Simulation of the Nonlinear Thermal Behavior of Metal Oxide Surge

8/14/2019 Simulation of the Nonlinear Thermal Behavior of Metal Oxide Surge

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306 IEEE Transactionson Power Delivery Vol. 9, No. 1. January 1994

SIMULATION OF THE NONLINEAR THERMAL BEHAVIOR OFMETAL OXIDE SURGEARRESTERS USING A HYBRID FINITE DIFFERENCE AND EMPIRICAL MODEL

F. R. Stockum, Senior Member, IEEEThe Ohio Brass CompanyWadsworth, OhioAbstract - A s imulat ion m ethod for determining temperaturesand heat f l ow in metal ox ide surge arresters (MOSA) ispresented. The meth od is val idated and a thermal s tabi l i tyappl ication is discussed.Keywords: Arrester, thermal, simulation.

INTRODUCTIONThe determinat ion o f internal temperatures in electr icalapparatus such as surge arresters and bushings is ofcons iderable impor tance. Excess ive temperatures can lead todamage or fai lure of the dev ice. Test ing of the fu l l s ize dev iceis cost ly and in the case of large surge arresters it i s notgeneral ly feasible. Therefore, sectio ns of arresters wh ich arethermal l y i nsu la ted a t the ends as show n in Fig. 1are normal lyused in the tests . Even then, t he amount of test ing that ca n bedone requi res cons iderat ion of the t ime and cost involved.These factors have resul ted in the development of analogmodels to help s tudy thermal condi t ions in bushings and metaloxide surge arresters 11.21.Analog models use thermal res is tances and thermalcapaci t ies represented by electr ical equivalents which areconnected in a netwo rk to s imulate the thermal behaviorof thedevice. Whi le this approach wo rks wel l in sol id mater ials whe reonly conduct ive heat f low is involved, s igni f i cant di f f i cul t iesarise in model ing the annular gas gaps of ten present inarresters.Heat t ransfer red across a gas gap by radiat ion is propor tionalt o t h e 4th pow er of the absolute temperatures on ei ther s ide ofthe gap according to the Stefan-Bol tzmann law. Convect iveheat t ransfer in an annular space involves Grashof and Prandltnumbers raised to f ract ional powers. Compl icat ions of thesek ind usual ly lead to compromises to make the analog modelsl inear whic h m ay reduce the temperature range. It is, how ever,

poss ible to construct a thermal model based on phys ical lawsthat is funct ional over a wi de range of temperatures.Using the s im ulat ion technique, a large var iety of interest ingand use ful s tudies of th e thermal behavior of ar resters can beconducted.THERMAL MODEL OF MET AL OXIDE SURGE ARRESTERS

In larger arresters, it i s a wel l es tabl ished pract ice tocons ider only radial heat t ransfer . This can be just i f ied exper i -mental ly a nd theoret ical ly 121. Therefore, a major assumpt ionin the mo del is completely radial heat f low . Wi th this assump-t i on in mind, a verbal descr ipt ion of the thermal model will begiven now and later the mathem at ical vers ion will be developed.93 WM 044 8 PWRD A paper recommended and approvedby the IEEE Surge Protective Devices Committee ofthe IEEE Power Engineering Society for presentationat the IEEE/PES 1993 Winter Meetin g, Colum bus, OH,January 31 - February 5, 1993.August 27, 1992 ; made available for printingNovember 10, 1992.

Manuscript submitted

PHENJLIC STUDPH EM L I C PL ATETH EW L IN SUL ATION

AYG X 12 COPPER WIREPHENJLIC STUDPHEMLIC P u r F l f f i E R SPR l f f iSTEEL DISKW R C E L A I N M U S fiVARISTORS 9 s - m n i wCORK GASKETTEFLON H E A T SHIELDSTEEL DI S KAYG 2 COPPER WIRE

-PHENOLIC PLATEI I OPPER TEWI NALI I I

Fig. 1 T h e r m a l t e s t m o d e l of a MOSA.

G A S G A P

HOUS I NG

C O N V E C T I O NH E A T T R A N S .M E T A L O X I D EV A R I S T O A SR A D I A T I O NH E A T T R A N S .

I

Fig. 2 Section of a MOSA.Most of the t ime, a gapless metal ox ide var is tor ar resterfunct ions electr ical ly as a column of capaci tors with dissipationfactors in the range of 1 t o 10 percent. W i t h l o w loss levels,

