Mitigation of Stability Problem in a Boost Converter having an Input Filter.

Transcription

1 Mitigatin Staility Prlem in a Bt nverter having an Input Filter..A. Nwu, M.Eng. and.. Ama, Ph.. epartment Electrical Engineering, Univerity Nigeria, Nukka, Nigeria. cajethannwu@yah.cm epartment Phyic and Atrnmy, Univerity Nigeria, Nukka, Nigeria. grg_chira@yah.cm ABSTAT Thi paper preent a theretical analyi the taility tatu a t cnverter having an input ilter uing a mallignal equivalent circuit mdel. The additin an input ilter ditrt the dynamic repne the aic cnverter mdel, wing t the preence in the reulting traner unctin dulepair cmplex cnjugate ple, and a pair let halplane cmplex cnjugate zer. The glitch cnequence in the vicinity ilter renant requency nticed in the Bde plt and the attendant reductin in phae margin i mitigated y the damping the input ilter. An imprved parallel damping apprach reulted in appreciale increae in the ytem phae margin. (Keywrd: input ilter, taility, damping, phae margin) INTOUTION Uually, a witching cnverter inject a pulating current i g (t) int the pwer urce v g (t) the cnverter. It ha een erved that the Furier erie the pulating current cntain harmnic at multiple the witching requency the cnverter []. The magnitude the higherrder harmnic can al e igniicantly aected y the current pike caued y dide revere recvery, and al y the inite lpe the witching tranitin. The large highrequency current harmnic i(t) can interere with televiin and radi receptin, and can dirupt the peratin neary electrnic equipment. T meet limit n cnducted electrmagnetic intererence (EMI) and t imprve the reliaility the ytem, it i neceary t add an input ilter t the cnverter. The rle the input ilter are t: () attenuate the witching harmnic that are preent in the cnverter input current waverm, () prtect the cnverter and it lad rm tranient that appear in the input vltage v g (t), therey imprving the ytem reliaility, and () prvide cmpliance with regulatin that limit cnducted EMI. Several cheme invlving twitched cnverter and quairenant cnverter are dcumented in the literature [] [4]. Other apprache aimed at cauing the cnverter input current i g (t) t e prprtinal t the applied input vltage v g (t) have al een dcumented []. An example uch an apprach emply a ullwave dide rectiier netwrk, cacaded y a dcdc cnverter. The cntrller mut caue the cnverin rati given in Equatin () t vary etween ininity (at the ac line vltage zer cring) and me minimum value (at the peak the ac line vltage waverm): v(t) V M(d(t)) () v (t) V in( ωt) r m The capaility prducing the M(d(t)) Equatin () i limited t t, uckt, SEPI, and c uk cnverter, ut till require minimal input EMI iltering. Thee cheme all all hrt addreing the prlem utlined in () and (), hence the need r a lwpa ilter having attenuatin uicient t meet cnducted EMI peciicatin at the cnverter input. The additin input ilter, nnethele, change the dynamic the cnverter, ten in a manner that degrade regulatr perrmance. The tranient repne i mdiied, and cntrl ytem may even ecme untale. The utput impedance may ecme large ver me requency range, pily exhiiting renance []. The linetutput, r audiuceptiility, may e degraded. The Paciic Jurnal Science and Technlgy 8

