Generalized Symmetrical Angle Pwm Technique For A.c

GENERALIZED SYMMETRICAL ANGLE PWM TECHNIQUE FOR A.C. VOLTAGE CONTROLLER Gama/M. Hashem*, und Mostafa K. Dowish** ’Deparrment o f Electrical Engineering, Ain Shams University, Cairo, Egypt ** Facully of information d Engineering systems, Leedk Metropolitan University, Leeds, U.K. ~ r m r c r l b a r . h ~ ~ n i ~ ~ ~i7r.darwish~~~rnU.3C.llk z~~~~~~~~~/.c~~ni Abstract - Conventional niethods of a.c. i~oltage controllers, such as on-off control and phme-ongle control are known io produce harmonic voltages in the O.C. szippiy l i t m This paper inimdures the use offorced roninrututed techniqires in a.c. voolrage controllers, tiame1jJ; symntetricd angle pulse width moddotion tecliniqiie. The sjw”trica1~v displaced piilses within the sinusoidal voliage woveform is adopted The advariiages of riniif displacement factor and high freqiiency harmonic currents which are euq, to filter, can be gained in ihe suggested control technique. The resrilting harmonic currents from the proposed techniqiie are ~nalyzedand compared on a basis of the phase-angle controlled technique. Simple LCjilters can be introduced in the supply input side of the voltage controllers to improve the qualip of the supply voliage woveform. 7he analysis of karmonic currents showed that noticeable reducrion as gained with increasing ihe number ofpiilses per halfcycle.

Index Term - A.C. Choppers, PWM, Harmonics

I. INTRODUCTION Large loads supplied from ax. voltage controllers used in soft starters, transformer controlled primary side for large electro-chemical rectifiers, fumaces, heaters, a.c. motors speed control and theatre dimmers all produce harmonic currents which have bad influence on the utility electrical network. Hannonic currents when passing through the source harmonic impedances produce harmonic voltages, resulting in source voltage waveform distortion [I]. Voltage synchronized equipment supplied from such polluted voltage sources may suffer from malfunctioning and operational failures. A.C. motors supplied from such voltage sources may over heat and produce parasitic torques. Also, high frequency harmonic voltages may cause overheating of reactive power compensating capacitors and lead to premature life time. Another drawback o f harmonic voltages and currents produced in ax. sources is the false operation of protection devices due to the jrd harmonic current interfering with zero sequence voltage components. These problems can be solved by using sophisticated advanced control schemes[2]-[9]. A new PWM control technique for ax. choppers is proposed. In this technique, a PWM switching function composed of 2 K pulses is introduced in each cycle of the ac source. The suggested symmetrical angle pulse width modulation SAPWM technique has the

advantages of unity displacement factor and better total current and total voltage harmonic distortion as well as better distortion factor DF. The SAPWM technique produces high frequency harmonic currents, which are easy to filter. This technique has the advantages of enabling linear control of the fundaxnental output voltage component. The higher the number ofpulscs per half cycle K, the higher are the Frequencies of harmonic currents and the easier is the filtering . The limitation in this technique is the increased switching losses of thyristors and other transistor switches, namely BJT’s, MOSFET and IGBT’s. The study in this paper considers only number of pulses per haIf cycle up to K = 21 pulses. The analysis in this paper concentrates on the fully controlled single-phase a.c. voltage controller. It applies equally well to three-phase controllers of singk-phase operating nature with one mode of operation, namely; four wire star connected loads or delta connected switches. The third harmonic current is present in the supply lines in this case. However, the analysis could be extended to three-phase ax. controllers of three-phase operating nature, with two modes of operation such as three-wire star connected loads or delta connected loads. Conventional forced commutated thyristor techniques could be used in the suggested controllers. Simpler circuits with better switching characteristics could be achieved using the gate turn off thyristors GTO’s. Since fumaces and heating loads supplied from a.c. voltage controllers are relatively large loads with large controllers, it is economically possible to use tuned LC filters across the a.c. line inputs to bypass unwanted hannonics and to reduce other hannonics. Theoretical comparison i s made with the conventional phase-angle control technique, and the computed performance indicates the superiority of the proposed technique.

11. THEORETICAL ANALYSIS The output current waveforms of the chosen different types of a x . voltage controllers are analyzed using Fourier analysis. Resistive loads are considered, since harmonic currents are the worst in this case and output current waveform can bc defined accurately. Phase-angle Control The conventional circuit diagram of a single phase a x . voltage controller with resistive load full-wave switch is used [I]. The waveforms of output load voltage and

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gating signals for thyristors TI and T2 are shown in Figure 1, at a tiring angle a =n/4. Therangeofthe firing angle a in this method of control is given as follows [I]: O
Figures 2 and 3 show the waveforms of the output load voltage and gating signals for thyristors T1 and f 2 from the a.c. chopper supplied resistive load for K=3, and K=4 respectively. It is clear from these figures that all the pulse widths having the same width. The width of afly pulse w i s calculated a5 follows :

The instantaneous line current can be expressed by Fourier analysis as follows

w=(--Za)

n=I

and since the current waveform has a half-wave symmetry, then

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K

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integration pervious equation yields to n - 1) n - l cos[( n 1) a J

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for n = 3, 5 , 7, ..

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for n = 1, (3) after integration yields to

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sin[( n + l ) a I n+l sin[( n I) aJ 1 n-I forn = 3, 5 , 7, .,. for n = 1, ( 6 ) after integration yields to IT .

