Optimum Design of the Current-Source Flyback Inverter for Decentralized Grid-Connected Photovoltaic Systems

Transcription

1 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 3, NO., MARCH Optimum Desig of the Curret-Source Flyback Iverter for Decetralized Grid-Coected Photovoltaic Systems A. Ch. Kyritsis, Studet Member, IEEE, E. C. Tatakis, ad N. P. Papaikolaou Abstract Two alterative modes of operatio for the curretsource flyback iverter are ivestigated i this paper. The discotiuous coductio mode (DCM), where a costat switchig frequecy (CSF) cotrol method is applied, ad the boudary betwee cotiuous ad DCM (BCM) that is itroduced for photovoltaic (PV) applicatios i this paper (where a variable switchig frequecy cotrol method is applied). These two cotrol methods are aalytically studied ad compared i order to establish their advatages as well as their suitability for the developmet of a iverter for decetralized grid-coected PV applicatios. A optimum desig methodology is developed, aimig for a iverter with the smallest possible volume for the maximum power trasfer to the public grid ad wide PV eergy exploitatio. The mai advatages of the curret-source flyback iverter are very high-power desity ad high efficiecy due to its simple structure, as well as high-power factor regulatio. The desig ad cotrol methodology are validated by persoal computer simulatio program with itegrated circuit emphasis (PSPICE) simulatio ad experimetal results, accomplished o a laboratory prototype. Idex Terms Curret-source iverter, dc ac power coversio, desig methodology, distributed geeratio, photovoltaics (PVs), sigle-phase grid-coected iverter. BCM CSF DCM d d p f S f s,max f s,mi f s,avg NOMENCLATURE Boudary (betwee cotiuous ad discotiuous) coductio mode. Costat switchig frequecy. Discotiuous coductio mode. Duty cycle of the primary semicoductor switch. Duty cycle value referrig to the switchig cycle that occurs at the time-area of ωt = /. Switchig frequecy of the primary switch (khz). Maximum switchig frequecy value of the primary switch for the BCM (khz). Miimum switchig frequecy value of the primary switch for the BCM (khz). Average switchig frequecy value of the primary switch for the BCM (khz). Mauscript received December, 005; revised July 6, 006. This work is supported i part by the Europea Social Fud (75%), i part by the Greek Geeral Secretariat Research ad Techology (5%), ad i part by the ANCO S.A. ad Eergy Solutios S.A. withi the framework of Measure 8.3 of the Operatioal Programme Competitiveers ad 3rd Commuity Support Programme (PENED 03400). Paper o. TEC A. Ch. Kyritsis ad E. C. Tatakis are with the Departmet of Electrical ad Computer Egieerig, Laboratory of Electromechaical Eergy Coversio, Uiversity of Patras, Rio-Patras 6504, Greece ( Kyritsis@ ece.upatras.gr; E.C.Tatakis@ece.upatras.gr). N. P. Papaikolaou is with the Helleic Trasmissio System Operator (HTSO) S.A., N. Smyri 7, Greece ( Npapaikolaou@desmie.gr). Digital Object Idetifier 0.09/TEC eff Iverter efficiecy. g S Curret-source coductivity (Ω ). g L =/f s L (Ω ). g L,avg =f s,avg L (Ω ). i S (t) Curret-source time fuctio (A). i dc (t) Trasformer primary widig curret time fuctio (A). I dc,avg Average value of the primary trasformer widig curret (A). i dc,p Trasformer primary widig peak curret value for a switchig cycle (A). L Trasformer primary iductace (µh). Trasformer turs ratio value. N ac Number of turs of the trasformer secodary widig (ac-side). N dc Number of turs of the trasformer primary widig (PV-side). P ac Power that is trasferred to the ac grid (W). P dc DC stage processed power (W). pf Power factor at the mais side after filterig. T S Switchig period of the primary switch (s). T hl Rectified lie period (s). T s,max Maximum switchig period of the primary switch for the BCM (s). T s,mi Miimum switchig period of the primary switch for the BCM (s). T s,avg Average switchig period of the primary switch for the BCM (s). t o Primary switch o-time (s). t o,p t o iterval value referrig to the switchig cycle that occurs at the time-area of ωt = / (s). t off Primary switch off-time (s). u ac (t) Mais voltage time fuctio (V). V ac,p Peak mais voltage value (V). V ac,rms RMS value of the mais voltage (V). V dc PV geerator voltage value at the maximum power poit (V). VSF Variable switchig frequecy. V S,p Peak voltage stress of the primary switch (V). V S,p Peak voltage stress of the switches at the mais side (V). w Iteger part of T hl /T s. λ Ratio V dc /V ac,p. θ = ωt. ω Mais agular frequecy (rad/s) /$ IEEE