the s teady s tate temperatures of the var is tors are only s l ight ly

0885-8977/94/$04.00 1993 IEEE


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above ambient. During surges or overvoltage s of sufficien tmagni tude, the var is tors become conduct ive and thei r lossesincrease. The resulting increase in varistor temperature causeshigher heat f low. The heat wh i ch c rosses the gas gap mu s texac t l y ma tch the n et (generated - absorbed) heat f low fromthe varistors. Th i s l eads to boundary cond i ti ons fo r wh i ch tw oequat ions can be wr i t ten.One equat ion s tates the requi rement that the heat leav ingthe var is tors be equal to the heat t ransfer red across the gasgap. A s indicated in Fig. 2, bot h convect ion and radiat ion arei nvo l ved in transferr ing he at across the gas gap and thus, a 4thorder equation is involved.The other equat ion s tates the requi rement that the heatleav ing the var is tor m ust equal the heat enter ing the hous ing onthe other s ide of the gas gap. S ince only cond uct ion is involvedin each material , the equation is l inear.These t w o equat i ons can be used to so l ve fo r twounknowns, v iz ., the temperatures at the OD of the var is tors andthe ID of the hous ing. Mathemat ical ly, th is involves f inding thecorrect root of a 4th order polynomial.The other boundary s i tuat ion is at the OD of the hous ingwhere the net heat f l ow f rom the hous ing mus t equa l the heatrejected to the atmosphere. Newton's cool ing equat ion can beused to calculate the heat rejected. Nicholas and Sels ing 131have developed curves for the heat t ransfer coeff ic ientsassoc iated with porcelain weathersheds. Us ing thesecoeff icients , the temperature at the outs ide of the hous ing canbe determined.In the sol id mater ials , heat f lo w is described by a par t ia ldi fferential equation cal led the heat equation. Fini te di fferenceapprox imat ions of the heat equat ion can be used to f ind thetemperatures at a set of radial locations for a series of t i m esteps. This process is val id for al l interior points in the varistorand housing. A t exter ior points , empi r ical equations and theboundary condi t ions discussed ear l ier are employed to comp utethe temperatures.A mul t is tep expl ic i t solut ion method can be employed.Star t ing wi th som e kno wn ini t ia l temperature dis tribut ion, t imeis incremented and a ne w set of temperatures in the sol idmater ials are calculated us ing the f in i te di f ferenceapproxim ations. Then, temperatures at the boundaries arecomputed and the process is repeated until results over thedesired duration have been obtained. The numbe r of radiallocat ions wh ere the temperatures are determined and the s izeof the t ime s teps are selected to give sat is factory accuracy.The t ime requi red for the calculations depends on the selectedintervals , the e f f ic iency of the com puter code and the speed ofthe computer .Fini te Difference ADproximation O f Heat Eqn.

In cy l indr ical coordinates wi th no var iat ion in the z or 0directions, the hea t equation ca n be expressed as:d o c * u=ko?? + * q , r > 0 , t Z 0 1)37 ar2

where: U is temperature ("C)t i s t ime ( 8 )r i s radius (cm )d is dens ity (g/cm 3)c is specific heat (W*s/"C/g)k is thermal conduct iv i ty (W/"C/cm)q i s power de ns i ty (W/cm3)The singulari ty (at r=0) in ( 1 ) can be el iminated by appl icat ion

of I 'Hospital 's rule w it h the result:

In the f in i te di f ference approx imat ion of the par t ia l d i f ferentialequations, t he derivatives are replaced by algebraic expressionssuch as the fol lowing:

where: p is a smal l increment in t ime SII i s a smal l increment in r (cm)i s a spatial indexj i s a t ime indexe l and e 2 are error termsIf p and 1 are chosen properly, it is possible to drop the errorterms. The general requi rement is to make the intervals smal lenough that t runcat ion er rors are smal l bu t large enough thatround off errors do no t affec t the results. In practice, i t is fair ly

easy to meet these requi rements.Using the above approximations for the partial derivatives,and replacing r by r i the heat equation can be expressed as:U / / * , /,I = k . + 1 , / - 2 4 . j k 1 . j k . + 1 J - Ui.jd * c * - P 12 r

Since there are tw o regions of sol id material , it i s convenientto use t w o var iables for temperature. In the varistor material ,U will be replaced by w and in the hous ing, the temperaturevar iable wi l l be v . The fol lowing def ini tions apply in the var is tormaterial:le t h12= k,/(d, c,) (cm 2/slR, = radius of varistor (cm)

N, = number of radial segmentsi = 1,2,..N, - 1j = 0,1, ....I = RJNl ( cm) (see Fig. 2)r, = i I cm)d, = densityc 1 = specific heatq = power dens i ty (losses)Heat equat ion 1 can be approx imated by

Let e, = p h12/12 nd solve for w , , ~ + ~ wi+l,/ Wi.w,.~., w,,/ +el wiel. 2 wi,/+ w ~- ,, ~)el p 9i dl Clrearrange to obtainw,+, =e, w ~ + , . ~ *1 ++ + ~ ~ , ~ * 1 - 2 + , )*el +

3)At the center of the MOV ( i=O), the approx imat ion for 2)s

WO,/+, ' h : . WlJ-2 ~aJ+wa- l , j ) 9P 12 dl * C l


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308By symmetry , wsl., = w ~ + , , ~o the equat ion at the center is

Solv ing for gives

In the hous ing material,let h = k,/(d,*c,) (cm2/s)R = ID of hous ing ( cm)