The amplitude of the resultant harmonic current is givenasI,= b, ' for n = 1 , 3 , 5 , ... (15)

IV. RESULTS

The amplitude of the resultant harmonic current is given as

1, = [ an2f b,?

1"'

(13)

forn = I , (12) after integration yields to

The integration yields to a =I

'1

; for n = I , 3, 5 , 7,

(9)

111. SYMMETRICAL ANGLE PULSE WIDTH MODULATION In the proposed symmetrical angle pulse width modulation technique SAPWM, the output voltage is controlled by controlling the width o l K pulses pcr half cycle. The pulses are symmetrically adjusted around the 90" axis and the first pulse is delayed by the firing angle a and the next pulse is delayed by twice a from the end of the pervious pulse, and so the rest pulses.

The suggested method was numerically verified through the extensive simulations using MATLAB/Simulink software package, To cvaluate the potential of the proposed PWM technique, the phase-angle control technique has been investigated for comparison. The phase-angle control technique, and the proposed SAPWM technique are applied to single-phase a x . voltage conwoller switches. The circuit data is as follows: a.c. supply voltage IS 220 Volts at 50 Hz, and the load resistance is 5 n. The harmonic spectnnn of the load current in case of phase-angle control technique is shown in figure 4, and for K = 5, IO, and 20 is shown in Figure 5 through Figure 7. For easy comparison, the fundamental current components in all figures, are kept constant at 0.9 P.U. (57.5 Amps.). Of course this P.U. current value occurred at different values of the firing angle a at each K, so the firing angle IS calculated accordingly. It can be

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noticed in these figures that the lower order harmonic currents is quite high in the case of low values of K, while they are eliininated or reduced with increasing the number of pulses per half cycle such as in the case K =-20 as shown in Figure 7. For easy comparison, each perfonnancc parameter of the a.c. voltage controller at different K values are drawn on the same graph. Figure 8 and 9 show the current T14D and current DF for different values of K as mentioned in the figures. Comparing these wavefonns it is obvious that the worst current THD and current DF is in the case of phase-angle control technique, while they, noticeable improved with increasing the values K. Figure 10 and I 1 show the fundamental and total r m s of load currents versus the firing angle rz for different values of K. Also in these figures, its clear that smooth controlling of the fundamental and total r1n5 of load currents can be achieved by using the proposed technique.

[RI El-Sabbc A. and Zcin El-Din A.," A Novcl AC Voltagc Rcpula8or." lECON'9R. Pwrreiling o j rhe 24" Anniial ~ ~ofrite IEEE. ~ v01.2.pp ~ 607-rii I~. f e [9] B. W. Williams," A symincirically modulstcd A.C. c h o p p L /€E€ Trari\ hd. Elecrion.. vo1.2Y.pp.181-I 85,1982.

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V. CONCLUSIONS

Figure I A.C. Voltage Controller wavefonns (Phase-angle control) a =d4

It has been demonstrated in this paper that the new proposed symmetrical angle pulse width modulation technique can be used to control the a.c. voltagel controller with the advantages of unity displacement factor and reduced lower order harmonics. Studying this technique at different values of K show that increasing the number of pulses per-half cycle K, noticeably! improves the performance of the a.c. voltage controller. I The switching patterns ,based on the proposed: technique is easily generated using a simple micro-! I I controller or a dedicated built in microchip. This work may be extended to study the performance' of a.c. voltage controllers supplied static resistive-' inductive loads, dynamic loads, as well as three-phase configurations.

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VI. REFERENCES

Figure 2 A.C. Voltage Controljer waveforms (SAPWM) K = 3, a = d l 2

[I] M. H. Rashld. *' Powcr Elcctronics ," Pren!ire-hal/ biter?ialional. l1fC 1993. 121 Dc-Hyun Jang: Gyu-Ha Choe and Ehsdmi. .W.." Asymmcirical PWM tcchniquc with harmonic climination and powcr factor, control in AC choppers." Poivei- Elrcrrunics, IEEE Ti~anractionh' u n . Volume: I O lssuc: 2 . Mar 1995 pp.175 -184. [ 3 ] Choc. G.-H. and Wallacc. A.K.: Park. M.-H.," An improvcd PWM tcchniquc for AC choppers ," Power Elrcfruttics, IEEE Twnsarfions o n , Volume: 4 lssuc: 4 , Oct 1989. pp. 496 -505 [4] Iiurriz. F.and Ladoux. P.," Phase-controlled multilcvcl convmcrs, based on dual s i r " associations." Power Elecrronics. lEE& Trunsooionx on. Volume: 15 Issue: I .Jan 2000. pp. 92 -102. 151 Ahmcd, N.A.. Amci. K. and Sakut. M A new configuration of single-phasc symmcincal PWM AC choppcr voltagc contmllcr :' Indirsrriu/ Eiectronics. IEEE Tronsaclrorts on , Volumc: 46 Issuc:' 5 , Oct 1 9 9 9 . p ~942 . -952. ! [6] Do-Hyun Jang and Gyu-HaChoc," lmprovctncnt of input pow% factor in AC choppers using asymmctncal PWM tcchniquc.", Indirstriui Electronirs. IEEE Transuclionx on , Volumc: 42 Issuc:; 2 , Apr 1995. pp.179 -185. I [7] Jang-Hyoun Youm and Bong-Hwan Kwon," Switching tcchniquc, for currcnr-controllcd AC-lo-AC convcncrs," Indusmal. Electronics. IEEE Transactions on, Volumc; 46 Issuc; 2 APT! 1999 . pp.309 -3 IS.

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Figure I 1 Fundamental Load rms Currents Versus Firing Angle a

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