PERFORMACE PREDICTIO OF EERGY EFFICIET PERMAET SPLIT CAPACITOR www.jee.ro RU SIGLE PHASE IDUCTIO MOTOR ijy Kur GHIAL Llit Mohn SAII Jsbir Singh SAII 3 Electricl Engineering Deprtent, tionl Institute of Technology, Kurukshetr, Indi. Eil: vijyghil@yhoo.co.in Electricl Engineering Deprtent, tionl Institute of Technology, Kurukshetr, Indi. Eil: lsini@gil.co 3 Electricl Engineering Deprtent, Deenbndhu Chhotu R University of Science & Technology, Murthl, Sonept, Indi. Eil: jssin@rediffil.co Abstrct: The perfornce of pernent-split cpcitor-run singlephse induction otor cn be evluted fro the equivlent circuit preters, which re derived fro dc test, no-lod test, lockedrotor test nd the winding rtio test. In the present work, the conventionl turns rtio hs been replced with coputed coplex voltge rtio for perfornce prediction of the c voltge controller fed cpcitor-run otor, t different firing ngles of tric. Two different energy efficient experientl schees, nely trditionl phse ngle control schee (with c voltge controller in series with both in nd uxiliry windings) nd dvnced phse ngle control schee (with c voltge controller in series with in winding lone), re used for perfornce observtion of the otor. It is observed tht for both the schees, the proposed perfornce prediction ethod gives perfornce vribles vlues closer to the experientl observtions in coprison to those obtined using the conventionl perfornce prediction ethods. Further, it is lso deonstrted tht lthough the conventionl preter estition nd perfornce prediction ethods did not show superiority of the dvnced c voltge control schee over the trditionl one, yet the proposed ethod does so. Keywords: AC Motors, Cpcitor otors, Equivlent circuits, Induction otors, Preter estition, Power seiconductor switches.. ITRODUCTIO Single phse otors re sll otors, ostly built in the frctionl horse power rnge. These types of otors re used for ny types of equipent in hoes, offices, shops nd fctories. In fct, the nuber of single-phse (frctionl horsepower) otors in use tody fr exceeds the nuber of integrl horsepower otors of ll types. The IEEE Stndrd 4-98 [] nd 4- [] provide the testing ethods for Single Phse Induction Motor (SPIM), but these do not provide ethod of extrcting the preters of Pernent- Split Cpcitor-Run Single-Phse Induction Motor (PSCRSPIM). For preter extrction of SPIM, except for cpcitor run otor, the no-lod nd locked-rotor tests re de with the uxiliry winding kept open. In cpcitor-run otor, however, uxiliry winding preters lso contribute in these test results even though rest of the procedure, to find the in nd uxiliry winding preters, reins the se s tht of plin SPIM [3]. The conventionl ethods [4-6] clculte the perfornce vribles by tking turns rtio of SPIM s sclr quntity, which is esured using the winding rtio test. However, the resulting perfornce vribles (line current, power fctor nd power) give error vis--vis experientl vlues, which in turn, fllciously copute the efficiency of the PSCRSPIM. Different schees hve been proposed to find out the equivlent circuit preters nd perfornce vribles for perfornce prediction of SPIM [4-3]. A detiled review of induction otor preter estition techniques with experientl nd siultion illustrtions, relted to online nd offline preter estition techniques hs been reported in [7]. Soe reserchers hve proposed online preter estition techniques such s lest en squre technique, prticle sw optiiztion technique, verging nlysis technique, eleentry lyer ethod, direct-online strting nd nturl slowdown tests etc.