IOSR Journal of Engineering (IOSRJEN) ISSN (e): 225-321, ISSN (p): 2278-8719 Vol. 5, Iue 3 (March. 15), V1 PP 11-15 www.iorjen.org Analyi of A 2-Phae Stator Winding By Winding Function Methodology * I.K.Onwuka, ** U.U.Uma, * G. C. Diyoke * Michael Okpara Univerity of Agriculture, Umudike, Nigeria. ifeanyikayonwuka@gmail.com ** AkanuIbiam Federal Polytechnic, Unwana, Nigeria. Abtract:A two-phae tator winding i preented here and analyzed. By two-phae, it i implied that the two tator winding are identical and diplaced in phae by 9 degree, and can upply ingle-phae load from either terminal. Firt, a tator winding wa preented for a pecified tator, and the winding ditribution analyzed with the aim of obtaining the mmf characteritic from it functional relationhip with the winding function.the particular tator winding preented in thi work wa found to be with low mmf harmonic level, and would perform acceptably when it form part of an ac machine, typically, a generator of induction or reluctance type in the low power range. Key word:two-phae, Winding function. I. INTRODUCTION With the world growing interet on reducing greenhoue effect and booting power upply to urban and remote area, intenive reearch i in the area of determining practical electromechanical converion device in both the low and high power range for eay and efficient converion of energy from unconventional energy ource to electricity. At the low power range, uch device are required to be rugged, near maintenance free, affordable, and uncomplicated, and providing good quality of power.along thi line, extenive work ha been done on ingle phae and three phae generator of induction and reluctance type. Self-excitation of thee generator i achieved by the action of capacitor connected to the terminal of the machine. For example, [1] dicued the performance prediction and analyi of a ingle phae elf-excited induction generator excellently. Alo, [2] preented a mathematical model by which the dynamic behavior of elf-excited ingle-phae reluctance generator can be uccefully predicted under different operating condition, while [3] wa minded of the teady tate analyi of the ame. Plenty reearch reult are alo available in three-phae autonomou reluctance generator in both the dynamic and teady-tate concern[4, 5, 6]. Generator in the low power range are uually ingle-phae machine and are uually two-winding machine having a main winding and an auxiliary winding. However, le i conidered of two-phae machine. By 2-phae tator winding, it i implied here that the machine i able to upply ingle phae load from the two tator terminal, with a phae difference of 9 o. The analyi employed i akin to aynchronou tator winding which ha a main and an auxiliary winding, of which the former ha more number of turn of conductor than the latter and occupie about two third of the tator lot [7]. The current in both winding are diplaced by an angle of 9 o. The baic difference i that the winding in thi work are of equal number of turn, and occupie equal number of tator lot. Such tator winding arrangement readily find application in autonomou production of electricity through renewable and non-conventional energy ource.a good deign will aim to realize a inuoidal tator mmf wave form with minimum harmonic content. Minimizing the tator mmf harmonic content i of great importance for many reaon, including minimizing voltage and current harmonic [8]. Stator loe are alo reduced. The focu of the preent work i to ugget a tator winding arrangement with clear analyi, howing a inuoidal tator mmf with reduced harmonic, of a two-phae machine. The interet i retricted to terminal rather than internal characteritic of the machine. Specification It i intended to obtain a tator winding deign for a 1hp, 2V, 2-pole, 2-phae machine. II. MACHINE DIMENSIONS With the method uggeted by [7] and [9], the dimenion of the tator can be determined to meet the above pecification, with a few aumption with repect to pecific magnetic and electric loading of the machine. Thee are conidered the main dimenion of the machine. It will be oberved however, that thi i a different reearch focu from the preent endeavor. Winding Decription International organization of Scientific Reearch 11 P a g e