2 8 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 3, NO., MARCH 008 I. INTRODUCTION AS MANY coutries have ratified the Kyoto Accord aimig at a reductio of gas emissios, there is a growig recogitio of the role that solar power ca play i the battle to reduce carbo dioxide levels. Nowadays, there are two potetial markets for electric power geeratio from photvoltaic (PV) systems: large-scale power plats sized up to several megawatts (large-scale electricity geeratio i desert regios with high isolatio, PV stad-aloe or grid-coected systems for professioal use, etc.) ad small-scale residetial applicatios, where the power productio usually varies betwee 0. ad 5 kw [] [3]. The residetial applicatios ca be used either as stad-aloe systems, where there is o access to the utility grid (electrificatio of remote villages ad islads, water pumpig i developig coutries, etc.), or as grid-coected systems (grid-coected PV buildig) [] [4]. I this case, the grid acts as a battery bak with a ulimited storage capacity. Therefore, the total geeratio capability of a decetralized grid-coected PV system will be better tha that of a stad-aloe system; as there is virtually o limit to the storage capacity, the geerated electricity ca always be stored, whereas i stad-aloe applicatios, the batteries of the PV system will be sometimes fully loaded, ad therefore, the geerated electricity has to be throw away. Sice the implemetatio of large-scale PV power plats is ot cost-effective yet, the use of several decetralized gridcoected PV systems is quite more appropriate as they ca also be easily istalled o buildigs [3]. The latest techology o decetralized grid-coected PV systems is the so-called ac PV module [5] [8]. A ac PV module is the combiatio of a sigle PV module ad a siglephase power electroic iverter. The iverter is mouted either o the rear side of the module or o the support structure ad is directly coected to the PV module. The beefits of this approach are ot oly the lack of power loss, due to mismatch betwee the PV modules, but also the lack of dc coectios, arcs, ad groud faults [7]. The cocept of ac PV module supports optimal adjustmet betwee the PV module ad the iverter, which may lead to a overall better performace. Beyod that, the istalled power ca be easily upgraded. Moreover, it has the possibility to become a buy plug device that ca be istalled eve by utraied idividuals. The power process uit of these systems is usually a sigle-phase cotrollable power coverter, ragig from W. The selectio of the appropriate coverter topology has to take ito accout the followig requiremets: high efficiecy ad high-power desity; low cost ad high reliability; compliace with the electromagetic compatibility (EMC) directives ad low-voltage regulatios [9]; IEEE Stadard IEEE Recommeded Practice for Utility Iterface of Photovoltaic Systems; IEEE 547 Stadard for Itercoectig Distributed Resources with the Electric Power System. The dc-to-ac voltage coversio ca be implemeted by ay sigle-step or multistep topology [5] [8], [0]. As it has bee show i [] [4], the so-called flyback iverter is rather a attractive solutio. As metioed i these papers, the iverter operates i DCM. So, it has to behave as a curret source whose value depeds o the mais voltage. However, a aalytical desig procedure, which will esure high-power desity ad wide exploitatio of PV-geerated power has ot bee preseted before. Cocerig the voltage-cotrolled curret-source modificatio requiremet, it is obvious that the iverter caot operate i cotiuous coductio mode where the trasformer is icompletely discharged durig a switchig cycle because i this case, it will become a load-idepedet voltage source. Thus, two operatio modes ca be used: the oe already preseted i [] [4] (DCM) as well as the boudary betwee cotiuous ad discotiuous (BCM) that is itroduced for PV applicatios i this paper. I the followig sectios, both DCM ad BCM modes of operatio will be aalytically ivestigated ad compared i order to establish their suitability for the developmet of a iverter with the smallest possible volume for a give power level. By this ivestigatio, the operatioal limitatios of both operatio modes will be emerged. Fially, a optimal desig strategy for wide PV-geerated power exploitatio is proposed for daily eergy productio maximizatio. The iverter will be studied without the presece of a maximum power poit trackig (MPPT) cotrol ad a isladig detectio scheme, sice the aim of this paper is to ivestigate the efficiecy, the total harmoic distortio (THD) reductio, ad the power desity that this iverter performs uder ay lie ad load coditios. Various MPPT cotrol methods [4], [5] ad isladig detectio schemes [6], [7] could be adopted for the case of the flyback curret-source iverter i both modes of operatio. II. VOLTAGE-CONTROLLED CURRENT-SOURCE MODIFICATION REQUIREMENT The basic idea of developig a flyback curret-source iverter for eergy trasfer from a PV system to the mais is to modify a curret source whose value depeds o the mais voltage i S (t) =g S u ac (t) () u ac (t) =V ac,p si ωt. () As show i Fig., this iverter performs eergy flow from the dc to the ac stage by usig two idetical secodary widigs. Each of them is able to trasfer eergy to the ac side durig a lie half cycle. For this reaso, two cotrollable switches are placed betwee these widigs ad the mais side. Both of them are appropriately cotrolled by the mais voltage, so as to coduct durig a lie half cycle. Thus, assumig that the L f voltage drop as well as the C f 50-Hz harmoic curret are egligible, for each lie half cycle, the equivalet circuit is that of Fig. (a), ad therefore, the system operates as a dc/dc flyback coverter with variable output voltage.

