Generation, Performance Evaluation and Control Design of Single-phase Buck-boost Differential-mode Current Source Inverters

Transcription

1 IET Renewable Pwer Generatn Generatn, Perfrmance Evaluatn and Cntrl Desgn f Sgle-phase Buck-bst Dfferental-mde Current Surce Inverters Jurnal: IET Renewable Pwer Generatn Manuscrpt ID: RPG Manuscrpt Type: Research Paper Date Submtted by the Authr: 3-Jul-05 Cmplete Lst f Authrs: Darwsh, Ahmed; Unversty f Strathclyde, EEE Hllday, Derrck; Unversty f Strathclyde, Electrnc and Electrcal Engeerg Wllams, Barry; UNversty f Strathclyde, Electrcal and electrnc engeerg Keywrd: DC-AC POWER CONVERTORS, SWITCHED MODE POWER SUPPLIES, PHOTOVOLTAIC POWER SYSTEMS, RENEWABLE ENERGY SOURCES, POWER ELECTRONICS, VARIABLE STRUCTURE SYSTEMS

2 Page f 3 IET Renewable Pwer Generatn Generatn, Perfrmance Evaluatn and Cntrl Desgn f Sglephase Buck-bst Dfferental-mde Current Surce Inverters Ahmed Darwsh, Derrck Hllday, Barry Wllams Electrcal and Electrnc Engeerg, Unversty f Strathclyde, Glasgw, UK ahmed.mhamed-darwsh-badawy@strath.ac.uk Abstract: Dfferental-mde verter tplges are prmsg fr renewable energy generatn as they ffer merts such as reduced sze f passve elements, hgh pwer densty, and reduced ttal cst. Sgle-phase buck-bst dfferental-mde current surce verters (DMCSI) can prvde flexble utput vltage abve r belw the put dc vltage, whch s necessary fr hgher effcency f mdern renewable energy applcatns. The cntuus put current f a DMCSI s apprprate fr maxmum pwer pt trackg peratn (MPPT) f phtvltac applcatns. Hwever, the perfrmance and cntrl f such cnverters has nt been dscussed detal. As a drawback, the ttal dc sde put current f a sgle-phase verter cnssts f a desred dc cmpnent and an undesrable ac cmpnent. Ths ac current cmpnent frequency s duble the utput vltage frequency and thus, affects MPPT resultg reduced ttal effcency. In ths paper, fve pssble DMCSIs are prpsed and cmpared terms f ttal lsses, maxmum rpple current, ttal harmnc dstrtn, devces and passve element ratgs. In addtn, the sldg mde cntrller s desgn and pssble methds f elmatg the put nd harmnc current are dscussed. A.5kW bdrectnal verter s used t valdate the desgn flexblty f the fve verters tplges.. Intrductn There s muntg ternatnal prclvty t reduce the cst and mprve the effcency f energy cnversn systems thrugh mdular structured renewable/dstrbuted systems []. Therefre, the need fr reducg cnverter sze and passve cmpnent values s pressg. Mrever, the cst f phtvltac (PV) systems s affected cnsderably by stallatn and matenance csts []. The verter tal and runng csts may reach abut half the tal PV system cst [3]. Mst dc-ac cnverters stalled PV systems requre large put flterg capactance, typcally wet electrlytc types. Replacg ths electrlytc capactr wth a plastc type creases relablty sgnfcantly as t s at least thrty tmes mre relable than electrlytc types, at the same peratg cndtns [4]. At rated peratg cndtns, the lfe tme f an electrlytc flter capactr s shrt cmpared wth ther verter cmpnents [5]. Thus, usg ths capactr hampers creased verall system relablty. The lfe tme f a capactr s halved fr every 0 C crease the peratg temperature [6]. Fr dc-ac cnversn, the vltage surce verter (VSI) s the mst cmmn cnverter tplgy where the utput ac vltage peak s always lwer than the put dc vltage and the utput ac current peak s always greater than the put dc current [7, 8]. Because f the VSI buck nature, a bst dc-dc cnverter may be stalled between the PV and the verters put fr vltage matchg and maxmum pwer pt trackg (MPPT) cntrl. Cnsequently, system vlume, weght, pwer lsses, and cst are creased [9,

