AN INFLUENCE OF SUPPLY VOLTAGE FREQUENCY ON DYNAMIC PERFORMANCE OF A SINGLE-PHASE CAPACITOR INDUCTION MOTOR

Transcription

1 Prace Nakowe Instytt Maszyn, Napędów i Poiarów Elektrycznych Nr 64 Politechniki Wrocławskiej Nr 64 Stdia i Materiały Nr Krzysztof MAKOWSKI*, Aleksander EICHT* indction otors, single phase, capacitor otors, circit odeling, silation, line freqency AN INFUENCE OF SUPPY VOTAGE FREQUENCY ON DYNAMIC PERFORMANCE OF A SINGE-PHASE CAPACITOR INDUCTION MOTOR The paper presents a odeling atheatical tool for prediction of characteristics and silating reslts of dynaic operation of the single-phase capacitor indction otor for different vales of the capacitor capacitance and for two widely sed vales of spply voltage freqency at no-load and rated load conditions. Developed atheatical odel of the capacitor indction otor was ipleented for calclation sing Matlab/Silink software. The silation shown the seflness of the odel for the process of designing single-phase indction otors. 1. INTRODUCTION Single-phase capacitor indction otors are coonly sed as a drive for lowpower fans, pps and copressors. Generally, they are indction achines of the syetrical rotor cage and two non-syetrical stator windings (the ain winding and axiliary winding with starting or rnning capacitor) spplied with the sae sinsoidal voltage sorce. In odelling perforance characteristics of the indction otors circit odels of lped paraeters are still often sed de to their siplicity and fast coptation. At first approxiation of the atheatical odels linearity of agnetic circit is assed and slotting of the stator and rotor are neglected [1, 3 4]. These odels ay be flly sefl for searching of better operating paraeters or showing direction of the searching in design optiization. In the paper a atheatical odel of the single-phase capacitor indction otor in the stationary dq syste is described which was ipleented for silation of the otor s start-p at no-load and application of noinal load torqe after starting fro no-load operation. The present paper deals with silations of dynaic characteristics * Politechnika Wrocławska, Instytt Maszyn, Napędów i Poiarów Elektrycznych, Wrocław, l. Solchowskiego 19, krzysztof.akowski@pwr.wroc.pl, aleksander.leicht@pwr.wroc.pl.

2 54 of a tested capacitor indction otor spplied fro sinsoidal voltage sorce of 30V at freqency of 50 and 60 Hz for different vales of capacitor capacitance placed in the axiliary stator winding. It shold be entioned that ains electricity in Erope, Astralia, Oceania, ost regions of Africa and Asia and few contries in Soth Aerica se the voltage of 0 40 V, 50 Hz. The voltage of 0 40 V, 60 Hz is sed in Soth Korea, Philippines, Per, soe regions of Brazil and in soe saller contries of Central Aerica, while ost of the North Aerican contries se V, 60 Hz.. DESCRIPTION OF THE TESTED MOTOR AND MATHEMATICA MODE The low power, single-phase capacitor indction otor was sed for coptational analysis. The otor has two stator windings: the ain (M) and the axiliary (A), of which agnetic axes are displaced by abot 90. The rnning capacitor (C) is plgged in series with the axiliary winding. The rotor has sqirrel cage of 11 bars, that are distribted niforly along circference. Table 1 lists the ratings and strctral data of the tested otor. Table 1. Ratings and data of the tested capacitor indction otor Rated power 0.09 kw Rated voltage 30 V Rated crrent 0.9 A Rated speed 840 rev/in Efficiency 0.55 Power factor 0.9 Freqency 50 Hz Torqe ratio 1.5 Nber of stator windings Rnning capacitor capacitance 3μF Connection of stator windings parallel Nber of poles: ain/axiliary winding / Winding layot: ain/axiliary winding single layer Rotor winding sqirrel cage Nber of slots: stator/rotor 18/11 aination aterial-generator sheet M A ainated core length 3 Since the axes of the both stator windings are orthogonal, the dq axes of the odel ay be aligned with axes of the windings, as illstrated in Fig. 1. The sqirrel cage rotor ay be represented as a pair of syetrical, short-circited coils [].

3 55 Fig. 1. Cross-section view and the dq odel of tested capacitor indction otor The circit odel of the capacitor indction otor can be described by set of differential eqations, written as follows [3 5]: di dt dm = R srr idm ω i r rr idr rr ω riqr rr dm di dt = ω i r dm R srr i rr ω ridr rr iqr rr rr qc dr di dt Rs = i dm ss Rr ss ω ri idr ωriqr dm (1) di qr dt = ss ω i r dm Rs i ω ridr R rss iqr qc where: dqc 1 = i dt C D f p ( idmiqr iidr ) r T dω r p = ω dt J J J rr ss, Rs = RM = RA, ss = sm sa = = and i dm, i are the direct- and qadratre-coponents of stator crrents, i dr, i qr are the direct- and qadratre-coponents of rotor crrents, dm, are the direct- and qadratre-coponents of stator voltages, qc is the voltage across the rnning capacitor, R s is the resistance of stator windings, R r is the resistance of rotor windings,

