Effects of Air Humidity on the Performance of a Polymer Insulator under Lightning Induced Voltage Conditions

Transcription

1 Effets of Air Humidity o the Performae of a Polymer Isulator uder Lightig Idued Voltage Coditios Mahdi Izadi *, Mohd Zaial Abidi Ab Kadir 2, Chadima Gomes 3, Mohd Syahmi 4, Maryam Hajihai 5,2,3,4,5 Cetre for Eletromageti ad Lightig Protetio Researh (CELP, Uiversity Putra Malaysia,Malaysia Eletrial Departmet, Islami Azad Uiversity, Firoozooh Brah, Ira * aryaphase@yahoo.om Abstrat_ Lightig idued voltage is oe of the importat issues pertiet to lie iterruptios i distributio lies.the behaviour of a polymer isulator uder differet weather oditios may affet the overall stability of a power flow i the lie. I this paper, the lightig idued voltage due to a typial sample of retur stroe urret o a distributio lie has bee ivestigated, ad the eletrial behaviour of a polymer isulator (0 V uder differet air humidity oditios was aalysed i detail. The results show that the air humidity has a diret effet o the eletrial performae of a polymer isulator uder lightig idued voltage oditios, whih redues the reliability of the system. Therefore, i desigig ew distributio lies ad i modifyig existig lies, various safety ad protetio parameters suh as determiig the ritial distaes aroud the distributio lies where lightig idued over voltage (LIOV may our, the humidity of air should be treated as a essetial iput parameter. Thus, the field propagatio alog a isulator based o reorded loal iformatio (weather oditios a be helpful ad should be tae ito aout i taig protetio measures. protetio level o the overhead power lie. I this study, the value of the lightig idued voltage o a typial 0 V distributio lie will be evaluated ad the eletromageti profiles alog a polymer isulator uder dry ad foggy weather oditios will be studied. The sum of two Heidler futios will be used for simulatio of the hael base urret ad the eletri urret model seleted is the Modified Trasmissio Lie with Expoetial deay model (MTLE to osider the urret behaviour at differet heights alog the hael. The basi assumptios i this study are listed as follows: i. The lightig is a vertial hael without ay brahes. ii. The groud odutivity is assumed to be perfet. iii. The surfae of the groud is assumed to be flat. Keywords_ Lightig eletromageti fields, Lightig idued voltage, Polymer isulator II. EVALUATION OF LIGHTNING INDUCED VOLTAGE I. INTRODUCTION Lightig idued voltage is oe of importat issues for osideratio i terms of lightig protetio of distributio lies whereby a lightig idued voltage will be reated alog lie by lightig striig ear a distributio lie ad also by ouplig betwee the eletromageti fields of the lightig ad the distributio lie. Several studies have evaluated the lightig idued voltage o a lie ad these studies usually osider the lie parameters, the striig poit ad the groud oditios[-6]. O the other had, the behaviour of a polymer isulator o a lie uder differet weather oditios a have a diret effet o the field profiles alog a isulator ad also affet the breadow value versus the lightig idued voltage. Therefore, by osiderig o lightig idued voltage i parallel with the isulator performae uder differet weather oditios (based o loal iformatio, a be helpful to set proper I order to evaluate the lightig idued voltage (LIV o a distributio lie as show i Figure, the hael base urret a be simulated usig the sum of two Heidler futios as expressed by Equatio ([7]. t i(0, t = [ i ( 0 t exp ( t i 02 η ( t t t 2 t ( t2 2 η 2 ( t t2 2 exp ( t t 22 ]( Where i 0, i 02 are the amplitudes of the hael base urret, t, t 2 are the frot time ostats, t 2, t 22 are the deay- time ostats,, 2 are the expoets (2~0, t η = exp [ ( t t2 ( t 2 ], η 2 = exp [ ( t 2 t t22 ( ]. t 2