A double-layer, integral-lot winding with chorded coil will be ued. Taking lot per pole, the tator number of lot i 24. Each lot hold 18 conductor, which could be of either or both phae. Winding were ditributed a near inuoidal a poible. Reference here include [7, 8, 9]. Furthermore, the winding of both phae are identical but diplaced from each other by an angle of 9 o.the winding clock diagram appear in figure 1.The following can eaily be oberved from the winding clock diagram: Number of lot = 24; Slot angular pitch = 15 o ; Phae belt = 1 lot pitch; Phae pread = 15 o ; phae hift = 9 o ; Number of pole =2; Pole-pitch = lot per pole. Aumption Each winding ection i aligned axially within the air gap. Thi i to ay that the wire i neither lanted in the circumferential direction nor tilted in the radial direction a it pae through the air gap. 11 1 A2 A1 B5 9 B4 A4 8 A5 7 A5 B2 B2 6 B1 B1 5 A4 4 B4 3 A2 B5 A1 2 1 φ 13 A1 A1 24 B5 A2 A2 B5 14 23 B4 B4 15 22 A4 B2 B2 A4 16 A5 21 A5 B1 B1 17 18 19 Figure 1: Winding Clock Diagram III. WINDING FUNCTION [1] oberved that the knowledge of the winding function for all winding together with the winding current eentially decribe the patial field ditribution in the gap of the machine. Moreover, it i well known that the winding function i the bai of calculating machine inductance. Obviouly, the harmonic S/No Table 1: The A and B-phae tator turn and winding function n a Coil pan Coil pan n ava N a nb n N avb b 1 6 2 9 3 9 4 5 18 6 18 7 8 9 5.25.75 23 6 7.5 1.875 9 11 4 6 6.375 2.625 9 7 3 4 7.5 4.5 6 5 1 6 9.75 8.25 19 2 8.25 9.75 7 3 2 4.5 7.5 6 2 17 3 2.625 6.375 9 3 4 4 3 4.5 7.5 11 6 2.625 6.375 1 4 1.875 7.5 3 3 4.75 5.25 5 2 3 7 2 19 7 2 5.25.75 5 41 3 7.5 1.875 7 1 4 3 International organization of Scientific Reearch P a g e
9 9 1 6 11 1.875 7.5 9 5 5 6 4.75 5.25 11 7 6 13 18 18 2 n n 54 54 a 1 ava a 6.375 2.625 11 13 6 4 7.5 4.5 23 19 6 37 2 N 18 9.75 8.25 n n b 8.25 9.75 avb N b content of both tator voltage and current depend on the hape of the air gap mmf due to the tator winding. Hence, tator winding analyi baed on winding function i preented here. Equation (1) repreent the relationhip between the air gap mmf, the winding function, and the tator current. Subcript repreent tator quantity, and N the winding function. mmf = N i 2 coφ (1) Where φ i an angular diplacement along the tator inner circumference. The winding function (WF) methodology developed in [11] wa employed in thi analyi. Table 1 how the turn and winding function for both winding, where n(φ ) and n ave are the turn function and the average turn function repectivley, given by: n φ = No. ofturninintegrationpat (2) n ave = 1 2π n φ 2π dφ (3) The winding function i then given by: N φ = n φ n ave (4) Together with the information under the Winding Decription, thee equation were adjuted to develop Table 1, integrating over the pan pecified. Alo, figure 2 and 3 how the actual winding function, in tair-cae form. Thee can alo be deduced from Table 1. Harmonic Analyi The method of Fourier erie [] wa applied to obtain the variou harmonic preent in the winding function expreed in Figure 2 and 3. The Fourier erie of the winding function wa performed and variou plot obtained uing the MATLAB tool [13]. The fundamental component of the winding function for the two tator winding are: N a = N co φ δ (5) N b = N in φ δ (6) Where, δ i the phae hift, and ubcript refer to tator variable. Figure 4 and 5 give a picture of the harmonic content in the winding function, up to the 5 th non-zero harmonic (odd harmonic only). Thi i a reflection of the ditortion that will be preent in the tator voltage and currentwaveform. It i put in better perpective by figure 6. International organization of Scientific Reearch 13 P a g e