[8-3], while others hve proposed offline preter extrction ethods such s vector constructing ethod, vector control schee using offline geneticlgorith routine, Lypunov function bsed stte observer, direct torque-controlled spce-vector-odulted ethod, extrpoltive, eqution error nd generlized identifiction ethod etc.[4-7]. Although vrious offline preter-estition techniques hve been proposed for single- nd three-phse IMs s becuse the offline identifiction is typiclly esier nd ore relible thn online ethods, yet little work hs been reported for the perfornce prediction of PSCRSPIM [8-3]. This pper is n dvnceent of the previous work [3] in which the jor thrust ws on proposing new coplex turn rtio (ned s CCR) which ws used to estite the preter nd hence the perfornce vribles. However, the present pper lys ephsis on evlution of efficiency of PSCRSPIM by dopting two different energy efficient experientl schees nd using the proposed ethodology. The ppliction of the proposed theory is bsed on the ssuption tht SPIM cn be represented s n idel trnsforer, with such trnsfortion rtio tht for which voltges re trnsfored in the direct rtio of turns, currents in the inverse rtio nd ipednces in direct rtio squred; power nd volt peres re unchnged. In this pper, in contrst to the conventionl pproch, the preters of in nd uxiliry windings re extrcted individully nd then using the Coputed Coplex oltge Rtio (CCR), the equivlent circuit of PSCRSPIM is developed. The perfornce vribles of the otor re then coputed t different firing ngles of tric. For coprtive study, two energy efficient experientl schees re pplied on PSCRSPIM, one of which is conventionl phse ngle control schee nd the other one is n dvnced phse ngle control schee. The coputed efficiency of the otor for the dvnced schee is shown to be better only using the proposed perfornce prediction ethod.
. PERMAET-SPLIT CAPACITOR-RU SIGLE-PHASE IDUCTIO MOTOR The PSCRSPIM hs two windings, one is known s in winding nd the other is clled uxiliry winding, s shown in Fig.. A cpcitor is connected in series with the uxiliry winding nd both the windings re connected in prllel with n AC supply source. These windings re geoetriclly displced in such wy tht the gnetic fields produced in spce re 9 prt. The gnetic field produced by the otor, tht pulstes in tie, but, is sttionry in spce, cn be resolved into two revolving gnetic fields tht re equl in gnitude, but, revolve synchronously in opposite directions. The induced e..f.s in the rotor due to the two revolving fields re in opposition to ech other. Fig.. Schetic representtion of PSCRSPIM. The slip in either forwrd or bckwrd brnches of the rotor is se t stndstill. Therefore, the strting torque developed by ech revolving field is the se nd the net torque developed by the otor is zero nd hence SPIM is not self-strting. An induction otor cn be de self strting, if the two windings re plced in spce qudrture nd re connected in prllel to single phse source, but, ipednces of two windings re de unequl to produce out-of-phse currents which, in turn, set up net unblnced revolving field. 