2 The taility prlem ariing rm the additin an input ilter i mitigated y intrducing damping int the input ilter and y deigning the input ilter uch that it utput impedance i uiciently mall [6] [7]. Input ilter are, in mt cae, required t perate nrmally when tranient r peridic diturance are applied t the pwer input. Such cnducted uceptiility peciicatin require that a deign r the damping the input ilter renance e inculcated, that input diturance d nt excite current r vltage within the ilter r the cnverter. ANAYSIS OF THE BASI ONVETE MOE When, r example, a ingle input ilter i added t a t cnverter a in Figure, the mallignal equivalent circuit mdel [8] i mdiied a hwn in Figure (). Vdˆ(t) vˆ g ( t ) I dˆ (t) vˆ g (t) (a) Input ilter () nverter : dˆ nverter : Vdˆ(t) vˆ(t) dˆ I dˆ(t) vˆ(t ) v g (t Input ilter () S () Figure : Additin a Single wpa Filter t the Input Terminal the Bt nverter. v(t) Figure : SmallSignal Equivalent Mdel the Bt nverter (a) Baic nverter Mdel, () With Additin Input Filter. mparing Equatin () with the tandard nrmalized traner unctin given y: g () Q ω ω The linetutput traner unctin the mallignal mdel the t cnverter, Figure (a), i tained y etting all the dˆ urce t zer. The urce vˆ g and the inductr are puhed thrugh the tranrmer t arrive at Figure. The linetutput traner unctin i given y: where g i knwn a gain, the alient eature the linetutput traner unctin are: g (4) ω, () π vˆ vˆ g dˆ 0 () Q (6) The Paciic Jurnal Science and Technlgy 9

3 vˆ g vˆ Figure : The Surce g and the inductr puhed thrugh the tranrmer. vˆ( ) ωz vd d (8) Qω ω The alient eature the traner unctin Equatin (7) which are derived y equating ceicient in Equatin (7) and (8) are: V d (9) V dˆ Idˆ vˆ( ) Figure 4: The dˆ vltage urce and the inductr puhed thrugh the tranrmer. The analyi the cntrltutput traner unctin vd i achieved y applying the principle uperpitin wing t the preence in the mallignal mdel mre than ne generatr that depend n dˆ. The cntrltutput traner unctin vd i tained y etting vˆ urce equal t zer. The dˆ g vltage urce and the inductr are puhed thrugh the : tranrmer t tain the circuit Figure 4. Further analyi which invlve individual etting the current and vltage urce t zer are made t arrive at the traner unctin given y: vd vˆ dˆ vˆ 0 g I V V (7) mparing Equatin (7) with the tandard nrmalized traner unctin given y: ω, (0) π Q () ω z, z () π The denminatr Equatin () and (7) are identical; hence vd and hare the ame ω and Q. The apprximate Bde plt the magnitude and phae the cntrltutput traner unctin vd and linetutput traner unctin are cntructed in Figure and Figure 6, repectively. EFFET OF UNAMPE INPUT FITE ON THE BOOST ONVETE TANSFE FUNTIONS In thi paper, we limited ur tudy the eect the input ilter n the taility the t cnverter mdel, t the variatin in the linetutput traner unctin. T determine the linetutput traner unctin in the preence the input ilter, we et all the dˆ urce t zer. The urce vˆ g, the inductr, and the ilter inductr and capacitr, and, repectively, are puhed thrugh the tranrmer t arrive at Figure 7. The Paciic Jurnal Science and Technlgy 0

4 80dBV Q 9.8 db vd vd 40dBV 80 0dB/decade (87Hz) k 0k 00 M (Hz) Figure : Bde Plt the ntrltoutput Traner Functin vd r the Bt nverter Mdel. 40dBV 0dBV 40dB 0dB 40dB 80dB d 4.4dBV 40dB/decade z (8.kHz) Q 9.8 db g.db 40dB/decade k 0k 00k M 87Hz (Hz) Figure 6: Bde Plt the inetoutput Traner Functin r the Bt nverter Mdel The linetutput traner unctin i a urth degree plynmial given in Equatin (). AMPIN OF THE INPUT FITE Several cheme are availale r the eective damping the input ilter. The chice any cheme depend amng ther actr n (a) the deire t prevent tranient and diturance in v g (t) rm exciting ilter renance, () the attainment deired ilter attenuatin, (c) the deire t minimize the ize reactive element [9], etc. In thi paper, a damping reitr, i cnnected acr the ilter inductr. The chice acr i t avid pwer diipatin in ince the dc vltage acr the inductr i zer. Hwever, the reulting traner unctin derived rm Figure 8 ater the uual manipulatin in the mall ignal mdel cntain a high requency zer. The reult cnnecting acr i that much the ilter attenuatin i prvided y. The linetutput traner unctin the cnverter mdel with damped input ilter i al a urth degree plynmial Equatin (4). vˆ g Figure 8: Additin t Figure 7. vˆ( ) vˆ g vˆ( ) Figure 7: The Surce vˆ g, the Inductr, and the Filter Inductr and apacitr puhed thrugh the Tranrmer. A mre practical and tandard apprach, hwever, i t cnnect a lw value, highrequency lcking inductr (uually, < ) in erie with the damping reitr. The highrequency lcking inductr al cntriute t the eective attenuatin prvided y the input ilter. The additin the inductr eectively t the ytem phae margin, Pm. A lw value damping reitr, reult in a very high value phae margin at an angular requency much lwer than the preinput ilter mdel value. T t the requency and till maintain reanale phae margin require an appreciale increae in the value the damping reitr. The Paciic Jurnal Science and Technlgy

