Nonlinear Eddy Current NDE and Theory Based on Vector Preisach Model in Rayleigh Regime

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Rodney Shannon Owens
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1 Nol Edd Cut NE d To sd o Vto s Modl lg g Noo Nkgw Ct fo Nodstutv Evluto ow Stt vst As ow 5 SA Astt. Ts sts ol to of dd ut NE sos ll to EC suts volvg fogt tls. T to tts t olt t t lowst otvl od. At ts lowst od t wll-kow lg lto sts dsg t o-l stt - lto t tt t s sttd to t s w t d flds udtol d lll to ot. ototl EC NE ols qu tso of lg s foul fo vto-vlud d flds. T s vto s odl d ots out tt t vto tso of t lg lto s otl t o of ostt wgt futo. T gv s-lg odl s l to lt o lss toug w EC ols solul o oto. wods: Edd Cut; Nol To; s-lg Modl ACS: 8.7.E 8.4.s d NTOCTON t s wll kow tt d sgls olltd dd ut (EC) stuts t olt w ld to fogt sls. T d () s sstll t ol-vlud to tw t outut voltg V d t dv ut d sts -ddt w t sto sst s l. A fogt sl tu () to -ddt toug ts ol sos to t tto fld. od to solt ts ol sos fo t sgl w odut d suts fo vg ut tst d t followg qutt dfd s () w s t u og ll. T qutt td olt dto us t vss fo l tls wl og o-vsg d -ddt fo ol tls. At NE C.C.. Lo d t st uto dosttd sussful ltos of t ol dd ut (EC) NE to suf l ttos of fogt sls w t olt dto ws sow to olt stogl wt t sl odtos of tst. Sfll t tod ws dosttd to fftv ot o s-dd stl sls d o g-ttu-odd N-3Al llo sls. To udstd t EC oo qutttvl t s NE tlk std slfd EC to sd o ufo dt fld d ld lf s. gl Mwll s qutos odutg du d E E ()

2 w do ot los tslvs utl osttutv - lto s gv tw t gt flu dst d t gt fld. W t du s o-gt l tl t l ltos olds. Fo fous tls t s ddtol ol t wt w t osttutv lto ds. (3) Fo t s of u-dtol ufo flds d w t fld s wk t sts t ol stss lto of lg s w ds [] t t t w t fld (t) swgs fo to d w t [] sg osods to t u [low] of t stss loo. lg s olt ostt s tl t ust s t tl lt s. T ol of ufo dt fld tg o ld lf s tl ws solvd t t lowst otvl od of olt t us of o oto. T odl lultos odud t tl sults of t olt dto qulttvl. Sussful EC odl dvlot fo t s dt tto ol otvtd us to gl t EC odl to od lss of EC NE ols. ft lg ot of lst EC stos volvs ft-od os w oft t ol soss du to t ft olt. owv t lg foul (4) s ll to gl EC ols w t flds t ufo o u-dtol. t s tus ss to fd vto tso of t lg foul (4). Ts ots out tt t vto s odl wt ostt wgt futo ovds t dd vto tso. Moov t sows tt t s ossl to lult t tdd foul fo vto-vlud o oto s ut. Followg ts toduto t t sto sts ol - lto t t lowst od of olt ts of t vto s-lg foul d ts o lss. T susqut sto sows ow to us t dg sult fo solvg t EC ol o oto. T fout sto woks out t EC ol ldll st got fo otss d sts ul dtos of t ol dto du to log od wt s l fo dwg svl olusos. ESAC-ALEG NONEA STEESS FOMLA Ts sto sts dvto of ol stss - lto à l lg s w s vld t t lowst otvl od of olt (lg g) d ll fo vto-vlud flds. W lso odut o lss of t sultg foul. Etso of lg s Foul to Two sos T fst d tl st s to td t lg ol - foul (4) to ult-dsol foul vld t lg g. Fo ts uos w stt wt t sl s foul [345] t t w t (5) dd w d w() l oto d wgt futo stvl. Ts s oologl odl of stss d wl g dstv d fll t qus ss ut to dt t wgt futo. t tud out tt ts dtto s stgtfowd t lg g.. t lg lto (4) follows Eq. (5) uo lt tgto w t wgt futo s st to ostt sfll w. W sll us ts ft s gudg l d dv t tso of u-dtol lg s foul to ultdsol foul sttg fo t vto vso of t s odl d sttg ts wgt futo to ostt. wt follows w wok wt t vso of t s-lg foul tus dvd fo t vto s odl [5] w ds (4)

3 t t dd d (6) w os s. T wgt s tk to ostt wl t ottll -ddt s of tl soto. o Alss of Vto s Modl T sod ott st s to odut o lss of t ol - ltos. T u-dtol sult ws kow l [.g. f. ].. w t dt fld udgos o osllto t os t wt fqu t outut fld t s lultd toug t lg foul (4) ts of Fou ss t (7) 4 t odd T osodg o lss - d out losd fo s wll. Cosd t ut o oto of t fo t ost t os t (8) w t t of t vto ts lltl lous. W ts oto s std to t s-lg foul (6) wt ostt wgt ν t outut fld lultd to t fo W t t t. (9) odd t oto dus to o osllto wl t s-lg foul lds gl t flds ssd ts of ft su of t F ;. Eltl 8 l Guss got futo w os k k 3 s s k 3 F k ;! k! s d w s s os. SOLTON OCEE VA ON AOXMATON () Gv t tod to lult t - lto w od to solv Mwll s qutos () fo fqu t lowst od of olt t us of o oto. Sfll w slt t totl fld to t l d ol ts odg to Eq. (3) d st Eq. () to