3 IET Renewable Pwer Generatn Page f 3 0]. Myrzk [] classfed the sgle-stage buck and bst verter tplges, whle [], buck-bst Z-surce verter tplges were prpsed and explaed. If tw pwer cnverters are cnnected a parallel-seres cnfguratn, they frm a dfferental-mde verter. Sme f these dfferental mde verters types are shwn [9], [3, 4]. The basc structure f a dfferental-mde buck-bst sgle-phase verter s shwn Fg.. The dfferental-mde verter tally appeared [3] as a bst verter, whle a dfferental buck verter s presented [5]. Knght et al. [] prpsed the dfferental sx-swtch buck-bst verter based n the Ćuk cnverter, but ts perfrmance was nt evaluated. Of the knwn tw-swtch tw-dde buck-bst reversble cnverters, there are fve cnverters that can prvde cntuus put currents and hence, mtgate the need fr large electrlytc put capactrs. These buck-bst cnverters are shwn [6] as C5, D, D, F5 and G5 and can be used as buldg blcks a dfferental-mde current surce verter (DMCSI). Besdes elmatg an unrelable large electrlytc capactr, cntuus put current swtched mde pwer supples (SMPS) enable safe and relable cnverter-grd cnnectn and they are attractve slutns fr energy cnversn systems terms f: ) vltage buck-bst peratn wth a flexble utput vltage range, ) cntuus put current, 3) hgh effcency, and 4) hgh frequency transfrmer cuplg pssbltes. Generally, cntuus put current cnverters are tme varant systems where the verall transfer functn descrbg the relatn between the put and utput vltages and currents depend n the swtchg perds f ts swtches. Ths results a cmplex stable desgn because the cnverter ples and zers travel thrugh a lng Nyqust trajectry [9], [7, 8]. In sgle-phase verters, the utput pwer demand reflects t the put sde and mples that the put current r vltage, r bth, carry a nd harmnc cmpnent [9]. Fr renewable energy surces, ths cmpnent wuld affect MPPT perfrmance and decreases the average pwer frm the system. The cnventnal slutn fr the harmncs the put dc current s t use a large ductr whch attenuates the even-rder harmncs [0]. Hwever, ths s nt a practcal slutn as the verter prduces hgh dc current whch requres a large, bulky put ductr. Research has been cnducted t elmatg the scllatg put current f a sgle-phase PV verter, and can be classfed t tw categres: ) passve elmatn wth passve crcuts and ) actve elmatn crcuts wth semcnductr devces []. An example f passve elmatn s presented [] where a secnd rder LC crcut s used as a ntch flter. Althugh such crcuts can reduce the even harmncs frm the put sde, they have tw ma drawbacks. Frstly, tme, devatn the passve element cmpnent values results reduced even harmnc attenuatn. Secndly, the capactr the PV current path results a dscntuus current

4 Page 3 f 3 IET Renewable Pwer Generatn cmpnent whch requres anther stage f flterg. An actve harmnc suppressn technque s presented [3], where the nd rder harmnc f the put current s elmated by a seres buffer cnverter tplgy. Ths paper presents the generatn f sgle-phase buck-bst DMCSIs frm ther buldg dc-dc blcks, prpses prper cntrl desgn fr each tplgy, and cmpares the pssble DMCSI tplges terms f features such as effcency, put current rpple, utput current ttal harmnc dstrtn (THD), and devce and capactr ratgs. Als the paper presents pssble methds fr decuplg the nd rder harmnc current cmpnents the prpsed DMCSIs wth and wthut extra pwer electrnc swtches and dscusses ther effect n passve element szes. Fg.. Basc structure f a buck-bst DMCSI.. System descrptn The put vltage dc surce s cnnected t tw bdrectnal buck-bst cnverters as shwn Fg.. Mst buck-bst cnverters prduce an utput vltage whch has an ppste plarty t the put vltage. Each cnverter prduces unplar vltage where: v ( t ) a = h av ha= H dc + H ac sωt v ( t) = ½ Vp [+ s ωt] a v ( t ) = h V b b h b( t ) = H dc + H ac s( ωt π ) v ( t) = ½ [+ s( ωt π )] b V p (a) (b) The utput vltage v g and current are: 3

5 IET Renewable Pwer Generatn Page 4 f 3 v ( t ) = v v = V sωt g b a p ( t ) = I s( ωt + γ ) The basc dc-dc cnverters wth cntuus put currents are shwn Fg.. All are reversble when usg tw swtch-dde pars. Fr all these cnverters, the pwer s transferred frm the put t the utput sde (r the ppste drectn) thrugh a capactr C whle strg energy the put and utput ductrs L and L. Fr cnverters C5, D and D, the utput shunt capactr C s ptnal (cnverters the utput t a vltage surce) as the utput current s cntuus. Hwever, C s mandatry fr cnverters G5 and F5 ( rder t average the utput vltage). Fr all the cnverters, the swtch and dde (S and D ) perate alternately when the pwer s transferred frm the put t the utput and the swtch and dde (S and D ) perate alternately when pwer s transferred the ppste drectn. t n s the perd when S r D cnduct current whle t ff s the perd where S r D cnduct. ( c) c a b e Fg.. Buck-bst cnverters wth cntus put current: (a) C5 (Ćuk), (b) D, (c) D, (d) F5, and (e) G5 (sepc). The swtch n-state duty rat f the cnverters δ s: t n δ = (a) t s d v c + r, L C/ + V S D - r, L L D C S v - 4

