Miroław DĄBROWSKI Andrzej RUDEŃSKI 62.33.333 62.37.78 EFFICIENCY DETERMINATION AND LOSSES SEGREGATION OF SINGLE-HASE INDUCTION MOTORS ABSTRACT Thi paper i concerned with the problem of accurate efficiency determination and loe egregation in inglephae capacitor induction motor. Segregation of loe in inglephae motor i more complicated than in three-phae motor, firt of all due to the bacward magnetic field component and the preence of the rotor current at zero lip. Thi ituation complicate the lo egregation in no load tet. In thi paper the uncertainty of efficiency determination method i conidered and a implified lo egregation procedure i propoed.. INTRODUCTION The ingle-phae induction motor with a cage rotor, two phae tator winding and tart capacitor or with two-value capacitor one for tarting C and one for running C n C i conidered. Miroław DĄBROWSKI Electrotechnical Intitute Department of Electrical Machine ożaryiego 28, 04 703 Waraw, OLAND e-mail: iel.nme@iel.waw.pl Andrzej RUDEŃSKI Electrotechnical Intitute Department of Electrical Machine ożaryiego 28, 04 703 Waraw, OLAND e-mail: iel.nme@iel.waw.pl ROCEEDINGS OF ELECTROTECHNICAL INSTITUTE, Iue 223, 2005
60 M. Dąbrowi, A. Rudeńi The tarting capacitor i turned off by a tarting witch while the running capacitor remain in erie with the auxiliary tator winding. The main tator winding and the econd called auxiliary winding are phae hifted patially by 90 0 electrical degree. The main and auxiliary winding magneto motive force produce together an elliptic wave which may be decompoed into a forward and a bacward travelling wave. Firt of all due to thi two magnetic field wave the efficiency determination and loe egregation of ingle-phae induction motor i more complicated a in three-phae motor. The motor examined in thi wor cover the power range from 0,25 W to ca. 5 W. In thi paper the election problem of efficiency determination method i conidered and the uncertainty of the obtained reult by thi method i conidered. 2. SELECTION OF EFFICIENCY DETERMINATION METHOD Generally there are two method of efficiency determination: the direct and the indirect method. In the direct method the input power in and the output power out are meaured and the efficiency i calculated by the formula: η = out () in or In the indirect method the following formulae are ued: η = out (2a) out + t η = in t (2b) in where t i the total power lo.
Efficiency determination and loe egregation of ingle-phae induction motor 6 If the part of individual power loe li are calculated then: t = li i= (3) where li i the I part of individual lo, which number i. In the analytical etimation of uncertainty (error) of the method following formula ha been ued [2]: n η X i X i η i= δ max = δ X i (4) After including the efficiency given by equation () into (4) we obtain: d d = δ (5) out in δ max + = δ + out in out in where d out ; d in ; δ out and δ in abolute and relative error of the output power and the input power, repectively. More complicated formula we obtain for the uncertainty of indirect method after including efficiency given by formula (2b) into (4): where δ t δ ( + ) η max = δ δ η in t (6) i relative error of the total power lo obtained e.g. by the calorimetric method [5]. If the loe are calculated a the um of all individual part, then the relative error hould be calculated by the formula [4]; δ li li i= δ ef = (7) li i= where δ li i the relative error of the part i of lo li.
62 M. Dąbrowi, A. Rudeńi For the comparion of both method accuracy an inequality i formulated with the uncertaintie given by formulae (5) and (6): δ out + δ in ( η) η ( δ + δ ) in t (8) After tranformation we obtain the following relation for the efficiency: η 2δ δ in in + δ + δ t out + δ t (9) If the efficiency of conidered motor fulfil the inequality (9) then the direct method mut be ued. However, if the efficiency i greater the indirect method will give more accurate reult. Auming that the relative error fulfilled the relation: δ = δ and p out in δ = δ (0) t t in where uually p >, and t >, then from the inequality (9) we obtain: + 2+ + t t η () p In the fig. the curve = f ( ) η for p a parameter are preented. If the t efficiency of teted motor i located in the area below curve the direct method of efficiency determination i preferred and if the efficiency i located in the area over thee curve the indirect method hould be ued. In thi method the individual part of loe ought to be determined, for intance by the meaured lo egregation in experimental manner. ROCEEDINGS OF ELECTROTECHNICAL INSTITUTE, Iue 223, 2005
Efficiency determination and loe egregation of ingle-phae induction motor 63 0.85 η 0.80 p = 2,6 = 2,2 =,8 =,4 p =,0 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0 2 3 4 5 6 t Fig.. The curve efficiency veru t for p a parameter 3. LOSSES SEGREGATION 3.. Introductory remar Single-phae induction motor, lie other electrical machine have loe aociated with their rotor and tator winding, with the alternating magnetic flux in the part of magnetic core and with friction and windage loe incurred through the rotation of the rotor and cooling fan. Lie all electrical machine, they alo have an additional power lo component, termed a well tray load lo, which ha many elemental ource and which i a reflection of the non-ideal nature of a practical made machine. A precie aement of loe by computation and alo by meaurement contitute a formidable ta due to complexity of the problem caued by exitence of forward and bacward magnetic traveling wave, magnetic aturation of magnetic core, higher field pace harmonic due lot opening in the tator and the rotor, mutually lot ewing, in effect in the rotor cage,
