Improvements in Power Quality and Efficiency with a new AC/DC High Current Converter

Transcription

1 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS Improvemens in Power Qualiy and Efficiency wih a new AC/DC High Curren Converer FRACESCO MUZI, LUIGI PASSACATADO Deparmen of Elecrical Engineering and Compuer Science Universiy of L Aquila Piazzale Ponieri, - L Aquila 67 ITALY muzi@ing.univaq.i luigi.passacanando@iscali.i Absrac: - A very flexible AC/DC converer feauring high-oupu curren, reduced volage ripple and highly adjusable curren conrol is described. The whole sysem consiss of four sages and uses a proper swiching echnique in conjuncion wih a feedbac conrol performed by means of a PID regulaor. Moreover, he buil prooype exhibis high efficiency and reduced harmonic polluion. In order o evaluae he harmonic disorion on he curren drawn from he supply newor, an FFT (Fas Fourier Transform) analysis is performed. Finally, experimenal and compuaion resuls for oupu currens up o 4A, which confirm he correc behavior of he proposed converer, are presened and discussed. Key-ords: - AC/DC converer, High direc-curren, FFT, Elecrical disribuion sysems, Power qualiy. Inroducion In he las few decades, a coninuous inegraion process beween elecrical sysems and power elecronic apparauses has been observed. Power elecronics, which has been applied so far mainly o energy end uses [], was recenly employed also in disribued generaion, namely phoovolaic and wind generaion. Acually, he ever-growing exploiaion of renewable sources requires ha volage and curren wave shapes should be compaible wih curren power disribuion. On he oher hand, new archiecures for modern elecrical sysems have been developed, and novel acive filering echniques and devices have been proposed, which will be able o change he power facor and o eliminae undesired harmonics as well [3], [4], [5], [6], [7]. In order o modify he power facor, eiher deerminisic digial echniques or probabilisic approaches were usually adoped [8], [9]. In addiion, AC/DC converers were acively researched in order o improve he power facor a reasonable coss. From his poin of view, boh he use of a PCB (Prined Circui Board) and implemenaion of a proper swiching conrol echnique allowed a drasic reducion of manufacuring coss. As a maer of fac, he adopion of hese echniques achieved over 9% cos reducion []. Unforunaely, he conrolled swiching produced elecromagneic emissions (EMI) causing disurbances o radio frequencies (RF). A number of sudies poined o a conrol procedure of power supply swiching wih modulaion echniques of he RPM ype (Random Pulse idh Modulaion) ha performed much beer han PM (Pulse idh Modulaion) []. Oher sudies aimed a reducing noncharacerisic harmonics []. Also resonan filers were proposed for high power AC/DC converers adoping yrisors, where a parallel resonance was used o obain amplificaion of seleced harmonics applying a sor of filering echnique [3]. Opimizaion sudies were also performed on AC/DC converers wih synchronous recificaion, ha can be used o supply elecrical machines requiring high direc currens, wih an aim o reduce losses a he oupu sage of he converer. In his case a MOSFET, which performs a role similar o a swiching power supply, and a resisive load are parallel-conneced a he oupu of he generaor. An AC/DC converer buil wih a synchronous machine and a parallel-conneced power MOSFET allow a reducion of he losses on he DC oupu supply sage [5]. In his paper a high curren AC/DC converer wih high qualiy performance is inroduced. The whole sysem is described and experimenal resuls obained from experimenal ess performed on a buil prooype are repored, analyzed and discussed. The proposed sysem The proposed converer is schemaically shown in Fig.. ISS: Issue 5, Volume 7, May 8