4 56 ss is the self-indctance of stator windings, rr is the self-indctance of rotor windings, is the stator agnetizing indctance, p is the nber of pole-pairs, D f is the viscos friction coefficient, J is the oent of inertia, T is the load torqe, ω r is the electrical anglar velocity of the rotor. 3. DYNAMIC CHARACTERISTICS The silation reslts in this section are obtained for the single-phase indction otor described in paragraph, spplied with sinsoidal voltage sorces of 30 V, 50 Hz and 60 Hz, at different capacitor capacitances, for free acceleration of the otor (T = 0) and applying the rated load (T = T N = 0.3 N ) after 0.7 s. The silations were perfored at the assption, that only oent of inertia of the otor J = kg and the viscos friction coefficient D f = N s were taken into accont. The otor starting wavefors obtained for capacitor capacitance of 3 µf are shown in figres 4. Fig.. The electroagnetic torqe T e (t) for C = 3 µf and a) f = 50 Hz, b) f = 60 Hz Fig. 3. The anglar velocity ω r (t) for C = 3 µf and a) f = 50 Hz, b) f = 60 Hz

5 57 Fig. 4. The intake crrent I(t) for C = 3 µf and a) f = 50 Hz, b) f = 60 Hz It can be noticed, that when the otor is spplied with voltage of freqency 60 Hz, the rotor rotates with higher no-load and rated speed. The otor s agnetic field rotates with synchronos speed abot 377 rad/s, copared to abot 314 rad/s for the line freqency 50 Hz. In addition to the average anglar velocity, the line freqency inflences also the shape of the rotating agnetic field in the achine s air-gap. Oscillations of the electroagnetic torqe (a reslt of an elliptical field) have noticeably lower aplitde at 60 Hz than at 50 Hz, especially when the otor operates nder rated load conditions. With the increase of the voltage freqency, ipedances of windings and rnning capacitor sitably change, crrents in ain and axiliary windings have siilar aplitdes and the rotating agnetic field is close to a circlar field. Electroagnetic torqe directly inflences the wavefor of the anglar velocity it s oscillations nder rated load conditions for 60 Hz have several ties lower aplitde than for 50 Hz and they are practically negligible. The no-load crrent aplitde for 60 Hz is also noticeably saller than for 50 Hz. The silation reslts for capacitor capacitances other than 3 µf are shown in figres Fig. 5. The electroagnetic torqe T e (t) for C = 4 µf and a) f = 50 Hz, b) f = 60 Hz

6 58 Fig. 6. The anglar velocity ω r (t) for C = 4 µf and a) f = 50 Hz, b) f = 60 Hz Fig. 7. The intake crrent I(t) for C = 4 µf and a) f = 50 Hz, b) f = 60 Hz Fig. 8. The electroagnetic torqe T e (t) for C = 6 µf and a) f = 50 Hz, b) f = 60 Hz

7 59 Fig. 9. The anglar velocity ω r (t) for C = 6 µf and a) f = 50 Hz, b) f = 60 Hz Fig. 10. The intake crrent I(t) for C = 6 µf and a) f = 50 Hz, b) f = 60 Hz It can be observed, that when the rnning capacitor capacitance is increased to 4 µf, the aplitde of the electroagnetic torqe s oscillation decreases for the otor spplied with voltage of freqency 50 Hz. The start-p tie also slightly decreases. However, for the line freqency of 60 Hz, the aplitde of aforeentioned oscillations increases, copared to 3 µf, becase the capacitor capacitance and line freqency inflence on the phase difference between the ain and axiliary windings crrents and also on the aplitdes of these crrents. Frther increase of the capacitance reslts in increase of aplitde of the electroagnetic torqe oscillations, and conseqently, the aplitde of the anglar velocity oscillations. 4. CONCUSIONS In the paper, the dynaic behavior of the single-phase capacitor indction otor spplied with a voltage of freqency of 50 and 60 Hz was presented. The silation

8 60 reslts showed, that for C = 3 µf, the line freqency of 60 Hz gives better reslts, as far as the oscillations of electroagnetic torqe and anglar velocity are concerned. Rnning capacitor capacitance of 4 µf yields better reslts for 50 Hz since for 60 Hz, the torqe s oscillations have higher aplitde. It shold be entioned, that the tested otor was designed for operation with line freqency of 50 Hz. The spply voltage freqency also affects steady-state characteristics when the otor is spplied with voltage of 60 Hz, the breakdown torqe is lower than for 50 Hz []. The presented atheatical odel of the single-phase capacitor indction otor ay be sed as an efficient atheatical tool for analytical prediction of perforance characteristics of the otor already before its anfactring. REFERENCES [1] YSHEVSKI S.E., Electroechanical Systes and Devices, CRC Press, 008. [] EICHT A., Wpływ pojeności kondensatora pracy jednofazowego silnika indkcyjnego z poocniczy zwojenie kondensatorowy ze względ na dobroć rozrch, Magisterska praca dyploowa, IMNiPE, PWr., Wrocław 010. [3] MAKOWSKI K., WIK M.J., Silation of dynaic and steady-state operation of the single-phase capacitor indction otor, Electrical Review, No. 10, 009, Poland, pp [4] MAKOWSKI K., An analytical odel and paraeters of single-phase indction otor, Modeling, Silation and Control, A, AMSE Press, Vol. 1, No., 1989, pp [5] ŚIWIŃSKI T., Metody obliczania silników indkcyjnych, PWN, Warszawa 008.