A novel single-phase ac to high voltage dc converter based on Cockcroft-Walton cascade rectifier

Transcription

1 PES29 A novel ingle-phae ac to high voltage c cverter bae Cockcroft-Walt cacae rectifier Chung-ming Young an Ming-hui Chen epartment of Electrical Engineering Natial Taiwan Univerity of Science an Technology Taipei Taiwan R. O. C. 6 young@ee.ntut.eu.tw Abtract Thi paper propoe a novel ingle-phae ac to high voltage c cverter bae Cockcroft-Walt cacae rectifier with ly aing e bi-irectial witch an e boot inuctor. Thi paper alo erive a new metho of circuit repreentati for Cockcroft-Walt cacae rectifier which implifie the equivalent circuit an i cvenient for imulati. Compare with cvential Cockcroft-Walt rectifier the propoe cverter provie halfwave ymmetric an low-itorte line current autable power factor at the ac ource an regulate c output voltage. Unit power factor i achieve by the average-current metho an the c output voltage i regulate by a PI compenator. Moreover thi paper employ a igital ignal proceor to implement a igital ctroller for operating the propoe cverter an a prototype with 5w rating i implemente for tet. Both imulati an experimental reult emtrate the valiity of the propoe cverter. Keywor-Cockcroft-Walt rectifier; high voltage c cverter; bi-irectial witch; power factor correcti I. INTROUCTION High voltage c power upplie have wiely applie in inutrie cience meicine military an epecially in tet equipment uch a X-ray ytem ut-filtering inulating tet an electrotatic coating []. Proviing the avantage of compactne an cot efficiency Cockcroft-Walt rectifier which i ctructe by a cacae of capacitor an ioe i very popular amg high voltage c applicati [2]. However traitial Cockcroft-Walt rectifier ha ome hortcoming uch a high-itorte an half-wave-aymmetric line current unregulate output voltage an a large amount of ripple [3]. Recently a number of high-frequency witching technique for the Cockcroft-Walt rectifier have been introuce to reuce the amount of ripple of output voltage for ingle-phae ytem but till have not improve the line current itorti problem [4]. Some power factor correcti technique for Cockcroft-Walt rectifier are evelope by the two-tage circuit to improve the line current itorti problem. Neverthele two-tage topologie incur higher cot an lo [5]. A three-tage cvential Cockcroft-Walt rectifier an the propoe cverter are hown in Fig. an Fig.2 vc vc3 v c vc2 vc4 v c 6 Fig. : The traitial three-tage Cockcroft-Walt rectifier repectively. The avantage of the propoe topology are a S v c Fig. 2: The propoe cverter with three-tage Cockcroft-Walt rectifier follow: ) The line current waveform ha half-wave ymmetry an low itorti which cvential Cockcroft-Walt rectifier can t achieve. 2) At any given intant there i ly e cucting emicuctor evice in the power flow path. 3) Proviing high tep up rate without uing a boot tranformer. 4) The ctrol metho of cvential boot cverter can be aapte for ue by the propoe cverter eaily [6]. Thi paper alo erive a new metho of circuit repreentati which will be etaile in ecti II for Cockcroft-Walt cacae rectifier. Thi new circuit repreentati implifie the equivalent circuit an i cvenient for igital imulati. The ctrol of power factor correcti an c output voltage regulati are preente in ecti III. For verificati thi paper employ a igital ignal proceor (TMS32F247) to implement a igital ctroller for the propoe cverter an a prototype with 5w rating i implemente a well. Both imulati an experimental reult 822

2 are hown In ecti IV. Finally in ecti V cclui i preente. PES29 II. ANAYSIS OF OPERATION Fig.2 how the propoe cverter which i upplie by a utility ac ource. The propoe cverter cit of a boot inuctor a bi-irectial witch( S ) with S operating in poitive-half cycle of the ource an operating in the negative-half cycle of the ource an a three-tage Cockcroft- Walt rectifier in thi cae. The well-known rectifier i ctructe by a cacae of tage with each tage ctaining two capacitor an two ioe. For an N/2-tage (N i an even number) Cockcroft-Walt rectifier there are N capacitor an N ioe. For cvenience both capacitor an ioe are ivie into o group an even group a enote in Fig. 2. In orer to tuy the teay-tate behavior for the propoe cverter the ioe cucting citi of the traitial Cockcroft-Walt rectifier i ecribe firt. Through imulati the capacitor voltage an ioe current are hown in Fig. 3 for poitive-half cycle an Fig. 3 for negativehalf cycle repectively. It can be een that even capacitor are charge an o capacitor are icharge through even ioe in equence uring the poitive-half cycle an vice vera uring the negative-half cycle. The cucting equence are 6 4 an 2 in the poitive-half cycle an 5 3 an in the negative-half cycle repectively. Fig. 4 how the correping current path for each cucting ioe with Fig. 4-(c) for poitive-half cycle an Fig. 4()-(f) for negativehalf cycle. Two ioe cucting phenomena are foun: ) there i at mot e cucting at any intant 2) the equence of cucting ioe i from right ie to left ie with even ioe cucting in poitive-half cycle an o ioe cucting in negative-half cycle. Accoring to above ecripti thi paper erive a new mathematic metho to analyze the operating of Cockcroft- Walt rectifier more generally an ytematically. Firt we introuce the ioe-cucting inex to etermine which ioe i cucting an which current path houl be taken. i given by S S v c = 6 : > > vc6 v c i = 4 : > vc5 vc6 > vc4 S v c i (c) = 2 : > vc5 vc6 vc3 vc4 S v c () = 5 : < > vc5 S v c i i i (e) = 3 : < vc4 vc5 > vc3 v c v c S v S 2 i i 6 i 4 i 2 v c (f) = : < vc4 vc5 vc2 vc3 Fig. 4: Correping current path for each cucting ioe in equence. Current path of i. Current path of 6 i. (c) Current path 4 of i. () Current path of 2 i. (e) Current path of 5 i. (f) Current path 3 i. of i5 i3 i Fig. 3: Capacitor voltage an ioe current of a three-tage Cockcroft- Walt rectifier. Poitive-half cycle. Negative-half cycle. 823