2 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS Iou Transformer Inverer Fig. Layou of he proposed four-sage sysem. The firs sage of he sysem consiss of a 6-diode passive recifier. The recified volage is applied o an inverer ha in is urn is made of an ulra-fas 6-IGBT able o commue up o Hz under cerain operaing condiions. The value of he recified volage was abou 5 V, neglecing a ripple ha can be reduced placing an acive recifier a he inpu erminaions of he inverer. Two serially-conneced capaciors, each of µf, were placed beween he DC bus and frame o achieve addiional volage smoohening. The modulaion echnique adoped o drive he inverer was srongly characerized by he 6-phase ransformer/recifier sysem used. The scheme of he hree-phase inverer is shown in Fig. where he phase-neural, phase-o-phase volages and command signals of he hree legs of he inverer are also repored. Fig. 3 Signals used o drive he inverer. Fig. 3 shows ha he volage ime period for each phase is 5 µs. Each phase erminal (phases a, b, c) is conneced by he respecive IGBTs for a maximum ime of 8,3 µs (depending on he command processed by he modulaion) o a +Vdc poenial while for he remaining 6,6 µs of he ime period he same erminal is conneced o ground. In oher words, each phase-neural volage (V a, V b e V c ) is a recangular wave having +Vdc ampliude and period of 5 µs. The duy cycle of his recangular wave can change beween a maximum of 33% (8,3 µs) and a minimum of % ( µs). Fig. 4 shows he hree phase-neural volages. Va Vdc Vb 8,3µs 8,3µs 5µs 8,3µs Vdc Vc Fig. Scheme of a hree-phase inverer. The modulaion echnique adoped o drive he hree legs of he inverer is shown in Fig 3. This echnique was implemened aing in mind he configuraion of he downsream ransformer. Vdc Fig. 4 Phase-neural volages of he inverer. ISS: Issue 5, Volume 7, May 8

3 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS The phase-o-phase volages are lined o he phase-neural volages by he following wellnown relaions: V ab V a - V b () V bc V b - V c () V ca V c - V a (3) I is also nown ha he phase-o-phase volages (V ab, V bc,v ca ) can assume boh posiive and negaive values, whereas phase-neural volages (V a, V b e V c ) ae up only posiive values. Fig. 5 shows he shapes of he (V ab, V bc, V ca ) phase-ophase volages. he sub-sysem shown in Fig. 6 is illusraed in Fig. 7. D D Fig. 7 oring scheme of he ransformer and AC/DC recifier. I Load L Load I Load Vab +Vdc -Vdc Vbc +Vdc -Vdc Of course, he L, L and L 3 inducors shown in Figs. 6 and 7 were used o smoohen he load curren. The whole sysem shown in Fig. is driven by a DSP (Digial Signal Processor), model dspic3f3 of he Microchip family [6]..3 Conrol scheme of he converer In order o obain he desired oupu curren values, he scheme of Fig. was compleed by a proper feedbac conrol sysem as shown in Fig. 8. Vca +Vdc -Vdc R S Recifier Recifier Fig. 5 ave shapes of phase-o-phase volages. T The phase-o-phase volage generaed downsream of he inverer is applied a he inpu erminaions of he 6-phase ransformer/recifier bloc shown in Fig. 6. L 3-Phase ewor Curren Reference A/D Iou* + - Iou PID duy 6-Phase d d d3 PM A B C L L 3 I Load bi A/D Converer A/D bi A/D Converer Hall Probe Fig. 8 Bloc diagram of he oupu-curren conrol sysem. Fig. 6 Six-phase ransformer/recifier bloc supplying he load. The ransformer reduces he volage while increasing he curren. The woring principle of The adoped conrol echnique was implemened by means of a PID regulaor. A bloc diagram of he adoped feedbac conrol is shown in Fig. 9. As already said in secion, he whole conrol sysem was implemened on a proper, DSPmanaged card. ISS: Issue 5, Volume 7, May 8