3 KYRITSIS et al.: OPTIMUM DESIGN OF THE CURRENT-SOURCE FLYBACK INVERTER FOR DECENTRALIZED GRID-CONNECTED PV 83 Fig.. High-frequecy sigle-stage curret-source flyback iverter. Fig. 3. Trasformer curret represetatio for the case of DCM operatio where costat switchig frequecy cotrol method is applied. The mai idea of this techique is to force the peak curret value of each switchig cycle to become proportioal to the siusoidal mais voltage. Fig. 3 shows the equivalet trasformer curret waveform. Obviously, whe S coducts [t o iterval, Fig. (b)], this curret flows through the primary widig, while whe S is off, it flows through the active secodary widig [t off iterval diode coducts; Fig. (c)]. Fially, durig the time iterval betwee the complete trasformer discharge ad the begiig of a ew switchig cycle, there is o curret flow through the trasformer. Durig o-time, the equivalet circuit is that of Fig. (b) (S is o ad D is off), ad the trasformer curret ca be calculated accordig to the followig equatio: di dc (t) V dc = L. (3) dt Thus, the peak curret value for a switchig cycle is Fig.. Equivalet circuit of the curret-source flyback iverter durig a lie half cycle. (a) Each lie half cycle. (b) Durig S o-time. (c)durig S off-time. III. BASIC ANALYSIS OF THE DCM OPERATION I this sectio, the DCM operatio will be aalytically ivestigated i order to coclude to its optimal desig scheme. This operatio mode has bee widely used i ac PV module applicatios maily due to its simplicity (eclipse of high-frequecy curret measure). Nevertheless, due to the uavoidable deadtimes o the trasformer curret feed, its use is limited to small power levels. i dc,p = V dc t o. (4) L Usig the duty cycle d = t o /T S parameter, (4) ca be rewritte as i dc,p = V dc d. (5) L f s Sice the peak trasformer curret value should have a siusoidal waveform i dc,p (t) =I dc,p si ωt, ωt [0,] (6) we ca coclude that the duty cycle has to be modified i such a way, so as to become d(t) =d p si ωt (7) where d p is the duty cycle value referrig to the switchig cycle that occurs at the time-area of ωt = /. The exact value of d p is determied by the desired output power level of the PV geerator by usig a referece sigal. Thus, i DCM operatio, where the switchig frequecy remais costat (CSF), the block diagram of the cotrol circuit is a simple pulse width modultaio (PWM) loop, as show i Fig. 4. The trasformer turs ratio value, where is = N dc N ac (8)

4 84 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 3, NO., MARCH 008 Fig. 4. Block diagram of the cotrol circuit for the DCM operatio (costat switchig frequecy). has to be appropriately selected so as to reassure that the iverter will always be i DCM. Thus, it has to be cofirmed that the t off iterval is smaller tha the time iterval betwee the switchig period ad the t o iterval for the maximum power level t off T s t o,p. (9) The calculatio of t off ca be doe by usig the equivalet circuit of Fig. (c) (S is off, S is o, ad D is o) u ac (t) = d[i dc(t)] L dt. (0) Sice the switchig period is much smaller tha the lie period, we ca assume that u ac (t) remais almost costat durig a switchig cycle. Accordig to (0) takig for grated that the trasformer curret becomes zero at the ed of t off iterval we ca express t off as (see Appedix A) t off = λ T s d p = costat () for ay switchig period withi the lie half cycle, where λ = V dc. () V ac,p Combiig (9) ad (), we ca coclude to the followig DCM criterio: d p + λ. (3) A. Ivestigatio of the Power Desity for DCM After the basic theoretical aalysis of the DCM operatio, where costat frequecy cotrol techique is applied, it is essetial to ivestigate the iverter-trasferred power desity i relatio with its operatio parameters, so as to result i a miimum iverter structure of high efficiecy. Assumig that the iverter has uitary efficiecy ad that the primary ad secodary trasformer leakage iductaces are egligible, the power that is trasferred to the power etwork P ac is equal to the power of the dc stage P dc P ac = P dc = P. (4) Cosiderig that the iverter is i steady state, we ca express the trasferred power as P = V dc I dc,avg (5) I dc,avg = T hl i dc (t)dt. (6) T hl 0 The above itegral ca be rewritte as I dc,avg = [ T s wts ] i dc (t)dt+ + i dc (t) dt+q T hl 0 (w )T s (7) where w is the iteger part of T hl /T s ad Q is the remaiig part of the itegral referrig to the begiig or edig of a lie half cycle ad hece, it ca be eglected. By usig (3), (7), ad (7) ad takig ito accout that ( ) ωt = (it s ) w i (8) T hl we ca coclude that (see Appedix B) [ I dc,avg = d pv dc w ( ] si ) f s L w w i = d pv dc = 4f i= s L 4 g Ld pv dc (9) where g L =. (0) f s L Combiig (), (4), ad (9), the trasferred power becomes d p P = Vdc = 4 f s L 4 d pg L Vdc. () Usig () ad (), we ca describe P as P = λ d p Vac,rms = f s L λ d pg L Vac,rms. () As it is show i (), the fudametal iverter curret that flows to the etwork (after the RF filter) is i phase with the mais voltage. For this reaso, we ca express the trasferred power as P = g S V ac,rms (3) Combiig () ad (3) we coclude that g S = g L λ d p (4) Thus, accordig to eq. (3) i order to trasfer power while remaiig i DCM, the followig equatio should be fulfilled: ( gs g L ) max = ( λ + ) (5) Fig. 5 shows (g S /g L ) max as a fuctio of with λ as parameter. The rage of parameter λ has bee selected cosiderig typical mais voltage values ad the PV geerators voltage values (which are used for ac PV module applicatios) at the maximum power [8]. I Europe, λ varies betwee ad 0.4, ad i USA, betwee ad As it is obvious, for give values of λ ad g L, the trasferred power depeds strogly o the trasformer turs ratio. However, as icreases, there is saturatio o the power icrease, ad thus, there is a upper