64 M. Dąbrowi, A. Rudeńi interbar (tranvere) rotor current particularly in two-pole motor. However, power loe computation require a great amount of computation effort. For ingle-phae induction motor cheaper experimental invetigation of loe and implified lo egregation i recommended. In thi paper only experimental method of loe egregation are conidered. 3.2. Lo egregation method given in literature The firt propoal for load loe egregation in ingle-phae capacitor induction motor announced Veinott in the paper [0]. In hi wor a combined experimental and analytical method i decribed which i elaborated under following aumption: harmonic pace magnetic field are paed over; permeability of the iron part are independent of the magnetic flux denity; primary winding leaage reactance i equal to the econdary winding leaage reactance. Veinott repect that: the no-load econdary copper lo cannot be neglected; the rotor copper lo under load condition cannot be computed directly from the lip and output power a in a polyphae induction motor, uing the formula + ( ) wr = out m (2) where m i the mechanical lo and i the lip. it i neceary to determine certain fundamental parameter of the motor, firt of all the open-circuit reactance X 0, the hort-circuit reactance X l and the rotor reitance tranformed to the primary main winding R r. The way propoed by Veinott for determining thee parameter and for the iron lo eparation from no-load and hort-circuit tet reult i criticized by Koch [6]. Koch pointed out that the parameter X 0, X l, and R r are from the lip
Efficiency determination and loe egregation of ingle-phae induction motor 65 frequency and the magnetic core aturation dependent. He ha preented a ymmetrical component method for lo calculation and in what way one can tae into conideration the loe caued by higher field harmonic of forward and bacward magnetic traveling wave. The method propoed by Van der Merve [; 9] i baed on the principle of upplying the ingle-phae motor from a ymmetrical voltage upply. The auxiliary winding voltage U a i 90 ahead of the main winding voltage U a = a U m uch that the current: I I m a = (3) a where a i the ratio between main and auxiliary winding effective turn. The given by Veinott experimental method of winding ratio tet i a follow [0]. The motor run at rated voltage U m on the main winding only and the auxiliary voltage U a i meaured. After them upon the auxiliary winding the voltage U a 0, 2Ua i impreed, then the voltage U m acro the main winding i meaured. The effective winding ratio we can obtain from the formula: a U U = a a (4) Um Um It i intereting that Štepina [8, alo in the boo in Czech printed in 957] recommended upplied the auxiliary winding with the voltage U a, 2U a. The lip and the magnetic field condition in both cae hould be nearly the ame. In the method propoed by Van der Merve in fact pure forward traveling field condition are provided. The 90 hifted voltage ource i obtained with two tranformer connected in erie: one in Scott connection and econd a regulated autotranformer. Again hort-circuit at low voltage and no-load teting i exercied. Moreover, ideal no-load operation (at zero lip) i performed by uing a drive at ynchronou peed. The ymmetrical voltage method doe not have to deal with the bacward field and thu the rotor current ha a ingle frequency f r = f. Conequently the in effect i neglected. The trouble i that during variable load operation, the bacward field exit in a real machine and thu the rotor in effect i preent.
66 M. Dąbrowi, A. Rudeńi 3.3. ropoed lo egregation procedure The loe egregation method propoed in thi wor i nearly imilar to the method decribed by Štepina [8], and i baed only on experimental reult. The reearch program conit of three part a follow.. Meaurement at ynchronou rotation The teted motor i driven by a dynamometer (e.g. by a ynchronou motor with torque tranducer). The mechanical lo (friction and windage loe) i meaured at no-load and no upplied tator winding. The next tet i carry out after upplying the main winding with the rated voltage U m and the input power inm0, the input current I m0 and the torque T 0 i meaured. In thi cae only the bacward field i preent and thu it may be claimed that the in effect in rotor cage i accounted for. The driven torque i: T + 0 = T m T bf 0 (5a) where T m i the mechanical lo torque and T bf i the bacward field torque: T bf 2R 2 = r Ibf (5b) 2 π n 2 where n i the ynchronou peed, R r i the rotor reitance referred to the tator main winding, i lip, and I bf i the bacward current component equal: I bf = 0,5Im0 (5c) For the lip = 0 the torque i: 4 2 T bf 0 = Rr Im 0 (6) 2 π n From equation (5a) and (6) we get the rotor reitance with repect of in effect: n R = 8π (7) r ( T0 T ) m I 2 m 0