4 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS Curren Reference bi A/D Converer A/D Iou* + - Iou PID A/D duy bi A/D Converer d d d3 PM Hall Probe Fig. 9 Bloc diagram of he feedbac conrol of he curren. The oupu curren value was moniored using a conrol sraegy consising of a PID regulaor wih a sof-sar echnique. Since he oupu load is conneced o smoohing inducances, in order o avoid sudden changes of he oupu curren, he program emulaing he PID regulaor was compleed wih a proper secion able o manage curren changes smoohly. As a maer of fac, he conrol acions fine-uned he rise and fall frons of he oupu curren in order o proec he smoohing inducances conneced downsream he ransformer agains negaive consequences. In addiion, Fig. 9 shows ha he inpu quaniies of he feedbac secion are he oupu curren values obained from a measuremen sysem placed proximally o he load, and of course also he curren exernal preesablished reference value. Measured currens and reference curren are analogical in naure. Consequenly, hese curren signals mus be ransformed ino digial daa o be sen o he DSP, which jusifies he use of -bi converers placed inside he DSP. The oupu signals produced by he feedbac secion are d, d and d 3, which in heir urn drive he hree legs of he inverer in accordance o he previously explained echnique. 3 Harmonic analysis of he curren drawn from he supply newor The ever-growing complexiy of elecrical sysems requires he developmen of apparauses able o monior and regulae woring condiions coninuously. For his reason, compuaion algorihms were implemened ha, on he basis of measuremens a cerain sysem poins were able o esablish he real-ime woring sysem sae [6], [7], [8], [3], [4]. The daa supplied from he measuremens and acquired on elecrical apparauses can be properly processed by means of a number of algorihms such as he FFT algorihm, which is commonly used o improve he qualiy of samples obained from he measuremen sysem [9], [5]. In his paper, he FFT is used o monior he harmonic conen of he wave shape of he curren drawn from he supply newor. The algorihm processes curren samples acquired by means of a measuremen sysem placed beween he newor and he inpu erminaions of he hree-phase recifier as shown in Fig.. ewor R S T iing() iing() iing3() Recifier 3-Phase Fig. Currens acquired by he measuremen sysem for he subsequen FFT analysis. For simpliciy reasons, in he following he performed harmonic analysis is illusraed only for he R-phase curren, since he shapes of all currens of he hree-phase sysem are equal and shifed from one anoher. Assuming he series i in (n)i in (n ) obained from he coming samples of he measured i in () curren, he DFT (Discree Fourier Transform) can be expressed as: Iin f i n e jπ fn ( ) in ( ) (4) where f is he frequency sample inerval (compued using he following relaion: f/ ) and is he sampling ime. The inverse discree Fourier ransform is: iin n f I f e jπ fn ( ) in ( ). (5) In order o simplify relaion (4), he quaniies and f can be omied obaining he following noaion: Iin i n e j π n / ( ) in ( ) (6) ISS: Issue 5, Volume 7, May 8

5 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS In he same way, relaion (5) can be wrien as: i in in ( n) I ( ) e j πn / (7) The compuaion complexiy of relaion (7) is O( ). If he number of samples is no a prime number, i is possible o opimize he compuaion by properly grouping some operaions depending on he facorizaion of. In his case, a faser algorihm can be obained, which also causes FFT o be equivalen o a fas DFT. The maximum reducion in ime compuaion aes place when is a muliple of, i.e. p. In his case, he Cooley-Tuey algorihm can be applied. The complexiy of his algorihm, also nown in lieraure as FFT- or radix-fft, is O( log ), [], [], []. 3. The FFT algorihm The FFT algorihm is opimized o perform he DFT (Discree Fourier Transform) in less ime. The DFT in is urn represens he applicaion of he Fourier ransform on he discree form. Generally speaing, he Fourier ransform applied o a coninuous funcion f() on he ime domain supplies as a resul a coninuous funcion F(f) on he frequency domain as shown in his relaion: F + ( f ) jπf f () e d (8) The inverse of he Fourier ransform, which allows o pass from he frequency domain o he ime domain, is shown in he following relaion: f + ( ) F(f ) e df jπf (9) I is useful o remember ha funcions f() and F(f) are coninuous funcions in he ime and frequency domains, respecively. Le us suppose o operae in he ime domain on a discree funcion, which means an x(n) funcion consising of a sequence of (,..., ) samples, usually defined as x(), x(),, x(), as when measuremen samples are acquired. The examined x(n) discree funcion is a monodimensional array (vecor) having dimension equal o. The Fourier ransform heory can also be applied o he x(n) discree funcion; in his case he algorihm is named Discree Fourier Transform (DFT), and is repored in he following relaion: X() n x(n) e j π n,..., () Relaion () allows o pass from he x(n) ime domain o he X() frequency domain. For he inverse operaion, ha is o say, passing from he f frequency domain o he n ime domain, he Inverse Discree Fourier Transform (IDFT) mus be used, as repored below: x(n) X() e j π n n,..., () I mus be always ep in mind ha, similarly as for relaions (4) and (5), also in relaions () and () he sample inervals (boh in he ime domain ( ) and frequency domain ( f)) can be assumed as uniary values. In his case, formulas () and () are in heir exended forms as follows: ( f ) x( n ) X x ( n ) f X( f ) wih f. e e j π f n j π f n The X() componens are imaginary numbers, which acually represen he modules and phases of he sinusoidal componens of he x(n) samples. The DFT allows o pass from x(n) o X(), whereas he IDFT shows he x(n) relaion as a sum of X() sinusoidal componens e frequency per sample cycle. j π n, wih The above explanaion concerns he DFT applied o a vecor of measured samples such as (x(), x(),,x()). In his case he DFT is also defined as mono-dimensional. In pracical cases, he Fourier ransform may someimes need o be applied o a number of vecors obained from differen (x n, x n,,x nd ) ime inervals. In such cases he DFT is defined as muli-dimensional, bu is menioned only for compleeness and was no used in he examined cases. In order o compue he X() hrough relaion () direcly, a number of arihmeical operaions equal o O( ) are required. In his case some operaions lined o relaion () can be grouped in order o obain a less complex, faser algorihm. If he Fourier Transform is applied o a discree signal composed of samples, a facorizaion of can be made, ha is some operaions will be adequaely grouped so as o reduce compuaion ime ISS: Issue 5, Volume 7, May 8

