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 to ly o u. I t, w oo uul to o oluto o t ou w ow low ol. T to o t ut jto tqu t Nwto-Ro oulto w tt ul tlty ov o wt ovtol to. Futo, t l l wt t tut to u. It lo olv t u-to loo t o oluto o tuto yt. T, w ut oto to t oo lot w tlly ov t ov y u t u o t tto outtol ot o tto. T to l to vl t ult t. Ix T--Dtuto two, Aytl t ou w lo low, Cut jto to L I. INTRODUCTION o low lulto ov ltu t l o ll volt ut o t ow yt. Mto u u-sl, Nwto t oul Nwto-Ro ( t ol oot o otv qu two v t tool o t lo low ly o out y. Mot o t ly v ou o t l oto. Howv, t tuto two ul v low R/X to. I, joty o tuto two ul u to ul lo, yty to l two l ut. T tt o tuto yt ll o tv ow low to. A u o to v ly vlo o t ol. Rtly, ut jto quto v u lo wt o t o ow t quto. t l vlo w oulto o ul t ow yt utlz t Nwto-Ro to tul oot []. T wo l tt t to vy tl t oxtly % tt t t ot xt to. Atolly, t t lty to t t tut to u olv t u-to loo t o oluto o t tuto yt. I, t to w ov to lu FACTS v ot o otoll []. Evtully, t tqu t [] w o to lu out w t oulto []. T t ot llow lu t utl w ou t oulto. T tqu tt ul tlty ov o wt ot ovtol to []-[]. Tu, t ou otvto to ou o t o v o ovt. I t, w t ott t tqu t ltto lot. T, w ut oto to t lot w tlly ov t ov y u u o tto outtol ot o tto. Rult ot o vl tu o ly ou o lo low lot to ul yt o t ol ovt. II. FOUR WIRE OWER FLOW TECHNIUE ASED ON THE CURRENT INJECTION METHOD AND THE NEWTON-RAHSON FORMULATION A vouly tt, t ou o ovt o to olly vlo y ot. Fo ull to o t tqu wll t o o t to []-[]. H, w jut v tt lot to lt t lly w wll ot t to ov t ov tvly y u t u o t tto t out lu t t o t outto. I t to t ut jto quto wtt tul oot ult o 8 yt o quto. T Jo tx oo o 8 8 lo t t tutu o t ol tt tx w xt o u t lt o t o ol lo t to o t oo ol tt tx. T lt o t ol lo ut t vy tto o to t lo ZI ol t t lt lult volt o to o. T olyol lo ol t ott, ott ut ott ow lo ly. I tul oot, olx vlu o volt ut u o t l y oot. Nol 78 X/6/$. 6 IEEE 899 SCE 6
tt tx t oo to oot: j I I Y ji j T lot o t ovtol lo low to w o t ut jto tqu Nwto-Ro oulto uz ollow: St : Itlzto; o lt tt t tl volt o ll o oul qul to t oot o volt. St : Clulto o t ut t o ll o o (-(5. St : Tt o ov; x{ I }< t o to t 7 l o to t xt t. St : Cout t Jo tx o ( o (6 (7. T o ol lo (lt o t o t o (7 ut o to t lo ZI ol t t lt lult volt o to o y u t x xo. St 5: Clult t olx volt t o (. St 6: Ut t olx volt o to t lult t. It t tto out o to t. St 7: t t ult. To t t u, t tv ow to o w tt vl. R to [] [] o o tl. : Colx volt t o, t {,,, } t Ω : St o o tly ot to o : Colx volt t o, {,, } : Nutl olx volt t o ( J J J ( ( J J J ( J ( J ( J ( ( ( ( ( ( t t t t t t t t ( ( ( ( J ( J ( ( ( ( ( ( t t t t t t t t ( ( ( I I I t t t t t t t t ( ( ( I I I t t t t t t t t ( ( (6 III. MODIFYIN THE ALORITHM TO IMROE THE SEED Y REDUCIN THE NUMER OF ITERATIONS AND THE AMOUNT LUS THE TIME OF THE COMUTATIONS T Jo tx, J, t t tutu o t ol tt tx. T vt t utlz t ov Nwto-Ro lot ou to % u o wt tt o t t outo Nwto-Ro ow low []. O t ot t lt o t ol lo o ll o t yt' o ut ut t vy tto o to t lo ZI ol t t lt lult volt o to o w ll o l out o outto t. Ou oluto ovo t vt. Fotutly, u t out o t lulto t t o t lo low outto ot t oly ovt. Futo, t oo oto u t u o totl tto o lo low ol w tl u t outtol ot v o. Ou oto tt ( ( (5 (7 9
