A Boost Converter Design with Low Output Ripple Based on Harmonics Feedback

A Boost Con verter Design w ith Low Output Ripple Based on Harmonic s Feedback Haifeng Wang * , Member, IEEE Penn State Univ ersity New Kensington, PA, US * hzw87@ psu.edu Abstract - C onventional boost converters are essential to connect low - vol tage energy source such as batte ry with high v olta ge D C bus in Electric Vehi cles due to its si mple constructi on and hi gh conver sion effi ciency. H owever, larg e output cap acitor banks mus t be used in orde r to reduce t he outp ut vo ltag e rippl es whe n an inv erter i s connec ted to a bo ost converter. In a typica l series hy brid electric vehi cle powertrain, signifi cant voltage and current pertur bati ons wi ll impa ct on batte ry sy stem p erforma nce a nd res ult i n co nsid erable po wer l oss . To address this i ssue, this pa per proposes a ne w control strategy for ripple reduc tion i n the dc - l ink of power electronic converters . In the propos ed met hod, an obs erver i s des igned to adaptiv ely esti mate the dc - link volt age an d current harm onics . The ha rmoni c terms are mult ipl ied by optimi zed ga ins t o control the conv erter’s duty cycle by negative f eedback law. Entire control model for t he p ropose d converte r is illust rate d and robust ness i s veri fi ed. Simul ati on and expe riments show that original volt age and cur rent ri pple magni tude can be reduced significa ntly . Keywords: power electroni cs, observer, feedbac k control 1. Introductio n Elect ric Veh icles such as pu re EV a nd hybrid EV are attractiv e to provide en vironmentally frien dly transpo rtation with rene wable energy. Fi g .1 shows the electrical sy stem configuration in EVs, inclu ding pow er DC - DC con vert er, i nver ter, mo tor a nd bat ter y. Fig .1. EV power convers ion a rchit ec ture Most of the E Vs have both high power dc co nvert er and lo w power conve rter . T he first o ne supplies el ectri c m otor an d th e se cond on e is u sed f o r ventila tion, light ening and other de vices [1, 2] . I n electrical vehicle applic ation s, the major load is typically an inve rter fol lowed by a m otor [3, 4] . The pres enc e of rip pl e an d nois e is an imp orta nt co nsid eratio n in DC co nve rter appl ica tio n s [5] . T he noise s have two compo nents. The first happens at the fundamenta l switchi ng freq uency cal led as ripp le. The second nois e occurs at the very high freque ncy ringing that o ccurs dur ing s witchi ng transitions . The ripple and noise leve ls can be sufficient ly high to advers ely affect other devi ces and parts c onnect ed to the convert er if the ripple are l eft unfilt ered. If electric vehicl es are integrated with electrical grid, the charg ing and dischar g ing circuits w ill induce extra ripples in the orde r of twice the gr id freq uency [6, 7] . Ripp les in t he dc - link are undesirable si nce they cause di stortion a nd pow er l oss , an d gen erate unn ecessary t orque r ipple s . The high freq uency curre nt ripples will enter t he electr ic v ehicl e’s bat te ry sy stem to age battery and deteriora te the a nions’ state of e quilibr ium [6, 8 , 9] . To red uce ri pp le s , interlea ved boost conver ter is widely investigated . But it n eeds shif t sever al chann els so that it has more components and weight as w ell as gener ates high er frequ ency r ipples and losses due t o chan nels’ switch [10] . For ty pical ap plic ation s wher e ripple s a re n o t critic al, they can be filter ed by adding addit ional ceram ic capa cito rs to the DC - D C o utput e nd and input end. B ut t he capacitanc e could be too