b-phae harmonic magnitude a-phae harmonic magnitude Winding Function, Nb (phi-) Winding Function, Na (phi-) 4 - -4-1 2 3 4 5 6 7 Stator circumferential poition, phi- in radian unit Figure 2: Actual Winding function of the a-phae winding 4 - -4-1 2 3 4 5 6 7 Stator circumferential poition, phi- in radian unit Figure 3:Actual Winding Function of the b-phae winding 5 4 3 1 1 3 4 5 a-phaeampled harmonic Figure 4:Harmonic of the a-phae winding function 5 4 3 1 1 3 4 5 b-phae ampled harmonic Figure 5:Harmonic of the b-phae winding function A comparion between the reultant winding function (um of all the harmonic including the fundamental component) and the fundamental component of the winding function, hown in figure 6, reveal that the approximation of the fundamental component to the reultant winding function i quite cloe. Hence, thi can be ued for inductance calculation of the machine. Thi plot i found identical for the two phae, except that they are diplaced in phae by 9 o. It i oberved that the fundamental component i ame for both winding, with the following phaor value: International organization of Scientific Reearch 14 P a g e
Winding Function, Na (phi-) N a = 55.8254.139rad (7) N b = 55.8254 1.4399rad (8) If the cloe approximation of the fundamental harmonic to the reultant winding function i accepted a the eventual winding function, then the effective number of tator turn will be taken a N = 55.8254. It i clear that the influence of winding deign feature which have not been conidered in the analyi are accounted for in N. 4 Reultant winding function funamental component a-phae - -4 b-phae - 1 2 3 4 5 6 7 Stator circumferential poition, phi- in radian unit Figure 6:Comparion between the reultant winding function and the fundamental component of the function. IV. CONCLUSION It mut be oberved here that aliency ha no influence on the form of the winding function [1], o that the tator winding here realized can be adapted to a round-rotor or a alient-pole machine. The particular deign of the tator winding preented in thi work ugget minimal current and voltage harmonic. Alo, the analyi here preented how that with little lo of accuracy, the fundamental component of the winding function can be adopted for inductance calculation of the machine. Again, it i clear that the two-phae tator preented in thi work will perform acceptably when it form part of an electric machine, typically, a mall generator. A earlier mentioned, thi generator could be of induction or reluctance type. It i therefore preented here that a two-phae ac generator of variou power rating can be deigned and ued for dometic and certain farm proceing activitie in the low power range. The author think thi will lead to a better utilization of the tator lot. REFERENCES [1]. Bhim Singh et al, Improved Steady State and Tranient performance with optimum excitation of Single-phae elfexcited Induction Generator, Electric Machine and Power Sytem, 28:591-4,. [2]. S.M. Allam, M. A. El-Khazendar, and A.M. Oheiba. Dynamic analyi of a elf-excited ingle-phae reluctance generator, ElectricPower Component and Sytem, 34:725-738, 6. [3]. J. Chen and P. Famouri. Single-phae elf-excited reluctance generator, part I: Steady-tate analyi, Electr. Power ComponentSytem, vol. 31, pp. 9-147, 3. [4]. Ben-Hail, N., and Rabinovici, R., Three-phae autonomou reluctance generator, IEEE Proc. Elect. Power Appl., Vol. 148, No. 5, pp. 438-442, September 1. A. K. Tandon, S. S. Murthy, and G. J.Berg. Steady-tate analyi of capacitor elf-excited induction generator, IEEE Tranaction on Power Apparatu and Sytem,vol. PAS-13, no. 3, pp. 6-618, March1984. [5]. T. F. Chan. Steady-tate analyi of a three-phae elf-excited reluctance generator, IEEE Tranaction on Energy Converion, vol. 7, no. 1, pp. 223-23, March 1992. [6]. Mittle, V. N., and Mittal A., Deign of Electrical Machine, Standard Publiher Ditriibutor, Delhi, 6. [7]. Paul C. Kraue, Oleg Waynczuk, Scott D.Sudho_. Analyi of Electric Machinery,IEEE Pre, New York, 1995. [8]. JuhaPyrhonen, TapaniJokinen, Valeria Hrabovcova, Deign of Rotating Electric Machine, John Wiley and Son Ltd, 8. [9]. P. S. Bimbhra, Electrical Machinery, Khana Publiher, Delhi, Seventh Edition, 8. [1]. Obe, E. S. Nnadi, D. B and Eke, J. Inductance and Airgap Flux denity of asynchronou Reluctance Machine uing theactual Machine Geometry, NSE TechnicalTran. Vol. 44. No. 4, pp.49-63, 9. [11]. Erwin Kreyzig. Advanced EngineeringMathematic, John Wiley and Son, Inc,New York, 1979. []. MATLAB. Mathwork7 :Natic, Pennylvania, USA. International organization of Scientific Reearch 15 P a g e