R, = OD of hous ing ( cm)N, = number of radial segmentsi = 1,2,..N, - 1j = 0 , l . ...s = (R, - R,)/N, (c m ) (se e Fig. 2)r, = R, + i * s (c m)d = densi tyc, = speci f i c heatHeat equat i on (1 ) ca n be approx imated byv/,/+,VI,/ = . (V/+l . ,-2 VI,, + V / - l . J + VI+,,, - VI,, ]P S 2 s r l

h,'vi, /*, vi , /+p - Vi*,,,-2 v/./+v/-,,/+-1I+, / - v/Solv e fo r v,,,+, S 2 R, .IS

Let e = p hZ2/s2 nd le t den = R,/s + i, Then1Vi,/+1 = vi+l, l ( 1 -Iden e, +(5)

In the mul t is tep solut ion process, the temperature at theboundar ies ( r = R,, r = R and r = R,) can no t be calculatedby the equat ions developed so far. As discussed earlier,boundary cond i t i ons are used to compute these th reetemperatures.

A, is the corresponding hous ing area (cm')The f i rs t heat balance equation equates the heat f lo w o uto f the var is to r to the heat f l ow i n to the hous ing wh i c h i sequ i va len t to say ing the med ia be tween the tw o i s non-absorbing. The fol lowing terminology is needed to wr i te theremaining equat ions:voll = vo lume o f l as t segment in varistor.v012 = volume of f i rs t segment in housing.w j p l u s l ( N , - l ) = tempera ture a t nex t to l as t node inv j p l u s l ( 1 ) = temperature at f i rs t inter ior node in housingwj(N,) = temperature at the last node in the var is tor forv j (0 ) = t e m p a t ID of hous ing fo r t im e s tep j.AB is absolute zero temperature.

the var is tor for t ime s tep j + 1.fo r t ime s tep j + 1 .t ime s tep j.

There is a correspondence between some of th e n ew terms andthose used in the earl ier equations, e.g., wj (N ) is the sam e aswIeN nd v j p l us l (N-1) i s the same as The new nota t ionwill mak e the next equat ions eas ier to w r i te a nd fac i l i tatecomputer code generat ion.The heat balance equat ion can be s tated as:

heat rejected b y var is tor = heat received by hous ingThis heat is the sum of three components in the outer sect ionof the var is tor and the sum of t w o c o m p o n e n ts in the innersect ion of the hous ing. These compon ents are ident i f ied in thefol lowing equal i ty .conducted + generated - absorbed = conducted + absorbed

The m athemat ical vers ion is :( w j p l u s l ( N , -l ) - (T , -A B ) ) k , * A ,-vol l ' + I(T, -AB- wj(N, ) c , d, vol l -(T, -AB-v jp lus l (1 ) ) * k , * A ,(T , -AB-v j (O) ) *c , *d ;vo lZ

PS

PADDlication of Boundary ConditionsIn an annular space, G rober and Erk 141s ta te tha t the to ta lheat Q, (W) t ransfer red by conduct ion and convect ion ca n bedetermined f rom:

0, = 2 t7 k, (T,- T,) ' /lOg(R,/R, ) 6)where: k i s an apparent thermal co nduc t iv i ty (W/cm/"C)T, is the tempe rature at the var is tor OD (K )

T i s the tempera ture a t the hous ing ID (K)L is the l ength of the var is tor (cm)The apparent thermal conduc t iv i ty , k depends on the produc t

of the P randt l number (N and a spec ial Grashof number (NGJraised to a f ract ional powe r. The formulas involved, wh ich areat t r ibuted to Kraussold [51, are described in [4].The heat t ransfer Q, ( W ) in an annular space b y radiat ion isg i ve n b y B r o w n a n d M a r c o [61Q , = o * F , * ( T ; ' - ~ )A , ( 7 )

where: is the Stefan-Bol tzmann constant (W/cm2/K4 )Fe = [1 / , + (A,/AZ) ( l /, - 111.E i s the emiss iv i ty of the var is torE , i s the emiss iv i ty of the hous ingA, is the late ral varistor area (cm')

Let F1 = k, A,/s +c, d volZ/p and isolate T(AS+v jp lus l ( l ) ) k , *A , (AB+v j (O) )c, d, vo12S PT , * F l = +

vol l q + (wjplus1 (N,- 1) - T, -AB)) k , A , -I( T1 AB - wj(N,) c, d, vol l

PL e t F 2 = AB + vjplus S( 1 1 1 k, A, AB+ v j (0 ) ) c , d, vol lP

Solve for T k * A * d ,* v o l l7 , = f Z + v o l l - ( T 1 - A B ) * [ , c l IF1 F1 8 F l p * F 1w j p l u s 1(N, 1 k , * A , w j ( N, ) c , d, vol l1 - F l p * F l1 F l p 9 ~ 1k * A c1 * d , v o l lL e t M I =2 ;Lef X I =T I AB