6 Page 5 f 3 IET Renewable Pwer Generatn The vltage cnversn rat between the utput and put vltages (h) can be expressed as: v δ h= = = (b) V δ The fve buck-bst cnverters can be serted t the cnfguratn blcks Fg.. The tme varyg duty rats f the cnverters can be deduced frm the desred utput vltages as: ha hb δa( t) = and δb( t) = h + h + a 3. Cnverter perfrmance cmparsn In ths sectn, the fve sgle-phase buck-bst DMCSIs are dscussed and cmpared terms f: ) verall effcency, ) put current rpple, 3) swtch and dde currents and vltages, 4) utput current THD, and 5) capactrs vltage stresses. T avd duplcatn and prlngatn, the mathematcal analyss fr nly the C5 (Ćuk) cnverter wll be presented detal whle the fal cnclusns fr the remag fur cnverters wll be summarsed. 3.. Pwer Lsses Tw sgnfcant lss surces wll be cnsdered ths analyss. The frst s the cpper (I R) lss the put and utput ductrs and the secnd s cnverter semcnductr devce lsses. Cnsequently, the rt mean square (rms) currents the ductrs as well as the average current the ddes shuld be derved. The currents thrugh ductrs L and L can be expressed as functns f the utput current, vltage and duty rats as shwn Table. Table Currents thrugh the cnverter s ductrs Tplgy Current thrugh L Current thrugh L b (3) C5 D δ = δ δ = L = δ δ L = D L= δ F5 G5 δ = L = δ δ δ = δ 5

7 IET Renewable Pwer Generatn Page 6 f 3 s always greater than whle δ δ s greater than when δ> 0.5 and less than when δ< 0.5. δ Fr C5 cnverters, as an example, the stantaneus put current a and b f each cnverter s: b a ( t ) v δ = =, ( t ) V δ a a a a ( t ) v δ = = ( t ) V δ b b b b V p V p ( t ) = ½[ + s ωt ] I s( ωt + γ ) V V V pi = {½ csγ + ½ cs( ωt + γ ) + s( ωt + γ )} V V p V p ( t ) = ½[ + s( ωt + π )] I s( ωt + π+ γ ) V V V pi = {½ csγ + ½ cs( ωt + γ ) + s( ωt + γ + π )} V The puts current a and b are rewrtten as: a( t ) = I + I s( ω t + γ ) + I cs(ω t + γ ) b( t ) = I + I s( ω t + γ + π ) + I cs(ω t + γ ) I I I V p I = ¼ V V p I = ½ V V p I = ¼ V csγ If the parastc resstances f the ductrs (L and L ) are assumed as r and r, the cpper lsses are: lss _ P = ( I + ½I + ½ I ) r lss _ ut = ½ P I r The pwer lsses thrugh the swtches can be apprxmated as: (4a) (4b) (4c) (5) (6) sw = DF D + n rms P V R I where I rms av I H dc H ac H dc ( ), δav H dc H ac 3δ I I D = ½ I, D = π π where V DF s the dde frward threshld vltage and R n s the devce dynamc resstance. (7) 6

8 Page 7 f 3 IET Renewable Pwer Generatn The ttal pwer lss f each verter s: and the verter effcency s: P = [ P + P + P ] (8) ttal lss _ lss _ ut sw V p I η = 00 V I + P p ttal The swtches pwer lsses the fve verter types are the same as they all have dentcal current and vltage wavefrms. The cpper lsses as well as devce average vltage and current are summarzed Table. Table Cpper lsses and swtch peratg cndtns Type C5 G5 D D F5 Cpper lsses x r L L ( +) 3 6 Parameter (9) Swtch averages S and D S and D Vltage Current Vltage Current 8 '' '' '' '' 8 + ( +) '' '' '' '' Table 3 Parastc cmpnent values and crcut cndtns '' '' '' '' '' '' '' '' Value Rated pwer.5 kw Swtchg frequency f s = 50 khz Input ductr L = mh, r = 80 mω Output ductr L = mh, r = 80 mω Input vltage V = 00 V Output vltage V p = 00 V Output current angle γ = 0º Dde frward vltage V DF = V Transfer capactr C = 0µF Output capactr ( G5 and F5) C = 0µF A MATLAB smulatn fr the effcences f the fve verters at dfferent put vltages and utput currents wth the verter parastc values s shwn Fg. 3a. C5 and G5 verters have the hghest effcency. The effcences f D and F5 are better than D the hgh put vltage regn whle D s 7