6 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS considerably and obain a fas algorihm of he DFT. The mos widely used algorihm of his ind is he Cooley-Tuey algorihm, which is based on he divide e impera principle, ha is o say a DFT is cu recursively off any dimension where is a number of smaller DFT having dimensions and, respecively. Le us suppose o have samples (x(), x(),, x()) obained from a measuremen process and o perform he DFT on his vecor. If he sandard DFT algorihm is applied in order o compue all he samples (X(), wih,,, ), he number of complex muliplicaions o be performed is equal o. In case he periodiciy of he exponenial funcion j πf e cos( πf ) + j sin( πf ) is exploied, i is possible o use he same complex muliplicaions many imes, which allows he above menioned facorizaion of he number of muliplicaions. In order o perform he FFT algorihm, he firs operaion is o separae he X() former / frequency samples from he laer / samples wih,,,, where each X() erm is obained from he summaion of relaion (). The second operaion is a subdivision inside relaion () of he erms wih even indexes from hose wih odd indexes as shown in he following relaion. ( ) X x(n) e x(n) (n) j π n + wih,,...,. n x(n) x(n + ) n (n + ) j π () From relaion () he posiion e can be assumed. In his case relaion () becomes: K X( ) X( ) + x(n + ) ( ) + X ( ) n X wih,,...,. n (3) ih relaions () and (3) only he / frequency samples are considered (X() (,,, /) and inside heir relaion () even erms were separaed from he (+) odd erms. The subsequen / samples of X() can be expressed hrough he following relaion: + X + X + + X + (4) wih,,...,. As previously menioned, in order o reduce he number of muliplicaions of he DFT algorihm, he periodiciy of he exponenial funcion ϕ e j cos( ϕ) + j sin( ϕ) is exploied obaining he FFT. Acually, he complex muliplicaions used for he compuaion of he former / samples X() wih (,,, /) can be reused also on he compuaion of he laer / samples X() (/, /+,, -) by using proper linages beween erms wih even and odd indexes, respecively. The decimaion relaions a he basis for he procedure are he following: X + X( ) (5) + X + X where,,...,. ( ) (6) The equaliy of relaion (6) can be undersood wih he following relaion: e (+ ) j π e e j π (+ ) j π e e j π n j π e e j π j π (7) Finally, he samples X() (,,, of he measures (n) (,,, ) can be obained hrough he applicaion of he FFT algorihm implemened wih relaions: ( ) X ( ) + X ( ) X (8) X + X( ) X( ) (9) where,,...,. Relaions (8) and (9) show ha he former / samples X() (,,, ) change only he sign of he algebraic sum beween he erms X ; his allows o obain also X ( ) and ( ) ISS: Issue 5, Volume 7, May 8

7 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS he laer erms of he succession X() (wih, +,..., ). Fig. shows he operaion reducion by applying he Cooley-Tuey algorihm. In his siuaion, he reference curren esablished for feed-bac conrol was A. Fig. shows ha he AC/DC oupu curren follows he reference value imposed by he conrol sysem, if a very small ripple facor is negleced. Figs. 3, 4 and 5 show he oupu curren wih an inpu reference of he conrol sysem ( I ref ) of A, 3A and 4A respecively, wih a load of R LOAD.3 Ω. 3 Fig. Decimaion process of he Cooley-Tuey algorihm. hen samples are available, i is possible o operae a series of subsequen halved cus o compue he sample X(). If is a power of : p wih p. i is possible o have a number of halved cus equal o log (). For each cu he number of complex muliplicaions are. Finally, for a number of p samples, he number of operaions necessary o apply he FFT algorihm is log while he muliplicaions necessary ( ( )) O for he DFT algorihm are ( ) O. 4 Experimenal and compuaion resuls Fig. shows he wave shape of he oupu curren coming from he six-phase AC/DC converer when a resisive load of R LOAD.3 Ω is applied. Fig. 3. Converer oupu curren wih an inpu curren reference of A. Fig. 4. Converer oupu curren wih an inpu curren reference of 3 A. Fig.. ave shape of he curren presen downsream of he six-phase AC/DC converer (oupu curren A). Fig. 5. Converer oupu curren wih an inpu curren reference of 4 A. ISS: Issue 5, Volume 7, May 8

