Predictive middle point modulation: a new modulation method for parallel active filters

P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales, Juan M. Ca asco, Juan A. Sánchez, Luis Te ón, Leopoldo Ga cía F anquelo. DEPT. OF ELECTRONIC ENGINEERING. UNIVERSITY OF SEVILLE Escuela Supe io de Ingenie os. Camino de los Descub imien os. Isla de la Ca uja. Se ille, Spain el: 954 48 73 74. ax: 954 48 73 73 e-mail: pe ales@g e.esi.us.es, [email p o ec ed], shanshe@g e.esi.us.es, syl@g e.esi.us.es, leopoldo@g e.esi.us.es Keywo ds Ac i e il e s , Modula ion s a egies, Powe ac o co ec ion, Powe Quali y Abs ac When designing an Ac i e il e , using a cu en -con olled ol age sou ce in e e , he e a e wo main asks : o gene a e an app opia e e e ence, o nulling ha monic cu en and eac i e powe , an , on he o he side, o gene a e a swi ching pa e n ha pe mi s o ollow he e e ence as close as i can be done. P edic i e Middle Poin Modula ion (PMPM) is a no el modula ion echnique, specially sui ed o Ac i e Fil e s. This me hod is de i ed om p edic i e Dead-Bea con olle , imp o ing i s dynamic esponse and cu en e o . Simula ion esul s con i m he alidi y o he p oposed me hod. Expe imen al esul s will be p o ided in he inal pape . I. In oduc ion PWM me hods ha e became e y popula on cu en -con olled ol age sou ce in e e s (CC_VSI). Many open-loop and closed-loop me hods ha e been desc ibed in li e a u e [1], [2], [3], [4]..., ocused mainly on mo o con ol, o gene ically con ol o elec onic loads. When he ‘load’ is he public g id, special conside a ions had o be aken in o accoun , as he p oblem is qui e di e en : • S a ing ha ol age on public g id is igid, he CC-VSI ac s pu ely as a cu en sou ce. • i is e y easy o de elop a simpli ied model o he en i e sys em, and hen use a p edic i e con ol me hod. • When using a Space Vec o me hod, ec o s 0 and 7 (ze o ol age ec o s) a e no in e changeable, and should be conside ed as he o he ec o s. Also, depending on he applica ion and opology o he in e e , a pa icula modula ion me hod could be be e o wo se. Dealing wi h ou wi ed – h ee legged sys ems, he use o Space Vec o modula ion ins ead o classic pulse wid h modula ion is no jus i ied in e ms o simpli ying algo i hms, as i is necessa y o use some 3D ec o modula ion, no a simple 2D ec o modula ion. In addi ion, in ou -wi ed sys ems each leg can be con olled sepa a ely, con e ing he con ol p oblem in con olling h ee 1-phase in e e s This pape p oposes a new me hod o calcula ing commu a ion ime o each leg o a h ee phase, ou wi e in e e , commonly used in Shun Ac i e Fil e s, as shown in Figu e 1. Fi s , in sec ion II, we p esen an o e iew o he shun ac i e il e case in s udy, in o de o s a e some conside a ions abou he modula ion Fig. 1: 3-phase 4-wi e in e e L L L C1 C2 T1 T2 T3 T4 T5 T6 R S T N _________________________________________________________________________________________________________________ P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales __________________________________________________________________________________________________________________ EPE 2001 - G az P. 1 me hod desi ed. Then, in sec ion III we p esen he simpli ied model o he in e e connec ed as a shun ac i e il e , and based on ha model, we p esen he basic equa ions o he new modula ion s a egy. In sec ion IV we p esen some simula ion esul s and compa ison wi h o he me hods. In sec ion V we show he expe imen al p o o ype, unde de elopmen by now, in which he algo i hm will be es soon. Finally, in sec ion VI we p esen some conclusions abou modula ion s a egies o ac i e il e s. II. CC-VSI used as Shun Ac i e Fil e When using