L e t F3 = z -+ d i 9 q wiplus1 (N,- 1 1 k , A ,

F1 F l 1 F lwj(N, c , d, voll

p F 1


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309of the last element, A, the sur face area of the outer elementand T as the tempera ture o f the ou ter hous ing surface a t times tep ( j + I ,he equat ions for th e three components are:(1 ) Heat conducted in las t hous ing segment:

k , (v jplus1(N,-l ) - T, ) A, l s(2) Heat absorbed in las t segment:

(vjplus 1(N2- ) - vj(N,-1 ) ) c2 d, vol31p(3) Heat rejected to the env i ronment a t a temperature of TF:

( T3- TF) H *A,The heat balance is then

(vjplus 1 N2- - T3) k , A, I s - v jp l us (N,- 1 ) -vj(N,-1 ) ) c, d v0/3 /p = ( T, - TF H A, ( 1 1 )

Define PT3 asPT3 = (vj(N,- 1 - vjplus 1(A ,- 1 1 c, d2 v o I 3 l p

Subst i tute PT3 n ( 1 1 ) and solve for TT, = vjplus 1(N,) = TF-H +PT3IA, +v j p / u s l ( N , - l ) g k , l s ) l ( H + k , l s ) ( 1 2 )

Then the equat ion fo r T, is: T = F 3 - M 1 X1 8)The second heat balance equat ion equates the hea t f lo w ou tof the var is tor to the heat cross ing the air gap. The wor dequat ion isconducted - absorbed + generated = radiated + eff .conducted

The m athemat ical vers ion (af ter factor ing) is :wjplus 1(N,-1 k , A wj(Nl c, d, v o l l

I P) + v o l l Q =k A * d 1 8 v o l l(T, AB) 2I P

Note tha t AIF3 Fl =F2 + v o l l q + w j p l u s l (N, 1 ) k , -Iwj(N, c , d, vo/lP

soF3 F?-F2-X 1 M I F 1 =A 1 D Fe ( ( X I +AB 4 -

(F3-M1 X I 4) + L 2 R k , ( X ?+AB-

Let K K l = A , * o * F , a n d K K 2 = 2*n*k;Ulog(R,/R1)Expand 9) s a 4 t h order polynomial0 = X 1 4 ( K K l - K K l M 1 4 )+ X 1 3 4 KK1 (AB +F3 M1X 1 2 * ( 6 K K 1 * A B2 - 6 * K K 1 F 3 2 * M 1 2 )+ +X1 * ( M 1 * F 1 + 4 * K K l *A B 3 + 4 - K K l O F ~ ~ O M ~K K Z . M l +KK2)+KK1 (AB4 - F34)+ K K 2 ( A B - F 3 ) + F 2 - F3 F1

The po l ynom ia l can be w r i t ten in a s tandard fo rm by us i ng thefol lowing coeff ic ients :P4 = K K l ( 1 - M 1 4 )P3 = 4 * K K 1 (A B + F 3 * M l 3 )P1 = 4 . K K l ( A B 3 + F 3 3 * M 1 ) + K K 2 * ( 1 + M 1 ) + M 1 OF1PO = K K l ( A B 4 - F 3 4 ) + K K 2 ( A B - F 3 ) f F 2 - F 3 F 1Now, the equat ion isP2 6 * K K 1 * ( A B 2 - F 3 3 0 M 1 )

X 1 4 * P 4 + X 1 ~ * P 3 + X 1 ~ * P 2 + X 1P l + P O = 0 10)Finding the correct ro ot of 101, gives the temperature at theOD of the var is tors . There are several wa ys to f ind the rootand a good choice is New ton's method. Once X 1 is obtained,the abso lu te tempera ture a t the ID o f the hous ing can be foundf r o m 8). ubtract AB to com plete the calculat ion.The thi rd and last boundary condi t ion is the one at the OD ofthe hous ing. Reference [31 prov ides informat ion necessary todetermine he at transfer co efficients (HI for porcelain housings.In serv ice, condi t ions suc h as wind veloci ty and solar heatingare involved. In the laboratory , the var iat ion in H is smal l anda f ixed value is usual ly sat is factory .

The last heat balance equat ion equates the heat f low out ofthe last (outer ) hous ing element to the heat rejected to theatmosphere. The heat ex i t ing the last hous ing element is theheat conduct ion produced by he temperature di f ference acrossthe element minus the absorbed heat. Wi t h vo13 as the volume

Al l the equat ions (31, 41,61, 81,10)a n d ( 1 2 ) necessary tocomp ute the temperature at points along the radius for t >0 areno w avai lable. Computer code necessary to per form thes imulat ions was generated us ing these equat ions.The output f rom one imp lementa t i on o f the s imulat ioninc ludes tabulat ions (discussed later) and graphs of the types h o w n in Fig. 3 and Fig. 4. A s imulat ion usual ly cons is ts of aheat ing per iod and a recovery per iod. A separate graph isassociated with each period. These graphs are outpu t to thecomputer m oni tor whi le the s im ulat ion runs and later saved byscreen dumps. They cons is t of plots of temperature v s radiusat a ser ies of t ime points . The ver t ical ax is is radial dis tancemeasured f rom the center l ine of th e ar rester and the hor izontalax is is temperature o ver an appropr iate range.

