Harmonics Phase Shifter for a Three-Phase System with Voltage Control by Integral-Cycle Triggering Mode of Thyristors

Transcription

1 America Joural of Applied Scieces 5 (11): , 2008 ISSN Sciece Publicatios Harmoics Phase Shifter for a hree-phase System with Voltage Cotrol by Itegral-Cycle riggerig Mode of hyristors I. Badra, A.L. Mahmood ad M.. Lazim Departmet of Electrical Egieerig, Philadelphia Uiversity, Jorda Abstract: I itegral-cycle triggerig mode of voltage cotrol, subharmoic as well as higher order harmoic compoets are geerated i the load voltage waveforms of a three-phase system. hese harmoic compoets are foud to be ubalaced i phase displacemet. he correctio of the ubalaced phase displacemet agles of a particular subharmoic or higher order harmoic for this type of triggerig is ivestigated to solve the limitatio of use of this importat type of cotrol as a drive ad may other idustrial applicatios. I this research a ew phase shiftig techique is proposed to correct the ubalaced phase displacemet agles i the three-phase system. his techique depeds o shiftig the waveforms of either phase B or phase C or both by multiples of 2π. A microprocessor-based harmoic phase shifter is desiged ad tested with three-phase resistive ad iductio motor loads. It is foud that there is a well agreemet betwee the theoretical ad experimetal results ad it is believed that the maor problem of harmoics phase ubalaces associated with the itegral-cycle triggerig mode of thyristors whe used with three-phase circuits have bee solved i the preset research. Key words: Harmoics, itegral cycle cotrol, power electroics, phase agle correctio, phase shifter, ac motor speed cotrol INRODUCION Load voltage cotrol by meas of switchig a pair of iverse parallel coected thyristors or triac is well established. It is customary to use modes of thyristor triggerig kow as itegral-cycle triggerig whereby burst of complete cycles of curret are followed by complete cycles of extictio [1-4]. Itegral-cycle triggerig results i coductio patters that cotai subharmoics of the supply frequecy ad so costitute a form of step-dow frequecy chagig that ca be cosidered as a form of frequecy chager. Also itegral-cycle triggerig results i a cosiderable reductio i the amplitudes of the higher order harmoics as compared with other triggerig techiques ad it is possible that Radio Frequecy Iterferece (RFI) is egligible [2]. he phase-cotrol switchig ca produce higher order harmoics ad heavy irush curret while switchig o i a cold start [5], while itegral-cycle cotrol circuits have the advatage of low irush curret due to zero voltage switchig ease i costructio ad low hardware cost. herefore, itegral-cycle cotrol loads have bee widely used i resistive loads, such as heaters, ove, furaces ad spot welders [6-8]. Also it is used i speed cotrol of siglephase iductio motor [9] ad dc series motor [10]. As a frequecy chagig scheme, itegral-cycle triggerig was foud ot feasible for applicatios i the three-phase systems exploitig this techique for ac motor speed cotrol [11]. his is because the amplitudes ad phase displacemet agles of the higher order harmoic ad subharmoic compoets of the itegralcycle cotrolled waveform are determied by the coductio period N ad the cotrol period ad the order of the idividual harmoic. he three-phase aalysis of voltage ad curret waveforms ad phase relatioships of the geerated harmoic ad subharmoic compoets for differet circuit cofiguratios are described i [12,13]. Cosider a three-phase resistive load with lie voltage cotrol as show i Fig. 1. he resultig threeload voltage waveforms are idetical ad so are the three-load curret waveforms. he supply frequecy compoets are foud to be balaced, sice they are 120 o apart i time-phase while the phase displacemet agles of a particular subharmoic or higher order harmoic are ubalaced [11,12]. Due to the ubalaced phase relatioships of the subharmoic compoets, these compoets represet a source of trouble whe these voltage waveforms are used to feed ac machies for speed cotrol purposes [11]. I this research a attempt is made to study the phase ubalaced Correspodig Author: I. Badra, Departmet of Electrical Egieerig, Philadelphia Uiversity, Jorda 1580