9 IET Renewable Pwer Generatn Page 8 f 3 better than bth when the put vltage s lw. Generally, the effcency f all verters decreases as the put vltage decreases (sce semcnductr vltage drps becme mre sgnfcant). a b c Fg. 3. MATLAB smulatn f DMCSIs: (a) effcency, (b) put current rpple I, and (c) utput current rpple I 3. Input current rpple Input current rpple s the maxmum change f the stantaneus current arund ts average value. Fr energy cnversn applcatns lke PV, fuel cells, etc., rpple causes harmncs and pwer lss the verall system, s shuld be reduced. Ref [4] demnstrates that put current and vltage rpple versely affects the ttal pwer extracted frm PV systems. In the structure Fg., the put current rpple s nt cnstant and changes durg the 50/60Hz current cycle. The maxmum current rpple ccurs at the peak value f the cnverter s duty rat. The maxmum rpple current fr the dfferent verters are presented Table 4. Fg. 3b shws plts f maxmum rpple currents at dfferent peratg cndtns. C5, G5 and D cnverters have the same put current rpple versus put and utput vltage. Bth D and F5 have the 8

10 Page 9 f 3 IET Renewable Pwer Generatn same put current rpple versus utput current and vltage. As an mprtant advantage, the rpple cntents f the put current D and F5 are small cmpared wth the ther DMCSIs. Table 4 Maxmum Input current rpple Tplgy nrmalsed C5 D D F5 ( + ) I ts 4 ( + ) 4 C ( V + V ) ( + ) I ts 4 ( + ) 4 C ( V + V ) p p G5 ( + ) 3.3 Output current rpple The utput current dstrtn can be classfed t lw frequency and hgh frequency dstrtn. Lw rder current dstrtn appears because f the nn-lear nature and hgh system rder f the prpsed verters and can be remved wth apprprate cntrl lps as dscussed [9]. The hgh frequency current and vltage rpple the utput sde s because f the swtchg actn. These hgh frequency rpple cmpnents are dependent n the cnverter tplgy the dfferental-verter descends frm. Fr the same passve element cmpnent values, the utput current rpple can be expressed as Table 5. The peak utput current rpple I f the dfferent verters are smulated Fg. 3c. The hgh frequency rpple cmpnent f the utput current I D s sgnfcant cmpared wth the ther cnverters, wth the same passve element values. Ths leads the DMCSI emergg frm the D cnverter havg lwer ttal harmnc dstrtn (THD) than the ther verters, prvded the lw rder current cmpnents are elmated wth prper cntrllers. 9

11 IET Renewable Pwer Generatn Page 0 f 3 Table 5 Output current rpple Tplgy nrmalsed C5 D D F5 G5 ( + ) ( + ) I 4 ( + ) ts 4 C ( V + V ) ( + ) p I L 4C V ( + ) I L 4 C ( V + V ) p 3.4 Capactr C vltage stress Knwledge f the vltage stresses n the energy transfer capactr C s mprtant fr ts selectn. Fr sme verters, the vltage acrss C cnssts f a dc-bas plus a susdal vltage cmpnent (fundamental) whle fr ther cnverters, the vltage acrss C s nly dc. Inverters usg F5 and G5 have lwer capactr vltages stresses than C5, D and D. Table 6 summarze the capactr vltages stresses fr each cnverter, terms f the surce vltage and dfferental susdal utput maxmum vltage, V p. Table 6 Vltage stress acrss capactr C (see Fg. ) Tplgy dc-bas Susdal vltage (fundamental) Peak Vltage C5 V + V p ½V p s ωt V+ V p D V + V p ½V p sωt V+ V p D V + V p ½V p sωt V+ V p F5 V 0 V G5 V 0 4. Cntrl desgn Fr several applcatns, buck-bst DMCSIs requre rbust, effcent and fast cntrl methds. Ths s because each phase cnverter prduces ac vltage supermpsed n a dc bas vltage. Thus, the devatn f the utput dc vltage cmpnent may cause utput dc current cmpnents whch are undesrable the verter systems. Because the prpsed systems are f hgh rder, varable structure cntrl [5] (VSR) s an attractve cntrl slutn. In ths sectn, sldg mde cntrl (SMC) [5], whch belngs t the famly f VSR technques, wll be dscussed when appled t the prpsed DMCSIs. The mathematcal V 0

12 Page f 3 IET Renewable Pwer Generatn analyss wll be presented detal fr the C5 based system and fllwg the same apprach, the fal blck dagrams and cntrl equatns wll be stated fr the ther fur verter types. SMC frces the system states t track predefed trajectres whch le n the desred reference values [5]. SMC havg fast dynamcs and ts rbustness t system parameter and states varatns are mprtant features. The cntrl structure ams t drve the verter s utput current n a specfed surface. Frst, the large sgnal average mdel f C5 cnverter can be btaed frm the cnverter s dfferental equatns the n and ff mdes as fllws (cntuus cnductn mde (CCM) f all passve reactve cmpnents s ensured because the cnverters are reversble): ) S OFF and S ON (0 < t <t ff ) ) S ON and S OFF (t ff < t <t s ) d r = V - - v dt L L L dv c = dt C d r = - - v dt L L c d r = V - dt L L dv c = dt C d r = - v - - v dt L L L c The equatns can be averaged ver the swtchg tme t s as: (0) () d r - u = V - v dt L L L dv c u - u = + dt C C d u r = - v c - - v dt L L L c u = { S n 0 S ff () By averagg the dscrete varable u n t s as u eq = δ, the average state space mdel the cntuus cnductn mde CCM s:

