Research Paper MODELING AND SIMULATION ANALYSIS OF SOLAR PV ENERGY SYSTEM WITH LUO CONVERTER USING STATE-SPACE AVERAGING TECHNIQUE

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1 enkatesan et al., nternatnal Jurnal f Adanced Engneerng Technlgy E-SSN Research Paper MODENG AND SMUATON ANAYSS OF SOAR P ENERGY SYSTEM WTH UO ONERTER USNG STATE-SPAE AERAGNG TEHNQUE Sundarrajan enkatesan, Manmaran Saraanan Address fr rrespndence Assstant Prfessr, Alagappa chettar llege f Engneerng and Technlgy, Karakud, Tamlnadu, nda Prfessr, Thagarajar llege f Engneerng, Madura, Tamlnadu, nda. ABSTRAT Ths paper presents a mdelng and smulatn analyss f phtltac (P) system wth hgher rder D-D UO cnerter usng state-space aeragng technque. The UO cnerter has the nn-nertng utput and ts utput ltage can be mre r less than nput ltage wth the nput current beng cntnuus. The nherent nput flterng prpertes f UO cnerter ges better utput ltage and current wth reduced rpples and ncreases the effcency as cmpared t exstng fundamental D-D cnerters. The state-space methd s used t mdel the UO cnerter. The P panel smulnk mdel s deelped based n the sngle dde equalent crcut f the P mdule. The cmbned P panel mdel and state-space mdel f UO cnerter s smulated under aryng enrnmental cndtns usng MATAB SMUNK. ncremental cnductance maxmum pwer pnt trackng (MPPT) algrthm s used t erfy the perfrmance f the UO cnerter n a P system. A crcutry smulatn s perfrmed under the same test cndtns t aldate the state-space mdel. The smulatn result shws that state-space aeragng technque yelds smlar perfrmance as the result frm crcutry mdel. The state-space technque s easer t mplement as cmpared t crcut mdel. n addtn, the cntrller desgn fr cnerter n P system wth ether smple r cmplex hgher rder system such as UO cnerter s easly pssble. KEY WORDS Hgher rder pwer cnerter, ncremental cnductance, UO, MPPT, and state-space aeragng methd.. NTRODUTON: n recent year mre attempts has been made t lcate renewable clean energes n the cuntres all er the wrld t meet the energy demand. The slar energy wll play an mprtant rle n alleatng the energy crss, t decreasng the enrnmental pllutn and mprng the green huse effect, hence tremendus grwth n the past decade. The sgnfcant research attentn n slar P energy system s fcused because f mre relable and easy t nstall [-3]. Hweer, the slar P energy system has lw cnersn effcency, because f the utput pwer f slar cells manly depends n factrs such as temperature and rradance. T maxmze the utput pwer f P and prde a cnstant r regulated utput ltage, there are a number f MPPT technques [4] and D D cnerters are emplyed and play a tal rle n slar P system [5]. Dfferent MPPT technques hae been deelped and publshed such as hll clmbng/ perturb and bsere (P&O), ncremental cnductance (nc-cnd.) methd, fractnal pen crcut ltage, fractnal shrt crcut current, Fuzzy lgc and neural netwrks [6- ].These technques dffer n many aspects such as requred sensrs, tme, cmplexty f the algrthm t track the MPP, mplementatn cst and the ease f mplementatn. Amng these mst suggested MPPT algrthms hll clmbng/ P&O and nc-cnd. algrthm are the center f attentn because f ther smplcty and ease f mplementatn. P&O algrthm s nt precse enugh because t fals t quckly track the MPP under fast aryng atmspherc cndtns and they perfrm steady-state scllatns at MPP, whch cnsequently waste the energy []. The nc-cnd. methd s the ne whch exhbts better perfrmance than ther technques [3, 4]. n ths algrthm, the array termnal ltage s always adjusted accrdng t ts alue relate t the MPP ltage by measurng