4 E E T soluto oss o oto llows us to tt t. (). t s gt ut sou dd t soluto oss ods s follows: () Tu t ol t off d lult t t od flds fo gv st of ol uts s usul l ol. () st t sultg -t od fld to t s-lg foul d lult t -st od. (3) Clult t -st od flds s t sod l ol wt usd s t gt ut sou. (4) Fll lult t totl fld s su of t -t d -st od flds d/o t -t d -st od ds d stvl s dd. Fo l t olt dto lultd s wt ou oto. dv () NONEA EC MOELNG FO LAEE CLNCAL O ts sto w wll s t soluto odu dsd t dg sto fo ototl EC ol.. ft lg ols woud oud ldl od of ft lgt. Sfll osdd s ld ldl od osstg of l fod oud o w t o s d of ol tl (.g. stl) wl t l s d of l tl (.g. dd stl tt s otl l) [FGE ]. Col () () ft lgt od V FGE. llustto of t odl ofguto wt ul ol(s) lg ld ldl od w t o go s d of ol tl wl t l go s d of l tl. Flds t Ld Cld W fst ot t t od flds ft sttg =. T ol dus to t wll-kow l ol [.g. f. 6] d t fld solutos wtt ts of Fou oots t l dto. Eltl t flds ssd ts of t odfd ssl futos s

5 d (3) (3) (3) (3d) w w todud svl ottos: k t. (4) T sso fo t -t od d otd sll. W t l t o lss of t dg sto d out t fst od ol fld fo t -t od fld toug t s-lg foul (). T sults tsfod k to t Fou s fo t susqut us. W t ot t fst od solutos solvg t sod l ol usg s t sou ts t. T fst od suf fld d t d otd odgl. t s otto t d E E d (5) (5) d (5) (5d) Nolt dto: Coutd Fo t ttl ssos t dg susto w out ds t -t d fst ods d t olt dto odg to Eq. (). t s stgtfowd ul tsk o w stl t outto soltg otl vos fo t odfd ssl futos [7]. W v os s dd l tto ol s l d outd t olt dto s t futo of ltv dv ut tst. To sf t outto s d out fo t u

6 Nolt dto ut tst of. A d fo t s dts gg tw d 4 wt t ts tultd TALE low. FGE sts tl sult outd t 3. TALE ). ts d t vlus usd t l outto. t T t Vl t Vlu v Col dus 6-8 [] v Col Lgt l [] v Col # Tus v Col dus [] v Col Lgt l [] v Col # Tus Cld dt 3 [] tl lt s s 6.6 Codutvt s s 7.5 [%ACS] tl lt o o.5 Codutvt s o 8.86 [%ACS] Nolt o 5.93 [/O].6%.5% ().4% ().3% ().% (d).% ().% v tst [d] Co ol 3 4 FGE. Coutd olt dto lottd gst t dv ut tst to / t d ut fo t s dts of () (o ol) () () (d) 3 d () 4 dv t 3. CONCLSONS oluso t s sow tt t vto s odl ovds ss fo foultg ol dd ut (EC) odlg. Sfll w v foud tso of lg s - lto to vto-vlud ol stss foul t t lowst otvl od of olt w of oosg ostt wgt futo t vto s odl. Sod w v sow ow to lult t sultg vto - lto ltl fo t ut fld udgog vto o oto d otd ltl ssos of t outut ol fld ssd ts of ft su of got futos. Td w v std soluto odu of t EC ol o oto solvg l ols tw t t t d st ods of olt wl usg t - lto to lk t t d st od solutos. Fout w v ltl sd t soluto odu v o oto fo ld ld ol dtg t olt dto sg fo log s-dd od. t sould kd tt dtld ttl dstos dd fo t olt osto of ts EC odlg tod t tsk g dfd to ulto lsw.

7 ACNOWLEGMENTS T uto wss to ddt ts to t o of t lt ofsso old O. Toso wo s t ld t d sou of ougt fo. Ts wok ws suotd t NSF dust/vst Cootv s og of t Ct fo Nodstutv Evluto t ow Stt vst. EFEENCES. Lod lg los. Mg (887)... M. oot Fogts Nw ok: V Nostd F. s tsft fü sk (935) Mgo EEE Ts. Mg (986) Mgo Mttl Modls of stss d T Altos Nw ok: Elsv C. V. odd d W. E. ds J. Al. s (968). 7..E. Aos "A Suout kg fo ssl Futos of Col Agut d Nogtv Od" Sd Ntol Loto ot SAN85-8 M 985.

Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks

Three Phase Asymmetrical Load Flow for Four-Wire Distribution Networks T Aytl Lo Flow o Fou-W Dtuto Ntwo M. Mo *, A. M. Dy. M. A Dtt o Eltl E, A Uvty o Toloy Hz Av., T 59, I * El: o8@yoo.o Att-- Mjoty o tuto two ul u to ul lo, yty to l two l ut. T tt o tuto yt ult y o ovt