13 IET Renewable Pwer Generatn Page f 3 d r ( - δ ) dt L L L V dv c ( - δ ) 0 δ = v c dt C C v d r 0 δ - 0 dt L L L The C5 cnverter s nt able t be cntrlled drectly frm the utput current; nly the put current can be drectly cntrlled. Ths can be understd frm the effect f the tw swtches S and S n the cnverters currents. Fr all the cnverters Fg., S affects the put current drectly whle S has n drect effect n. Fr ths reasn, the reference value f the cnverter utput current s wrtten terms f. The sldg surface S can be chsen as: = + + (4a) = + + =0 (4b) where α, α and α 3 are cnstants and e, e and e 3 are the cntrller errr sgnals, wrtten as: (3) = = = ( + ) = = = + Fr the pre-stated cntrllablty ssues, the reference put current s re-wrtten as: (5a) (5b) =( ) (6) where K s a cntrl cnstant. If the frequency f s assumed small cmpared t the swtchg frequency, can be cnsdered cnstant durg ne swtchg perd and ts dervatve can be cnsdered as zer. Substtutg (3) and (6) t (5a) yelds: - r K δ ( - δ ) K r K e & = V + + v c (- + ) + + v L L L L L L δ r e & = - v c + + v L L L 3 - ) - e & = (K +)( Substtutg (7) t (4a) and slvg fr δ gves: (7) + + c V ( r K ) v ( K r ) v K K ( ) u eq = δ = v c ( + K ) α3 Kα+ α ( K + ) α3 K= L, K = L, and K3 = L α L α α (8)

14 Page 3 f 3 IET Renewable Pwer Generatn The resultant sldg mde cntrller frm (8) s shwn Errr! Reference surce nt fund.a. The cntrller gas K, K and K 3 are respnsble fr steady state regulatn, scllatn and settlg tme. The desgner has three degrees f freedm t chse the ga values. Hwever, t must be cnfrmed that these values ensure trackg f the predefed trajectry. Ths s cnfrmed by fulfllg tw exstence cndtns [6]: Cndtn (Lyapunv): when S>0 then <0 and u= Frm (8): Ths mples that: -V + ( r K ) + v + ( K r ) + v K + K ( ) < v (K + ) (9) c 3 c -V + r $ K v K + K r $ + K v$ + K ( ) < 0 (0) c 3 Cndtn : when S<0 then >0 and u=0 Frm (8): Ths mples that: c 3 -V + ( r K ) + v + ( K r ) + v K + K ( ) > 0 () -V + r K + v+ K r + K v+ K ( ) > 0 () c 3 Equatns (0) and () are referred t as exstence equatns. The sldg mde cntrllers fr the ther verters are smlarly btaed. The blck dagrams f the ther fur buck-bst DMCSIs are shwn Fg. 4 whle the asscated exstence equatns are lsted Table Expermental results The system cncept, presented mathematcal analyss, and smulatns, are valdated wth a.5kw DMCSI as Fg., wth the parameters Table 3, cntrlled wth TMS30F80335 DSP. Fg. 5 shws the expermental rg, whle Fg. 6 shws the expermental results fr the presented analyss and dscussn fr the buck-bst DMCSIs when cntrlled by sldg mde cntrl and cnnected t the grd (V p = 00V) at unty pwer factr (γ=0). The effcences f the fve buck-bst DMCSIs at dfferent utput pwer are shwn Fg. 7a. As frm the smulatn Fg. 3, the effcences f the C5 and G5 are the hghest. D and F5 have effcences hgher than D fr lwer utput pwer whle D has a hgher effcency at hgher utput pwer. Fg. 7b shws the THD f the fve verters wth respect t utput pwer. 3

15 IET Renewable Pwer Generatn Page 4 f 3 a b c d e Fg. 4. Blck dagrams f DMCSI sldg mde cntrllers: (a) C5, (b) D, (c) D, (d) F5, and (e) G5 Fg. 5. Expermental setup 4