~ Arrester Temperat ures - Heating P e r i o d10 P o w e r I n u t 900 att5D u r a t i o n 220 Se c

I I i n c r e a s i p q ' r i m e - 4-R3

6 I 0 0 140 I S 0Temperature, Des C

Fig. 3 Simulat ion output to the moni tor dur ing theovervoltage period.VAL1DATlO NS

Val idat ion s tudies involve per forming exper iments whichproduce resul ts that c an be compared to the s imulat ion output .I f the agreement be twe en the tw o methods i s sa ti s fac tory,then the s imu la t ion m ay be used in studies where condi t ionsare s imi lar t o those use d in the val idat ion process.Tw o val idat ion s tudies are repor ted. One s tudy comparesthe s imulat ion output with empi r ical resul ts dur ing heat ing andcool ing per iods of the thermal model (F ig. 1) . The second s tudyus ing va r is tors with s igni f i cant ly di f ferent loss levels.


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310I Arrester Temperatures - Coolins PeriodI I Voltage Level: ncav

2 0 60 100 140 180 2 2 0Temperature, Deq C

Fig. 4 S imula t ion o u tput t o the mon i to r dur i ng the recoveryt ime per iod.

Character iz ina Var is tor LossesThe losses in a varistor depend o n several variables includingtempe rature, electr ical stress, and prior service. Wh en avar is to r i s made to change s ta te f rom a high level of conduct ionto a l ower l eve l o f conduc t i on in a fe w seconds, the equat i onf o r p o w e r loss i s complex. Howeve r , several minutes af tersuch a s tate change, the losses at a constant vol tage becomepr imar i ly an exponent ial funct ion o f temperature.

P=A e x p ( u e (1 3 )where A and U are constantss the tempe rature ( "C)P i s power loss (W)The cons tants fo r (13) ca n be obta ined exper imenta ll y b yapp l yi ng an overvo l tage to a co l um n of var is tors unt i l reachingthe highest temperature of interest and then measur ing thep o w e r a t a reduced vol tage (usual ly MCOV) for a ser ies oftemperatures as the var is tors cool . Typical resul ts f rom onetest fol low:

0 , "C 209 203 1 9 5 1 8 2 1 7 3 1 6 3 1 5 5 1 4 6P , W 1 0 7 8 1 6 5 40 28 20 1 6 1 2A regress ion analys is on these data gives the fol lo wing resul ts :Constant (A) 0.07 183Correlat ion coeff ic ient R ) 0 . 9 9 8 9 7

Coeff ic ient 0 ) 0 . 0 3 4 7 7Good correlat ion (R - 1) be tw een the ac tua l and pred i c tedvalues for P is indicated, so, ( 13) a n b e u s e d in the s imulat ionto compu te var is to r losses dur ing recovery at MCOV.Thermal Mode l

The thermal m odel cons is ts of a shor t sect ion o f an ar restera s s h o w n in Fig. 1. The insulated ends of the sect ion have athermal res is t iv i ty z 2.9 "C*mZ/W. Leads through theinsulat ion are .0021 m dia x .1 m long copper wi re. With th i sconstruct ion, the losses th rough the ends o f the mode l a regene ral ly negl igible. The dimen sions of the test spec imens seeFig. 2) w e r e R , = 3.85 cm, R = 5.64 cm, R, = 8.26 cm, andL = 9.6 cm.

ini t ia l temperature of 6 0 "C. Then the appl ied vol tage isreduced to the cont inuous opera t ing l eve l (MCO V) and powerconsumpt i on is moni tored until an end condi t ion is reached.F rom the i nverse o f ( 13). n est imate o f temperatures dur ingthe per i od a t M COV ca n be obta ined us i ng the measured powerlevels . These temperatures and po we r levels are thencompared with values obtained in the s imulat ion output .The s imula t ion ou tput i nc ludes powe r consumpt ion o f thevar is tors , p ow er f low across the ai r gap and temperatures atselected locat ions for a series of t ime intervals. A samp le ofthe output f r om a 46 min s imula ti on with 220 s of hea t ing at900 W is given in Table 1.II TASLE 1 - PARTIAL OUTPUT R O M A SIMULATION

T i m, Power, W

220II240 28.3 82.4 188.6 196.6 69.3300 26.7 78.1 196.4 194.4 71.6II ,p , ;; 188.4 184.7 I168.9 168.21600 44.8 168.9 167.8 78.9II 1800 8.7 41.6 164.3 163.3 78.7