5 KYRITSIS et al.: OPTIMUM DESIGN OF THE CURRENT-SOURCE FLYBACK INVERTER FOR DECENTRALIZED GRID-CONNECTED PV 85 Fig. 5. (g S /g L ) max as a fuctio of λ ad for the DCM operatio. Fig. 6. V S,p /V ac,p ad V S,p /V ac,p as a fuctio of λ ad,forthedcm operatio. limit for its value. This limit ca be calculated from (5) for the case that -value becomes ifiite ( ) gs g L = λ max. (6) The above aalysis leads to the followig coclusio; for a specific λ value, ay operatio poit, which is located at the area uder the correspodig curve of (g S /g L ) max, is a feasible solutio i order to trasfer a give power, while remaiig i DCM operatio. However, accordig to (3), the best selectio of operatio poits occurs whe there is equality, which meas that the (g S /g L ) max curve poits are the optimum oes, leadig to the maximum power desity. The appropriate selectio of the exact operatig poit depeds o costructioal parameters. The way i which the selectio of the trasformer turs ratio affects the desig of the iverter is discussed ext. The trasformer turs ratio affects the maximum voltage value across the semicoductor switches. I more detail, by usig the equivalet circuit of Fig. (c), the voltage stress o the switch at the PV geerator side ca be calculated accordig to the followig equatio: V S,p = λ +. (7) V ac,p Fig. 6 shows V S,p /V ac,p as a fuctio of with λ as parameter. By studyig this figure, we coclude that there is a strog limit o the -value selectio. Although, accordig to Fig. 5, the best -value selectio, for a give λ, is the closest oe to the startig poit of saturatio area; this value may lead to uacceptable large voltage stress o the primary switch S. Cocerig the maximum voltage across the semicoductor switches at the mais side, it ca be calculated by usig the equivalet circuit of Fig. V S,p = λ +. (8) V ac,p Additioally, the -value selectio also affects the maximum peak curret value o the primary switch S, as show from the combiatio of (5), (3), ad (9) [ I dc,p =4 + λ ]. (9) I dc,avg By studyig the above two equatios, we coclude that there is a strog limit o the -value selectio; a small -value may lead to uacceptable large curret value for the primary switch S ad to excessive voltage stress o the semicoductor switches S,S 3. Thus, the exact -value that has to be adopted depeds o the acceptable (permitted) voltage value across the semicoductor switches ad the acceptable peak curret value for the S switch. Combiig the aforemetioed remarks, the trasformer turs ratio must be selected betwee 0. ad.8 i Europe ad betwee 0.3 ad 5.5 i USA. This selectio limits the maximum voltage across the semicoductor switches uder kv ad the maximum peak curret through the primary switch S at the very most te times higher tha the average value of the primary trasformer widig curret. I this way, the meaig of the term acceptable area for Europe, which is show i Fig. 5, is clarified. IV. BASIC ANALYSIS OF THE BCM OPERATION The ew operatio scheme that is itroduced for PV applicatios i this paper, leads the iverter to the boudary betwee cotiuous ad DCM of operatio. Thus, the switchig frequecy ecessarily varies durig a lie half cycle to achieve complete trasformer discharge without ay time itervals of zero trasformer curret flow. So, for the case of BCM operatio, a variable switchig frequecy (VSF) cotrol techique must be applied.

6 86 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 3, NO., MARCH 008 Fig. 7. Trasformer curret represetatio for the case of BCM operatio (variable switchig frequecy). The basic equatios for the BCM scheme ca be derived by a aalysis similar to the previous case. The equivalet trasformer curret waveform for this case is show i Fig. 7. Obviously, the mai differece betwee this mode of operatio ad the DCM scheme is that, i BCM, a ew switchig cycle begis each time the trasformer curret reaches zero T s (t) =t o (t)+t off (t). (30) Durig t o, the equivalet circuit is that of Fig. (b), ad so, the peak curret value ca be described by (4). Sice the peak curret waveform should be a siusoidal oe, the t o iterval should be modified as t o (t) =t o,p si ωt (3) where t o,p is the t o iterval value referrig to the switchig cycle that occurs at the time-area of ωt = /. Additioally, Fig. (b) ad (0) stad for the descriptio of the off-time iterval. So, t off becomes t off = λ t o,p = costat (3) for each switchig cycle. Fially, accordig to (30) (3), the switchig period value ca be expressed as ( ) λ T s (t) =t o (t)+t off = +siωt t o,p. (33) Accordig to (33), the maximum ad miimum switchig frequecy values durig a lie half cycle are f s,max = T s,mi = f s,mi = T s,max = T s = ωt=0 = T s ωt= λ t o,p (34) ( λ + ) t o,p. (35) Fig. 8 shows the block diagram for the BCM scheme. Sice the switchig frequecy varies, a variable frequecy cotrol techique is applied. Cotrary to DCM operatio, the cotrol loop is more complex sice it demads sesig of both the primary ad secodary trasformer currets. Nevertheless, this more complicated cotrol loop reassures that the circuit will ot eter cotiuous coductio mode (CCM) regio uder ay coditio, because the begiig of a ew switchig cycle demads the complete trasformer discharge. Fig. 8. Block diagram of the cotrol circuit for the BCM operatio (variable switchig frequecy). A. Ivestigatio of the Power Desity for BCM As discussed i the previous case, the trasferred power will be calculated by usig (5) (8). Combiig these equatios with (3) (33), we ca express the trasferred power as P = Vdc t o,p si θ ( )dθ = V ( ) dc λ t L 0 λ o,p F. +siθ L (36) I order to obtai a expressio similar to the DCM case, the average switchig frequecy f s,avg will be itroduced f s,avg = (37) T s,avg T s,avg = T s (θ)dθ, θ = ωt. (38) 0 Combiig (33), (37), ad (38), f s,avg becomes f s,avg = ( ). (39) t o,p λ + Furthermore, the fuctio F (λ/) of (36) ca be aalytically calculated accordig to the followig formula: ( ) λ F = si θ ( )dθ = λ +siθ λ ( ( ) λ λ ) + S 0 (40) where (see Appedix C) ( ) λ S = dθ 0 λ +siθ (λ ) (λ ) arcta, for λ > =, for λ =. ( ) ) arcta h λ, for λ < ( λ (4)