2 E x (x, y, z, t = E x (x, y, z, t t t {a m F (x, y, z, t = t, z = h m,i i= m= a mf (x, y, z, t = t, z = h m,i} U(t r2 z 2 (3 E z (x, y, z, t = E z (x, y, z, t t t {a m F 2 (x, y, z, t = t, z = h m,i i= m= a mf 2 (x, y, z, t = t, z = h m,i} U(t r2 z 2 (4 Figure.. The geometry of problem The urret behaviour at differet heights alog the hael a be studied usig the MTLE model as preseted by Equatio (2. O the other had, the lightig geerated eletromageti fields i the x ad z axis (based o Figure 2 a be estimated usig the aalytial field expressios as expressed by Equatio (3 ad Equatio (4[8,9]. I(z, t = I (0, t z v P(z u(t z z is the temporary harge height alog lightig hael, I(z,t is urret distributio alog lightig hael at ay height z ad ay time t, I(0,t is hael base urret, P(z is the atteuatio height depedet fator (for MTLE urret model is exp(-z'/λ, v is the urret-wave propagatio veloity, is the upward propagatig frot veloity, u is the Heaviside futio as defied by u (t z = for t z 0 for t < z { Figure 2. Coordiatio of lie with respet to lightig hael (2 E x is the eletri field at x-axis, E z is the eletri field at z-axis, tis the time step, t is the umber of time steps, = 2 t = ( t t t =,2,, max h i for m = ad m = a m = { 2 h i for others h i for m = ad m = a m = { 2 h i for others is divisio fator(>=2, h i = h i = { βχ 2 {(t i t i (βt i z 2 ( r χ 2 (βt i z 2 ( r χ 2 } βχ 2 { (βz t i (βt i z 2 ( r χ 2} for i = βχ 2 {(t i t i (βt i z 2 ( r χ 2 (βt i z 2 ( r χ 2 } βχ 2 { (βz t i (βt i z 2 ( r 2} χ for i = { (m h i h h m,i = { m=,i (m h i for i = (m h i h h m,i = { m=,i (m h i for i = R = x 2 y 2 (z z 2, A = t R z, v R A 2 = exp ( t z v, t 2 A 22 = exp ( R t z v t 22.

3 F = I 0 P(z x(z z A 2 4πε 0 η 0 [( A t ] { (A t (3 2 t 2 2 3t 2 RR 2 2 t 2 2 R ( A t 3 2 ( ( A t 2 [( A 2 t ] 3([( A t ]( A t ( A t R 4 [( A t ] I 02P(z x(z z A 22 { ( A 4πε 0 η 02 [( A t2 ] 2 t 2 R 3 [( A t ] t 2 ( 3 2 ( A t 2 2 [( A t ] 2 2((A t 2 [( A t ]( A t 2 t t 2 R 3 [( A t ] t2 (3 2 t t 22 RR 2 2 R 5 2 t ( A t2 3 2 ( ( A t2 2 [( A 2 t2 ] 3([( A t2 ]( A t2 ( A I F 2 = 0 P(z A 2 4πε 0 η 0 [( A t 2 R 4 [( A t2 ] t ] 2( A t (t t 2 t R2( A t t 2 R t t 2 R 3 2 t 2 2 R 3 [( A t2 ] t2 2 ( 3 2 ( A t2 2 2 [( A t2 ] 2 A 2(( t2 2 [( A t2 ]( A t2 2 t 2 t 22 R 3 [( A t2 ] { (x2 y 2 [( A t ( 3 2 t t 2 3t t 2 R t R 2 ( A t ( 3t 2 R2t 2 R 2 ] 2 t t 2 2 R 5 A ( (x2 y2( t 2 2 t 2 R 3 (x 2 y 2 [2 2 t 2 R( A t 2 2 3t t 2 ( A t 2 ( t 2 R( A t 2 2 2t R( A t 2 ] 2t t 2 R 2 ( A t 2 2 t 2 t 2 R 4 [( A t ] 2 2 (x 2 y 2 ( A t t 2 R 3 [( A 2 } t ] I 02 P(z A 22 4πε 0 η 02 [( A t2 ] { (x2 y 2 [( A t2 ( 3 2 t 2 t t 2 t 22 R t 2 R 2 ( A t2 ( 3t 2 22 R2t 22 R 2 ] 2 t 2 t 2 22 R 5 2( A t2 (t 2 t 22 t 2 R2( A t2 A t 22 R ( (x2 y2( t2 2 t 2 t 22 R 3 2 t 2 2 R 3 (x 2 y 2 [2 2 t 22 R( A t t 2 t 22 ( A t2 2 ( t 22 R( A t t 2 R( A t2 2 ] 2t 2 t 22 R 2 ( A 2 2 (x 2 y 2 ( A t t 2 2 R 3 [( A 2 } t2 ] 2 t 2 2 t 22 R 4 [( A t2 ] The values of the LIV o the power lie a be estimated usig differet ouplig models suh as Agrawal, Taylor ad Rahidi models whih use differet field ompoets as urret ad voltage soures alog the lie for geeratio of the LIV. The Taylor ouplig futio a be expressed by Equatio (5 [,2]. } } t2 2 I this study, the aalytial lightig idued voltage expressio (based o sum of two Heidler futios was used to evaluate the LIV alog the lie usig Equatio (6 whih is based o the Taylor ouplig model [0]. V(x, t = t = [A RS A 2 RS A 3 RS ]U(t x2 d 2 h 2 (6 x = (tx 2 h 2 d 2 2(tx q x, x m = x (m x, qis divisio fator (>=2, 2 for m = ad m = q m = { for others h = h, is divisio fator (>=2 h = E z (x, z, d, t = t dz A RS A RS 0 = 2 h b m m = [E z (x, y, z = (m h, t t {a m F 2 (x, y, z i= m= = (m h, t = t, z = h m,i a mf 2 (x, y, z = (m h, t = t, z = h m,i}u(t r2 z 2 ] (tx 2 h 2 d 2 2 = 2 2(tx E x (η, h, d, t η x dη x = 4 x q m m = (tx 2 h 2 d 2 h E z (x, z, d, tdz 2(tx E 2 x (η, h, d, t η x dη 0 x v(x, t = x 2 E x (η, h, d, t η x U(t dη [ (t x2 h 2 d 2 2(t x ] x2 d 2 h 2 E x is the eletri field at x-axis, E z is the eletri field at z-axis, h is height of lie, is light speed i free spae, d is radial distae betwee striig poit ad lie, x is observatio poit alog power lie, t is time (5 [E x (x = x m, y = d, z = h, t x m x t {a m F (x = x m, y = d, z i= m= = h, t = t x m x, z = h m,i a mf (x = x m, y = d, z = h, t = t x m x, z = h m,i} U(t x m x x m 2 d 2 h 2 ]