5 4 ) ( ) ( () 4 ) ( ) ( ) ( (4) The eneit increaing the i that there i n pwer diipatin in it ince the dc vltage acr the inductr i zer. The reulting linetutput traner unctin i a ith rder plynmial and cntain a high requency zer and i given y: K J H F E B A 4 () where, A (a) B () E (c) F (d) (e) H () J (g) K (h) ISUSSION OF SIMUATION ESUTS Sme imulatin were run t veriy the taility cnditin the three mdel tate the cnverter: preinput ilter mdel, additin input ilter mdel, and damped input ilter mdel. Tet technique emplyed in the imulatin include Nyquit plt, Bde plt, and tep repne plt. ata r the aic cnverter mdel ued th in the analyi and imulatin are hwn in Tale. Filter inductr, and capacitr, value were elected t meet peciicatin while damping reitr wa iteratively gt thrugh erie imulatin run. The Nyquit plt, Bde diagram, and tep repne r the preinput ilter cnverter mdel are hwn in Figure 9. The Bde diagram, Figure 9 (), indicate a tale ytem with a pitive phae margin and ininite gain margin. The tranient repne the ytem, The Paciic Jurnal Science and Technlgy

6 Figure 9 (c), t a tep input hw that a teady tate wa achieved in le than tw ecnd ater the tranient excitatin. Tale : ata r the Baic nverter Mdel. Input vltage, V g 48.V uty cycle, 0. Inductr, 800uH apacitr, 000uF ad reitr, 90Ω Switching perid, T 00u Filter inductr, 00uH Filter capacitr, 470uF amping reitr, 0Ω (a) Surce: [0] Figure 0 hw the taility plt r the aic cnverter mdel with the input ilter added. In the vicinity the ilter renant requency, Figure 0 (), the traner unctin cntain a dulepair cmplex ple, and al a pair let halplane cmplex cnjugate zer. Thee caue a glitch in the magnitude plt, with a cntriutin 80 lead t the phae the riginal plt. When the 80 cntriuted y the additin input ilter i added t 80 cntriuted at high requency, (ω/ω ) >, y the tw ple the riginal vd, a high requency phae aymptte 0 i tained. The intrductin the input ilter lethited the aic cnverter angular crner requency rm ω 4 rad/ t ω 40 rad/, with a reulting decreae in quality actr, Q, rm 98 t 8. The tranient repne the ytem t a tep input, Figure 0 (c), hw an extra 0 ecnd delay ere teady tate wa attained. In Figure (a), it i explicitly evident that the j0 pint wa nt encled y the Nyquit plt. The glitch in the magnitude plt in the vicinity the ilter renant requency which dipped t aut 0dB wa reduced t elw 0dB y damping the input ilter, Figure (). At an ptimum value,ptimum 0Ω, the highrequency pikelike quality actr, Q, experienced an appreciale damping, hwever, t the detriment an increae in the lw requency Q. At thi,ptimum, the phae margin i aut 0. at an angular requency 99.4 rad/ec. When a 0μH highrequency lcking inductr wa cnnected in erie with,ptimum, the phae margin re t 6.69 at an angular requency 7.64 rad/ec. (c) () Figure 9: Staility Plt r the Baic nverter Mdel (a) Nyquit Plt, () Bde Plt, (c) Step epne Plt. The Paciic Jurnal Science and Technlgy

