RECHARGING LARGE CAPACITOR BANKS. H. R. Shaylor Brookhaven National Laboratory

Transcription

1 RECHARGING LARGE CAPACIOR BANKS H. R. Shaylor Brookhaven Naional Laboraory he power bill for a large lina suh as ha proposed for he AGS onversion would be in he order of $100, 000 per year. his is for an 0. 6 mse pulse lengh and.30 pps, and an 8,000 hour year. I also assumes fairly high effiieny in he rf power sages. A ypial ".meson faory" would involve a power bill en imes as grea. A simple mehod of reharging a modulaor ondenser bank or sorage line from zero vols o a given volage would be o use a sandard d power supply and a series resisane o limi he urren. Suh a irui would dissipae as muh energy in he resisane as i supplied o he ondenser bank, and he power bill would hen be doubled. Clearly hen i is very worhwhile o design ondenser reharging iruis wih view o ahieving a high reharge effiieny, any improvemen of a few pel;" en or more will be signifian. he modulaor energy sorage sysem usually akes he form e iher of a delay line or a single ap13.ior bank. Afer onsidering he alernaives i was deided ha he.single apaior bank is he mos suiable alernaive when (a) he pulse lengh was oo long o permi he use of a pulse ransformer, and (b) i was neessary o modul13.e he d plae volage Oll he rf amplifier in order o onrol he rf a mpliude in he lina ank, () he rf power amplifier was some sor of riode wih a de plae vola ge around 30 kv. he reasons for his hoie will no be enumeraed he r e. Furher praial onsideraions show ha he opimum hoie of apaior bank size is no one whih sores wiee he energy delivered o he load, alhough his is he smalles bank in erms of energy sored. A apaior bank ha droops abou 100/0 during he disharge, and sores abou five imes he energy delivered o he load is a beer hoie. Reharge Analysis he basi irui upon whih he analysis has been made is shown in he irui diagram: 50

2 swih losed a '" 0 R Power Eo Supply L i C e - E ~ El 1 Cirui Diagram he ondenser is disharged by he load irui (no shown) o VO:8.g:e E' he reharge is effeed by losing he swih a ime ": O. A VElriable C1Jrren i flows and he ondenser volage e rises from E a :.: 0 o E1 a1; ". A ime he urren now is inerruped eiher by opening be s\~fihs or by some oher means. he poviler supply volage is Eo' 3.nd he energy dissipaed in he irui from ime 0 o ime is DR' Arrangemen of formula In order o show ha he analysis is df;penden only upon he relaive' values of L, C and R, he resuls have been normalized. he apaior urren i beomes a dimensionless quaniy i n i ---- (El - E) C 51

3 he apaior volage e beomes n = e and he energy dissipaed in he resisane U R beom,~s N = R (E - E ) o 1 C he effiieny of he reharging irui an be obaine,direly from NR sine Energy dissipaed Energy supplied o apaior N R hus for a apaior wih 100/0 volage droop during disharge, an NR value of 1 will gi.ve a 50/0 loss. he irui has been analyzed for he values of energy dissipaed in R (N R ), he maximum apaior volage (N C ), he peak harging urren. (N m ), and he harging urren a he end of he reharge period (N). he laer urren is signifian sine i deermines he.rae. Of hange of ondenser volage a swih off, and hene he ime olerane. requiremens for a given volage auray. he analysis falls naurally ino wo ases, one when Q is greaer han one-half, and he oher when i is less. In he Q > 1/ ase, were i no for he P9wer supply reifiers, he apaior.volage would be a damped periodi funion of ime; however, he derease in apaior volage afer he firs peak is aompanied by a reversal ofllie. harging urren, and he reifiers u off a his poin.leaving he. apaior harged o he p eak volage. hus, if he irui is no inerruped by he swih, he r e eharge period will be one-half of he ringing period, he urren a his ime will be zero, and he apapior volage will be greaer han (or in he limi equal o) he reharge volag'e. he formula relaing o he Q :> 1/ ase assumes ha he harge is erminaed by urren reversal a h.e end of he firs half yle, and shown in he firs summary able. 5

4 SUMMARY 1 >- -. ~R - -- LC 4L n..!!..-(.l+ 1 ) i N p - P e sin " i '" N.r == 0 1 N (1 n "" - - e e - P 1 (os - +- P ) sin ") e - E - 1 E E E1 - E N., E - E 0 '" P e NR...L (1 - N e - P ) (E - E ) C U = 1 N R R 53