3. Proposed Perfornce Estition of PSCRSPIM In the forl prctice, for perfornce prediction of the PSCRSPIM, the preters of the in winding re first coputed nd then in winding referred uxiliry winding preters re coputed using the turns rtio. However, in the present work, for coputtion of efficiency of the otor, the totl input ipednces of both the windings re coputed seprtely using the no-lod nd locked rotor tests nd using the coputed coplex voltge rtio (CCR) insted of the conventionl turns rtio. The conventionl sclr turns rtio,, in ters of constnt voltge trnsfortion rtio is given by: I priry sec ondry = = = () I sec ondry Min priry Rotor Auxiliry where, nd re the no. of turns of in nd uxiliry windings, respectively. C For the coplex trnsfortion rtio, the in www.jee.ro nd uxiliry windings self induced e..f.s, ( Ec nd E c ) t rted voltge, cn be coputed s [3]: = I () ( ) ( ) Ec Z ins Ec I Z ins = (3) where, Z ins, Z ins re the totl input ipednces nd I, I re the phsor currents of the in nd uxiliry winding equivlent circuits, respectively. As on ppliction of rted voltge on the one winding, such e..f. is supposed to be induced cross the other winding, which kes the currents of two windings in inverse rtio of turns, therefore, equtions () nd (3) cn be rewritten s [3]: I Ec = ( Z ins ) (4) E ( ) I = (5) c Z ins The coputed voltge induced cross the one winding would then be in the direct rtio of rted voltge pplied cross the other winding. The turns rtio in ters of coplex voltge trnsfortion rtio thus cn be obtined s: E = c = (6) = (7) = Ec where, nd re line voltges pplied to in nd uxiliry winding, respectively. Multiplying equtions (6) nd (7), the coputed coplex voltge rtio CCR,, is thus given by [3]: E c = (8) Ec The sclr turns rtio,, will now be replced with this observed coplex voltge rtio,, tered s CCR. This trnsfortion rtio is then used for developing the coplete equivlent circuit s shown in Fig. nd for evluting the perfornce vribles nd hence the efficiency of PSCRSPIM. The stedy stte theticl odel of the otor consists of the syste of equtions which govern its stedy stte opertion under ll operting conditions. As shown in Fig., the following equtions cn be written [3]: E f Eb = IZs E f Eb j j (9) = I Z Z E E je je () ( s c) f b f b where: E = Z I () f b f b E = Z I () E f = Z I (3) f
Eb = ZbI (4) The in nd uxiliry winding voltges re clculted by the ppliction of Kirchhoff s voltge lw to the equivlent circuit. Substituting fro equtions ()-(4) into equtions (9) nd () yields: = Z Z Z I j Z Z I (5) ( s f b ) ( f b ) j( Z f Z b ) I ( Z s Z c ( Z f Z b ) I = (6) Min nd uxiliry winding currents ( I nd I ) cn be obtined by solving (5), (6) s follows: ( Z Z) I = (7) Z Z Z Z I ( Z Z ) = (8) ZZ ZZ R s j X s j X / j X / Fig.. Proposed equivlent circuit of PSCRSPIM where, Z, Z, Z nd Z re coputed s: Z R f j X f = Zs Z f Zb (9) [ Z f Z b ] [ Z f Z b ] Z [ Z Z ] Z = j () Z = j () * = Zs c f b () Z - R b j X b Forwrd brnch R f j X f The line current is coputed s: I L = Re [ I I] (3) On pplying input voltge,, to PSCRSPIM, the power consued by the otor is given by: P in = I L cosθ (4) The power fctor cn be coputed s: pf = cosθ (5) Bckwrd brnch - - - R b j X b R s j X s R c j X j X j X c where, θ, is the power fctor ngle between www.jee.ro the pplied voltge nd the line current. For PSCRSPIM the totl ir gp power is defined s: P= P gf P gb (6) where, P gf nd P gb re forwrd nd bckwrd gp powers nd re expressed s: P = Re( E I je I ) (7) gf f f P = Re( E I je I ) (8) gb b b By inserting (7) nd (8) in to (6), the totl ir gp power cn be obtined s: P = P g I gf I Pgb = ( I I )( R f Rb) ( R R ) sin( θ θ ) f b (9) The developed power is given by: P = S P (3) d ( f ) g The output power is then clculted by subtrcting