the ncremental and nstantaneus array cnductance f the P mdule. n D-D cnerter perspecte, all exstng cnerter tplgy used n slar P-based system such as buck, bst, buck-bst and hgher rder cnerters UK,SEP cnerters hae ts wn unque characterstcs and are emplyed n a number f applcatns such as electrc tractn, electrc nt J AdEngg Tech/l. /ssue /Aprl-June,6/ ehcles, and dstrbuted D systems such as space statns, shps, and arplanes, [5-7].Mst f the applcatns need extremely lw rpple n ltage and current fr battery perated prtable deces. Basc cnerters are nt sutable fr many applcatns whch requred lwest rpple, hgher and lwer utput ltage cmpared t nput and hgh effcency. The hgher rder cnerters such as UK,SEP and UO cnerter s better ne, but UK cnerter prduces the utput ltage hgher r lwer than the nput ltage, wth reerse plarty [8],[9]. The prblem can be crrected easly, but ths wll netably lead t the ncreased n sze and cst f the cnerter. At the same tme, the SEP and UO cnerter des nt suffer frm ths prblem. The lterature des nt hae suffcent reprt f D-D UO cnerter and ts dynamc perfrmance n cnjunctn wth slar P panel fed energy system. Durng the past tw decades, dfferent mdelng f the D-D cnerters has been carred ut by researchers t ncrease the pwer cnersn effcency n P system [-]. The PWM and aeraged swtch mdel strateges are based n equalent crcut manpulatn. The state-space mdel s the mathematcal mdel that prdes a dynamc mdel f a physcal system. n the statespace aerage (SSA) technque, dfferental equatns fr a system are wrtten n canncal frm (matrces).hence, t s cnenent fr analyzng cmplcated cnerter tplges thrugh state space mdelng prcess f hgher rder cnerters. n ths paper, nc-cnd. algrthm wth fxed step sze s used fr smulatn. D-D UO cnerter tplgy s cnsdered fr analyss and the statespace mdel fr a nn-slated furth-rder D-D UO cnerter s dered and the result cmparsns are made wth crcut mdel n terms f P and cnerter utput ltage and current fr arus rradatn cndtns and at cnstant temperature. By usng ths mdel, system matrces are dered, and a MATAB cdng s wrtten t extract the releant transfer functns partcularly the aud susceptblty f the cnerter and cntrl-t-utput transfer functn f the D-D UO cnerter and ts stablty s analyzed thrugh bde plt.

2 enkatesan et al., nternatnal Jurnal f Adanced Engneerng Technlgy E-SSN MATHEMATA MODE FOR P MODUE: The basc structural unt f a slar mdule s the P cells. t s an electrcal dece that cnerts the energy f lght drectly nt electrcty by the phtltac effect. A sngle dde equalent crcut mdel f a slar cell s shwn n Fg.. t s mdeled by a current surce, a dde and tw resstrs. The dde s cnnected n parallel t current surce; the phtn energy ncdent n the P cell generates current. The current surce ( ph ) s prprtnal t the amunt f energy ncdent n P cell [3-5]. whse specfcatn detals are gen n Table. Fg. (a) & (b) presents the current-ltage (-) and pwer-ltage (P-) characterstcs f the P panel under dfferent slar rradatn cndtn at a cnstant temperature f 5. (a) Fg.: Equalent sngle dde mdel f a slar cell The - and P cures f the P are btaned by the equatn (-5). The P cell lght generated current ph depends n the slar rradatn and temperature as gen by () ph Gk [ sc K ( Tp Tref )] () The P mdule reerse saturatn current s gen by rs e ( c sc q N KAT s p ) () The mdule dde saturatn current ares wth the cell temperature and s gen by (3) rs T [ T p ref 3 q * E ] exp[ BK g { T ref T (3) The slar cell utput current s gen by (4) p ph Equatn (4) can be rewrtten by substtutng frm equatn (-3) and btaned as N * N [exp{ q * ( R )} ] p P ph