5 Here P is a funion of Q, and is defined as half he naural periodiiy of he irui. N' he value of ni a ime is zero. N is he reharge volage raio. Boh urren and volage are damped rigonomerial funions of ime. NR is a funion of P (and hene Q) only. In he Q < 1/ ase he apaior volage rises asympoially owards he reharging volage,. so he reharge period is assumed o be erminaed afer ime by opening he swih. hus here is a finie urren flowing a ime and he final apaior volage is always less han he reharge volage. he formula relaing o he Q < 1/ ase is shown in he seond summary able. In his ase he reharge period is no uniquely deermined by Q and C as in he Q ::. 1/ ase, so he period has o be speified. I has been normalized (somewha arbirarily) as he quaniy V = L. S is RC a. funion of Q, hosen so as o avoid he use of omplex noaion. he oher symbols used are similar o he Q ::. 1/ ase. N may be found by puing " in he ni formula.. he urren and volage are exponenial funions of ime, and NR is a funion of Q and. Reharging Power Supply A praial power supply wou1d no deliver a smooh de volage as assumed in he analysis, bu a reified n volage. However, suh a supply would be a leas six phase and he ripple would be less han 150/0, so resuls alulaed for he de ase would be reasonably aurae. he power supply would also have a finie inernal impedane.(generally induive) and his impedane will, of ourse, add o a ny exernal resisane and induane in he irui. he exa relaionship of he powe r supply ransformer leakage induane and resisane o hose values found as soure impedane in a omplee muliphase power supply is no lear, bu i is probable ha a resisane ha would aoun for he supply d regulaion in series wih he leakage induane per reifie r phase would give he.orre value of soure impedane. 54

6 SUMMARY Q=!J1 <! R C V.. - RC = J 1-4Q V n i.. N S -V (e(l+s) -V _ e(1-s) ) i - -V 1 (1-S) ne -; [1 + (5-1) } -V 1 e (1+S)] (- + 1) - S -4V (1-S) (1 - S) } + S ] 55

7 Evaluaion of Resuls Sine he evaluaion of formula by inspeion is a diffiul menal exerise, i was deided o program he Brookhaven ompuer o plo ou he resuls. Copies of hese resuls are shown in he nex few diagrams. Figure 1 shows he variaion of urren and volage wih ime for Q values of O. 7 and 5. he Q = 5 ase shows he urren as a sine urve and he volage as a osine urve. he Q = 0.7 ase shows heavily damped versions of he same urves. Figure shows N ' he reharge volage raio; N m, he peak o average urren raio; and N R, he loss faor; varying wih Q for he Q. > 1/ ase. For he Q < 1/ ase, Figures 3, 4 and 5 show he variaio.n of urren wih ime. hey show Q values of O. 5 and 0. 1, and /Re values of O. 5, 1 and 3. Noe ha he definiion of is quie differen from ha in he Q > 1/ Case, so he values of i in he wo ases have no orrespondene. I will be seen ha as he reharge period -L... is made RC shorer, he Q = 0.1 urve shapes a.pproah he simple.rc exponenials. For he Q < 1/ ase he values of No N' NR and N m a re shown as :(unions of IRC raher han Q, sine he r e harge period is he more signifian para meer. Figure 6 shows N and N' a.nd Figure 7 shows NR and N m.. I may be seen from he plos ha he dissipaion value NR is always greaer han one for Q<1/, and less han one for Q > 1/. wofurher poins may be seen in he Q > 1/ ase; wih inreasing Q.he dissipaion dereases oward zero, and he maximum ur ren during he r e harge p er i od 1m dereases oward /; his would seem o indiae ha he highes aainable Q is he ideal. siuaion. However, wih high Q values he NC raio ends oward, and his leads o an unsable reharge volage in ha when he a.paior bank is disharged o an unusually low vola ge (e. g. beause of a parj.al breakdown) hen he bank is reharged o a. higher v olage han normal.. In he exreme ase onside r a bank whih normally has a 10% droop and would require a reharge vola.ge E of abou 95% of he maximum apaior volage E 1. If suh a irui w ere Jlisharged o zero volage hen he apaior bank would heoreially reharge o 1. 9 imes he normal m aximum volage, whih ould be very dangerous. A praial ompromise would seem o be a irui designed o give a Q a lile above 0.5, say O. 75. his would give a dissipaion value of 0.9, whih means a power loss of 4. 7% during he reharge of a 10% droop; 56