the rottionl losses, P rot, fro the developed power s follows: Pout = Pd Prot (3) Therefore, the efficiency cn be clculted s: Pout η = (3) P in In this section, coplete equivlent circuit, perfornce vribles including the efficiency of the otor hve been clculted using the CCR. 4. EXPERIMETAL ALIDATIO, RESULTS AD DISCUSSIO In order to verify the theoreticl findings, two PSCRSPIMs, s given in tble, hve been tken for study. The perfornce vribles of otors re coputed using dc, no-lod nd locked rotor test results. Motor Tble : Specifiction of fn otors oltge Power Frequency Rted () (W) (Hz) speed (rp) C (µf) 3 65 5 4.57 3 6 5 4 5. Two different energy efficient experientl schees re shown in Fig. 3() nd 3(b). Fig. 3() is the trditionl wy of phse ngle control by using the tric bsed c voltge controller between the supply voltge nd the otor. An dvnced schee for phse ngle control is depicted in Fig. 3(b), in which the tric bsed c voltge controller is inserted in series with in winding nd the otor uxiliry winding is directly connected to the supply voltge. By vrying the firing ngle of the tric, different voltges re chieved for both the schees. The perfornce vribles (such s current, power nd power fctor) of PSCRSPIMs hve been esured with YOKOGAWA WT 3 Precision power 3
nlyzer nd further the efficiency hs been deduced theoreticlly. The results for current, power nd power fctor re obtined t different firing ngles, using two different energy efficient experientl schees. The experientl results obtined re then copred with conventionl preter estition techniques [4-6] nd the proposed perfornce prediction ethod s shown in Figs. 4-5. In these Figs., the curves corresponding to the brcketed references in the legend re obtined by using the ethods given therein. Also, - nd - in legend refer to phse ngle control schee- nd phse ngle control schee-, respectively..6.45.3.5 www.jee.ro 3 6 9 5 8 Experientl- Proposed- [4-] [5-] [6-] Fig. 5. Current of otor- using schee- with proposed nd Auxiliry 5 AC Supply Min Rotor C 9 6 3 () 3 6 9 5 8 AC Supply Min Auxiliry Rotor C Experientl- Proposed- [4-] [5-] [6-] Fig. 6. Power of otor- using schee- with proposed nd 5 (b) Fig. 3. () Trditionl phse ngle control: Schee-. (b) Advnced phse ngle control: Schee-. The inferences tht cn be drwn fro these results re iteized long with the results s below: For both the experientl energy efficient schees, t different firing ngles, the perfornce curves due to the proposed perfornce prediction ethod re closer to the experientl ones in coprison to the conventionl theoreticl preter estition ethods [4-6], s shown in Figs 4-5..6.45.3.5 3 6 9 5 8 Experientl- Proposed- [4-] [5-] [6-] Fig. 4. Current of otor- using schee- with proposed nd Power fctor 9 6 3 3 6 9 5 8 Experientl- Proposed- [4-] [5-] [6-] Fig. 7. Power of otor- using schee- with proposed nd.8.6.4. 3 6 9 5 8 Experientl- Proposed- [4-] [5-] [6-] Fig. 8. Power fctor of otor- using schee- with proposed nd 4