2 A v LA v LA 2v B v LB v LB 2π 4π Phase A ax Phase B C v LC 2π 3 ax v LC N Fig. 1: Four-wire star-coected load with lie cotrollers characteristics of the subharmoics as well as the higher order harmoics geerated due to itegral-cycle triggerig ad to fid a ew phase shiftig techique that is capable of correctig the ubalaced phases based o microprocessor implemetatio [14]. HE PROPOSED PHASE SHIFING ECHNIQUE Figure 2 shows the waveforms of the load voltages for the case whe usig itegral-cycle cotrol with cotrol period = 2 ad coductio period N = 1, for the circuit show i Fig. 1 with R-L load. Let the otatio 1, 2, 3 deote the three phases A, B ad C respectively. hus the load voltage (v L ) for ay th phase will have the geeral form [12]. γ 2π N + φ + γ vl = 2 Vsi( ωt γ ) ωt (1) where = 1, 2, 3 γ = 0, γ = 2 π/3, γ = 4 π/ φ = ta 1 ωl R Fourier aalysis of Eq. 1 results i the followig mathematical expressios: for, the dc compoet is: 2 V a 0 = 1 cosφ π [ ] (2) he amplitude c of th order subharmoic or higher order harmoic as well as its phase displacemet ψ are foud as follows: 2π4 π 33 Phase C Fig. 2: ypical load voltages for phases A, B ad C a b γ cos cosφcos 2π N + φ + γ 2 V = π( ) si φsi ( 2π + φ + γ ) ( ) γ si cos φsi 2π N + φ + γ 2 V = π( ) + si φcos ( 2π + φ + γ ) c = a + b c 2 2 ( ) 2 1/ 2 2 cos ( 2π N + φ) cos φ 2 V = π( ) + si ( 2π N + φ) si φ ψ = ta ψ = ta 1 1 a b γ cos cosφcos ( 2π N + φ + γ ) si φsi ( 2π + φ + γ ) γ si cosφsi ( 2π N + φ + γ ) + siφcos ( 2π + φ + γ ) ax (3) (4) (5) (6) For =, the supply frequecy compoet, the Fourier coefficiets are: 1581

3 a = 2 V cos 2( 2 N ) si cos( 2 ) 4 γ π + φ γ φ + γ π b = 2 V si 2( 2 N ) cos si( 2 ) 4 γ + π + φ γ φ + γ π (7) (8) 2 V 1/ 2 c = 2( 1 cos2 ) 4( 2 N )( 2 N si 2 ) 4π φ + π + φ π + φ φ (9) a 1 ψ = ta (10) b It is foud i [15] that the th frequecy compoet of load curret i phase A (ψ 1 ) leads that of phase B ο ο (ψ 2 ) by 120 ad (ψ 2 ) leads (ψ 3 ) by 120 also. However, if the phase displacemet of the th phase (γ ) is shifted accordig to the followig relatioship: γ = γ + 2π m (11) where, γ represet the ew shiftig agle ad m = 1,2,..., 1. m = 0, γ = 0, γ = 2 π/3, ad γ = 4 π / his ew value of γ do ot affect the amplitude ad phase agle relatioships of the supply frequecy compoets at the load voltages. It ca be see from Eq. 5, that the amplitude of the th harmoic is idepedet of γ, which meas that, the variatio of γ does ot affect the harmoic amplitude spectrum of the th phase. Oly the phase displacemet agle ψ of the th harmoic is chaged as could be see from Eq. 6. he phase displacemet agle ψ of the th harmoic varies with the variatio of m. Now after shiftig the load voltage waveform of phase B or C or both of them by multiple of 2π the th frequecy compoet of load curret i phase A (ψ 1 ) leads that of phase B (ψ 2 ) by + (12) Ο Ο ( m 2) Fig. 2 are show i Fig. 3 ad 4 respectively. It is see that, the phase displacemet agles of the subharmoics ad the higher order harmoics are ubalaced. Now, if the phase displacemet agle of phase B, i.e., ψ 2 is shifted by 180 the the phase displacemet agles of the 1st harmoic (25 Hz) ad the 5th harmoic (125 Hz), as for example, become balaced. he ew values of ψ 2 for the 1st, 3rd ad 5th harmoics which are ψ 12 = 210 o, ψ 32 = 270 ad ψ 52 = 150 o respectively give the value m 2 = 1 ad the ew value of γ 2 is equal to 480 o. he harmoic amplitude spectrum ad the phase displacemet agles of the supply frequecy compoet remais uchaged with the ew value of γ 2, while the phase displacemet agles of the 1st, 3rd ad 5th harmoics chaged as show i Fig. 5a, c ad d respectively. It is foud that this shiftig techique makes the phase displacemet agles of the th harmoic order balaced (120 betwee the phases) except whe is a multiple of 3 where i this case the phase displacemet agles become i phase for all values of N ad except whe is a multiple of 3. Also it is oticed that the phase shiftig of the phase displacemet agles used i this techique do ot deped o the value of N. his meas that, the values of γ 2 ad γ 3 that makes th order harmoic balaced for certai values of N ad ca make it balaced as well for the same value of with N = N-1, N-2,, 1. able 1 shows the values of m 2 Amplitude (per uit) F requ e c y (H z) Fig. 3: Harmoic amplitude spectrum for = 2 ad N = 1, R-load ad (ψ 1 ) leads (ψ 3 ) by: able 1: he phase displacemet agles for typical values of ad N N m 2 m 3 Ο Ο ( m 3) (13) he harmoic amplitude spectrum ad the phase agle relatioships for the load voltage waveforms of