16 Page 5 f 3 IET Renewable Pwer Generatn Table 7 Cntrl and exstence equatns C5 D + + c V ( r K ) v ( K r ) v K K ( ) u eq = δ = v ( + K ) c -V + r $ K v K + K r $ + K v$ + K ( ) < 0 c 3 c 3 -V + r K + v + K r + K v + K ( ) > 0 + c eq = vc K V V + r K K vc+ vc+ K r + K v+ K 3( ) > 0 u V (K ) (r K ) v (K ) (K r ) v K K ( ) D u c 3 K V V + r K K v + K r + K v + K ( ) < c eq c + + c+ c > V ( K ) ( r r K ) v ( K ) ( K r ) v K K ( ) = v + v K V V ( r r ) K K v v K r ) K v K ( ) 0 c 3 K V V + ( r + r ) K K v + K r + K v - v + K ( ) < 0 F5 u eq + + c V ( r K ) v ( K r ) v K K ( ) = K (v + v ) c c 3 V + r (m) K + v + K r + K v + K ( ) > 0 G5 u eq c c 3 V + r K K v - v + K r + K ( ) < 0 -V + ( r K ) + v c ( K r ) + v + K 3 ( ) = v + v c c 3 V r K K r K 3( ) V + r K + v K r + v + K ( ) > < 0 D has the lwest THD whle C5 and D have the hghest. Bth D and F5 have the lwest put current rpple. Hwever F5 and G5 requre utput capactr C, whle the vltage stresses acrss the termedate capactrs F5 and G5 are lwer than the stresses the ther verters. The relatnshp between the put current rpple and the ttal effcency fr the PV systems are t be cnsdered further publcatns. 5

17 IET Renewable Pwer Generatn Page 6 f 3 a b c d Fg. 6. Expermental results: (a) C5, (b) D, (c) D, (d) F5 and (e) G5. e 6

18 Page 7 f 3 IET Renewable Pwer Generatn S S S S Eff (%) S THD (%) S S S S S a Fg. 7. Expermental plts f DMCSIs: (a) effcency and (b) THD. b 6. Dc sde harmnc flterg Sgle-phase verters draw and delver scllatg pwer, wth the secnd-rder current harmnc (supermpsed n an average dc current) the dc lk (the dc sde), dependent f the pwer flw drectn. In lw pwer applcatns, such as small-scale PV systems fr mcr-grds, flterg s requred at the dc sde because the harmnc current cmpnents wll sgnfcantly affect PV MPPT. In [], a twswtch tw-dde reversble bst cnverter can actvely elmate the secnd rder harmnc cmpnent frm the put f the PV r EV system currents as shwn Fg. 8a and the energy can be stred temprarly an utput capactr C HC. Hwever, ths harmnc cmpensatr (HC) methd requres an addtnal pwer electrnc cnverter whch adds t the ttal cst and cntrl cmplexty. The stantaneus pwer equatn f the dfferental buck-bst verter wth an HC can be wrtten as: I I s HC = peak HC ½ P ( t ) = P ( t ) + P ( t ) HC V I = ( t ) V + v ( t ) ( t ) V I V s HC g V p I = ½ cs ωt V V p I = ½ V v ( ) ( ) ( )= g t t HC t I s V (3) 7

19 IET Renewable Pwer Generatn Page 8 f 3 + CHC VHC (f) LHC V (f) + V - HC a b - v g + a b - Buckbst(a) + s Harmnc a Cmpensatr V L - s Buckbst(b) Buckbst(a) Buckbst(b) C b v b = b v a = + a C f=50hz f=50hz v a v b + - v g + f=00hz f=00hz c d Fg. 8. nd harmnc elmatn f DMCSI: (a) actve elmatn wth addtnal pwer electrnc cnverter [], (b) actve elmatn wthut addtnal pwer electrnc cnverter, (c) cntrl fr the prpsed methd, and (d) expermental results fr C5 DMCSI wth the prpsed methd. 8