7 (a) (a) () () Figure 0: Staility Plt r the Baic nverter Mdel with Undamped Input Filter (a) Nyquit Plt, () Bde Plt, (c) Step epne Plt (c) (c) Figure : (ntinued n Next Page). The Paciic Jurnal Science and Technlgy 4

8 e. IEEE Tran. Pwer Electrn. 7(): h, J.., J. W. Baek,.Y. Jeng,.W. Y, and K. Je Nvel ZerVltage and Zer urrentswitching Full Bridge PWM nverter Uing Tranrmer Auxiliary Winding. IEEE Tran. Pwer Electrn. : Hamda, S., T. Mrimt, T. Matuhige, and M. Nakaka A New Inverter Tplgy High Eicient StSwitching PWM nverter, Prc. IEEE PES n Prdic, A., J. hen,. Makimvic, and.w. Erickn. 00. SelTuning igitally ntrlled wharmnic ectiier Having Fat ynamic epne. IEEE Tran. Pwer Electrn. 8(): (d) Figure : Staility Plt r the Baic nverter Mdel with amped Input Filter (a) Nyquit Plt, () Bde Plt, (c) Step epne Plt, (d) Imprved amped epne. Thrugh an iterative prcedure, a inal ptimum value, ptimum KΩ, wa elected. Figure (d) diplay the imprved Bde repne the ytem. In additin t a dulepair cmplex ple and a pair let halplane cmplex zer, the traner unctin al cntain ne each negative real ple and zer. They th cmine t cntriute a 60 lead t the phae the riginal plt. When the 60 cntriuted y the damped input ilter i added t 80 cntriuted at high requency, (ω/ω ) >, y the tw ple the riginal vd, a high requency phae aymptte 80 i tained. The lwrequency Q wa eectively damped. The phae margin. at an angular requency 64.4 rad/ec wa achieved. EFEENES. Erickn,.W. and. Makimvic Fundamental Pwer Electrnic, nd ed. Kluwer Academic Puliher: New Yrk, NY.. Hamada, S. and M. Nakaka. 00. A Nvel ZerVltage and Zerurrent Switching PWM nverter With educed nductin 6. Erich, S. and W. Plivia Input Filter eign r urrentprgrammed egulatr. IEEE Applied Pwer Electrn. n Erickn, Optimal Singleeitr amping Input Filter. IEEE Applied Pwer Electrn. n Nwu,.A. Unpulihed. StateSpace Averaging a Nnideal Bt nverter. Unpulihed Jurnal Paper. 9. Middlerk, eign Technique r Preventing Input Filter Ocillatin in SwitchMde egulatr. Prceeding Pwercn. :A. A. 0. Nwu,.A A Mdel Uninterruptile Pwer Supply (UPS) Sytem. Unpulihed M.Eng. Thei. epartment Electrical Engineering, Univerity Nigeria. ABOUT THE AUTHOS ajethan A. Nwu tained hi B.Eng. and M.Eng. degree in Electrical Engineering rm Univerity Nigeria, Nukka, Nigeria, in 994 and 004 repectively. He i preently wrking tward the Ph.. degree in Electrical Engineering. He i currently a lecturer in the epartment Electrical Engineering, Univerity Nigeria, Nukka, Nigeria. Hi reearch interet include pwer electrnic cnverter and renewale energy technlgie. erge. Ama, Ph.. i in the epartment Phyic and Atrnmy, Univerity Nigeria, Nukka, Nigeria. Hi reearch interet are The Paciic Jurnal Science and Technlgy

9 ndened Matter and Material Science (magnetim, upercnductivity, nancience and nantechnlgy) and Slar Energy (phtvltaic and renewale energy). Ama i married with children. SUESTE ITATION Nwu,.A. and.. Ama Mitigatin Staility Prlem in a Bt nverter having an Input Filter. Paciic Jurnal Science and Technlgy. 9():86. Paciic Jurnal Science and Technlgy The Paciic Jurnal Science and Technlgy 6