4 (a) (b) (c) (d) Fig. 4: Phase displacemet agles for = 2 ad N = 1, R-load (a): Phase displacemet agles for the 1st harmoic (25 Hz) (b): Phase displacemet agles for the supply frequecy compoet (c): Phase displacemet agles for the 3rd harmoic (75 Hz) (d): Phase displacemet agles for the 5th harmoic (125 Hz) (a ) (b ) (c ) (d ) Fig. 5: Phase displacemet agles for (a): 1st harmoic (25Hz) (b): supply frequecy compoet (50Hz) (c): 3rd harmoic (75Hz) (d): 5th harmoic (125Hz) 1583

5 Fig. 6: Schematic circuit diagram ad m 3 which make the phase displacemet agles of the th harmoic either balaced or i phase for typical values of ad N. his techique caot correct the phase displacemet agles of a particular subharmoic or higher order harmoic if is a multiple of 3. A D PRACICAL IMPLEMENAION he schematic diagram of the microprocessorbased harmoic phase shifter for itegral-cycle cotrol is show i Fig. 6. After reducig the three-phase supply voltage by the step-dow trasformers ( 1, 2 ad 3 ), the Zero Crossig Detector (ZCD) circuits produces the 180 pulses to a 8085 microprocessorbased system. he microprocessor ow ca sese the zero-istat of the ac supply. he the coductio of the triacs started by sedig high pulses to the gate drive circuits (the gate drive circuit used from [16] ). he output of each gate drive circuit is coected to pulse trasformers ( 4, 5 ad 6 ), that are used to isolate the microprocessor circuit from the power circuit. I order to esure successful triggerig of the triac the trigger voltage must be maitaied for the etire coductio period. his ca be achieved by usig a square pulses at high frequecy ad these pulses are geerated by the 1584 F OU v IA H Fig. 7: Waveforms of sigals at differet poits i the cotrol circuit timig circuit. A NAND gate is used to modulate the higher frequecy pulses with the mai coductio pulse. Figure 7 shows the sigals at differet stages i the cotrol circuit for phase A programmed for a coductio period of 1 cycle out of two. he square pulse E goes through a buffer circuit that is foud ecessary for the elimiatio of the dc bias geerated i the comparator. he microprocessor seds a square