8 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS The resuls obained confirmed he correc behaviour of he proposed sysem. The wave shape of he R-phase curren upsream of he non-acive hree-phase recifier is shown in Fig. 6. The value of he curren pea is abou 36A while he T period of he curren wave is ms, corresponding o a frequency of 5 Hz. Table Harmonic analysis of he curren drawn from he supply newor. Harmonic order Frequency[Hz] Ampliude[A] 5, 7,95 5,, , 8, ,, ,, ,,3 7 95,,7399 Finally, able shows he efficiency of he proposed converer. Fig. 6. ave shape of he R-phase curren drawn from he newor. The resuls of he FFT analysis applied o he phase curren of Fig. 6 are shown in Fig. 7. Fig. 5. Resuls of he FFT applied o he R-phase curren drawn from he newor. The ampliude of he fundamenal frequency and oher harmonics are repored in able. These resuls give rise o he following observaions. The frequency of each subsequen harmonic is - Hz greaer han he previous one, saring and proceeding alernaively from he fundamenal frequency. As concerns ampliudes, he fundamenal aes up a value of A/, where A is he pea ampliude of he wave shape of he curren drawn by he converer. The second harmonic aes up a value of A/, he hird harmonic A/3, he fourh harmonic A/4 and so on. Table Efficiencies of he four-sage converer for differen values of he oupu currens. Iou[A] Pin[] Pou[] η 3,7 74,8, , , ,5 657, ,57 875, ,7 5 Conclusions A new ype of an AC/DC high curren converer composed of four sages was presened. The firs sage performed an AC/DC conversion while he second and fourh sages employed a specific swiching procedure performing a DC/AC and AC/DC conversions, respecively. The fourh sage was supplied by an elecric ransformaion secion which was acually he hird sage. The inverer commued wih a 4 Hz carrier frequency, and a 6-phase sar recifier was conneced downsream he ransformer. Experimenal laboraory ess on a converer prooype validaed he correc behaviour of he new archiecure. Also a harmonic analysis of he curren drawn from he supply newor was performed using he FFT algorihm, and finally he shapes of he recorded oupu currens were repored and discussed. The proposed sysem could be effecively employed in fields requiring very high DC currens, such as elecric racion and elecrochemical applicaions. References: [] S. u, L. B. Zhou, S.H. Huang, A sudy on doubly-fed inducion machine wih bidirecional AC/DC/AC converer, Universiies Power Engineering Conference, 4 UPEC ISS: Issue 5, Volume 7, May 8