bi g and vary greatly . In this case, a star tu p prob lem coul d aris e. The output fil ter vol u me w ill be incr eased by adding the extra output capa citors to reduce the output ripple s . I n addition, if “L C” filte ring n etw ork is applie d t o filter rip pl e s , the inductance and the frequenc y of network should be sta ggered with the DC - DC freq uency to avoid mutual interfer ence. Moreover experiments indicates that the vo ltage ripple increases w ith the decreas ing of the ind uctance in small inductanc e condition. The refore, ther e is no doubt that sim ple LC filter cannot ens ure the converter to meet the desired rip pl e requi rements . In noise sensitive appl ications, a need for low r ipp le perform ance is more t han the c onv ert er c an pr ovi de on its own. An external proporti onal - integral fil ter is rec ommen ded to be co nne cte d to t he con vert er’s outp ut. T he fir st step is to cho o se a large va lue of inductor . But l arge induc ta nce will r eq uire a lar ge capacit ance and th e r es pons e of th e fi lter c oul d be significantly slowed. Adding a n ultra - lo w - noise lo w - dro pout regulator or LDO to the converter outp ut is another way to ge t low noise and ripp le in converters. B ut the LDO can only handle a lim ited current that i s usually about 1 A and needs requi r ed capa cito r s along with it. For exa mple, a regu la r LDO an d re qui red c om pon ents nee ds 4 6.8 m m 2 P CB boar d spa ce an d the cost is m ore t han $ 5 f or e ach LDO. T hi s paper prop os es a method to reduce DC - LIN K rip pl e for a ty pical tw o - sta ge conver ter inverter drive circuit that consists of a boost conv ert er c ascad ed by a thr ee - pha s e full br idge inverter and a motor, as depi cte d in Fig. 2. Co mpared with the pre vious wor k [11] , the new ly pro pos ed 7 th orde r au ton om ous LTI control sy stem is applie d to a batter y po wered mo to r drive system . This paper applie s thi s observer based meth od to reduce in ducto r cu rren t harm onics besi des DC - LINK vo ltage ri pples . Moreov er, th e vo lta g e and current harmonic s frequ ency in t he ob ser ver ca n be adapti vely up da ted accord ing to the r eal - time sp eed o f the motor . This p aper al so co mp are s th e r educ ed ri pp l e magnitude with circuit analy sis to prove the effecti veness of the m ethod. Fig .2. Circ uit topol ogy f or a BLDC motor dr iver powere d by a boos t conver ter . 2. Feedback Contr ol design for robus t referenc e tracking and ripple r eduction 2.1 Extractin g rippl e harmon ics v ia an observer Suppo se the above boost converter - inver te r cir c uit is a linear - time - in vari ant (L T I) sy stem repres ented b y its state. I f the sy stem is observable, its state s such as voltag e and cur rent can b e re con str ucted or eva luat ed by an obs erv er. In what fo llows, the se ction expla in s how the dc - link harmoni cs are related t o t he sta te o f the LTI system. T hen t he constructio n of observer follows from st andard p rocedur e [11] . At steady stat e, the dc - link voltage   can be expre ssed as   (  ) =   +    cos (  +   )   (11) W her e   is t he aver ag e of   ,   and   are t he magnitude and p hase for the n - th o rder harmonic . β (measur ed in radians) is the frequency of the dc - link rip pl e and is adaptively ad justed based o n motor speed ra tio . T he fir st t hr ee harm onics w ill be s ufficient and they can be used to signi ficantly reduce th e ri pple. So the pape r consider s only the fir st thr ee harmonics. Then   (  ) =   +   cos (  +   ) +   cos (2  +   ) +   cos (3  +   ) (1 2) DC - LINK volta ge   and in