6 pulses through PB0 of the 8155 with ON/OFF ratio equal to N/(-N). EXPERIMENAL RESULS he cotrol circuit show i Fig. 6 was built ad tested i the laboratory with a three-phase balaced resistive load. Fig. 8 ad 9 show oscillograms of the load voltage waveforms v LA, v LB ad v LC for the case whe = 4 ad N = 2 before ad after the applicatio of the phase-shiftig techique respectively. It is obvious that the phase-shiftig procedure does ot affect the wave shapes of the load voltage or curret. he system was tested also with a three-phase, cage-type iductio motor described i Appedix A. he stator widigs were coected i 4-wire, starcoected form. Practically this type of voltage cotrol, i.e. itegral-cycle, is foud to produce some problems to the motor such as oise, vibratio ad heat risig to the motor widigs. hese problems become severe especially at high voltages ad whe the motor rus cotiuously. However, able 2 shows the speed measuremet of the motor s at differet values of N ad usig a digital tachometer before ad after the phase displacemet agles correctio i additio with the frequecy of rotatio for each case that is calculated usig the followig equatio of the three-phase iductio motor speed [17] : will produce its ow speed. his meas that after the correctio of the phase displacemet agles of the first harmoic, the motor bega to rotate at the desired subharmoic frequecy. he three-phase iductio motor is loaded by a dc dyamometer available i the laboratory to examie the performace of the motor uder load coditio. he dc V o lta g e sc a le V /D IV. im e sc a le 1 0 m s/d IV. Fig. 8: Load voltage waveforms of phases A, B, C respectively before the correctio of the phase displacemet agles f s = 120 (14) p where, p = umber of poles ad f = supply frequecy. It is importat to metio that the motor rotates i the reverse directio for some cases after the correctio of the phase displacemet agles ad this is due to the variatio i the phase sequece after the correctio of the phase displacemet agles. However, the above results show that, the motor speed s is chaged after the correctio of the phase displacemet agles. his is because the phase displacemet agles of the first harmoic become balaced, i.e. separated by 120 o i time phase ad it Voltage scale 400V/DIV. ime scale 10ms/DIV. Fig. 9: Load voltage waveforms of phases A, B, c respectively after the correctio kof the phase displacemet agles able 2 : he speed measuremet of motor s at differet values usig phase-shiftig techique ad friquecy of rotatio of each sace s (r.p.m.) before Frequecy of s (r.p.m.) after Frequecy of Frequecy of the usig shiftig rotatio (Hz) usig shiftig rotatio (Hz) 1st harmoic (Hz) N techique (Experimetal) techique (Experimetal) (heoretical)

7 Fig. 10: Coectio diagram for separately-excited de dyamometer (r.p.m.) Curve il (A) Fig. 11: Speed-curret characteristic Am. J. Applied Sci., 5 (11): , 2008 Curve 1 dyamometer is coected as a separately excited machie as show i Fig. 10. he specificatios of the 3-phase motor ad the dyamometer are give i Appedix B. he field widig of the dyamometer is coected to a 220V dc source ad the field curret is set to the maximum permissible value. he motor speed s is the measured at differet values of load curret (i L ) for = 4 ad N = 2 for both before ad after correctio cases of ψ, the results are show o curve1 ad curve 2 i Fig. 11 respectively. It is foud that, the motor speed is reduced after the correctio of ψ ad this is obvious sice the motor rotates at the 1st harmoic frequecy. he highest value of the load curret show o curve2 is less tha that o curve1, this is because the geerated e.m.f. i the dyamometer proportioal to motor speed s ad ay reductio i the speed leads to further reductio i the geerated e.m.f. which i tur reduces the load curret. Also ay reductio i the value of the load resistace R i order to icrease the load curret at a certai value of V AH 1586 leads to a reductio i the speed. his limitatio i the loadig machie performace does ot allow us to take further readigs to reach maximum loadig of the motor. CONCLUSION he ubalaced sets of subharmoic ad higher order harmoic voltages geerated by itegral cycle cotrol techique create severe problems for ac machies as they foud to cause excessive heat, mechaical vibratios ad oise. herefore, this type of cotrol was abaded as a ac motor speed cotroller sice may years ago. he proposed phase shiftig techique i the preset work is a try to solve the iheret limitatio of this importat type of cotrol by shiftig the secod ad third phases of the three-phase system by multiples of 2. his techique is foud to be more suitable tha usig the phase-agle cotrol scheme to correct the ubalaced phase displacemet agles of the geerated harmoics. he last scheme is foud to cause ubalaced harmoic amplitude spectrums for the three phases. It is foud, from the theoretical ad practical tests, that the performace of the three-phase iductio motor with phase corrected voltage waveforms is very similar to that whe fed from balaced siusoidal voltages of the same amplitude ad frequecy whe usig the proposed phase-shifter. Fially, it is believed that the maor problems associated with itegral-cycle triggerig cotrol techique, whe used for speed cotrol of ac motor, have bee solved i the preset work. ACKNOWLEDGMENS he authors wish to ackowledge the support ad ecouragemets give by Ass. Prof. Xavier Kestely ad all the staff of the L2EP laboratory i ENSAM school of egieerig i Lille City -Frace. REFERENCES 1. Gallagher, P.J., A.B. Barret ad W. Shepherd, Aalysis of sigle-phase rectified thyristor cotrolled load with itegral-cycle triggerig. Proc. Ist. Elec. Eg., 117 (2) Ligard, B.W., R.W. Johso ad W. Shepherd, Aalysis of thyristor cotrolled sigle-phase loads with itegral-cycle triggerig. Proc. Ist. Elec. Eg., 117 (2): Gallagher, P.J. ad W. Shepherd, Operatio of two parallel coected thyristor cotrolled resistive loads with itegral-cycle triggerig. IEEE ras. Id. Electro. Cotrol Istrumetatio, IECI-22 (4):