an CC-VSI o build a shun ac i e il e , he e a e some conside a ions ha should be aken in o accoun , ela ed o modula ion me hod. The main cha ac e is ics ha make his necessa y a e: • The shape o he e e ence cu en o be ollowed is no sinusoidal a all. I has, indeed, all he ha monics o he load, and uses o ha e e y sha pen slopes. • The load, as commen ed be o e, is he public g id, which is mos ly a ol age sou ce and a li le se ies impedance. • I is e y impo an o ack he e e ence as quick as i can be possible, because he compensa ion e ec i eness depends on i . • The e ec i eness o compensa ion lays on he wo sides - he gene a ion o he e e ence and he acking o his e e ence- o he p oblem. The e o e a balanced solu ion mus be p o ided be ween a pe ec –bu slow- e e ence gene a o and a quick acking me hod ha makes impossible o calcula e he app op ia e e e ence. The en i e sys em can be ep esen ed as in igu e 2. In his pic u e we can see he public g id, ha will be conside ed as a non-ideal ol age sou ce, wi h i s se ies impedance; also, he load will be a hy is o ec i ie , wi h a high 5 h , 7 h and 11 h ha monic, and low powe ac o (a ound 0.87); The il e i sel will be implemen ed wi h he CC-VSI, di ided in o e e ence gene a o and e e ence acking. The pe o mance o a modula ion echnique can be measu ed in so many di e en ways [3], and depending on he applica ion designed, some c i e ia had o be conside ed mo e impo an han o he s. Fo he Ac i e Fil e (AF) applica ion, he mos impo an c i e ion could be a as esponse, because he shape o he e e ence o be ollowed is e y sha p in ce ain egions and e y la in o he egions. Also, i is e y impo an o educe high equency ha monics gene a ed by he in e e , as he AF is designed o educe THD o a load. Fig. 2: Gene al block diag am Z L LOAD REFERENCE GENERATION (DSP) MODULATION TECHNIQUE 3-PHASE 4-WIRE V-SOURCE INVERTER + - D Q Q i S i L i F N Public G id (3-phase + neu al) Ac i e Fil e _________________________________________________________________________________________________________________ P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales __________________________________________________________________________________________________________________ EPE 2001 - G az P. 2 The p oblem is e y di icul o a o d, because he e e ence gene a o is no o ally decoupled om he acking me hod, and he e a e many e ec s ha had o be aken in o accoun , as he e ec o dead imes, he e ec o o he sys ems in e e ing wi h ou il e , o he public g id impedance, among o he s. The e o e, an app oxima ion should be con enien , a leas as a s a ing poin . III. P edic i e Middle Poin Modula ion App oxima ed model In o de o e alua e he pe o mance o di e en modula ion me hods, a Simulink model o he en i e sys em was buil . The ollowing conside a ions ha e been made: • Sou ce (ne ) impedance is much less han he se ies induc ance o he Ac i e Fil e . • Capaci o ol ages s ay cons an on a sample ime • Sou ce ol ages also emains cons an on a sample ime • Each phase is decoupled om he o he wo, and i s cu en depends only on he posi ion o i s swi ches and on he ol age o he ne on i s phase. Really, he ou h conside a ion could be de i ed om he second one, as he DC-LINK is he only poin o connec ion be ween phases. Using his simpli ica ions, he sys em was linea ized pe phase using he basic scheme shown in Figu e 2. Fo his scheme, he main equa ions ha gi es cu en on phase , depending on he posi ion o swi ches T1 and T2 a e s a ed in Eq.1 whe e V is he line ol age(phase o neu al) , nulling he e ec o sou ce impedance, i is phase cu en o he il e , and VC1 and VC2 a e ol ages ac oss he upside and downside