duct or cu rrent are t he out put of a 7 th order a utonomous LTI system. Define S =        0 0 0 0 0 0 0 0 0  0 0 0 0 0  0 0 0 0 0 0 0 0 0   0 0 0 0 0  0 0 0 0 0 0 0 0 0   0 0 0 0 0  0        (13) G = [ 1 1 0 1 0 1 0 ] (14) And den ote th e st ate of th e L TI sy stem as x  R  , then let’s analy ze the vol ta ge   first:   =  ,  󰇗 =  ,  ( 0 ) =   (15) The t w o des cri ptions (1) an d ( 2) a re rel ated vi a the following eq uations: v  = x  ( t ) , x  = v  (16)   cos (  +   ) = x  ( t ) , 󰇣 x  x  󰇤 =  b  cos   b  sin    (17)   cos ( 2  +   ) = x  ( t ) , 󰇣 x  x  󰇤 =  b  cos   b  sin    (18)   cos ( 3  +   ) = x  ( t ) , 󰇣 x  x  󰇤 =  b  cos   b  sin    (19) This m eans t hat each h armoni c can be recon st ru cte d by two of the state v ariables. S ince th e pair (S,G ) is obs erva ble , all its states can be recon st ru cte d from its o utput   , which can be eas ily meas ured by AD conv erters . It fol lows that, th e averag e of   , all its ha rmonics a nd their derivatives can be ext ract ed fr om   via a n obser ver in table 1 . Based on the techno lo gy dealing with unwanted periodi cal signals [2, 12] , the feedback cont rol w ill be constr ucted using no t only the har monics w hich are repr es ented by x 2 , x 4 and x 6 , but als o their der ivatives, x 3 , x 5 and x 7 . Table 1 Funda me ntal a nd ha r monic s fo r the D C volta ge. Funda me ntal Com po nent   First Order Harmon ic b  cos   First Order Harmon ic Der ivativ e b  sin   Second Order Ha rmonic b  cos   Secon d O rder Har moni c Der ivativ e b  sin   Thir d Or der Har monic b  cos   Thir d Or der Har monic Der ivativ e b  sin   2.2 Estim ation of the h armonic s v ia observer Let the state of the obs erver be z a nd the inp ut be   : z 󰇗 = ( S  LG ) z + L   ( 20 ) Let the observer error be e = z  x , and e 󰇗 = ( S  LG ) e . T his im plies th at the observe r erro r will go to 0 as t tends t o infin ity if S − LG is stab le. L is the observe r gain. Due t o measurement error s, noise, high - frequenc y switching r ipple, the gai n L should be kept within reas onable rang e for accep tabl e conv ergen ce ra te and av oid ove r ampl ify ing nois es . When t he estim ation error e i s suff iciently sm all, the obs erv er state z is be ver y clos e to state x o f t h e LT I system . The harmonics of   and thei r deriv atives can be extract ed from the state z. Then state z can be used for d u ty c yc l e feedback control. 2.3 Using t he es timate d harmo nics for feedback Suppo se that the c urrent i L of the inductor L dc i s repr es ented b y a volta ge acros s a resi stor . Le t th e desir ed dc - lin k v oltage be   . A s im ple feed back to achie ve robust tracking is D = D  + k  ( i   i  ) + k         +            ( 21 ) W here D is th e duty cycle for th e low side MOSFET of the half - bridge for the dc - dc con vert er and D 0 is a n ominal duty cy cle. i L0 is the nominal inductor current. To red uce dc - link voltage r ipple, an extr a term Kz is added in the abo ve feedba ck co ntrol: D = D  + k  ( i   i  ) + k         +            +  ( 22 ) 2.4 The d iscreti zed obser ver a nd dig ital implement ation T he LTI system needs to be discretized for implementatio n in a d igital pr ocessor . Let t he sampling time be T and the discretized state is x [ k ] = x ( kT ) . T he discretized LTI syste m is   [  ] =  [  ] ,  [  + 1 ] =    [  ] ,  [ 0 ] =   ( 23 ) W here   =      =        1 0 0 0 0 0 0 0 cos  T sin  T 0 0 0 0 0  sin  T cos  T 0 0 0 0 0 0 0 cos  T sin  T 0 0 0 0 0  sin  T cos  T 0 0 0 0 0 0 0 cos  T sin  T 0 0 0 0 0  sin  T cos  T        (24) Sim ilarly , t he state observer is constructed as  [  ] =    [  ] +   (   [  ]   [  ] ) ( 25 ) Wher e L d is c ho sen so the eige nval ue s of S   L  G are withi n t he uni t d isk to keep stable. A simple rule is to choos e the desired eigenvalues wit hin t he unit dis k but v ery c lose t o those of S  , which a re a ll o n the unit disk. Let the e ige nva lues of S  be   , i = 1,2, . . ,7. the eigenvalues of S   L  G at   , i = 1,2, . . ,7. wi t h 0 <  < 1 . If the sampling time is v ery small, then  shoul d be very close to 1, f or exam ple, great er th an 0.99. Notice that S  is 7 b y 7 ma tr i x . T his may s l o w do wn the co mputation in a digital signal p rocess . T o reduce computation time, the system is decomposed i nto o ne fi rst - order sy stem and 3 second order sys tems . 2.5 Sys tem simul ation and Key performa nce eva luation The p rop ose d con tr ol sy stem block diagram is shown i n Fig.3. E ach block in Fig. 3 is ex panded in Fig. 4 for det ails . Fig .3. Bl o ck diagra m for t he ent ire co nt rol sy stem Fig .4. Expanded bl ock di agra m of l ow harm onics boost conve rter - inver ter m otor cont rol m odel The nom inal operating c ondition w as chosen at V s =12V, and V dc =28 V. This re quires the duty cycle for the dc - dc boo st conv ert er to be D 0 = 0.42. And the inductor current for L dc be i L0 =0.9A. The fe edback control was found to be D = D   0. 08 ( i   i  )  0. 06        +          ( 26 ) w here v  is the referen ce val ue for the dc link voltage v  . The coeff icien ts were caref ully d esigne d based on a good transient per formance and re asonable steady sta te behavi or. For exam p le, if the coef fici ent for i L − i L0 is l arge, th e duty cy c le will be noisy since the inductor curre nt has large high - frequenc y switching ripple. If this c oefficient is red uced, there w ill be larger overshoo ts in inductor current and v dc . T he co effi cien t for v dc − v ref should be kept small due to t he constraint on the duty cycle and the noises. Increasing the gain f or the integr ator may increas e the overshoots and the ripple siz e. And the duty cycle D is constr ained w ithin [0, 0.8] via a saturat ion function as D must less than 1. For digital im plementation, the paper firs t constr ucted a di scret ized obser ver to e xtr ac t the firs t orde r, the s eco nd - ord er harmoni cs and third - ord er as well as their deriv atives from the state of a 7 th order LTI system. S ince t he r eal r ipple freq uenc y i s 400Hz ,  =  × 400 = 2512ra d /s . With sam pling frequen cy of 18 kHz , the sam p ling peri od i s T = 5. 56 × 10  s . A nd the S  is ex pressed as below : S  =        1 0 0 0 0 0 0 0 0. 9903  0. 1392 0 0 0 0 0 0. 1392 0. 9903 0 0 0 0 0 0 0 0. 9610  0. 2756 0 0 0 0 0 0. 2756 0. 9610 0 0 0 0 0 0 0 0. 9123  0. 4066 0 0 0 0 0 0. 4066 0. 9123        (27) The desired eigenval ues for S d − L d G ar e ob tained by scaling the eige nvalues of S d with 0.99 [11] . U sing pole placem ent algo rithm, L d i s computed as L  =        0. 0098 0. 0195 0. 0019 0. 0192 0. 0037 0. 0189 0. 0047        (28) A s the Fig. 5 shows, t he dc - link voltage is decom posed i nt o a dc com ponent an d harmoni cs by the built observer . Recall that th e first - order and seco nd order harmoni cs corresp ond to z 2 , z 4 and z 6 of the obse rver. z 3 , z 5 a nd z 7 are similar to z 2 , z 4 a nd z 6 but with some ph ase sh ift . Let’s com pare the origin al v dc signal and reco nstructed signals from obser ver states. Fig. 6 (a) shows the ori ginal v dc ( top , bl ue cur v e) a nd t he rec o nstr uc ted v dc (middle, red curve) . Th e estim ati on error i s also plotted as the bl ack curv e at t h e b ot tom of the figur e. The compari