8 4. Shepherd, W., hyristor Cotrol of ac Circuits. Bradford Uiversity Press, Eglad. 5. Syed Jamil Asgher, M., fie power cotrol by discotiuous phase-cotrolled switchig. IEEE ras. Circuits Syst., 46 (3): Chu Li, J.A.M. ad J.A.M. Wilsu Xu, O the ambiguity of defiig ad measurig iterharmoics. IEEE Power Eg. Rev., pp: Moha, N.,. Udelad ad W. Robbis, Power electroics. 2d Ed. New York: Wiley. 8. Krei, P., Elemets of power electroics. New York: Oxford Uiv. Press. 9. Krisha, R., B. Ilago, S. Selvarary ad S. Guasekara, Sigle-phase iductio motor speed cotrol with itegral-cycle switchig. IEEE ras. Id. Electro. Cotrol Istrumetatio, IECI-27 (4): Fetih, N.H., G.M. Abdel-Raheem ad G.A. Girgis, Speed cotrol of a DC series motor usig a itegral-cycle cotrolled sigle traic. IEEE ras. Eergy Coversio, 3 (3): Lazim, M.. ad W. Shepherd, Aalysis of iductio motor subected to osiusoidal voltages cotaiig subharmoics. IEEE ras. Id. Appli., IA-21 (4): Lazim, M.. ad W. Shepherd, hree-phase circuits with voltage cotrol by itegral-cycle sigle-phase mode triggerig of thyristors. IEEE ras. Id. Appli., 46 (5): Lazim, M.., Modulatio techiques i the speed cotrol of electric motors. Ph.D. hesis, Uiversity of Bradford, Eglad. 14. Mahmod, A.L., Microprocessor-based phase shifter for itegral-cycle cotrol. M.Sc. hesis, Al- Nahrai Uiversity, Iraq. 15. Yog Nog Chag, Gerald homas Heydt ad Yazhou Liu, he Impact of switchig strategies o power quality for itegral cycle cotrollers. IEEE ras. Power Delivery, 18 (3): Arifur Rahma, Syed Eamul Haque ad Ibrahim Abdul Rahma AL-Gadhi, A digital selfcompesatig method for itegral-cycle power cotrol of rl loads. IEEE ras. Id. Electro. Cotrol Istrumetatio, IECI-27 (2): Nasar, S.A. ad L.E. Uewehr, Electromechaics ad Electric Machies. Joh Wiley ad Sos, Ic. 1587