9 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS 4 39h Inernaional, Vol., 6-8 Sep. 4, pp [] Z. ang, L. Chang, PM AC/DC boos converer sysem for inducion generaor in variable-speedwind urbines, Elecrical and Compuer Engineering, 5 Canadian Conference on, -4 May 5, pp [3] F. Muzi, C. Buccione, S. Mauone, A new archiecure for sysems supplying essenial loads in he Ialian High-Speed Railway (HSR), SEAS Transacions on Circuis and Sysems, Issue 8, Volume 5, Augus 6. [4] B. R. Lin, D. J. Chen, Single-phase neural poin clamped AC/DC converer wih he funcion of power facor correcor and acive filer, Elecric Power Applicaions, IEE Proceedings, Vol. 49, Jan., pp [5] F.C. Qun Zhao Lee, T. Fu Sheng, Volage and curren sress reducion in single-sage power facor correcion AC/DC converers wih bul capacior volage feedbac, Power Elecronics, IEEE Transacions on, Vol. 7, July, pp [6] R. Morrison, M.G. Egan, A new modulaion sraegy for a buc-boos inpu AC/DC converer, Power Elecronics, IEEE Transacions on, Vol. 6, Jan., pp [7] L. Bor Ren, H. Chun Hao, Single-phase converer wih flying capacior opology, TECO 4 4 IEEE Region Conference, Vol. 4, -4 ov. 4, pp [8] K. Y. Lee, H. Y. Hsu, Y. Lai, Simple Digial- Conrolled AC/DC Converer wih Power Facor Correcion for Universal Inpu Applicaions, Indusrial Elecronics Sociey, 7 IECO 7. 33rd Annual Conference of he IEEE, 5-8 ov. 7, pp [9] E. gandui, P. Sicard, Probabilisic models of harmonic currens produced by welvepulseac/dc converers, Power Delivery, IEEE Transacions on, Vol. 9, Oc. 4, pp [] S. Saponara, P. Terreni, Cos-effecive design of AC/DC converer wih programmable poweramplificaion, Indusrial Technology, 4 IEEE ICIT '4 4 IEEE Inernaional Conference on, Vol., 8- Dec. 4, pp [] J. Mahdavi, S. Kaboli, H. A. Toliya, Conduced elecromagneic emissions in uniy power facor AC/DC converers: comparison beween PM and RPM echniques, Power Elecronics Specialiss Conference, 999 PESC 99 3h Annual IEEE, Vol., 7 June- July 999, pp [] A.. Segura, P. B. Sanchez, Experimenal measuremen of non-characerisic harmonic power generaed by hyrisor pulse-conrolled AC/DC hree phase converers, Indusrial Elecronics, 996 ISIE '96, Proceedings of he IEEE Inernaional Symposium on, Vol., 7- June 6, pp [4] P. Maavelli, Design aspecs of harmonic filers for high-power AC/DC converers, Power Engineering Sociey Summer Meeing, IEEE, Vol., 6 July, pp [5] T. Masuawa, M. Shioyama; omura, J.; eumeyer, C.; Tsuji-Iio, S.; Shimada, R., Synchronous recifier using power-mosfet for high curren AC/DC converer sysem, Fusion Engineering, 9h Symposium on, -5 Jan., pp [6] F. Muzi, A new digial power condiioner o improve qualiy and safey in elecrical disribuion sysems, IEEE-PES General Meeing, June 6-, 4, Denver, Colorado, USA. [7] S. D Oavi, F. Muzi, L. Passacanando, A real-ime predicion procedure of he sae of an elecrical disribuion sysem, 6h SEAS Inernaional Conference on Applicaions of Elecrical Engineering, Isanbul, Turey, May 7-9, 7. [8] F. Muzi, L. Passacanando, A real-ime monioring and diagnosic procedure for elecrical disribuion newors, Inernaional Journal of Energy, (a AU, orh Alanic Universiy Union, Journal), Issue, Vol., 7 [9] I. D. Lu, P. Lee, Use of mixed radix FFT in elecric power sysem sudies, Power Delivery, IEEE Transacions on, Vol. 9, July 994, pp []H. Sorensen, D. Jones, C. Burrus, Real-valued algorihms for he FFT, Acousics, Speech, and Signal Processing, IEEE Inernaional Conference on ICASSP '87, Vol., Apr.987, pp [] D. Sundararajan, M. O. Ahmad, Swamy, M..S., Vecor compuaion of he discree Fourier ransform, Circuis and Sysems II: Analog and Digial Signal Processing, IEEE Transacions on [see also Circuis and Sysems II: Express Briefs, IEEE Transacions on], Vol. 45, April 998, pp [] M. Puschel, Cooley-Tuey FFT lie algorihms for he DCT, Acousics, Speech, ISS: Issue 5, Volume 7, May 8

10 SEAS TRASACTIOS on CIRCUITS AD SYSTEMS and Signal Processing, 3. Proceedings. (ICASSP '3). 3 IEEE Inernaional Conference on, Vol., 6- April 3, pp [3] C. Barolei, G. Fazio, F. Muzi, S. Ricci, G. Sacerdoi, Diagnosics of Elecric Power Componens: an improvemen on signal discriminaion, SEAS Transacions on circuis and sysems, Issue 7, Volume 4, July 5. [4] F. Muzi, An alernaive FMECA procedure o design disribuion sysem reliabiliy, SEAS Transacions on Power Sysems, Issue, Volume, ovember 6. [5] F. Muzi, C. Buccione, S. Mauone, A new archiecure for sysems supplying essenial loads in he Ialian High-Speed Railway (HSR), SEAS Transacions on Circuis and Sysems, Issue 8, Volume 5, Augus 6. ISS: Issue 5, Volume 7, May 8