20 Page 9 f 3 IET Renewable Pwer Generatn The energy (P HC dt) flws frm the put sde and s stred the utput capactr C HC the +ve half cycle f HC and v HC (t) creases frm V HC () t V HC (f). In the -ve half cycle f HC, the same energy flws frm C HC back t the dc supply leadg v HC (t) t decrease frm V HC (f) t V HC (). Ths energy cyclg can be expressed as: ½t HC HC = HC HC HC 0 V ( t ) dt ½ C [ v ( f ) v ( )] where t = and v ( ) = V f V p I v HC ( f ) = V + π f C HC HC HC V p I v HC ( f ) = v + π f C HC The prpsed sgle-phase buck-bst DMCSIs have the capablty t decuple the nd rder harmnc current cmpnent wthut addtnal pwer electrnc devces. Frm Fg. 8b, an addtnal cntrller frces energy scllatg at 00/0 Hz t be stred stantaneusly the utput capactrs C (whch are necessary fr F5 and G5 verters and ptnal fr C5, D and D verters). The cntrller must ensure that ths stred energy des nt affect the utput vltages and currents. Therefre, tw vltages wth the same magntude, phase-shft and 00/0 Hz frequency are supermpsed acrss the utput capactrs. Wthut decuplg the duble-frequency pwer, the utput stantaneus pwer s: (4) p( t ) = S 3 csγ S cs( ωt γ) where S = V p I where Q s the reactve pwer absrbed by the lad The cnverter utput vltages, v a and v b shwn Fg. 8b, can be expressed as: P v ( t ) = ½V + ½V sω t + V s( ω t +ψ ) a p p Q v ( t ) = ½V + ½V s( ω t +π ) + V s( ω t +ψ ) b p p (5) (6) Because they are f same magntude V, frequency f, and phase shft ψ, the secnd rder cmpnents the utput vltages v a and v b d nt affect and are nt seen by the lad vltage v g and current. That s, the secnd rder cmpnent s elmate the utput v a v b. Fr the C5 DMCSI example, the ttal reactve pwer stred the ductrs (L and L ) and capactrs (C and C ) the dfferental verter can be wrtten as: 9

21 IET Renewable Pwer Generatn Page 0 f 3 d a d b d dv ca dv cb dv a dv b Qs ( t ) = L( a + b ) + L + C ( v ca + v cb ) + C ( v a + v b ) (7) dt dt dt dt dt dt dt T elmate the nd rder harmnc current suppled frm the put dc surce, the ttal stred energy the verter shuld be zer. Equatg Q t Q s equatns (5) and (7) and slvg fr V and ψ leads t: ψ = tan V ω p 4S csγ S csγ = ω C V csψ C V p d (8) where C d = C+C Hwever, elmatg the duble frequency scllatg pwer wll generate 4 th rder scllatg pwer Q 4th : 4th Q = ωv s(4ω t + ψ ) (9) The emergg 4 th rder scllatg pwer wll generate 4 th rder scllatg current the put sde and needs an addtnal cntrl lp fr elmatn. In Fg. 8c, a prprtnal-resnant (PR) cntrller s mplemented rder t ensure suppressn f the nd and 4 th rder harmncs frm the put current. As the cntrller s fast dynamcs are nt mprtant, the ga values f the PR cntrller (K p and K r ) can be selected much lwer than the ma lp values rder t avd teractn. Fg. 8d shws the perfrmance f ths cntrller wth C = 50µF where t remves 75% f the nd rder harmnc cmpnent the put current. Fg. 9a shws the vltage stress acrss the decuplg capactrs (C HC and C ) fr the tw actve methds, wth and wthut pwer electrnc devces, at dfferent utput current and capactr values. Stress n Capactr (V) x Capactr (C r CHC) (Farad) Wthut Pwer Electrncs Wth Pwer Electrncs I(A) Lad Pwer (W) a b Fg. 9. nd harmnc elmatn f DMCSI : (a) vltage stress acrss the decuplg capactr (C r C HC ) fr actve elmatn methds and (b) dfferental-mde C5 verter effcency wth nd rder harmnc currents actve elmatn technques Wthut Pwer Elect. Cnverter Wth Pwer Elect. Cnverter 0

22 Page f 3 IET Renewable Pwer Generatn Usg addtnal pwer electrncs results lwer stress n the capactr C HC (lwer plane Fg. 9a) than n C wth the secnd methd (upper plane Fg. 9a). Hwever, Fg. 9b shws that the effcency f the secnd methd s hgher, sce devce pwer lsses f the addtnal pwer electrnc cnverter decrease effcency. 7. Cnclusn The paper vestgated sgle-stage sgle-phase verters based n tw dfferentally cnnected reversble buck-bst cnverters whch have advantages when embedded renewable energy generatn systems. The verters have a lw dc sde rpple current, wthut recurse t electrlytc capactr flterg. The buck-bst cnverters have nnlear hgh rder transfer functns where the dynamcs depend n the peratn pt and the duty rat, whch cmplcates cntrl desgn. A nd rder harmnc dc sde put current cmpnent dsturbs MPPT, hence reduces ttal effcency. In ths paper, fve tplges fr DMCSIs were prpsed. Wth ther peratn, features, and cntrl desgn usg sldg mde cntrl were vestgated and verfed. The C5 and G5 based verters have the lwest pwer lss, hence the hghest effcences. Hwever, they experence hgh put current rpple and may requre hgher put ductrs values. The D and F5 cnverters have gd effcency at hgher put dc vltages whle the effcency deterrates at lwer put vltages. The effcency f the D verter s lwer than D and F5 at hgh put vltage but s better at lwer put vltages. Frm the devces ratg pt f vew, the fve verters tplges have the same perfrmance. Usg the same passve element values, D s fund t have the lwest THD the utput vltage and current wavefrms. D and F5 verters have lw put rpple current whch s attractve feature fr PV systems. F5 and G5 verters have the lwest capactr vltage stresses, hence smaller and cheaper capactrs can be used. A new actve methd t suppress the nd rder harmnc put current frm the DMCSIs wthut addtnal pwer electrnc cnverters s prpsed. The nd rder reactve pwer s decupled usg the verter utput capactrs the ac sde. Cmparg the prpsed technque wth a pwer electrnc based actve elmatn methd, the prpsed methd avds the pwer lsses asscated wth an addtnal pwer electrnc cnverter, whch reduces system effcency. An expermental unversal sgle-phase verter was used t valdate the theretcal and mathematcal analyss. Detaled verall cntrl analyss, cludg MPPT peratn, as well as the effect f grd sde mbalance, cmmn mde vltage, and lw rder harmncs are yet t be cnsdered.