Power fctor.8.6.4. 8 5 9 6 3 www.jee.ro 3 6 9 5 8 Experientl- Proposed- [4-] [5-] [6-] Fig. 9. Power fctor of otor- using schee- with proposed nd.8.6.4. 3 6 9 5 8 Experientl- Proposed- [4-] [5-] [6-] Fig.. Current of otor- using schee- with proposed nd Power fctor 3 6 9 5 8 Fig. 3. Power of otor- using schee- with proposed nd.8.6.4. Experientl- Proposed- [4-] [5-] [6-] 3 6 9 5 8 Experientl- Proposed- [4-] [5-] [6-] Fig. 4. Power fctor of otor- using schee- with proposed nd.8.6.4. 3 6 9 5 8 Power fctor.8.6.4. 3 6 9 5 8 Experientl- Proposed- [4-] [5-] [6-] Fig.. Current of otor- using schee- with proposed nd 75 4 5 7 35 3 6 9 5 8 Experientl- Proposed- [4-] [5-] [6-] Fig.. Power of otor- using schee- with proposed nd Experientl- Proposed- [4-] [5-] [6-] Fig. 5. Power fctor of otor- using schee- with proposed nd In trditionl phse ngle control schee, both in nd uxiliry winding currents re non-sinusoidl (on ccount of presence of tric in both the pths) nd hence input current hronics increses, which in turn increse the copper loss due to hronics. For both the otors, the experientl input current for schee- is ore thn s for schee-, s shown in Figs. 6 nd 7, respectively. 5
.6 8 5 www.jee.ro.4. 9 6 3 3 6 9 5 8 Current- Current- Fig. 6. Coprison of experientl currents of otor- using schee- nd schee-, t different firing ngles. 3 6 9 5 8 Power- Power- Fig. 9. Coprison of experientl powers of otor- using schee- nd schee-, t different firing ngles..8.6.4. The bsence of hronics flux in uxiliry winding eliortes the displceent fctor, which iproves the power fctor for the dvnced phse ngle control schee s copred to trditionl phse ngle control schee, s shown for both the otors, in Figs. nd, respectively. 3 6 9 5 8 Current- Current- Fig. 7. Coprison of experientl currents of otor- using schee- nd schee-, t different firing ngles. For dvnced phse ngle control schee, the uxiliry winding current is sinusoidl (due to bsence of tric in this pth) nd the in winding current is distorted. Hence, the phsor su of in nd uxiliry winding currents contins fewer hronic, which further lessens the copper loss due to hronics. This decreses the consued input power which cn be seen for both the otors in Figs. 8 nd 9, respectively. Power fctor.8.6.4. 3 6 9 5 8 Fig.. Coprison of experientl power fctors of otor- using schee- nd schee-, t different firing ngles. Power fctor- Power fctor- 8 Power fctor.8.6.4. 4 3 6 9 5 8 Power- Power- Fig. 8. Coprison of experientl powers of otor- using schee- nd schee-, t different firing ngles. 3 6 9 5 8 Power fctor- Power fctor- Fig.. Coprison of experientl power fctors of otor- using schee- nd schee-, t different firing ngles. Although, the experientl observtions distinctly nifest the superior perfornce of the dvnced phse ngle control schees s evidenced fro Figs. 6-3, nevertheless, the deficiency ppers while the otor preters re extrcted using the conventionl ethods [4-6], the resulting perfornce vribles (line current, power nd power fctor) give error vis--vis experientlly esured vlues. However, the 6
perfornce vribles derived fro proposed ethod give less error to the experientl vlues. By exerting the conventionl [4-6] nd proposed ethods to the studied sple otors, for both the energy efficient schees, the efficiency versus firing ngle is obtined s in Figs. nd 3. The observtions of these Figs. revel the following points: The efficiency of the otor using the conventionl ethods [4-6], shows no iproveent even while using the dvnced phse ngle control schee. This indictes the deficiency of the conventionl theoreticl perfornce prediction ethods. The efficiency of the otor shows superiority of schee- over schee-, using the proposed ethod, which is in coplince to erlier work [8] nd lso confirs the vlidity of the nlyticl findings. Efficiency Fig.. Clculted perfornce of otor- using schee- nd schee- with proposed nd conventionl results, t different firing ngles. Efficiency 4 3 3 6 9 5 