. In case when the lghtnng current s fed at the center of the grd all voltages are consderably saller, as n Fg. 9. Fg. llustrates voltages under sae condtons as n Fg. 7, but for ore conductve sol wth ρ = Ω. and ε r = 36. Ths exaple llustrates that better conductvty of the sol has very large nfluence on the reducng of the voltages n the cable sheld. Fg. llustrates the nfluence of the lghtnng current pulse shape. The condtons are sae as n Fg. 7, but the lghtnng current pulse has uch saller steepness (T = /35 µs, Fg. 3). As t s well known, large nduced voltages are phenoena related to fast varyng currents, and slower varyng currents nduce saller voltages. 7. TRANSIENT GROUND POTENTIAL RISE The GPR dfference between the sheld s end ponts has donant nfluence on the total voltage along the sheld. Fg. 2 shows the nfluence of the earthng grd sze on the axal transent GPR at the feed pont. The grd sze has large nfluence on GPR after the transent perod, that lasts for about one to few µs, but has sall nfluence durng the transent perod. Results ndcate that, for the analyzed cases, the effectve area of the grd at the te when the axu GPR occurs, s very sall and ay be approxated as not uch greater than about x 2. Fg. 3 shows that saller conductor separaton can be used to reduce the transent GPR only f eshes are Fg. 8. Influence of the cable routng on voltage along the sheld (cable route -3). (Sybols are sae as n Fg. 7.) v/i (k/ka) /I 4 3 v/i (k/ka) Fg. 9. Influence of lghtnng current feed-pont locaton on voltage along the sheld (cable route -2-3): lghtng current s njected n the center of the grd. (Sybols are sae as n Fg. 7.) Fg.. Influence of sol conductvty on voltage along the sheld (cable route -2-3): ρ = Ω., ε r = 36. (Sybols are sae as n Fg. 7.).5.5

5 v/i (k/ka) GS GS2 GS GS6 6 2 GS v/i (k/ka) (a) GS GS2 Fg.. Influence of lghtnng current pulse shape on voltage along the sheld (cable route -2-3): T = /35 µs. (Sybols are sae as n Fg. 7.) saller that the effectve area of the grd. It can be seen n Fg. 3, that aong the analyzed cases, only grd wth 3 square eshes, n saller area near the feed pont, substantally reduces the axal GPR. Fg. 4 llustrates the possblty to reduce the nduced voltage by decrease of the conductor separaton n an area near the lghtnng current feed pont. The potental dfference coponent of the voltage s lower, whle the feld couplng coponent s antaned hgh, whch results n reducton of the total voltage along the cable sheld. 8. CONCLUSIONS. A ethod for coputer analyss of transent voltages coupled to shelded cables n H substatons subjected to lghtnng s presented. The ethod cobnes the antenna and crcut theory approaches. Antenna odel s used to copute voltages and currents n the sheld, whle crcut odel ay be used for evaluaton of the voltages coupled to the cables. 2. Ground potental dfference and feld couplng coponents of the voltage along sheld are opposte, whch results n saller total voltage than predcted solely on ground potental dfference analyss. 3. Greatest nfluence on the reducton of voltages has factors beyond control, such as: larger sol conductvty and saller lghtnng current pulse steepness. 4. Possbltes to substantally reduce the nduced voltages due to the currents n earthng syste are: saller earthng conductors separaton n the effectve area around lghtnng current feed ponts, cable routes near earthng conductors, and sheld routes and bondng away fro the edge. 5. Presented coputer odel ay be used n analyss of the worst case scenaro (subsequent stroke, dry sol, corner feed pont) and for optzaton of the protectve easures, concernng the earthng syste and the sheldng. 2 GS3 GS6 GS (b) Fg. 2. Influence of earthng grd sze on transent GPR at feed pont. Sol s wth ρ = Ω. and ε r = 9, and njected current pulse n the corner of the grd wth T =.25/ µs. (a) Analyzed grds. (b) Noralzed transent GPR v/i (k/ka) GS4 GS6 GS64 GS GS24 GS6, GS64 GS (a) GS4 GS TIe ( µ s) (b) Fg. 3. Influence of earthng grd conductor separaton on transent ground potental rse at feed pont. Sol s wth ρ = Ω. and ε r = 9, and njected current pulse n the corner of the grd wth T =.25/ µs. (a) Analyzed grds. (b) Noralzed transent GPR.