3 PES29 where { x k } = max { x } k v for v > k = N < k = 3... N ( ) Fig. 5: The general equivalent circuit of the propoe cverter i a et of poible cucting inexe an it element are given by x k k for k 2 = k for k > 2 v for k > 2 v c( k ) c( k ) () c( k ) > vc( k ) (2) v where v c(k ) i the voltage of the k-th capacitor an will be given later. Although there are ictinuou-cucti an ctinuou-cucti moe that can be operate in thi cverter ly the latter i cucte in thi paper. et be the cucting tate of the bi-irectial witch an i given by ( S = an v = ( S = off an v > ) or ( S > ) or ( S 2 2 = an v = off an v < ) < ) Cequently Fig. 5 ketche the general equivalent circuit of the propoe cverter an the ifferential equati of line current i given by (3) i = [ v ( )( vcel )] (4) t where i the line current an ( v col ) repreent the erie voltage of even(o) capacitor that are the left ie of the cucting ioe. Both an v col are epenent an are given by (5) an (6) repectively where y ( y ) i the larget (mallet) integer not larger (le) than y. / 2 vc(2i) for vcel = i= for = (5) / 2 v col = v c (2i ) i= (6) Moreover vce2 an v co2 repreent the erie voltage of even an o capacitor repectively that are the right ie of the cucting ioe an are given by (7) an (8). N / 2 vc( 2i) for N v = (7) cer i = / 2 + for = N N / 2 vc(2i ) = i = / 2 + for / 2 N / 2 for / 2 = N / 2 Summing (5) an (7) we can obtain the output voltage the total voltage of all even capacitor o cel cer (8) v = v + v (9) The current equati of each even an each o capacitor are given by () an () v t v t ci c = ( ) i i Ci [( i ] = ) C v R o () () where C i i the capacitance of the i-th even capacitor an C i the capacitance of the -th o capacitor an i an are given by (2) an (3) i = = < i for i i = N (2) < for = 3... N (3) When i = C i i the right ie of the cucting ioe an i icharging through the loa. When i = C i i the left ie of the cucting ioe an i icharging for ( ) i < or i charging for ( ) i >. When = C i the right ie of the cucting ioe an i floating. When = C i the left ie of the cucting ioe an i charging for ( ) < or i icharging for ( ) i >. From above erivati of the operati of the propoe cverter there are four operati moe of the propoe cverter epite the number of the tage of the Cockcroft- Walt rectifier. Fig. 6 how the equivalent circuit of the four operati moe with Fig. 6 an correping to poitive-half cycle an Fig. 6(c) an () correping to negative-half cycle. For Fig. 6 an (c) which are moe an moe 3 with = the boot inuctor i charge by the ac ource an the even-group capacitor upply the loa. For Fig. 6 which i moe 2 with = the boot inuctor an the ac ource tranfer energy to the rectifier an part of ocapacitor are icharge while part of even-capacitor are charge. The charge an icharge capacitor are etermine by. With the ame energy tranferring the charging an icharging citi of moe 4 are oppoite to 824