2700 6.6 31.2 138.7 136.9 76.8

66.366.368.483.184.766.064.2

Compar isons of exper imental resul ts and s imulat ion outp ut areprov ided in Table 2.The temperatures in column three of Table 2 are obtained byapp l yi ng the i nverse o f (1 3) to the m easured pow er l eve l s ofco l umn 2. The temperatures in c o l u m n 4 are f rom athermocouple (TC) imbedded in the edge o f a thin meta l d i sk inthe varis tor s tack. The temperatures in c o l u m n 5 are f rom thes imulat ion ( see co lumn 4, Table 1 for a part ial l ist). The largestd i f fe rence between the s imu la ti on tempera ture ( co l um n 5) andthe TC tempera ture ( co l um n 4) i s 3 "C or about 1.8 percent.The graphical compar isons in Fig. 6. indicate good agreementamong the th ree m ethods .Another par t o f the va l i da t ion s tudy wa s a compar i son o f themax imu m computed tempera ture o f the hous ing wa l l with theva lue f rom a m ax imum tempera ture i nd i c i ta t i ng s t r i p a t tachedto the i ns ide wa l l of the hou s ing dur ing the test . In he presentexample, th e temperature s tr ip recorded a ma ximu m valueb e t w e e n 7 7 "C a n d 82 "C whi ch is cons is tent with the largestvalue (78.9 "C) in colum n 6 of Table 1.

In the present case, the po we r t ransfer across the ai r gap issevera l t imes m ore than the losses in the var is tors dur ingthe MCO V per i od ( compare va lues in co lumn No. 2 andco lumn No. 3 a t t imes > 220 s n Table 1 ) and the var is tor

Compar isons Of Resul tsThe va l i da t ion tes ts s ta r t by app l yi ng an overvo l tage tha tdevelops a constant input po we r for a per iod of t ime suf f ic ientto reach a selected var is tor temperature, e.g., 19 9 "C from an


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311(column 2) f i rs t decreases and th en increaseswith a net changeof 2W. The output f rom the s imulat ion indicates cont inuousincreases in var is tor power loss ( co l umn 3) nd temperature(column 6). here is a relat ively constant pow er t ransfer in theai r gap (column 4).

TABLE a - TH-AL ANCE OF HGH LOSS VARISTORS

II IITAU 2 - m i VALUES

FOR THE VWDATlON OF TdAe I

aec Power, W Regrea. Thrmocpl. Simul.270 . 29.28 20 0 188 197

Time. I Varistor VARISTOR TEMPERATURES,*C

7 208001200

18.38 17 8 179 18213.84 172 174 17711.11 183 188 1898.497.27 164

167 168161 163

210024002700

2 T e G e r a t u r e s f r o m T a b l e 2 .I I I I I

7.27 147 147 1488.87 144 142 1426.88 139 137 137

mE 2 2 0g 19E 3, 16

1 3 0LE 1 0 0 6 12 18 24 3T i m e , S e cFig. 6 Compar ison of three temperature determinat ionsdur ing 40 minutes of recovery at MCOV.temperatures cont inual ly decrease. A n interesting s i tuat ionar ises whe n the p ow er t ransfer across the ai r gap is less thanor equa l to the power loss in the varistors. This case isdiscussed next.A Thermal Stabilitv ADDliCatiOn

The condi t ions requi red for thermal s tabi l i ty wereinvest igated us ing var is tors with di f ferent levels of powerlosses characterized as "high" and "normal". Each type ofvar is tor wa s subjected to a heat ing per iod fol low ed by a per iodat MC OV s imilar to the f i rs t s tudy. Opposi te resul ts wereobtained in t h e t w o c a s es a n d t h is l a d t o a statement of thenecessary and suf f ic ient condi t ions for thermal s tabi l i ty .

Case 1 - Hiah Loss Varistors:

Varistor

206 20088 204 200 II

420 I y I I ,: I 204 201640 204 202

86 91 206 20300 103

780 109 208 208840 113 113 82 207 207

The three curves in Fig. 6 sho w the complex behavior of thethermal system in th is quas i -s table s ituat ion. The upper curvein Fig. 6 show s the measured power loss decreases for about3 min, remains relatively constant f o r about 2 min and thenincreases. The power loss f rom the s imulat ion (middle curve) ,which, as prev ious ly discussed, is not programme d to exact lydupl icate the varistor 's loss characteristics r ight after a statechange, increases f rom a beginning levelo f 84 W and coinc ideswith the m easured power loss curve af ter about 14 min. Thea ir gap pow er (bo t tom curve) i s a lways be low the loss curvesa t a relatively constant leve l of about 81 W. These conditionsresult in increasing varistor temperature as i nd i ca ted b y thecurves in Fig. 7 and thus , the sys tem i s unstab le w hen thevaristor losses exceed power transfer across the air gap.

P o w e r V a l u e s f r o m T a b l e 31 5 0 I I - * - E m p i t i c a l Column 2 ) I I13110

e

g 950 3 1200 3 4 0 48 62 7 6 9 0 0T i m e , S e c

Fig. 6 Power loss and pow er t ransfer curves in an unstablesi tuation.