Proposed- Proposed- [4-] [4-] 5 4 3 Fig. 3. Clculted perfornce of otor- using schee- nd schee- with proposed nd conventionl results, t different firing ngles. For quntittive result nlysis, en bsolute percentge error (MAPE) of perfornce vribles (current, power nd power fctor) with respect to experientl observtions using conventionl [4-6] nd the proposed ethod for both the otors nd phse ngle control schees re depicted seprtely, in Tble II. MAPE = [5-] [5-] [6-] [6-] 3 6 9 5 Proposed- Proposed- [4-] [4-] [5-] [5-] [6-] [6-] E E T (33) where, E www.jee.ro, is the experientlly esured perfornce vrible nd T, is the theoreticlly obtined perfornce vrible. This tble deonstrtes tht the MAPE of perfornce vribles with respect to experientl observtions using the proposed perfornce prediction ethod is less thn tht using the conventionl perfornce prediction ethods. 5. CASE STUDY The equivlent circuit preters hve been deterined nd hence perfornce vribles re evluted for four-pole PSCRSPIM with the following rtings nd dt: -4, 65 W, 5 Hz, 4 rp. Direct dc test, no-lod test nd locked rotor tests hve provided the following dt: R s= 357.4 Ω, R s = 357.4Ω, P = 65.7W, L 37.976W, C =.57µF, R s = 78.5Ω, given the following dt: L = 4, I L =.79A, LR = 65.43, I LR =.3A, P LR = R c =.4Ω. Winding rtio test hs E = 4, E = 98, E =34, E =96. Experientlly esured perfornce vribles re: =4, I L =.7A, P in=65w, pf =.99. This otor is tken for detiled nlysis fro section, depicted in Tble I s otor. At rted voltge nd zero degree tric firing ngle, the line currents of the otor for both the schees, for obvious reson, re sinusoidl. Consequently, the equivlent circuit preters nd perfornce vribles of the otor for both the schees would rein se. At ny firing ngle other thn zero degree, the line current of otor for schee- nd in winding current of the otor for schee- becoe non-sinusoidl. Hence, for the cse study, the equivlent circuit preters nd perfornce vribles of the otor re evluted for both the schees t rted voltge on sixty degree firing ngle of the tric. The vlues of line current, power fctor, power consued nd efficiency hve been evluted in Tble III, using the conventionl [4-6] s well s the proposed techniques. 6. COCLUSIO Conventionl preter estition ethod for PSCRSPIM is indequte to find the perfornce vribles like input current, power fctor nd power consued nd hence towrds the overll perfornce prediction of the otor t different firing ngles of tric (for tric bsed c voltge controller). The proposed ethod trets the turns rtio s coplex quntity tered s CCR nd the perfornce vribles of the otor hve been clculted using this coplex quntity. The conventionl nd proposed ethods re used to find the equivlent circuit preters, input perfornce vribles nd hence for the coputtion of the otor efficiency. Two experientl energy efficient schees hve been used to observe the otor perfornce t different 7
firing ngles of tric. However, with the conventionl perfornce prediction ethods, the input vribles show devition fro the experientl results obtined nd the estited efficiency violtes the thee of superior perfornce of the otor with dvnced phse ngle control schee. The proposed perfornce prediction www.jee.ro ethod not only give the perfornce vribles closer to the experientl results but lso confor to the superiority of the dvnced phse ngle control schee, which vlidte the nlyticl findings. Tble : Men Absolute percentge error with respect to experientl Perfornce vribles MAPE Motor MAPE Motor Schee Schee Schee Schee Current ([4]) 35.939 54.84 7.664 4.8938 Current ([5]) 35.48 53.94 5.533 4.493 Current ([6]) 89.53 96.63 3.665.9956 Current (Proposed). 