23 IET Renewable Pwer Generatn Page f 3 8. References [] Thmsn, M., Infeld, D.G.: 'Impact f wdespread phtvltacs generatn n dstrbutn systems', Renewable Pwer Generatn, IET, vl., n., pp.33 40, March 007 [] Knght, J., Shrsavar. S., and Hlderbaum, W.: 'An mprved relablty Ćuk based slar verter wth sldg mde cntrl', IEEE Transactns n Pwer Electrncs, vl., pp. 07-5, 006. [3] Nak, R., Mhan, N., Rgers, M., and Bulawka, A.: 'A nvel grd terface, ptmzed fr utlty-scale applcatns f phtvltac, wd-electrc, and fuel-cell systems', IEEE Transactns n Pwer Delvery, vl. 0, pp , 995. [4] 'Relablty Predctn fr Electrnc Equpment',Dc. MIL-HDBK- 7X, Dec. 99. [5] Hngb, M., Jh-Sheng, L., Quanyuan, F., Wensng, Y., Cng, Z., and Z. Zheng: 'A Nvel Valley-Fll SEPIC- Derved Pwer Supply wthut Electrlytc Capactr fr LED Lghtg Applcatn', IEEE Transactns n Pwer Electrncs, vl. 7, pp , 0. [6] Hu, S., S, L., Xue Hu, T., Wu, C., and Ng, W.: 'A Nvel Passve Offle LED Drver Wth Lng Lfetme' IEEE Transactns n Pwer Electrncs, vl. 5, pp , 00. [7] Puukk, J., Sunt, T.: 'Dynamc prpertes f a vltage surce verter-based three-phase verter phtvltac applcatn' Renewable Pwer Generatn, IET, vl.6, n.6, pp.38,39, Nvember 0 [8] Gu, X.Q., Wu, W.Y.: 'Imprved current regulatn f three-phase grd-cnnected vltage-surce verters fr dstrbuted generatn systems' Renewable Pwer Generatn, IET, vl.4, n., pp.0,5, March 00 [9] Darwsh, A., Hllday, D., Ahmed, S., Massud, A.M., and Wllams, B.W.: 'A Sgle-Stage Three-Phase Inverter Based n Ćuk Cnverters fr PV Applcatns' Emergg and Selected Tpcs Pwer Electrncs, IEEE Jurnal f, vl., pp , 04. [0] Kjaer, S.B., Pedersen, J.K., and Blaabjerg, F.: 'A revew f sgle-phase grd-cnnected verters fr phtvltac mdules' IEEE Transactns n Industry Applcatns, vl. 4, pp , 005. [] Myrzk, J.:'Nvel verter tplges fr sgle-phase stand-alne r grd-cnnected phtvltac systems' Pwer Electrncs and Drve Systems, 00. Prceedgs., 00 4th IEEE Internatnal Cnference n, 00, pp vl.. [] Peng, F.Z.: 'Z-surce verter' Industry Applcatns Cnference, th IAS Annual Meetg. Cnference Recrd f the, 00, pp vl.. [3] Mehrnam, S. and Mazumder, S.K.: 'Dscntuus Mdulatn Scheme fr a Dfferental-Mde Cuk Inverter' Pwer Electrncs, IEEE Transactns n, vl. 30, pp. 4-54, 05. [4] Caceres, R.O., Barb, I.: 'A bst DC-AC cnverter: analyss, desgn, and expermentatn' IEEE Transactns n Pwer Electrncs,, vl. 4, pp. 34-4, 999. [5] Dalan, C., Gulg, W.: 'Dfferental Buck DC-DC Chpper Mde Inverters Wth Hgh-Frequency Lk' IEEE Transactns n Pwer Electrncs, vl. 6, pp , 0. [6] Wllams, B.W.: 'Generatn and Analyss f Canncal Swtchg Cell DC-t-DC Cnverters' IEEE Transactns n Industral Electrncs, vl.6, n., pp , Jan. 04

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