son show s the effectiv eness of the obs erver and t hat the 7 th - order model is sufficient for the dc - link voltage. A close up view of the comparison is shown in Fig. 6 (b) . I t is obvious that the curve for the origi nal v dc is fuzzy and thick, due to the high fre quency switchi ng ripple. In c ontrast, the r econstruc ted v dc is clean an d ripple f ree , indic ating that t he high freq uency switching rip ple has been filte red out du e t o effect of the obse rver. Sinc e the fo u rt h - order harmonic is negligible at steady stat e, t he syst e m only need feedbac k the stat e z 2 , z 3 , z 4 , z 5 , z 6 and z 7 to cal culate the duty cycles . A stat e feedba ck is designed b y ad din g two m ore te rm s to as : D = D   0. 08 ( i   i  )  0. 06        +           0.3z  + 0.2z   0.1z  + 0.2z   0. 03 z  + 0. 14 z  (29) Fig .5. Estimated the d c - link volta ge and its harmonic s (a) (b ) Fig .6. (a ) reconstructed dc - link vo ltage, the original , and the err or; ( b) C lose - up vi ew of recons truct ed dc - link volta ge i n red an d the original in blue The las t tw o coefficien ts are obtained th rough trial and err or. Firs t, th e term for z 3 is set t o 0. By using one di me n sional sea rch an d sim ulation, it is found that t he rip pl e i s minimum when the coefficient of z 2 wa s - 0. 25 . Another one d imensio nal search with the coeff icient of z 2 fixed at - 0. 25 prod uced a value of − 0. 4 for z 3 . T hen other c oeffici ents are dete rm ined in th e sam e way . It should be noted that both terms for z 2 and z 3 are neede d to m inimize ripple si ze. If t he t erm for z 3 i s dis carde d, th e mi nim al rippl e size in creas es. This means that the deriva tive of the first order harmonic also helps to r educe the rippl e size. The same appli es to other har monics. In order to eliminate the output volta ge overshoot and vibra tion at the beginning b ecause o f the observer feedba ck, a delay elemen t i s add ed to the obs erver feedb ack loop with 0.1s. To obser ve the e ffect mo re obvi ous ly , m ore loa d is con n ect ed to t h e m otor . T he load torq ue change increas es the DC - link vo ltage and the voltage ripp les. To reduce th e voltag e rip ple, observe r based control begin to work at 0.1 second. Simulin k is used to con duct t he simu lation of the pro pose d contr ol sy stem. Th e sampl ing ra te can be chosen as 18 kHz . We use 24V DC as the output voltage of boost co nverter to drive 24 V BLDC m otor used i n an experim ent . T he dc - link vo ltage ge nerat ed by th e boos t c onv ert er c ont roll ed by t wo differe nt co ntro l ler s is plotted in Fig . 7 . Fi g.7 (a) sh o w s the volt ag e ri pple redu cti on by switc hing to the har monics feedba ck contr ol ler . The voltage ripple peak to peak value i s quic kly reduced 53 % from 0.37 V s hown in Fig. 7 (b) to 0.17 V sho wn in Fig.7 (c). The response in Fig. 6 clearly shows the reductio n in r ipp le si ze a fter the harm o nic te rm s are fe d back to the du ty cy cle co ntro l ler a fte r t > 0.1 s. Similar to volt age ripple reduction principl e, 3 - order harmoni cs are used in negat ive feed back w ith proper gain to red uce the inp u t curre nt rippl e. T he new ob server feedback gain i s gained by one dimensio nal search a nd si mulation. Curre nt ripple observer based cont rol ler be gin s to work at 0. 