7.8.388.3543 Power ([4]) 4.8 8.63 3.5933 43.5943 Power ([5]) 39.99 8.383 4.693 3.876 Power ([6]) 8.9 8.789 8.955 8.47 Power(Proposed) 4.494.98 8.653.9798 Power Fctor ([4]) 65. 7.894 59.65.699 Power Fctor ([5]) 65.4 8.74 6.37 8.984 Power Fctor ([6]) 35.939.944 6.6 8.6973 Power Fctor (Proposed) 35.48 4.669 59.846 5.599 Tble 3: Cse study solutions (At 6 degree firing ngle) using conventionl nd proposed technique Preters Schee- [4] Schee- [5] Schee- [6] Schee- [Proposed] Schee- [4] Schee- [5] Schee- [6] Schee- [Proposed] R 78.5 78.5 78.5 78.5 78.5 78.5 78.5 78.5 s X 34. 34. 68.44 34. 34. 34. 68.44 34. s X r 34.3 34. 34. 34. 34. 34. 34. 34. R r 37.76 357.7 67.8 535.63 37.7 357.7 37.7 535.63 5.6784 5.67 ot Used 5.67 5.67 5.67 ot Used 5.67 b X 67.8 67.8.7 67.8 67.8 67.8.7 67.8 Z 38.9 f j633.49 336.6 j6.6.4 j5 57.85 j73.45 53.3 j77.35 6. j7.64.5 j5.7 86.94 j76.99 Z 93.47 b j7.94 89.88 j7.9 8.65 j3.5 3.67 j39.63 9.63 j7.5 85. j6.68 867.67 j3.4 3.5 j38.75 Z 357.4j34. s 357.4j34. 357.4 j68.44 357.4 j34. 357.4 j34. 357.4 j34. 357.4 j68.44 357.4 j34. Z 779.5 ins j695.65 783.9j683. 57 378.5 j5.96 747.66 j787.37 7. j779.8 76.36 j77.54 377.34 j5.66 674.3 j834.96 ot Used ot Used ot Used 83.48 ot Used ot Used ot Used 83.48 b X ot Used ot Used ot Used 5759.7 ot Used ot Used ot Used 5759.7 Z f ot Used ot Used ot Used 384. j83.3 ot Used ot Used ot Used 49.8 j63.8 Z ot Used ot Used ot Used b 4.44 ot Used ot Used ot Used 376. 8
j3.9 www.jee.ro j3.64 Z s ot Used ot Used ot Used 357.4 j34. ot Used ot Used ot Used 357.4 j34. Z ins ot Used ot Used ot Used 94. - j99.56 ot Used ot Used ot Used 936.9 - j38.34 I ot Used ot Used ot Used.3 - j.7 ot Used ot Used ot Used.3 - j.7 I ot Used ot Used ot Used.5 - j.6 ot Used ot Used ot Used.5 - j.6 E c ot Used ot Used ot Used 63.56 - j66.64 ot Used ot Used ot Used 63.56 - j66.64 E c ot Used ot Used ot Used 9.35 j9.97 ot Used ot Used ot Used 9.35 j9.97 E 4 4 4 ot Used 4 4 4 ot Used E 98 98 98 ot Used 98 98 98 ot Used E 34 34 34 ot Used 34 34 34 ot Used E 96 96 96 ot Used 96 96 96 ot Used.99.994.994 ot Used.994.994.994 ot Used ot Used ot Used ot Used.65 - j.8 ot Used ot Used ot Used.65 - j.8 I L.9.9.55.7.7.7.53.6 P 44.67 45.5 7.47 6. 4.99 4.3 7.4 59.4 in pf.98.99.99.98.98 P 4.5 3.78 8.78. 8.38 8.8 87.84.3 cu P 3.65 3.65 3.65 3.65.85.85.85.85 cl P 4.46 4.73 6.37.44 4. 4.46 5.95.48 fwl Po 9.37 9.96 4.63.5 4.7 5.8.76 3.33 η.97..48 3.65.5.3.9 37.6 References [] IEEE Stndrd Test Procedure for Single-Phse Induction Motors, IEEE Stndrd 4, 98. [] IEEE Stndrd Test Procedure for Single-Phse Induction Motors, IEEE Stndrd 4,. [3] Ghil. K., Sini L. M., Sini J. S.: Preter Estition of Pernent-Split Cpcitor-Run Single-Phse Induction Motor Using Coputed Coplex oltge Rtio. In: IEEE Trnsction on Industril Electronics (4), vol. 6, no., Februry 4, p. 68 69. [4] Mtsch L. W.: Electrognetic nd Electroechnicl Mchines, Hrper nd Row, ew York, 997. [5] Toro. D.: Electric Mchines nd Power Systes, Prentice Hll, 988. [6] Brosn G. S., Hyden J. T.: Advnced Electricl Power & Mchines, Sir Isc Pitn & Sons Ltd., London, 966. [7] Toliyt H. A., Levi E., Rin M.: A review of RFO induction otor preter estition techniques, In: IEEE Trnsction on Energy Conversion (3),, vol. 8, no., June 3, p. 7 83. 9
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