6 v/i (k/ka) ACKNOWLEDGMENT The work was partally supported by the Mnstry of Scence of Republc of Macedona. REFERENCES 6 [] R. Anders, Interference Probles on Electronc Control Systes, (Electra, No. 83, 982) [2] A. Strnad, C. Reynaud, Desgn As n H Substatons to Reduce Electroagnetc Interference n Secondary Systes, (Electra, No., 985, pp. 87-7) [3] R. Cortna, L. Pandn, G. Pellegrn, Evaluaton of the Electroagnetc Interference on the Power Plant and Substaton Auxlary Equpent, (CIGRE 988, Paper 36-) [4] R. Cortna, A. Porrno, P. C. T. van der Laan, A. P. J. van Deursen, Analyss of EMC Probles on Auxlary Equpent n Electrcal Installatons due to Lghtnng and Swtchng Operatons, (CIGRE 992, Paper 36-32) [5] H. Mtan, Magntude and Frequency of Transent Induced oltages n Low-oltage Control Crcuts of Power Statons and Substatons, (IEEE Transactons on Power Apparatus and Systes, ol. 99, Sept/Oct 98, pp ) [6] D. E. Thoas, C. M. Wggns, T. M. Salas, F. S. Nckel, S. E. Wrght, Induced Transents n Substaton Cables Measureents and Models, (IEEE Transactons on Power Delvery, ol. 9, October 994, pp ) [7] E. F. ance, Couplng to Shelded Cables, New York: Wley, Fg. 4. Influence of earthng grd conductor separaton on voltage between ponts and 3 along the sheld. (Sybols are sae as n Fg. 8.).5 [8] S. Benda, Interference-free Electroncs, Broley: Chartwell-Brat, 99 [9] A. L. aner, Ipulse Characterstcs of Coplex Earthngs, (Electrcal Technology n URSS, ol., 966, pp. 7-7, also n: Electrchestvo, No. 3, 966, pp ). [] M. Raaoorty, M. M. B. Narayanan, S. Paraeswaran, and D. Mukhedkar, Transent Perforance of Groundng Grds, (IEEE Transactons on Power Delvery, ol. PWRD-4, Oct. 989, pp ) [] A. P. Melopoulos and M. G. Mohara, Transent Analyss of Groundng Systes, (IEEE Transactons on Power Apparatus and Systes, ol. PAS-2, Feb. 983, pp ) [2] L. Grcev and F. Dawalb, An Electroagnetc Model for Transents n Groundng Systes, (IEEE Transactons on Power Delvery, ol. PWRD-5, No. 4, October 99, pp ) [3] L. Grcev, Coputer Analyss of Transent oltages n Large Groundng Systes, (995 IEEE/PES Suer Meetng, Portland, OR, IEEE Paper 95 SM PWRD) [4] R. G. Olsen and M. C. Wlls, A Coparson of Exact and Quas-Statc Methods for Evaluatng Groundng Systes at Hgh Frequences, (995 IEEE/PES Suer Meetng, Portland, OR, IEEE Paper 95 SM PWRD) [5] L. Grcev, Coputaton of the Lghtnng Current Dstrbuton Along Metallc Tubes n Frequency Doan (2st Internatonal Conference on Lghtnng Protecton, Berln, Gerany, 992, pp. 27-2, Paper 4-) [6] L. Grcev and. Arnautovsk, Transent oltages Couplng to Cables n Metallc Tubes, (22nd Internatonal Conference on Lghtnng Protecton, Budapest, Hungary, 994, Paper R 5-3) [7] R. F. Harrngton, Feld Coputaton by Moent Methods, New York: The Macllan Co., 868. [8] Mousa, A. M., The Sol Ionzaton Gradent Assocated wth Dscharge of Hgh Currents nto Concentrated Electrodes, (IEEE/PES 994 Wnter Meetng, New York, NY, U.S.A., February, 994, IEEE Paper 94 WM 78-6 PWRD). [9] L. Grcev, Analyss of the Possblty of Sol Breakdown due to Lghtnng n Coplex and Spacous Groundng Systes, (22nd Internatonal Conference on Lghtnng Protecton, Budapest, Hungary, 994, Paper R 3a-7) [2] IEC Internatonal Standard 32-, Protecton Aganst Lghtnng Electroagnetc Ipulse. Part : General Prncples, 995. [2] S. Rao, J. H. Whnnery, and T. an Duzer, Felds and Waves n Councaton Electroncs, New York: Wley, 965.