capaci o s. Modula ion S a egy The e a e many me hods o modula e a signal using Pulse Wid h Modula ion echniques. A iangula wa e o m is commonly used, which is compa ed wi h he signal o be modula ed, and he compa ison decides wha swi ch has o be u ned on. The p esen me hod is a a ia ion o he classical suboscila ion me hod known as p edic i e Dead-Bea con olle [5]. In ha me hod, he in e e ol age is chosen in o de o null cu en e o a he end o he sample pe iod. Tha me hod p esen s some disad an ages o using in Ac i e Fil e s: • The e e ence is eached a he end o he pe iod, so he delay is, a leas , one sample ime. • The e o is no dis ibu ed symme ically, so he in eg al e o is no ze o. Now, we will y o minimise wo pa icula pe o mance c i e ia, specially impo an o ac i e il e s, as s a ed be o e: • The cu en e o , measu ed as he in eg al o he di e ence be ween cu en e e ence and ac ual cu en . • The delay be ween e e ence and cu en , measu ed as he ime in which he cu en equals he e e ence. Fig. 3: Simpli ied Sys em Model Eq 1. L C1 C2 V T2 T1 Vc1 Vc2 I )(:, :, 221 121 V Vc d di LonTo T V Vc d di Lo TonT +−=⋅ −=⋅ _________________________________________________________________________________________________________________ P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales __________________________________________________________________________________________________________________ EPE 2001 - G az P. 3 F om his poin , we calcula e commu a ion ime, using linea ized equa ions, in o de o minimise bo h delay ime and cu en in eg al e o . The a ge is o ge an a e age cu en , du ing a sample ime, equal o he e e ence we a e acking. In Figu e 3 is shown he e olu ion o cu en on a sample ime, in a ypical iangula PWM suboscilla ion me hod. whe e: 1, 2 : pe iods when he uppe and lowe swi ch a e connec ed, espec i ely. T: Commu a ion pe iod. ia , ib , ic: wa e o ms o he cu en in he h ee in e als o a commu a ion pe iod, (no ha ing in coun dead imes) I0: Ini ial cu en , measu ed a he beginning o a commu a ion pe iod. I1 ,I2 ,I3: Final cu en s a he end o each in e al. The a e age cu en in he in e al could be calcula ed as ollows : whe e 1 and 2 a e he ime whe e swi ches T1 and T2 a e u ned on, espec i ely. Le us conside ha ol age o e capaci o s a e balanced, so VC1 a e equal o VC2. Then, a e age cu en can be calcula ed as: Finally, i we wan IAV o be equal o he cu en e e ence, being I0 ac ual (measu ed) cu en , hen 2 can be calcula ed as: The e a e some ad an ages di ec ly de i ed om he use o his modula ion: • The a e age cu en o e he sample ime is equal o he e e ence calcula ed. • The e e ence, i sel , is eached a he middle o he sampling ime. Tha ea u e gi es he name o he me hod (P edic i e Middle Poin Modula ion, PMPM). Eq. 2 Eq. 3 11 1 122 1 2 2 2 1 011 1 1 2 1 0 2/ 000 2/ 0 )··(;)·()( ;)··(;)·()( ;)·()( · 2 212 V VcII V VcI i V VcII V VcI i V VcI i d id id id iIT LL c LL b L a c T b aAV −+=+−= +−=−+= +−= ⋅+⋅+⋅=⋅= ∫∫∫∫ [] Vc V VcT L II AV ⋅⋅−−⋅⋅ ⋅ += 20 2)( 2 1 Vc TV Vc II Vc L AV ⋅ ⋅− +−⋅= 2 )( )( 02 Eq. 4 d iiI T e )·( 0 ∫−= ε Eq. 5 I e I 0 I 1 I 2 I 3 2 /2 2 /2 1 T i i c ( ) i b ( ) i a ( ) Fig. 4: Cu en e olu ion _________________________________________________________________________________________________________________ P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales __________________________________________________________________________________________________________________ EPE 2001 - G az P. 4 • he in eg al e o , de ined in Eq. 5, is null, supposing all magni udes ixed o e one commu a ion pe iod, because is null on each pe iod. • I is e y as and simple o calcula