7 KYRITSIS et al.: OPTIMUM DESIGN OF THE CURRENT-SOURCE FLYBACK INVERTER FOR DECENTRALIZED GRID-CONNECTED PV 87 Fig. 9. (g S /g L,avg ) as a fuctio of λ ad, for the BCM operatio. Usig () ad (36) (4), the trasferred power fially becomes P = g S V ac,rms λ = g L,avg ( ) λ + ( λ + [ λ + ( ) λ S ( ) ] λ Vac,rms (4) leadig to the followig relatio betwee g S ad g L,avg : [ g S λ = ) g L,avg λ ( ) λ + S where ( ) ] λ (43) g L,avg =. (44) f s,avg L Fig. 9 shows (g S /g L,avg ) as a fuctio of with λ as a parameter. Comparig with Fig. 5, the power trasfer that ca be achieved i this mode of operatio is sigificatly higher tha that of the DCM operatio for the same values of λ ad ; the power trasfer limit for this case is give by g S = λ. (45) g L,avg A compariso betwee (45) ad (6) shows that usig BCM operatio (assumig g L ad g L,avg have similar values), the power trasfer becomes twice the maximum power trasfer of the DCM operatio. Therefore, the use of BCM istead of DCM mode, for a specific power level, leads to a trasformer volume decrease of approximately 50%. This importat advatage highlights that BCM is the most suitable mode of operatio for the developmet of reduced-size efficiecy-effective ac PV modules iverter. After the basic theoretical aalysis of the BCM operatio, it is essetial to ivestigate the ifluece of the parameters λ ad i this operatio scheme. Sice the switchig frequecy Fig. 0. Ratio of switchig frequecy badwidth ad f s,avg as a fuctio of ad λ for the BCM operatio. Switchig frequecy badwidth as fuctio of (a) with λ as a parameter ad (b) λ with as a parameter. of the switch at the PV geerator side is ot costat, there is aother limitatio cocerig the values of λ ad ; i Fig. 0(a), the switchig frequecy badwidth is show as a fuctio of with λ as parameter. Apparetly, for a give λ, as the value of icreases, the switchig frequecy badwidth also icreases, ad f s,max becomes sigificatly higher tha f s,mi (especially for practical λ-values i PV applicatios). The above remark ifers that the selectio of the trasformer turs ratio sigificatly affects the selectio of the upper ad lower limit of the switchig frequecy, ad so, the desig of the iverter as well as the desig of the output filter becomes more complicated. Additioally, the upper limit of the switchig frequecy ought to assure that the semicoductor switches will operate withi their safe operatio area. Furthermore, i a real system, the value of λ varies because the irradiatio ad the ambiet temperature chages affect the PV

8 88 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 3, NO., MARCH 008 output voltage. Aalytically, for a give trasformer turs ratio, as it is show i Fig. 0(b), a PV geerator voltage decrease also leads to a switchig frequecy badwidth icrease (especially for high values), thereby limitig the use of BCM scheme accordig to the aformetioed remarks. Last but ot least, the maximum permitted peak curret value of the primary switch S is effected by the t o,p value, accordig to (4). Additioally, the average switchig frequecy of the mai switch S depeds also o the selectio of t o,p.imore detail, f s,avg is a fuctio of t o,p as show i (39). Takig ito accout (34), the adopted value of t o,p has to reassure that the semicoductor switch S will operate withi its safe operatio area for the maximum switchig frequecy. So, a compromise amog f s,avg, f s,max, ad the maximum peak curret values has to be made. V. COMPARISON BETWEEN DCM AND BCM Followig the theoretical aalysis, a compariso betwee BCM ad DCM modes is give i this sectio. The most importat coclusios ca be summarized to the followig remarks. BCM is the oly feasible solutio for high-power levels. The cotrol loop i BCM is more complicated tha i DCM sice it demads the sesig of both trasformer curret parts. However, the fact that the trasformer has to be completely discharged before the begiig of a ew switchig cycle reassures that the iverter will ot eter CCM. The sesig of both trasformer curret parts ca be realized with the usage of curret trasformers, similar to curret-mode cotrol, peak curret cotrol, ad curret limitig applicatios, sice both currets have appropriate high-frequecy switchig waveforms [9] []. The use of curret trasformers is particularly useful because galvaic isolatio is achieved betwee the measured quatity ad the cotrol circuit, while the short-circuit curret is limited. Fially, the total cotrol circuit cost sigificatly decreases due to the usage of these iexpesive curret sesors. DCM has a very simple cotrol loop. This fact reduces the total cost, establishig it as a attractive solutio for lowpower PV applicatios. Its small power process capability limits its use at a lower power rage compared to BCM for agivevolume. The fact that the trasformer curret is ot measured may lead uder heavy load or trasiet coditios the iverter i cotiuous coductio, ad so, a short circuit will take place. Thus, the iverter should be very carefully desiged i order to reassure that uder ay circumstaces it will ot eter CCM. The irradiatio ad the ambiet temperature chages affect both DCM ad BCM operatio, leadig to dimiished trasfer power, due to the PV geerator voltage decrease. Despite this fact, i DCM operatio (where the switchig frequecy is costat), the mais curret harmoic cotet is ot affected by the aforemetioed chages. I BCM operatio, the filter desig is more complicated i geeral, sice it has to cutoff frequecy values that deped o lie ad load coditios. O the cotrary, the filter is less Fig.. Typical power characteristic for a solar module; proposed cotrol strategy for a ac PV module. distressed compared to DCM operatio, sice the harmoic cotet is distributed i a large frequecy rage. So, BCM operatio presets smaller THD tha DCM [9]. Accordig to the earlier remarks, it is obvious that the cotrol loop i BCM mode is more complicated; however, this cotrol loop does ot lead to ay sigificat cost icrease (compared to the DCM cotrol loop) sice iexpesive curret trasformers are used. Cosiderig that the use of curret trasformers limits short-circuit currets ad that the trasformer volume icrease is isigificat, we coclude that practically, without ay cost icrease, the use of BCM operatio doubles the iverter-processed power. The icrease of the electric power per uit square meter of a PV cell module, due to the differet solar cell techologies, establishes BCM scheme as the most appropriate mode for PV applicatios with the smallest possible volume. Fig. shows a typical power characteristic of a solar module for costat temperature ad varyig irradiatio. Ay PV power decrease (due to irradiatio decrease) calls for a decrease i t o,p value; so, the average switchig frequecy as well as the upper ad lower frequecy limits take cosiderably higher values tha the rated oes. Thus, BCM operatio is suitable for power levels greater tha a certai limit, as show i Fig.. For lower power levels, DCM operatio is used i order to exploit all the available PV geeratio. Moreover, this combiatio of BCM ad DCM operatio, proposed i this paper, establishes the flyback iverter as a global solutio for ac PV module applicatios for wide power rage. VI. DESIGN PROCEDURE FOR OPTIMAL POWER TRANSFER DENSITY For low-power level PV applicatios, DCM is the most attractive solutio accordig to the aforemetioed remarks. I these