Efficiency determination and loe egregation of ingle-phae induction motor 67 The rotor reitance can be obtain from the one phae hort-circuit tet (at zero peed) if the main winding i upplied by low voltage. The iron lo i practically equal zero and: R r = I ml 2 ml R m (8) where ml i the input power, I ml i the hort-circuit current in the main winding, and R m i the direct meaured main winding reitance. In thi cae the in effect in the rotor cage i repected only at the frequency 50 Hz. The iron core lo i: 2 2 I 0 = 0 m Fe m RmIm Rr (9) 0 2 2. Meaurement at no-load For to determine the um of iron and mechanical loe the no-load tet may be performed at different value of the main winding voltage U m below rated value, until the current I m0 tart increaing. A for the three phae induction motor, the eparation of mechanical and core loe may be done by taing the ordinate at zero peed to the rather trait line dependence 2 of ( Fe + m ) veru U m. The core lo i, in fact, dependent on the e.m.f. E m not on input voltage U m, and on the magnetic field ellipticity. The field ellipticity decreae with load and thi i way, in general, the core loe are practically attributed to the forward field component. 3. Meaurement at rated load There are two main operation mode to tet the ingle-phae induction motor on load: the motor mode and the generator mode. Under the motor mode the electric input in, and the output mechanical power, out are meaured. The mechanical power i in fact calculated from the meaured torque T out and from the peed n: out = 2πnT out (20) In thi paper i aumed that the mechanical and core loe at load are the ame a at no-load tet. The loe in the main and auxiliary winding are
68 M. Dąbrowi, A. Rudeńi calculated directly on the bai meaured reitance and current. The lo in rotor caued by the bacward current component approximately i 2 I load = m rbf bf (2) Im0 0 where I mload i the meaured load current and I m0 i the current at ynchronou peed a in the equation (6). The lo in rotor caued by the forward current component my be calculated on the bai of mechanical output [7]: ( + 0, ) = out m + (22) rbf rff 5 The difference between total loe by direct input/output meaurement under load and by egregation method i a meaure of tray load loe. The tray load loe in the ingle-phae motor tend to be maller than in a three phae motor becaue the ratio between full load and no-load current i maller. 4. CONCLUSIONS In thi paper the election of efficiency determination method of inglephae capacitor motor i preented. The no load tet of thi motor i done with the auxiliary phae open, after the motor tart. Due to the bacward field component, even at zero lip the rotor current lo i not zero. Thi ituation complicate the loe egregation. The calculation of rotor reitance from zero peed tet at 50 Hz produce a value that i acceptable for computing on load performance of the motor, becaue it i meaured at an average of forward and bacward rotor current frequencie: 0,5 [ f + ( 2 ) f ] = f Alo the propoal for the motor tray load loe election i preented. The tray load loe in ingle-phae motor are mall than in a three phae motor.
Efficiency determination and loe egregation of ingle-phae induction motor 69 LITERATURE. Boldea I., Naar S. A.: The induction Machine Handboo. CRC re, London, New Yor, 2002. 2. Dąbrowi M.: Choice of Efficiency Determination Method for Electrical Machine. roceed. of International X Sympoium on Micromotor and Servodrive. Rydzyna, pp. 64 69, 996. 3. Dąbrowi M., Dąbała K.: Extenion of power balance in an induction motor. (In olih). rzegląd Eletrotechniczny, no. 2, pp. 309 35, 997. 4. Dąbrowi M., Dąbała K.: Accuracy of efficiency determination of electrical machine. (In olih). rzegląd Eletrotechniczny, no., pp. 269 272, 999. 5. Dąbrowi M., Ogonowa-Schweitzer E.: Accuracy lo meaurement in induction motor by calorimetric method. (In olih). rzegląd Eletrotechniczny, no., pp. 280 282, 2000. 6. Koch I.: Die metechniche Betimmung der Einzelverlute von leinen Indutionmotoren. ETZ-A, H., S. 696 700, 965. 7. utoła J., Śliwińi T.: Deign and operation of one-phae motor. (In olih). WNT, Warzawa, 964. 8. Štepina J.: Die Einphaen-Aynchronmotoren. Springer-Verlag, Wien, 982. 9. Van der Merve C., Van der Merve F. S.: Study of Method to Meaure the arameter of Single hae Induction Motor. IEEE Tran., vol. EC-0, no. 2, pp. 248 253, 995. 0. Veinott C. G.: Segregation of Loe in Single-hae Induction Motor. A.I.E.E. Tran., pp. 302 306, December 935. Manucript ubmitted 0.07.2005 WYZNACZENIE SRAWNOŚCI I ROZDZIAŁ STRAT MOCY W JEDNOFAZOWYCH SILNIKACH INDUKCYJNYCH Miroław DĄBROWSKI, Andrzej RUDEŃSKI STRESZCZENIE raca dotyczy zagadnień związanych z doładnym wyznaczanie prawności oraz rozdziału trat mocy w jednofazowych ilniach ondenatorowych. Rozdział trat w ilniu jednofazowym jet bardziej złożony niż ilniach trójfazowych, przede wzytim ze względu na wytępowanie pola magnetycznego przeciwbieżnego oraz prądu w wirniu nawet przy poślizgu zerowym. Ta ooliczność w zaadniczy poób ompliuje rozdział trat przy próbie biegu jałowego. W pracy jet rozpatrywana niepewność pomiarowa wyznaczania prawności oraz podana jet propozycja uprozczonej metody rozdziału trat mocy.