4 V i (V 3 = 2 E x (η, h, d, t η x dη (t x2 h 2 d 2 2(t x = 4 x A RS x q m [E x (x = x m, y = d, z m = = h, t x m x t {a m F (x = x m, y = d, z i= m= = h, t = t x m x, z = h m,i III. ELECTROMAGNETIC PROFILES ALONG A POLYMER INSULATOR UNDER DIFFERENT WEATHER CONDITIONS I this paper, the values of the eletromageti fields alog a polymer isulator uder a idued voltage i dry ad foggy oditios will be studied. A 0 V polymer isulator was seleted as show i Figure 4. The parameters of the isulator are tabulated i Table 2 as follows [-3]: a mf (x = x m, y = d, z = h, t = t x m x, z = h m,i} U(t x m x x m 2 d 2 h 2 ] b m = { 2 for m = ad m = for others x = x(t x2 h2 d2 2(t x, q x m = (t x 2 h 2 d 2 2(t x (m x. Figure.4. Polymer isulator (a. osidered isulator ad b. the observatio poits Table.2. Parameters of polymer isulator a dimesios b eletrial parameters a Table shows the hael base urret parameters that were used i this study based o Equatio (. The lightig idued voltage o the distributio lie based o Figure is illustrated i Figure 3 assumig a radial distae of r=50 m ad a odutor height of 0 m. Table..The hael base urret parameters based o sum of two Heidlerfutios[7] i 0 (A i 02 (A τ (μs τ 2 (μs τ 2 (μs τ 22 2 λ V (μs (m (m/s b Parts of Isulator Dimesio Shed diameter (mm 48/8 Shed-to-shed spaig (mm 50 Struture Height (mm 250 Mi Nomial CreepageCreepage distae 420 (mm Parts Material Relative permittivity (ε r Relative Permeability (μ r Volume Coduti vity (σ S/m Fittigs Alumiium x 0 7 Sheds Silioe rubber 3 x 0-7 Core Fiberglass 5 x Time( s Figure 3. Evaluated idued voltage at r=50m ad h=0m The eletri field distributio of the isulator uder dry oditio a be obtaied from Figure 5. Moreover, the eletri fields at differet poits alog the isulator for dry ad foggy oditios are demostrated i Figure 6 ad Figure 7,

5 respetively with the weather parameters obtaied from Table 3 [-3]. Material Table.3. The eletrial parameters of air Relative Relative permittivity (ε r Permeability (μ r Volume Codutivity (σ S/m Dry x 0-4 Foggy x 0-4 Similarly, the mageti fields at differet poits alog isulator for dry ad foggy oditios are demostrated i Figure 8 ad Figure 9, respetively. Figure.8. The mageti field profile alog isulator uder dry oditio Figure.5. The eletri fields alog isulator uder dry oditio Figure.9. The mageti field profile alog isulator uder foggy oditio Figure.6. The eletri field profile alog isulator uder dry oditio Figure.7. The eletri field profile alog isulator uder foggy oditio A ompariso betwee Figure 6 ad Figure 7 ad also Figure 8 ad Figure 9 shows that the air humidity has a diret effet o the field values at differet parts of the isulator ad this a redue the eletrial performae of the isulator whe subjeted to a lightig idued voltage. The results show that the air humidity a have a effet i terms of ireasig the eletri field i the rage % at differet poits alog the isulator. Moreover, the values of the mageti fields ireased uder foggy oditios ompared to dry oditios i the rage of % at differet poits alog the isulator. Therefore, whe the humidity of the air ireases, the hae of eletrial breadow will also be ireased. I additio, i order to set the proper level of lightig protetio o a distributio lie, osideratio should be give to the evaluatio of the lightig idued voltage o the lie ad also a estimatio of the ritial distae for the idued overvoltage is importat [4,5]. Therefore, appropriate osideratio of the effet of air humidity o the eletromageti profiles of polymer isulators should be give, ad taig the due redutio fator ito aout a be helpful for desigig ew lies or improvig existig distributio lies.