P ( p prs )/ Rsh (5) where p :Output ltage f a P mdule () p :Output current f a P mdule (A) ph :ght generated current n a P mdule (A) G k :nstant whch s equal t µ/; µ :rradatn( rradatn leel) (W/m ) O :Dde saturatn current (A) q :Electrn charge (.6-9 ) k :Bltzmann cnstant (.38-3 J/K) K :Temperature c-effcent at shrt-crcut current Sr s.7a / A=B :p-n junctn dealty factr =.6 T p :ell peratng temperature n ⁰ T ref :ell reference temperature at 5⁰ R s :Slar cell seres resstance (Ω) R sh :Slar cell shunt resstance (Ω) S :P mdule shrt-crcut current at 5 and W/m E g :Band gap fr slcn =. e Ns :Number f cells cnnected n seres n the mdule Np :Number f cells cnnected n parallel n the mdule The slar panel utput pwer depends n the ltage and current btaned at ts utput termnals and there exsts ne peratng ltage at whch the slar panel can prduce maxmum pwer. A 4W P mdule s taken as the reference mdel fr smulatn setup, sh p p s p } (b) Fg. (a): - and (b) P- characterstcs f 4W slar panel under aryng rradatn cndtn at 5. Table Electrcal specfcatn at W/m and 5 (4-Watt slar panel) Parameter alue Rated pwer 4W ltage at maxmum Pwer(mp) 7.4 urrent at maxmum Pwer(mp).9A Open crcut ltage(c).8 Shrt crcut current(sc).45a 3. MAMUM POWER PONT (MPP) TRAKNG: 3.Bascs and ad Matchng f MPPT Technque: P mdule has a maxmum pwer pnt fr a gen temperature and nslatn. Fg.3 shws the P mdule drectly nterfacng t lad. f a lad lne crsses ths pnt, maxmum pwer wuld be transferred t the lad and t s well knwn that the P- characterstcs has nly ne pnt where pwer s maxmum, and the crrespndng ltage s MPP and current s MPP. The ptmum alue f lad resstance s btaned by P ltage and P current at MPP and s gen by equatn (6). Fg.3: P mdule drectly nterfacng t ad The ptmum resstance f P mdule s descrbed as MPP Rpt MPP (6) The lad resstance f the crcut s, O R O (7) where MPP s the maxmum P ltage at MPP and MPP s the maxmum alue f P current at the MPP, and are the cnerter utput ltage and current nt J AdEngg Tech/l. /ssue /Aprl-June,6/77-777

3 enkatesan et al., nternatnal Jurnal f Adanced Engneerng Technlgy E-SSN respectely. When the alue f lad resstance (R ) matches wth that f R pt maxmum pwer transfer frm phtltac panel t the lad wll ccur. The bjecte f the MPPT s t make the lad resstance f the P mdule t be equal t the ptmal resstance f the slar panel. R pt R n rder t achee the abe, and extract the maxmum pwer frm P panel, D-D cnerter s nserted n between the P panel and lad and ts duty cycle s ared. n ths paper D-D UO cnerter s used. The ltage gan f the hgher rder UO cnerter s gen by D n D where D s the duty cycle f the cnerter. The aratn f the duty cycle s nt nly regulatng the utput ltage but als can be used t ary the nput sde mpedance f the cnerter. The D-D cnerter can be cntrlled t present ptmum mpedance at the P array termnals whch facltate maxmum pwer extractn frm an array. Ths feature can be apprecated by nspectng the nput sde mpedance (R n ) expressns fr the cnerters. The nput mpedance f the hgher rder D-D UO cnerter can be calculated by R D D n R D D (8) The equatn (8) ndcates that by changng duty cycle, the nput mpedance (R n ) f cnerter shuld be equal t the ptmum mpedance (R pt ) at whch the system s wrkng at MPP. 3. mplementatn f nc-nd. Methd: The nc-nd. methd s based n the fact that the slpe f the P array pwer cures as shwn n Fg. 4. t s zer at the MPP, pste n the left f the MPP, and negate n the rght, as gen by reference ltage at whch the P array s frced t perate. At the MPP, ref equals t MPP. Once the MPP s reached, the peratn f the P array s mantaned