9 KYRITSIS et al.: OPTIMUM DESIGN OF THE CURRENT-SOURCE FLYBACK INVERTER FOR DECENTRALIZED GRID-CONNECTED PV 89 applicatios, aimig for a iverter with the smallest possible volume, the followig desig procedure has to be adopted. ) For give values of mais voltage, as well as PV geerator maximum power ad dc voltage, the value of λ parameter is calculated by (). ) Takig ito accout the remarks that have bee metioed for the trasformer turs ratio i Sectio III-A, we select the -value so as to lead the iverter withi the safe operatioal frame of Fig. 5, while keepig its power desity (g S /g L ) as high as possible for the specific λ-case. 3) From (3), we ca calculate the value of d p which reassures that uder ay circumstaces, the iverter will be able to remai i the DCM operatio. 4) Assumig that the iverter has uitary efficiecy, the maximum power trasferred to the etwork is equal to the PV maximum power, ad so, accordig to (3), the curretsource coductivity g S ca be calculated. 5) Afterwards, the g L -value ca be derived from (5) by usig the adopted -value ad the calculated curret-source coductivity. It is worth metioig that this g L -value is selected such that g S /g L becomes maximum for the specific λ ad values, as show i Fig. 5. 6) By substitutig the result of (5) ito (0), we obtai a expressio for the product of the trasformer primary iductace ad the switchig frequecy of the semicoductor switch S. Fially, we ca calculate the trasformer primary iductace by selectig the desired switchig frequecy of the S. Certaily, the selected switchig frequecy has to guaratee that S will operate withi its safe operatio area. However, for higher power level PV applicatios, BCM is the oly feasible solutio (as it has bee show i Sectio IV). O the other had, a cosiderable irradiatio decrease, ad cosequetly, a PV-geerated power decrease limits the use of BCM due to the switchig frequecy badwidth icrease (as it has bee show i Sectio IV-A). Thus, i such applicatios, a combiatio of BCM ad DCM operatio should be adopted i order to exploit all the available PV geeratio. This combiatio claims for the followig geeralized desig procedure. First of all, the iverter operatioal parameters are calculated for the case of BCM operatio. ) Cocerig the calculatio of the curret-source coductivity value, the parameter λ, ad the appropriate selectio of the trasformer turs ratio (takig also ito accout its limitatio by the maximum permitted voltage value across the semicoductor switches), the commets that have bee metioed for low-power level PV applicatios should be cosidered. For these calculatios, the give value of the mais voltage ad the maximum values of PV geerator power ad dc voltage should be used. ) The g L,avg -value is derived from (43) by usig the adopted -value ad the calculated curret-source coductivity. It is worth metioig that this g L,avg -value is selected such that g S /g L,avg becomes maximum for the specific λ ad values, as show i Fig. 9. 3) Replacig the result of (43) ito (44), a expressio for the product of the trasformer primary iductace with the average switchig frequecy of the semicoductor switch S is derived. 4) Fially, we ca calculate the trasformer primary iductace by selectig the cogruet average switchig frequecy of S, takig ito accout the remarks that were metioed for the t o,p i Sectio IV-A. Thereafter, the lower power limit for the BCM operatio should be defied. From (36), (34), ad the chose value of L, the power level wherefore t o,p leads to uacceptable f s,max value is derived. I this way, the lower safe power level for the semicoductor switch S is determied. Actually, the use of this mode of operatio should be siged off shortly before this power level. The trasitio betwee BCM ad DCM takes effect i this regio, i order to exploit the lower PV geeratio. Fially, the safe use of DCM depeds o the judicious selectio of d p,f S,i dc,p. For this PV geerator power level, the steps 3 6 of the DCM desig procedure have to be performed. Thus, the ew curret-source coductivity is determied, ad the aforemetioed parameters ca be calculated. Last but ot least, the above calculatios are acceptable, if the resultig i dc,p value does ot lead to excessive peak currets ad the resultig f S guaratees that S will operate withi its safe operatio area. Otherwise, a redefiitio of L value is required. The aformetioed desig methodology assures the smallest possible iverter volume for wide power trasfer to the public grid. VII. SIMULATION AND EXPERIMENTAL RESULTS The iverter operatio i the proposed BCM mode was experimetally examied o a 00-W laboratory prototype for the case of a PV geerator with 50-V costat dc voltage, 00-W maximum power, ad 0-V rms, 50-Hz mais voltage. The iverter operatio i the DCM scheme was examied o a 00-W laboratory prototype ad also with persoal computer simulatio program with itegrated circuit emphasis (PSPICE) simulatio results for the same values of PV geerator voltage, λ parameter, ad trasformer primary iductace values i order to prove that i BCM, the power trasfer that ca be achieved is sigificatly higher tha that of the DCM. For both modes of operatio, the iverter is studied without the presece of MPPT cotrol, sice the aim of this paper is to ivestigate the desig procedure uder ay lie ad load coditios. Cosiderig () ad (3), the value of λ is equal to 0.6, ad the value of the curret-source coductivity is equal to 4.3 mω (the maximum power that is trasferred to the etwork is 00 W). Accordig to the desig procedure that was preseted i the aforemetioed sectios, for the case of BCM operatio, the trasformer turs ratio is selected to be 0.5. The parameters, which lead to this -value, are a acceptable (maximum) voltage value across the semicoductor switches (V s,p 00 V, V s,p 70 V), a acceptable maximum peak curret value, ad the selectio of a ferrite core with a small volume. Takig for grated that the leakage of the trasformer is ot zero, the use of a 500-V MOSFET (for the low-voltage stage switch S ) is the cost-effective solutio i our case. The ferrite