6 IV. CONCLUSION I this paper, the values of the lightig idued voltage o a typial distributio lie were evaluated ad the behaviour of the eletromageti fields alog a polymer isulator uder dry ad foggy oditios was evaluated by applyig the lightig idued voltage as a exitatio soure of the isulator. The results show that the humidity of the air has a diret effet o the field values at differet poits alog a isulator ad also it a irease the hae of a eletrial breadow. Therefore, i order to protet the distributio lie ad to evaluate the isulatio level of the lie versus the idiret effet of lightig, osideratio of the loal iformatio iludig loal weather oditios is very importat ad taig a appropriate redutio fator ito aout a be helpful for desigig of ew lies or improvig existig distributio lies. REFERENCES [] A. Adreotti, A. Piero, ad V. A. Raov, "A New Tool for Calulatio of Lightig-Idued Voltages i Power Systems Part I: Developmet of Ciruit Model," Power Delivery, IEEE Trasatios o, vol. 30, pp , 205. [2] A. Adreotti, A. Piero, V. A. Raov, ad L. Verolio, "Aalytial formulatios for lightigidued voltage alulatios," Eletromageti Compatibility, IEEE Trasatios o, vol. 55, pp , 203. [3] A. Borghetti, J. Gutierrez, C. Nui, M. Paoloe, E. Petrahe, ad F. Rahidi, "Lightig-idued voltages o omplex distributio systems: models, advaed software tools ad experimetal validatio," Joural of Eletrostatis, vol. 60, pp , [4] F. Rahidi, "A review of field-to-trasmissio lie ouplig models with speial emphasis to lightigidued voltages o overhead lies," Eletromageti Compatibility, IEEE Trasatios o, vol. 54, pp , 202. [5] F. Rahidi, C. A. Nui, M. Iaoz, ad C. Mazzetti, "Ifluee of a lossy groud o lightig-idued voltages o overhead lies," Eletromageti Compatibility, IEEE Trasatios o, vol. 38, pp , 996. [6] N. Rameli, M. Ab Kadir, M. Izadi, C. Gomes, ad J. Jasi, "Evaluatio of Lightig Idued Voltage due to the Effet of Desig Parameters o Medium Voltage Distributio Lie," Jural Teologi, vol. 64, 203. [7] M. Izadi, A. Kadir, M. Z. Abidi, C. Gomes, ad W. F. W. Ahmad, "A aalytial seod-fdtd method for evaluatio of eletri ad mageti fields at itermediate distaes from lightig hael," Progress I Eletromagetis Researh, vol. 0, pp , 200. [8] M. Izadi, M. AbKadir, C. Gomes, ad W. Ahmad, "Numerial expressios i time domai for eletromageti fields due to lightig haels," Iteratioal Joural of Applied Eletromagetis ad Mehais, vol. 37, pp , 20. [9] M. Izadi, A. Kadir, M. Z. Abidi, ad M. Hajihai, "A Algorithm for Evaluatio of Lightig Eletromageti Fields at Differet Distaes with respet to Lightig Chael," Mathematial Problems i Egieerig, vol. 204, 204. [0] M. Izadi, M. Z. A. AbKadir, ad M. Hajihai, "O the Lightig Idued Voltage Alog Overhead Power Distributio Lie," Joural of Eletrial Egieerig & Tehology, vol. 9, pp , 204. [] T. Doshi, "Performae Aalysis of Composite Isulators up to 200 V a usig," Arizoa State Uiversity, 200. [2] M. Sato Zari ad D. Belavi, "A experimetal ad umerial study of the humidity effet o the stability of a apaitive erami pressure sesor," Radioegieerig, 202. [3] K. M. Elovitz, "Uderstadig what humidity does ad why," ASHRAE joural, vol. 4, p. 84, 999. [4] A.Piatii ad J.M. Jaiszewsi, "Lightig idued voltage o overhed lies-appliatio of the exteded rus model," IEEE trasatio o eletromageti ompatibility, 5, 3, [5] A.Piatii, "Lightig-Idued Voltage o overhead Power Distributio Lies," word meetig o lightig(womel, Mar 206.