The cond i ti ons show n in Table 3 x is t af ter heat ing high lossvar is tors for 220 s at 900 W in the thermal mode l and thenreducing the vol tage to MCOV. Dur ing the 10 min per iodcovered by Table 3, he measured power loss in the var is tors


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312

2 340 4 8 0 6 2 0 7 6 0 9 0 0

330420600

Fig. 7 Thermal runaway of high loss varistors during astabi l i ty test .

30.3 83 204 20428.3 80 20 1 20 123.2 73 184 106

Case 2 - Normal Loss Varistors:In the second tes t , the heati ng peri od a t 9 00 W wasex tended 10s or a to ta l t ime o f 23 0 s. This additional heatingensured that the var is tors we re at a higher s tar t ing temperaturethan in the f i rs t case. This made recovery more di f f i cul t andthus, more significant.

TABLE 4 - T H M A L PERFORMANCEOF NORMAL LOSS VARISTORSTime, Power. Watts Varistor Tamp. 'C

Varistor Pur Gap Experiment Simulation

300 33 4 207 206I1 II

900 18.2 64 186 186 ]1200 14.6 66 176 176II II1600 10.8 44 166 161

Temper at ur es f r o m Tab= 4 .2523

0

E- 21;;; 192L4 1 7 0E 15

2 5 3 0 86 119 1 5 2 0 185

Fig. 8 Recovery of normal loss var is tors f rom hightemperatures in a stabi l i ty test .

varistors resulted in the cool ing characteris t ics s how n by thecurves in Fig. 8. Dur ing the 3 0 m in recovery per iod the var is tortemperature decreased and s tabi l i ty w as assured.This analys is leads to the conc lus ion t hat af ter an excurs ionto a h igh temperature, the var is tor temperature wi l l decrease i fthe po wer t ransfer across the ai r gap is greater than the lossesin the varistor.CONCLUSIONS

The thermal behavior of a surge arrester can be s tudied wi t ha s imulat ion mod el that has been descr ibed and val idated. Thes imulat ion approach is useful n nvest igations where knowledg eof internal temperatures and po we r conditions are needed, e.g.,thermal stabi l i ty studies. It wa s shown tha t a f te r a temporaryovervol tage, s tabi l i ty is achieved i f and only i f the powertransfer in the ai r gap exceeds the power loss in the var is tors .W i th normal loss var is tors , recovery f rom temp eratures of 20 0C or higher is possible. How ever, high loss varistors did notrecover f rom a temperature of 20 0 OC. Using this approach, iti s possible to establ ish the highest al lowable temperature forvarious levels of varistor losses.Other appl ications of the simulation techn ique include studiesof tempora ry overvoltage (TOV ) capabi l i ty. Since there is awide range of overvol tage levels and durat ions plus thepossibi l i ty of prior energy duty, a large number of tests areneeded to develop TOV curves. S imulat ions can great ly reducethe amount of test ing that must be done.

REFERENCES[ l ] P. P. Heber t and R. C. Steed, "A High Vol tage BushingTherm al Performance Comp uter Model", IEEE Trans. on PowerApparatus and Systems, Vol . PAS-97, pp. 2219-2224,Nov /Dec 1978.[2] M. V. Lat, "Therma l Properties Of Me tal Oxide SurgeArresters", IEEE Trans. on Power Apparatus and Systems, Vol.[31 J. H. Nicholas and J. Selsing, "High Ampacity Potheads",EPRl Contract RP781 7-1 g. 50, Oct. 1975.[41 H. Grober and S Erk, "Fundamentals of Heat Transfer",New York, M cGraw-H i l l Book Co., Inc. , pp. 316-318, 196 1.161 H. Kraussold, "Wijrmeabgabe von zyl indrisehenFlussigkeitssehichte n bei natis l ieher Konvektion ", ForschungGebiete Ingenieurwesen, 1 934 .[ 6 ] A. I. B r o w n a n d S. M Marco, " Introduct ion to HeatTransfer" , New York, M cGraw-H i l l Book Company, Inc.

PAS- 102, pp. 2194-2203, July 1983.

F. Richard Stockum (SM) rece ived the B.E.E. degre e fro mThe Ohio State Universi ty in 196 0 and the M .S . degree i nmathemat ics f rom the U nivers i ty of Akron in 1 9 8 7 .Mr. Stoc kum has been employed by The Ohio Brass Co.s ince 1960 in a variety of engineering positions: currently, heis the Senior Test Engineer in the high vol tage laboratory .A Registered Professional Engineer in the State of Ohio,Stockum is a member of the IEEE Subcommi t tee on HighVoltage Testing Techniques and the honor society Tau Beta Pi.He is the author or coauthor of four IEEE papers including onegiven the IEEE PES "Prize Winning Paper"award.The measured var is tor losses are shown i n co l umn 2 o fTable 4. Comp ar ison of the losses wi th the ai r gap powertransfer in co lumn 3 shows about 60 W m o r e p o w e r w a srejected than was generated. This net loss of energy f rom the