e 2. In ac , we calcula e 2·Vc, and hen compa e wi h T·Vc o gene a e pulses, in o de o a oid di ision in eal ime calcula ions. IV. Simula ion Resul s Many simula ions we e pe o med wi h he linea ized model o he shun AF, in o de o p o e he alidi y o he me hod. Basically, a Bang-Bang me hod and he new PWM me hod a e o be compa ed. The elec ion o he Bang-Bang me hod as a e e ence o compa ison is mo i a ed by i s simplici y and i s ela i ely good esul s. I can be demons a ed ha Bang-Bang me hod is he as e me hod, in e m o calcula ion and one o he be e in e ms o con ollabili y. Nex , we p esen Fig 5: Simula ion esul s o Bang-Bang a 10kHz. (a) Cu en wa e o ms o load and sou ce side, (x axis in seconds , y -axis in am p e es ); ( b ) Sou ce Cu en S p ec um. ( x-axis in Hz , y -axis in p e cen o 1s ha monic ) ( a ) ( b ) Fig. 6: Simula ion esul s o Bang-Bang a 20kHz. (a) Cu en wa e o ms o load and sou ce side, (x axis in seconds , y -axis in am p e es ); ( b ) Sou ce Cu en S p ec um. ( x-axis in Hz , y -axis in p e cen o 1s ha monic ) ( a ) ( b ) 0.545 0.55 0.555 0.56 0.565 0.57 0.575 0.58 -40 -30 -20 -10 0 10 20 30 40 01000 2000 3000 4000 5000 6000 7000 8000 9000 0 1 2 3 4 5 6 7 8 9 02000 4000 6000 8000 10000 12000 14000 16000 18000 0 0.5 1 1.5 2 2.5 0.54 0.545 0.55 0.555 0.56 0.565 0.57 0.575 0.58 -40 -30 -20 -10 0 10 20 30 _________________________________________________________________________________________________________________ P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales __________________________________________________________________________________________________________________ EPE 2001 - G az P. 5 simula ion esul s o an ac i e il e applied o a hy is o ec i ie , cha ac e ised using ac ual measu es o he cu en . Figu e 5 and 6 p esen s esul s o simula ion using Bang-Bang me hod , a 10kHz and 20kHz o commu a ing equency. Wa e o ms o load (uncompensa ed) and sou ce (compensa ed) cu en s, and he FFT o he compensa ed cu en a e shown: Figu e 7 and 8 shows he same cu es, using PMPM me hod. I can be app ecia e ha ipple dec eases d ama ically, and Spec um is concen a ed on he commu a ion equency. I should be no ed ha no all he spec um g aphics ha e he same scale, in o de o gain p ecision, al hough his could leads o con usion. In Table I, he main esul s a e shown. he THD was calcula ed only wi h he i s 30 ha monics, o m 100Hz o 1500Hz, because he in e es o an ac i e il e is ocused on low o de ha monics. Fig. 7: Simula ion esul s o PMPM a 10kHz. (a) Cu en wa e o ms o load and sou ce side, (x axis in seconds, y -axis in am p e es ); ( b ) Sou ce Cu en S p ec um. ( x-axis in Hz , y -axis in p e cen o 1s ha monic ) ( a ) ( b ) Fig. 8: Simula ion esul s o PMPM a 20kHz. (a) Cu en wa e o ms o load and sou ce side, (x axis in seconds, y -axis in am p e es ); ( b ) Sou ce Cu en S p ec um. ( x-axis in Hz , y -axis in p e cen o 1s ha monic ) ( a ) ( b ) 0.54 0.545 0.55 0.555 0.56 0.565 0.57 0.575 0.58 -30 -20 -10 0 10 20 30 01000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 1 2 3 4 5 6 7 8 9 0.54 0.545 0.55 0.555 0.56 0.565 0.57 0.575 0.58 -30 -20 -10 0 10 20 30 00.2 0.4 0.6 0.8 11.2 1.4 1.6 1.8 2 x 104 0 0.5 1 1.5 2 2.5 3 3.5 _________________________________________________________________________________________________________________ P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales __________________________________________________________________________________________________________________ EPE 2001 - G az P. 6 Table I: Simula ion Resul s Me hod THD (<1500 Hz) 5 h Ha m. Bang Bang a 10kHz 11.96 % 3.4% Bang Bang a 20kHz 3.96% 2.3% PMPM a 10kHz 3.7% 2.07% PMPM