vy lo low ol t o tl tto o t vto o ut t o ll o t o ttl (x{ I ut - I vou }<, t Jo tx wo't ut t lt ut Jo wll u tll t o t lo low.. utl x{ I }< ou. I t w v u t o t o t ut t o o to w t o l t lt (, t Jo tx wo t ut. Fu ( t lot o ou o lo low to. t l w ot oly o't t t ult o t lo low ut lo u t out o t lulto t t o t lo low outto qu o ut t Jo. Elly t' t l wt l olt yt w t o o ut t Jo vy t ou. ut t' ot ll; t oo oto lo u t u o t tto to v t ult o vy lo low ol; oqut o t t outtol ot u v o. T u o t t tt y v to t l ult, ol volt lly tll ty t t l vlu w ot l t t tl vlu. R to t x w out tt ult o t uto o volt, t ol lt o t Jo, w ut vy tto o to t volt,. T tt t J - lly tou t lo low t ow. Now t o tl tto w lo o t o to tul ou (, w ou t l w o t lo low, t Jo oxt t l vlu utly ltou t lly lttl ll t t l vlu. Now w t t Jo tx ott, t t vlu lult o volt o J - I ll out t tl t lt u to v t l ult w tto. T oo o ovtol to u u-sl t t volt t ultl y ot ll lt to w lwy x uty [5]. To ulll ou, w o o lt ll w t lo o t o, ut t, ttl t lt, w wo't ut t Jo tx ow. I t wo o w v t t o oot o t o lt,, o o o t ot oot o t o lt,, o t. F.. Flowt o t o lot T oluto ll u to vl o: Ft w oul ot tt y o to t ult o t lo low ol t ut t (I. I tl t, t uto o I vy t t l t o t lo low. So t lo o t vto w u o t o I vto l ly otly tou t lo low t ow o tt t lo o o o to t l ult o t lo low ol. T, w t lo o ll, t l tt I v o vy ll. To, wt t ll I, t t o t vto t Jo o t ult o J - I, (, o ll lt wt o o o t vy ll ut t. I to ult o ov tow t oluto, t volt vto xtly. Tu, vto o t lt o t Jo tx, w t o t volt, o ll. So, ot ut t Jo tx t o t o I. ALIN THE MODIFIED ALORITHM TO TEST SYSTEMS AND COMARIN ITS EFFICIENCY WITH THE CONENTIONAL METHOD To llutt t tlty o ou oo oto, w v l ot t ovtol o lot to ou t two. T t l tt yt t [] o otto o t ovtol tooloy. Fu ( t yt. ou uqul t t lo ul, tolly to t ul, t o to l - w u o. Two ot tt two o u ( ( xo o t t o lt to l. T two two ou w yt v ou t ll o wt uqul. Sl l tto jut o lty. T lo ul t o l - o l -5 7 o yt t o l 5-7, o l 8- o l -5 5 o yt o o. T ot tt two t IEEE o tt [6]; t t 't utl w ou t ul u oly u to t 9
ul lo. W v xut t lot w w lt lvl o lu o.5 MHz C. T u o totl tto, t u o t t o ut t Jo tx t totl t o t lo low outto o t ou tt yt, ovtol o to uz tl (. W v l t o tqu o two o wt o o wt. O ou u o qul o lt ( ot ovtol o to t lo low ult t t o. Tl ( ow t uto t out o ut t Jo tx t o to. Alo t ow tt t u o totl tto. ot o t v l to t v o outtol x o tt t t o t outto u oly y o t oo oto. T vlu o tt ovt. T vlu o t 7 5 o tt yt v v 5% u. TALE I COMARISONS OF THE SEED AND THE COMUTATION TIME ETWEEN THE CONENTIONAL [] AND THE MODIFIED ALORITHMS o tt yt Cov. to 7 o tt yt Cov. to 5 o tt yt Cov. to IEEE o tt Cov. to Nu o t totl tto Nu o t Jo ut T o t lo low ( 88 9 7 9 9 8 8 8 5 9 8 797 85 9 F.. 7-u tt yt F.. -u tt yt F. 5. IEEE -u tt F.. 5-u tt yt. CONCLUSIONS I t, w oo uul to o oluto o t ou w ow low ol. T to o t ut jto tqu t Nwto-Ro oulto w tt ul tlty ov o wt ovtol to w u ow t quto. Futo, t l l wt t tut to u. It lo olv t u-to loo t o oluto o tuto yt. I t to t utl w ou o tly. T ot t tt t Jo tx t t tutu o t ol tt tx. A oto oo o t lot w tlly ov t ov y u t u o t tto outtol ot o tto. Rult ot o vl tu o 9
ly ou o lo low lot to ul yt o t ol ovt. I. AENDIX T lt o t o t o (7 lult o to t lo ZI ol t t lt lult volt o o: ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( II. REFERENCES []. A. N., J. L. R., J. Co,. M. Cot, N. Mt, "T- ow low lulto u t ut jto to", IEEE T. ow yt, vol. 5, o.,. 58-5, My. []. M. Cot, J. L. R., N. Mt, "A ut Nwto- Ro ow low oulto o ut jto", Eltl ow y yt, vol.,. 5-,. [] D. R. R. o, L. R. Aujo, J. L. R.,. A. N., J. Co, "Fou w Nwto-Ro ow low o t ut jto to", o. IEEE ow E Soty ow yt o xoto, vol.,. 9-. []. A. N., J. L. R., J. Co, M.., F.. o, "Iovt t Rtto o u o T- Dtuto ow Flow", IEEE T. ow Dlvy, vol. 9, o.,. 89-896, Al. [5] I. J. Nt, D.. Kot, Mo ow Syt Aly, Mw- Hll, 98. [6] IEEE o tt, IEEE ow E Soty, Dtuto Syt Aly Suott. [Ol]. Avll: tt:// 9