at ths pnt unless a change n Δ s nted, whch s due t the change n atmspherc cndtns. The algrthm decrements r ncrements ref t track the new MPP. At the MPP, n cntrl actn s needed, therefre the adjustment stage wll be bypassed and the algrthm wll update the stred parameters at the end f the cycle as usual. The nc- nd. technque s used the nstantaneus cnductance and the ncremental cnductance t generate an errr sgnal = + () Frm (), we knw that e ges t zer at the MPP, but t s rarely ccurs n practcal mplementatn, and a small errr s usually acceptable. n ths paper the errr alue e s taken as.. Measurements f the nstantaneus P array ltage and current requre tw sensrs, whch can easly keep track f preus alues f ltage and current and make all the decsns as per the flw chart; duty cycle s ared accrdng t the algrthm. Fg.4: Basc f nc-nd. MPPT methd = ( ) = + = + The equatn (9) can be rewrtten by, = ;at MPP > ;left f MPP < ;rght f MPP (9) The MPP can thus be tracked by cmparng the nstantaneus cnductance (/) t the ncremental cnductance (Δ/Δ) as shwn n flwchart as gen n Fg.5 fr nc-nd. algrthm MPPT. ref s the Fg.5: Flwchart f nc-nd. algrthm MPPT 4. MODENG OF D-D UO ONERTER USNG STATE-SPAE TEHNQUE: The state-space-aeragng apprach [6] s wdely used t dere the expressns and analyss fr the small-sgnal characterstcs f PWM-cntrlled D- D cnerters. t cnssts f state equatn and utput equatn that reeals the characterstcs f the partcular physcal system. t exhbts the dynamc behar f a system r swtchng cnerter usng cmputer smulatns, whch s ery useful n the desgn f cntrllers. The peratn f the state-space mdel f the cnerters are descrbed by the fllwng basc state equatns ( t) Ax( t) Bu( t) Y ( t) x( t) Du( t) () where, x(t) = The state arable, u(t) = The nput ectr, parameter A s the state matrx, parameter B s the nput matrx, s utput matrx and D s the transtn matrx. n an electrcal system, the methd t dentfy the set f state arables s by dentfyng the number f nt J AdEngg Tech/l. /ssue /Aprl-June,6/77-777

4 enkatesan et al., nternatnal Jurnal f Adanced Engneerng Technlgy E-SSN nt J AdEngg Tech/l. /ssue /Aprl-June,6/ energy strage elements. Wth that, the nth rder f the system can als be knwn. Usng ths state-space aerage mdel f D D cnerter, ne can btan the small sgnal mdel and transfer functn f cnerter, whch wll be ery useful n the desgn f clsed-lp cntrller usng arus cntrl technques [7 8]. The mst superr adantages f D-D UO cnerter s capactr () assures the galanc nsulatn between nput and utput. The shrt crcut r breakdwns f the lad d nt affect slar panels. The addtnal flter elements n the UO-cnerter elmnate the utput rpples and enhance the utput ltage leel effectely [9]. Hweer, ths type f cnerter s stll under research wth regard t ts usage n ndustral and dmestc applcatns. 4. States-Space Equatn: Fg.6(a) shws a hgher rder D-D UO cnerter, whch s used as the pwer stage nterface between the P mdule and the lad. The UO cnerter can perate ether n cntnuus cnductn mde (M) r dscntnuus cnductn mde (DM) dependng n the current flwng thrugh. n ths paper M mde f peratn s cnsdered. The D-D cnerter has tw mdes f peratn. ()When the swtch S s clsed (ON), n ths mde, the capactr releases energy t the utput. () When the swtch S s n OFF, the current drawn frm the surce becmes zer, and current flws thrugh the dde t charge capactr.the equalent crcut f the UO cnerter when swtch s ON and OFF state as shwn n Fg.6 (b)&(c). (a) (b) (c) Fg.6: rcut dagram f (a) UO cnerter (b) Swtch ON cndtn (c) Swtch OFF cndtn The furth rder elementary UO cnerter made up f tw nductrs and tw