2 second. T he inductor current under the mod ified controll er is plotted in Fig.8. T he induc tor curre nt ri pp le reducti on is sho wn in Fig.8 (a). The ripp le peak to peak value i s reduce d 3 0 % fr o m 1.7 A sho wn in Fig. 8 (b ) to 1.2 A sho wn in Fig. 8 (c) . (a) The vol tage r ippl e r educt ion (b) T he or ig ina l vo ltag e r ipp le clo se - up view (c) The red uced voltag e rip ple c los e - up view Fig. 7 . Dc - link voltage rippl e is reduced from 0.37 V to 0 .17V . (a) Ind ucto r cu rrent ripple reduction (b) The origina l current ripp le close - up view (c) The reduced current rip ple close - up view Fig . 8. Indu ctor current ripple peak t o pea k val ue reduce d from 1.688A to 1.156 A To compare the reduced ripple magnitud e in simu lation with ci r cuit an aly sis results , the v o ltage ripple an d cur rent ripp le a re cal culated in next sec tion s. 2.6 Output Volta ge Rip ple Anal ysis To calcu late a mini mum output capac it ance , t he desir ed output vo ltage rippl e percenta ge is set to 1 % of the ra ted output voltage [1 0] . B ased o n Table 2, the o utput capaci tor values for the desired output volta ge rip pl e i s as b elo w :   ( min ) =   (  )      =  .   .     .  = 0. 000337  = 3 37  (7) So a 470  capacitor i s determined to be the output ca pacitor in the tes t. The ES R of the output capa cit or add s mor e rip pl e s. So the total voltage ri pple is given with the equat ion:   (   ) =   󰇣     +    󰇤 = 0. 67  (8) Table 2 Compon ents in the sim ulati on model C out (min) =3 37  minimu m output capacita nce Iout (max)= 2. 65 A maxim um output cu rrent D = 0.55 du t y c ycl e fs = 18 kH z minim um switc hing fr eque ncy ΔV out =0.24 V desir ed outpu t voltage ri pple 󰇛 with _ ESR) = 0. 67  With additional out put volta ge ripp le d ue t o capac ito rs ES R ESR = 0.1o hm equ iva lent s eri es resi st anc e of the out put capa citor  l =1. 28 A induc tor ripp le curren t V in = 13.9 V typic al input voltage Vout =24 V desi red outpu t voltage L = 0.0 0033 H select ed induc tor valu e 2.7 Input Current Ripple Analy sis The resistance of a CM OS s witch in the closed positi on, re ferre d to as t he on - resistance or R ON , chan ges de pe ndin g on the inp ut volta ge. T his beha vior is usua ll y undesirab le and can signi ficantly disto rt the input signal in some applic ations. A good esti mation for th e in duct or ripple curren t is 20% to 40% of the outp ut cur re nt.   = ( 0.2  0.4 )          = (0.9   1.8  ) (9) To calculate the maxi mum switch curr ent is to determine the inductor ripple cu rrent.   =       =  .  .     .  = 1. 28  (10) In sum, the voltage rip ple plotted in simulation is 0 .17 v ( or 0.7% of output DC v oltage) is better than the acc eptable volt age rippl e 0. 67 v calcul ated by a bove circuit analysis. In addition , in ductor curr ent ri ppl e of t he mode l is 1.1 6A (or 43 % of output current) i s also bett er than maximum sw itch current 1.28 A from the a bove circuit analysis. I n a research about t he interleaved boost con verter, t he voltage ripple varies from 0. 3% to 0.43% of outp ut DC vol ta ge when output pow er changes from 20 kw to 70 kw and t he inductor current ripp le var ies from 50 % to 30 % of maximum input curre nt when output power ch anges from 50 kw to 1 70 k w [1 3]. T heir ripple to DC signal ratios, in comparison, are clos e to our resu lts alt h ough the two converter s ’ circuit s and outp ut p owe r a re different. 3. Experiment al Ve rification The experiment circu it in an electric vehicle prototy pe includes DSP con trol ler, boost con ve rter - invert er , b attery and charger, mo t o r d rive r and m otor s sho wn in F ig.9 . Fig . 