8 u Z E Z a: Z n, Q-0.7 II /. -/ Y \ FIG No NR Q FIG. - a-o.s RC -0.5 FIG.3 I Q-05 RC _I Q-Ol RC or 05 FIG.4 Proeedings of he 1964 Linear Aeleraor Conferene, Madison, Wisonsin, USA 57

9 ol ~ ~~~~ 05 FIG u z 06 I- z FIG 6 R 10 9 Q' Q 0.1 N Q 0.5 ol-----~r~----~~----~ ~----~5 RC FIG. 7 58

10 and an NC raio of 1. 06, so under ondiions of omplee disharge he ondenser volage would rise only 6% higher han normal. he maximv m urren for suh a irui would be 1. 9 ime s he average urren and he irui would auomaially u off a zero urren when he reharge is finished. Alhough he danger of over-voling he apaiors is now removed, here would sill be he problem of high reharge urren in he even of reharging from z.ero volage, in whih ase he maximum urren would end o rise o 19 imes he normal urren. he reharge onrol equipmen would have o have some provision for reduing suh urren in he even of a flashover or rowbar, and also a sar''"up imes. here seems o be no advanage in using he Q < 1/ ase, exep on he grounds of simpliiy, or perhaps o obain a lower maximum reharge urren a he expense of greaer losses. I is of ineres o noe ha for he ase of Q < 1/ and IRC < 1, NR inreases wih inreasing Q. his is beause when he swih is opened wih a finie urren flowing, hen he LI energy in he induane a ha ime is dissipaed (presumably in he swihing ar) and hus is los o he irui. When /RC is less han one" he raio of energy sored in he induane o ha dissipaed in he resisane is suh ha inreasing he Q also inrea.ses he oal power loss. Variable Resisa.ne Reharging Mr. J. F. Sheehan of Yale Universiy ha,s suggesed a very ineres-kg alernaive o he LR urren limiing nework. his would replae he LR ombinaion wih a variable R, auomaially onrolled o keep he reharge urren onsan. he variable resisane would ake he form of a hard ube. he mos useful ase of his irui would be when.he reharge volage Eo is equal o he maximum volage El, and so he minimum variable resisane value is zero. his gh'e:s a dissipaion value NR of 1. 0, so he power loss would be similar o he Q '" 0.75 ase: oulined above. he maximum urren raio N m is now he ideal va1ue of 1. 0, he N r _ raio is 1. 0 and he urren a hf: end of he harge is zero sine here is no way for he apaior volage o rise above he reharge volage. Provided he urren onrolling aion is auomai., he only effe of reharging a fully disharged bank would be o prolong he reharge period. he main disadvanage would be he omplexiy of suh a irui as ompared wih a passive LR ombinaion. 59

11 Coninuousl;y Reharged Capaior S;ysems Some onsideraion has been gi.ven o he ase whih is ofen used; when reharge urren is no zero a he sar of he reharge period. his would our if he swih.was omied in he Q < 1/ ase, or if he disharge repeiion rae was greaer han wie he ringing frequeny in he. Q > 1/ ase. An analysis of he reharge urren in he laer ase has been arried ou. he arrangemen presens he diffiuly ha eah reharge yle depends upon he previous one, and here is no obvious indiaion as o how he urren a he sar of eah reharge period will onverge upon a seady value. Furhermore, his seady sae will be upse by any irregulariy in he pulsing rae. I is onsidered hen ha unless used wih a Q < 1./ and a large value of IRC, in whih ase he iniial reharge urren will be very small, he. oninuous reharge sysem is likely o give less sable operaion han one in whih he reharge urren is zero a he sar of he reharge yle. here would seem o be no real advanage of a oninuous reharge irui over one in whih Q is a lile greaer h"n 1/, and he reharge erminaed by urren reversal. Conlusions he opimum des.i.gn of a irui for reharging ondenser banks of he ype desribed above, would be one wih a Q value abou If an aive irui is aepable, hen a onsan urren irui would be preferable. I seems ha a oninuously reharged sysem would be le!3s sable han one in whih he reharge ime is onrolled. WHEELER: If you look a he figure here, 1m = 1. 9, and make a quik esimae of he peak power demand for a large insallaion, i urns ou o be of he order of 60 MW for he insananeous demand. his is r efleed ino he power line and he power ompanies will no bevery happy abou i. For his reason alone I hink i may b e neessary o go o a onsan urren- harging sysem. 530