capactrs and capable f wrkng n ether step-up r step-dwn mde. The state arables f the UO cnerter (x, x, x 3, x 4 ) are cnsdered as currents and, ltages c and c respectely. The state equatn deratn fr the UO cnerter fr the ON and OFF state f the swtch can be descrbed by the fllwng equatns (3) and (6) respectely. These equatns are expressed usng the swtchng functn, when the swtch s ON n n R () n R dt d (3) The utput equatn s expressed by (4), (4) Durng ff state, the state equatns are wrtten by (5) usng Fg 6(c), 4 3 R (5) n R dt d (6) The utput equatn, s expressed by (7) The state-space equatns hae been mplemented n MATAB/Smulnk, where the Smulnk blck s llustrated n Fg.7 5. SMUATON RESUTS AND DSUSSON: n rder t aldate the state-space mdel, a crcutry smulatn f the prpsed P system s cnnected n parallel wth the state-space mdel. Bth the statespace and crcutry mdels were deelped n MATAB/Smulnk as shwn n Fg. 8. The state-space mdel P system was smulated under dfferent rradance cndtns. The functn f the MPPT blck s t ensure that the system delers the maxmum pwer t the lad by aryng the duty cycle f the hgher rder D-D UO cnerter. The UO cnerter s fed by P surce and desgned fr 4W/4, under the nmnal maxmum pnt (rradance G = W/ m and temperature T = 5 ). Ths utput alue may change as the

5 enkatesan et al., nternatnal Jurnal f Adanced Engneerng Technlgy E-SSN Selectn f nductrs n,mn D max Δ f s n,mn Dmax Δ f s Selectn f apactrs Δ D f D max S max n mn 8 f s (8) rradance and temperature leel f P changes. The cmpnent f the UO cnerter used n the smulatn s calculated frm the equatn (8) and s gen n table.the D-D UO cnerter was desgned t perate at the swtchng frequency f 5 khz. Table Specfcatn f UO nerter mpnents Specfcatns nductr, & 69mH& 9mH apactr, & µf & 47µF Resste lad, R Swtchng frequency nput ltage 5 hm 5 khz Output ltage 4 at W/m T test the effecteness f prpsed P system, smulatn s dne fr arus enrnmental cndtns. The results f bth the state-space aeragng and the crcut mdel prde ery much clse results. The MPPT trackng features f nc- nd MPPT algrthm frm 6 t W/m at.sec s shwn n Fg.9. As the rradatn ares, the MPPT cntrller tracks the new maxmum pwer pnt and the pwer utput f the P array whch s 4W at 6W/m s ncreased t 4W at W/m. The ltage f the P mdule s ncreased frm 5. t 7.4 under that cndtn. Fg. 7:Open-lp state-space mdelng f UO D-D cnerter Fg.8: Oerall smulnk mdel f the prpsed system P Panel Pwer (W) P ltage () Fg.9:MPPT trackng features f nc-nd. MPPT algrthm frm 6 tw/m at.sec Y Plt Max.Pwer at w/m nslatn = 4W Max.Pwer at 6w/m nslatn= 4W Fg. : Smulatn results f UO cnerter n P sde at W/m P panel ltage and current nt J AdEngg Tech/l. /ssue /Aprl-June,6/77-777

6 enkatesan et al., nternatnal Jurnal f Adanced Engneerng Technlgy E-SSN Fg. shws the smulatn result f P panel ltage and current at rradatn leel f W/m.t s bsered that P ltage and current at MPP s 7.3 and.3 A respectely n steady state. The D-D UO cnerter prdes a dc ltage f 4 and current.6a fr the typcal resste lad f 5 hms as shwn n Fg. (a) & (b). The respnse tme f bth crcut and state-space mdel f the prpsed system slghtly dffer, the state-space mdel s.s faster than the crcut mdel. (a) (b) Fg.: The smulatn results f UO cnerter (rradance W/m ) (a) cnerter utput ltage (b) cnerter utput current (a) (b) Fg.:The smulatn results f UO cnerter (rradance 6 t W/m ) (a) cnerter utput ltage (b) cnerter utput current Fg.3 Smulatn results f the cnerter utput ltage and current fr the state space and crcut mdel fr aryng rradatn cndtn Fg.4: Bde plt f cntrl t utput transfer functn fr UO cnerter Fr dfferent alue f duty cycle nt J AdEngg Tech/l. /ssue /Aprl-June,6/77-777