9 . The electric vehicle prototype in test The detailed experiment parameters are shown in table 3 and table 4. Table 3 BLD C motor parameters Numbe r o f p hase s 3 Back EM F wav eform Trap ezoid al Sta tor phas e resi stan c e (ohm ) 0.41 Sta tor phas e indu ctan c e (H) 0.0007 To rque co nsta nt (N .M/A - peak) 1.4 Back EM F flat area (degrees ) 120 Ine rtia ( J(kg.m^2) ) 9.6 e-5 viscou s d amping ( F(N.m.s) ) 1e -3 pol e pair s 4 Table 4. ALM 12V7s EverSa fe™ b attery: lithiu m - ion batteries Ele ctrical Char acte ristics at 25°C 12V7s EverSaf e™ b att ery Nomin al Volta ge 13.2 V Nom inal Ca pacity 5 Ah Max. Charge Voltage 16 V Reco mmen ded Float Volt age 13.6 - 14.4 V Unde r - v olta ge Limit ( mi n) 8 V Cons tant Power Disc ha rge End Voltage 10V Pro duct Mode l AL M 12V7s, Si ngle U nit W hen motor runs at 100 0 rpm, the co nverter o utput 24 V vo lta ge to power the invert er and drive the motor. Experimental data sh ow th at the boost c onver ter output vol tage ripp le ca n be r ed uced by half. Fig.10 sh ows the volta ge ripple r eductio n by using the har monics feedb ack contro l. T he volta ge ripple peak to pe ak valu e is q uic kly r educed 46% from 0.67 V shown in Fig. 10 (a) to 0 .36 V shown in Fig.10 (b). T his red uc t ion r ati o is approxim ately e qual to the rati o of th e sim ulation exper iment, as demonstr ated in Fig. 6 . (a) (b) Fig. 10 . Conv ert er outpu t volt age ripp le in c lo se - up view : ( a) voltage harmo nics is not fed back to the duty c ycle controller ; (b ) voltage h armoni cs is f ed back to the duty cycle cont ro ller The pr oposed de sign ca n also be used to reduce inductor current rippl e in the b oos t conver ter . T he second te st uses a 0.1 ohm re sistor connec ted in seri es with a n inducto r t o meas ure th e current fl owi ng thro ugh the inductor. Fi g.1 1 plots the curr ent rippl e reduc tion by using the ha rmoni cs feedbac k control. The voltage ripple p eak to peak value is qui ckly reduc ed 22% fro m 306 m v without ha rmo n i cs te r m feedba ck cont rol in Fi g.1 1 (a) to 239 mv w ith the pro pose d h armoni cs f eedback control in F ig.11 (b ) . This rat io of ripple redu ct ion is clo se to the ra tio of the simulatio n exper iment, a s demons trated i n Fig. 7. (a) (b) Fig .11 . Ind uc to r current ripp le sampling wave for m in c lo se - up view: The sys tem d oes n ot u se har moni cs fee db ack in (a); the sy ste m u s es har moni cs fee dback c ontr ol in (b ) 4. Conclusi on The pap er address ed con verter rip ple reduct ion problems for a power system drive n by battery or other DC power so urce s . A cont rol stra teg y for re ducti on of the dc - link ri pple i s propo sed fo r a two st age boo st invert er. The m ain i dea i s t o use an observer to extract the har monics o f the dc - link vo ltage and curr ent to u s e the har monics for feedback contr ol of the dc - dc boo st converter. The mot or's speed i s sam pled and us ed to ada ptive ly ad jus t the freq ue ncy o f the har moni cs i n the observer. The effect iveness of the co ntrol design methods was validat ed by both simul ation an d expe ri ment s . T he results de velo ped in this p aper will find pos sibl e applic ation s in elect ric, hy brid and plug - in hybrid electric vehicles , wind systems and photovoltaic s ystems. Si nce the rip ple red uction i s achieved by f eedback control of observer stat es, the method can be applied to re duce other fix ed frequency ripples b esides voltag e and current ripp les . REFERENCES [1] A. N ahavand i, M. T . Hagh, M . B. B. Sharif ian, and S. Dan yali, " A Nonis olated Multi inp ut Mu ltiout put DC - DC B oost Conv erter for Elec tr ic Vehic le Ap pli cati on s," (in Engl ish) , Ie ee Tr ansactio n s on P owe r El ectro nics, vol. 30 , no. 4, pp . 1818 - 1835 , Apr 2015. [2] H. Jung , H. F . Wang, and T . S. 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