10 90 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 3, NO., MARCH 008 Fig.. Supplyig curret waveform at the iverter mais side (before filterig) for the case of DCM operatio (experimetal results). core that has bee selected is E4//5. The umber of turs for the trasformer primary widig is 9, while the umber of turs for the trasformer secodary widig is 58. Combiig (4), (43), ad (44), the selected average switchig frequecy of the semicoductor switch S is 3 khz, ad the trasformer primary iductace L is 85 µh. Furthermore, thet o,p is 3.3 µs, ad therefore, the maximum ad miimum switchig frequecies are 96 ad 3 khz, respectively. Fially, the maximum peak curret value of the primary switch S is 8 A, which is a acceptable value for the iverter power rage. For the case of DCM, takig ito accout that the maximum power trasferred to the etwork is 00 W, from (3), the value of the curret-source coductivity is equal to.066 mω. Combiig (0) ad (5), ad cosiderig that L =85µH ad =0.5, as for the case of BCM, the switchig frequecy of the semicoductor switch S is 40 khz. Equatio (3) shows that, i order to reassure that the iverter will ot eter CCM, the value of d p must be smaller tha So, the maximum peak curret value of the primary switch S is approximately 0 A. Figs. ad 3 show the experimetal iverter mai curret waveform before ad after filterig, for the case of 00-W costat active power trasfer at the mais side ad 50-V PV geerator voltage (DCM operatio). Measuremets were obtaied by usig the oscilloscope spectrum aalyzer HP ifiium Oscilloscope 500 MHz 3 Gsa/s ad the curret probe amplifier Tektroix AM 503 B. Furthermore, Fig. 4 shows the active power trasfer P as a fuctio of d p, i compariso with the correspodig theoretical ad PSPICE simulatio values. By studyig these results, we ca coclude that the theoretical aalysis is quite accurate, sice the divergece amog the simulatio ad experimetal results ad the correspodig theoretical values is slight. Moreover, Figs. 5 ad 6 show the iverter efficiecy eff as well as the power factor pf as a fuctio of the trasferred power at the mais side P ac, showig that the proposed iverter topology presets very high efficiecy ad power factor regulatio eve uder light load coditios. Simulatio ad experimetal results are very close due to the accurate models of the switchig devices that were used i PSPICE ad due to the fact that the switchig frequecy does ot exceed 40 khz. Obviously, Fig. 3. Supplyig curret waveform at the iverter mais side (after filterig) for the case of DCM operatio (experimetal results). Fig. 4. Trasferred power as a fuctio of d p for the DCM operatio (theoretical values, simulatio, ad experimetal results). if the switchig frequecy icreases beyod 00 khz, the expected divergece betwee simulatio ad experimetal results icreases too. Figs. 7 ad 8 show the experimetal iverter mai curret waveform before ad after filterig, for the case of 00-W costat active power trasfer at the mais side ad 50-V costat PV geerator voltage (BCM operatio). These experimetal results cofirm the theoretical aalysis i Sectio IV-A. For the same trasformer volume, the power that ca be processed by the iverter is doubled i the BCM mode compared to the oe i DCM case. Fig. 9 shows the harmoic cotet of the supplyig curret for the case of 00-W costat active power trasfer at the mais side. This figure shows that the proposed iverter topology presets very high-power factor regulatio ad very low total harmoic distortio (the third harmoic cotet is already 8.75 db lower tha the fudametal harmoic). Furthermore, Fig. 0 shows the iverter efficiecy eff as a fuctio of the trasferred power at the mais side P ac for BCM

11 KYRITSIS et al.: OPTIMUM DESIGN OF THE CURRENT-SOURCE FLYBACK INVERTER FOR DECENTRALIZED GRID-CONNECTED PV 9 Fig. 8. Supplyig curret waveform at the iverter mais side (after filterig) for the case of BCM operatio (experimetal results). Fig. 5. Iverter efficiecy as a fuctio of the trasferred power level for DCM operatio (simulatio ad experimetal results). Fig. 9. Harmoic cotet of the supplyig curret at the iverter mais side for the case of BCM operatio (experimetal results). Fig. 6. Iverter power factor as a fuctio of the trasferred power level for DCM operatio (simulatio ad experimetal results). Fig. 7. Supplyig curret waveform at the iverter mais side (before filterig) for the case of BCM operatio (experimetal results). ad DCM operatio, respectively, showig that the proposed iverter topology presets very high efficiecy i both modes of operatio but the trasfer capability is quite higher i BCM. I the followig sectio, the meaig of the terms BCM effective area ad DCM effective area, which are show i this figure will be explaied. I order to achieve a iverter with the smallest possible volume for 00-W trasferred power at the mais side, BCM techique is the advisable solutio accordig to the aalysis that was preseted i the precedig sectios. As trasferred power decreases, the average switchig frequecy as well as the upper ad lower frequecy limits take cosiderably higher values tha the rated oes accordig to Fig. 0. So, the switchig frequecy badwidth as well as the switchig losses (as a percetage of the geerated power) will icrease. This fact limits the use of BCM operatio beyod the power level of 00 W for the case of the specific experimetal iverter. I order to exploit the available PV geeratio uder 00 W, while keepig high efficiecy, DCM techique must be applied. This proposed scheme ca be used i geeral for ay PV applicatio. The exact border betwee BCM ad DCM operatio depeds o the specific applicatio ad the desiger s requiremets (frequecy badwidth, efficiecy, -value selectio, etc.)