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313T h e a s s u m p t i o n t h a t a m b i e n t r o o m t e m p e r a t u re w a su s e d fo r t h e e x a m p l e s g i v e n in the paper i s cor rec t . T h e

r e a s on f o r t h i s c h o i c e i s t h e s i m u l a t i o n r e s u l t s a r e co m p a r e dt o l a b o r a to r y t e s t r e s u l t s o n t h e r m a l m o d e l s ( s e e F ig . 1) o rv a l i d a t i o n o f t h e c a l c u la t i o n s. T h e u s u a l p r o c e d u r e f o rt h e s e t e s t s i n c l u d es h e a t i n g t h e t h e r m a l m o d e l in a n o v e nt o a u n i f o r m t e m p e r a t u r e o f 60 OC a n d t h e n t r a n s f e r r i n g t h eu n i t t o a t e s t a r ea w h i c h i s a t r o o m t e m p e r a t u r e ( u su a l lya b o u t 22 OC). T h e r e will a l m o s t a l w a y s b e s o m e i n i t i a lcoo l ing , par t i cu l a r l y a t the ou ts i de o f the hous ing underthese cond i t i ons . Th i s coo l i ng will o f t e n c o n t i n ue f o r s o m ep e r i o d o f t i m e e v e n a f t e r t h e v a r i s t o r s h a v e r e ac h e d h i g ht e m p e r a t u r e s a s c a n b e s e e n in Fig. 3, Fig. 4, a n d t h e l a s tc o l u m n i n T a b l e 1.In s e r v ic e , a w i d e v a r i e t y o f e n v i r o n m e n t a l c o n d i t i o n sc a n e x i s t as s u g g e s t e d b y D r . T h a l l a m a n d m e n t i o n e d in h ep a p e r . T h e h e a t t r a n s f e r c o e f f i c i e n t H) s n o l o n g e r a f i x e dva lue as it i s in the l abora tory . For tunate l y , cons iderab lei n f o r m a t i o n a b o u t t h e s e c o e f f i c i e n t s i s av a i la b l e i nReference 131 a n d p r o b a b l y f r o m o t h e r s o u r c e s . It i s as i m p l e m a t t e r t o i n c o r p o r a te b o t h a va r i a b le H c o e f f i c i e n ta n d d i f f e r e n t a m b i e n t t e m p e r a t u r e s i n t h e c a l c u la t i o n s.

I n t h e t i m e s t e p p e d s o l u t i o n o f t h e p a r t i a l d if f e r e n t ia le q u a t io n , t h e v a l u e o f n e a r l y a ny p a r a m e t e r c a n b e c h a n g e di n e a c h it e r a t i o n . W h e n a b o u n d a r y c o n d i t i o n i s i n v o l v e d asit is in t h i s d i s c u s s i o n , t h e c h a n g e s a r e m a d e in t h ea p p r o p r ia t e b o u n d a r y c o n d i t i o n e q u a t i o n w h i c h i s Eq n . 1 2i n th i s case.

T h u s , i f d e s i re d , s t u d i e s c o u l d b e m a d e t o d e t e r m i n e t h ee f f e c t s o f s o l a r r a d i a ti o n , a m b i e n t t e m p e r a t u r e , a n d w i n dv e l o c it y o n t h e m a x i m u m t e m p e r a t u re o f t h e v a r i s to r s fo rs t e a d y s t a t e a n d t r a n s i e n t c o n d i ti o n s .

Discussion

Rao S. Thallam Salt River Project, Phoenix, Arizona): Theauthors have presented a very useful analytical model for estimatingthe thermal behavior of metal oxide surge arresters. The model isbased on heat flow from the disk to the surrounding medium and tothe porcelain housing. Such model will be useful in the arrest erdesign and for estimating the arrester performance for specificapplications.It appears that in calculating the heat rejected to the atmospherethrough the porcelain surface, the authors assumed that the ambientair temperature is 200 C which is the room temperature. This seemsto be the reason for the strange result in Figure 3 that while the disktemp erature increases, the outside porcelain temperature decreaseswith time. An arrester therma l design is usual1 designed for thedirect sunlight considered. Under those conditions and with energypumped into the disks by applying overvoltage, the outsideporcelain temperature will either stay constant or will slightlyincrease if at all. Is ambient temperature a variable in equations 1 1)and (1 2) in calculating heat rejected to the atmosphere?Manuscript received March 1, 1993

maximum outdoor ambient temperature of 40B C with effect of

F. R. Stockum: I w o u l d l i ke t o t h a n k D r . T h a l la m f o r h i sc o m m e n t s a n d q u e st i o ns o n i m p o r t a n t t o p ic s w h i c h w e r eon l y b r i e f l y covered in t h e p a p e r . I h o p e t h e s e d i s c u s s i o n swill i n d i c a te h o w t h e m o d e l c a n b e u s e f u l i n s e rv i ceapp l i ca t i ons . Manuscript received March 30, 1993.

Simulation of the Nonlinear Thermal Behavior of Metal Oxide Surge

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