7 enkatesan et al., nternatnal Jurnal f Adanced Engneerng Technlgy E-SSN Fr btanng the dynamc respnse f the state-space mdel system, the rradance, G, was ntally set t 6 and ared t W/m at.sec as shwn n Fg. and Fg.3 shws the smulatn results f the cnerter utput ltage and current fr the state space and crcut mdel fr aryng rradatn cndtn. t s bsered that fr all rradatn leels bth cnerter utput ltage and current n crcut and state-space mdel ges clser result. 5. Dynamc Functn f the nerter: The dynamc perfrmance ndces f the cnerter are aud susceptblty and cntrl transfer functn, where the aud susceptblty f the cnerter measures the amunt f nput aratns that wll reach the utput as a functn f frequency and the cntrl transfer functn descrbes gan between the cntrl duty rat and the utput arable [3-3]. Aud susceptblty (F) f the UO cnerter can be calculated by (9), ( S) F q( S A) b g ( S) (9) The mst sgnfcant ne s, duty cycle-t-utput ltage transfer functn (G ), whch can be btaned by () ( S) G q( S A) f ( q q ) d( S) () where A A D A ( D) b b D b ( D) q q D q ( D) f ( A A ) ( b b ) n The system matrces are dered, and a MATAB M- fle cdng s wrtten t extract the releant transfer functns and s gen by equatn () and () fr D=.5. The bde plt f cntrl-t-utput transfer functn fr dfferent alues f duty cycle D f the UO cnerter s shwn n Fg.4.The gan margn(gm) and phase margn(pm) are bsered frm the bde plt. Fr hgher alue f the duty cycle where D.7, the system get stable as clearly shwn n plt fr the prpsed system. Smlarly the bde plt f aud susceptblty (F) f the UO cnerter s generated wth MATAB as shwn n Fg.5 and bsered that fr hgher alue f D s greater than.7 the system perfrmance s gd, whch are sgnfcant fr feedback cntrl desgn purpse. F 5765e S 4 878e 5 3.6e S 4e 3 4 S 6896e S 638e S 63e 3 () G 5765e S e S 37e e S 6896e S 638e S 63e 3 () Fg.5: Bde plt f aud susceptblty fr UO cnerter Fr dfferent alue f duty cycle 6. ONUSON: n rder t help the researcher n chsng and analyzng the best cnerter fr slar P system, ths paper reewed state-space mdelng f the nnslated D D UO cnerter wth MPPT algrthm. The smulatn enrnment MATAB/SMUNK s used t mdel the crcut, and learnt the dynamc behar f cnerter fr slar P system. Smulatn results cnfrmed the accuracy f the btaned mdel fr ths cmplex furth rder system and reduce the erall smulatn cnergence tme as cmpared t crcut mdel smulatn, snce the state-space mdel des nt nclude the effect f swtchng. The cmputatn and plttng f typcal transfer functns f a D-D UO cnerter prdes grund wrk fr cntrller desgn, and bde plts were presented t dentfy the stablty regn f the prpsed P system. nt J AdEngg Tech/l. /ssue /Aprl-June,6/ REFERENES. Mekhlef S S, Sadur R, and Safar A, A reew n slar energy use n ndustres, Renewable and Sustanable Energy Reews, l.5, pp ,.. Gaetan Marc, et al. The near future aalablty f phtltac energy n Eurpe andafrca n clmateaersl mdelng experments. Renewable and Sustanable EnergyReews, l.38,pp.76 6,4. 3. Alemán-Naa Gbrán S, et al. Renewable energy research prgress n Mexc: a reew Renewable and Sustanable Energy Reews, l.3, pp.4 53, Salas, Olas E,Barrad A, and azar A, Reew f the maxmum pwer pnt trackng algrthms fr stand-alne phtltac systems, Sl. Energy Mater. Sl. ells, l. 9, n., pp , Jul Sakumar S, JagabarSathk M, Manj P S, and Sundararajan G, An assessment n perfrmance f D D cnerters fr renewable energy applcatns, Renewable and Sustanable Energy Reews, l.58,pp ,6.

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