a 20kHz 2.25% 1.32% I should be no ed ha he THD is always g ea e in Bang-Bang han in PMPM, e en doubling he equency. The 5 h ha monic is shown as i is he g ea es ha monic in he load, and he smalle i emains in he compensa ed cu en , he be e is he me hod o acking he e e ence. V. Expe imen al Model An expe imen al model is being cons uc ed o inally alida e he simula ion esul s ob ained. I is based on a p e ious wo k o he au ho s [6], and basically consis on a h ee-phase IGBT ol age Sou ce In e e , connec ed hough a 380/220 au o ans o me . The DSP boa d, in his case, was composed by wo DSP-based boa ds. The i s o hem, based on he TMS320C31 om Texas Ins umen s, is used o calcula e an app op ia e e e ence, in eal ime (20kHz). The second one is based on he TMS320F243, o m Texas Ins umen s, which is a ixed-poin DSP wi h PWM modula o s buil in. In Figu e 9 a gene ic o e iew o he ins alla ion is shown, and in Figu e 10 a pic u e o he digi al sys em is shown, ma king he mo e impo an pa s o i . Fig. 9: Expe imen al model Fig. 10: Digi al Con ol Boa ds DSP BOARD iL iL R S T N LOAD Swi ching Signals iLs iL iF iFs iF V Vs V 220V-50Hz 220:127 iF V s VDC _________________________________________________________________________________________________________________ P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales __________________________________________________________________________________________________________________ EPE 2001 - G az P. 7 VI. Conclusions When dealing wi h non sinusoidal wa e o ms, specially wi h locally high slopes, no all he modula ion me hods shows good esul s. In he pa icula case o ac i e il e s, an ex a ca e ha e o be aken in choosing he modula ion me hod, as i con ibu es d ama ically o he success o no o he il a ion. The main cha ac e is ics o a modula ion me hod o be selec ed, in his a ea, will be a as esponse and a minimal e o in acking a e e ence, e en al hough he elec ical e iciency will be less han in o he me hods. A new me hod o modula ion, specially sui ed o Shun Ac i e il e s bu use ul in any g id- connec ed applica ion, is p esen ed. Simula ion esul s con i ms heo e ical conclusions, showing a e y good and as esponse. An expe imen al model is being inished, and soon we will be able o p esen expe imen al esul s, o con i m he alidi y o he modula ion me hod p esen ed. Re e ences 1. Joachim Hol z. “Pulsewid h Modula ion Techniques o Con olled AC D i es” Con e ence held on Ma ch, 3- 2000, in he E.S.I. Se illa. 2. M. A. Dzieniakowski, M. P. Kazmie kiwski, “Sel - uned uzzy PI Cu en Con olle o PWM_VSI”. P oc. EPE Con . 1995. pp 1308-1313. 3. Ma ian P. Kazmie kowski, Luigi Malesani, “Cu en Con ol Techniques o Th ee-Phase Vol age Sou ce PWM Con e e s: A Su ey. IEEE T ans. on Ind. Elec, Oc .1998. Vol 45, no 5, pp 691-703 4. Michael M. Bechm F ede Blaabje g, John K. Pede sen, “Random Modula ion Techniques wi h Fixed Swi ching equency o Th ee-Phase Powe Con e e s. IEEE T ans. on Powe Elec. July 2000, Vol 15, no 4, pp 753-761. 5. T. Kawaba a, T. Miyashi a, Y. Yamamo o, “Dead Bea Con ol o h ee-phase PWM in e e ”, IEEE T ans. Powe Elec onics, Jan. 1990 Vol 5, pp 21-28. 6. J.M. Ca asco, M. Pe ales, B. Ruiz, E.Gal án, L.G. F anquelo, “ DSP Con ol o an Ac i e Powe Line Condi ioning sys em”. EPE’97, ISBN 90-75815-02-6 _________________________________________________________________________________________________________________ P edic i e Middle Poin Modula ion: A New Modula ion Me hod o Pa allel Ac i e Fil e s Manuel A. Pe ales __________________________________________________________________________________________________________________ EPE 2001 - G az P. 8