4 moe 2. It ha to note that S i turne in moe an i PES29 ( ) v ref v err i avg u K v tri S Fig. 7: The ctrol cheme of the propoe cverter with PS-bae igital ctroller. ( ) unit line voltage ignal u i multiplie by i avg to obtain the reference ignal i for the current loop. The output of current ( ) TABE PARAMETERS USE IN THE SIMUATION AN EXPERIMENTS Symbol Range or type Note /5Vrm(6Hz) ac ource for tet/tet2 2.9mH boot inuctor f 2kHz witching frequency 8V c output voltage R 28 Ω loa S IXEH4N2 bi-irectial witch C ~ C 6 F capacitor ~ 6 SF26U ioe (c) ( ) v () Fig. 6: Four operati moe of the propoe cverter turne in moe 3. Some witching trategie can be taken for improving line current citi an regulating the c output voltage. III. IGITA CONTRO STRATEGY The ctrol cheme of the propoe cverter with igital ctroller i hown in Fig. 7 an there are two ctrol loop the voltage loop an current loop. The feeback ignal of the output C voltage filtere through a low-pa filter for eliminating the line frequency ripple i compare with et reference v ref. Then verr i fe to a proportial-integral ctroller to regulate the require reference currenti avg. The v c Fig. 8: Simulati reult of the propoe ytem. (25V/iv) (2.5A/iv) an (25V/iv) waveform. voltage waveform of each capacitor. compenator moulate with the triangular wave to generate PWM ignal for the bi-irectial witch. High-power-factor an low-itorte line current an regulate c voltage can be achieve cequently. 825

5 IV. Simulati an Experimental Reult Bae the mathematical moel an ctrol trategy ecribe in ecti II an III repectively a imulati program i cucte with the parameter hown in Table. Fig. 8 how the imulati reult of an an PES29 Magnitue(% of funamental) Magnitue(% of funamental) Harmic orer (c) Harmic orer () Fig. 9: Experimental reult. (V/iv) (A/iv) an (5V/iv) waveform for tet an t : 5m/iv. Spectrum of for tet. (c) (5V/iv) (25A/iv) an (5V/iv) waveform for tet2. () Spectrum of for tet2. Fig. 8 how the voltage of each capacitor. The imulati reult prove that the mathematical moel can repreent the propoe cverter incluing the famou Cockcroft-Walt rectifier correctly. A 5w prototype i alo built to verify the valiity of the propoe cverter. The ytem parameter ue in the experiment are ummarize in Table. For compari two tet with ame output c voltage an power are cucte. Tet i for the operati of cvential Cockcroft-Walt rectifier with Vrm/6Hz line voltage while tet2 i for the operati of the propoe cverter with 5Vrm/6Hz line voltage. Fig. 9 an (c) how the experimental reult of an for tet an tet2 repectively an the pectrum of are hown in the Fig.9 an () a well. From Fig. 9 it can be een that the line current of cvential Cockcroft-Walt rectifier ctain not ly 58% 3r harmic but alo about % an 7% of 2n an 4th harmic compent therefore the line current i highly itorte an i not half-wave ymmetric. The latter phenomen which rarely occur in traitial ioe-brige rectifier i mainly caue by aymmetric loa cnecti --- the loa i cnecte to the even-group capacitor. Accoring to the waveform of an it pectrum in Fig. 9(c) an () the line current i nearly inuoial an in phae with ; moreover the even harmic are almot eliminate. The power factor/total harmic itorti of tet an tet2 are.85/.59 an.99/.8 repectively. Thu the experimental reult how the valiity of the propoe cverter. V. CONCUSION A novel ingle-phae ac to high voltage c cverter bae Cockcroft-Walt cacae rectifier that can achieve the line current half-wave ymmetry an low itorti ha been introuce. By uing a ioe-cucting inex thi paper erive a new circuit repreentati that give a general form to analyze the Cockcroft-Walt rectifier an implifie the imulati proce. Reult of imulate an experimental work cfirm the valiity of the propoe cverter. The propoe cverter not ly mitigate the rawback of traitial Cockcroft-Walt rectifier but alo achieve high boot rate an high quality line current with ly ewitching tage. Although ly the ctinuou cucti moe i cucte in thi paper the ictinuou cucti moe will tuy further to a the variety of ctrol trategy for the propoe cverter in the near feature. REFERENCES [] M.. Bellar E. H. Watanabe an A. C. Mequita Analyi of the ynamic an teay-tate performance of Cockcroft-Walt cacae rectifier IEEE Tran. Power Electric vol. 7 pp July 992. [2] J. Tanaka an I. Yuzurihara The high frequency rive of a new multitage rectifier circuit in Proc. Power Electric Specialit Cf. 988 vol. 2 pp [3]. Maleani an R. Piovan Theoretical performance of the capacitorioe voltage multiplier fe by a current ource IEEE Tran. Power Electric vol. 8 pp April 993. [4] S. M. Sbenaty an C. A. Ventrice High voltage C hifte RF witchmoe power upply ytem eign for ga laer excitati in Proc. Applie Power Electric Cference an Expoiti 99 pp [5] J. Sun X. ing M. Nakaoka an H. Takano Serie reant ZCS-PFM C-C cverter with multitage rectifie voltage multiplier an ualmoe PFM ctrol cheme for meical-ue high-voltage X-ray power generator in IEE Proc. Electric Power Applicati vol. 47 pp Nov. 2. [6] S. Buo P. Mattavelli. Roetto an G. Spiazzi Simple igital ctrol improving ynamic performance of power factor preregulator IEEE Tran. Power Electric vol. 3 pp Sept

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