12 9 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 3, NO., MARCH 008 APPENDIX B i dc (t x )= i dc,p t x = I dc,p si ωt t o t o t x = V dc L f s d p si ωt T s d p si ωt t x = V dc t x L f s T s where t x = t (i )T s,i=,, 3... T s to i dc (t)dt = i dc (t x )dt x = V dc t x (i )T s 0 L t o 0 (B) = V dc t o L (B) t o = T s d p si ωt = T s d p si ωit s T s d p si w i. (B3) Fig. 0. Iverter efficiecy (experimetal results) ad switchig frequecy badwidth (theoretical results), as a fuctio of the trasferred power level for BCM ad DCM operatio (P ac,max is equal to 00 W). VIII. CONCLUSION Two alterative modes of operatio for the curret-source flyback iverter for decetralized grid-coected PV systems have bee ivestigated ad compared. A desig strategy for both the operatio schemes has bee proposed i order to achieve high-power desity. Moreover, this paper has highlighted, both theoretically ad experimetally, the optimum iverter behavior whe these two modes of operatio are combied, leadig to a global ad high-efficiecy solutio for wide power rage ac PV module applicatios. APPENDIX A Accordig to Figs. (c) ad 3, t off iterval ca be calculated by usig the followig equatio: t off = i dc,p(t) L u ac (t) = I dc,p si ωt L V ac,p si ωt = I dc,p L V ac,p (A) where i dc,p (t) is the peak secodary curret value ad L / is the secodary iductace value. Takig ito accout that t o = T s d(t) =T s d p si ωt I dc,p = V dc t o,p = V dc d p. L L f S (A) ca be rewritte as t off = V dcd p L f S V ac,p L = λ d pt S. (A) (A3) So, we coclude t off = λ T S d p = costat for ay period withi the lie half cycle whe λ remais costat. Due to the above equatios, (7) ca be rewritte as I dc,avg = T S d pv dc w ( si ) T hl f s L w i where w S w i= For λ > si ( w i ) = w ( ) λ = 0 = d pv dc f s L w w i= i= w i= si ( w i ) [ ( )] cos w i (B4) { = [( ) si w + ] } w w si w [ = ( ) ] si + w 4w si w = [ si ] w 4w si = w. (B5) dθ λ +siθ APPENDIX C ( ) λ = ta ( ) θ + (λ ) arcta (λ ) 0 = (λ ) arcta (λ ) = (λ ) arc cot (λ )

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Yim-shu, Techique for sesig iductor ad dc output currets of PWM dc dc coverter, IEEE Tras. Power Electro., vol. 9, o. 3, pp , May 994. A. Ch. Kyritsis (S 00) received the Dipl. degree i electrical egieerig from the Uiversity of Patras, Rio-Patras, Greece, i 003, where he is curretly workig toward the Ph.D. degree i reewable eergy sources. His curret research iterests iclude power quality improvemet ad reewable eergy sources issues. E. C. Tatakis was bor i Alexadria, Egypt, i 957. He received the Dipl. degree i electrical egieerig from the Uiversity of Patras, Rio-Patras, Greece, i 98, ad the Ph.D. degree i applied scieces from the Uiversity of Brussels, Brussels, Belgium, i 989. He is curretly a Associate Professor of power electroics ad electrical machies i the Departmet of Electrical ad Computer Egieerig, Uiversity of Patras. His research iterests iclude switch mode power supplies, resoat coverters, powerfactor correctio, electrical drive systems, photovoltaic systems, educatioal methods o electrical machies, ad power electroics. Dr. Tatakis is a member of the Europea Electroics Associatio, the Sociėtė Royale Belge des Electricies, ad the Techical Chamber of Greece. N. P. Papaikolaou received the Dipl. Eg. ad the Ph.D. degrees i electrical egieerig from the Uiversity of Patras, Rio-Patras, Greece, i 998 ad 00, respectively. He is curretly a special Scietific Staff Member with the Helleic Trasmissio System Operator (HTSO) S.A., N. Smyri, Greece, where he is egaged i power system aalysis. His research has bee cocered with power quality improvemet issues.