Direc Coupling of Power Acie Filers wih Phooolaic Generaion Sysems wih Improed MPPT Capabiliy G. Grandi, Member, IEEE, D. Casadei, Member, IEEE, C. Rossi Absrac - Phooolaic sources can be usefully combined wih power acie filers in order o regulae boh he acie and he reacie power injeced ino he mains. In his way, he sysem is able o compensae undesired load characerisics such as phase unbalances, power flickers, and low-order curren harmonics, improing he power qualiy. In order o aoid an inermediae dc-dc chopper, a direc coupling beween he PV panels and he dc-link of he olage source inerer is considered in his paper. The dc-link olage is coninuously regulaed beween upper and lower limis for racking he maximum power poin of he PV panels. The proposed MPPT algorihm is based on real-ime processing of curren and olage ripple of he PV source ha is generaed by he swiching operaion of he PWM inerer. The sysem performance is inesigaed emphasizing he ransien behaior in presence of sudden ariaions of he solar irradiance. The heoreical deelopmens are erified by realisic numerical simulaions. Index erms - Acie filers, Phooolaic cells, Power condiioning, Power qualiy, Solar power generaion. I. INTRODUCTION HOTOVOLTAIC energy seems o become one of he P mos imporan renewable energy resources in he near fuure, since i is clean, polluion free, and inexhausible. Due o he rapid growh in semiconducors and power elecronic echniques, he solar energy is of increasing ineres in elecrical power applicaions, and a large research aciiy has been carried ou in his field oer he las years. Nowadays, despie of he known adanages, he insallaion cos is sill high and he PV energy is no compeiie ye wih respec o he radiional fossil-based energy resources. Since PV panels hae relaiely low conersion efficiency, minimizing he losses in he power elecronic conerers, and maximizing he elecric power exraced from he PV source can subsanially reduce he whole sysem cos. On he basis of hese consideraions, in his paper he analysis is focused on a sysem opology wih a direc coupling beween he PV panels and he olage source inerer (VSI) employed o injec he solar power ino he uiliy grid. A block diagram of he corresponding PV generaion sysem is represened in Fig. 1. In his way, he need of an inermediae dc-dc chopper is aoided, increasing he efficiency and reducing he cos of he oerall sysem. In order o exrac he maximum power from he PV source his simplified srucure, he dc-link olage mus be regulaed according wih a maximum power poin racking algorihm (MPPT), which direcly acs on he conrol sysem of he VSI. In his case, he dc-link olage excursion should be limied G. Grandi, D. Casadei, C. Rossi are wih he Deparmen of Elecrical Engineering, Uniersiy of Bologna, ia Risorgimeno 2, I-4136 Bologna ITALY. (e-mail: elero@mail.ing.unibo.i. wihin a fixed range, o ensure correc power injecion ino he uiliy grid (lower limi, and o saisfy he olage insulaion requiremens of he power elecronic componens (upper limi. An improed MPPT algorihm is presened in his paper. I is based on he analogue processing of curren and olage ripple of he PV panels, which is generaed by he swiching operaion of he PWM inerer. The adanages of he mehod proposed in his paper are emphasized wih respec o he radiional ones, such as he perurbaion and obseraion mehod and he incremenal conducance mehod. The VSI can be conrolled such as an acie filer, conribuing o saisfy he power qualiy requiremens of he uiliy grid. In his way, he sysem is able o delier besides he solar power, reacie power and curren harmonics in order o compensae non-linear and/or unbalanced loads [1]. The conrol sraegy is based on keeping he source currens in phase wih he corresponding posiie sequence componens of he supply olages. This mehod leads o sinusoidal balanced source currens, regardless o source olage unbalance or disorion [2]. Numerical simulaions are presened for erifying he sysem performance in he case of sudden ariaions of he solar irradiance and/or he load power. II. MPPT ALGORITHM The goal of MPPT algorihms is o exrac he maximum power from he PV panels. Usually, he condiion p/ = is adoped o locae his operaing poin, since PV panels show a unique global maximum poin. A. Background and Proposed MPPT Algorihm As i is known, he i = i() characerisic of PV panel is affeced by enironmenal ariables, i.e., solar irradiance (I irr ) and emperaure (θ). In paricular, he shor-circui curren is approximaely a linear funcion of he illuminaion inensiy, i = i() PV array or subarray = dc C dc VSI inerer F L ac i F C F R F passie filer Fig. 1. Block diagram of he PV generaion sysem Z S S i S i L UTILITY LOADS
p o i o p ) i = i() p max esimae he incremenal conducance. A mehod based on he ripple analysis, called ripple correlaion conrol, useful o exploi gradien informaion for opimizaion purposes is described in [8]. In order o derie he proposed MPPT algorihm, le us o consider a generic periodic funcion x( haing he moing aerage componen x ( oer he period T, and he alernaie componen x ( ), i.e., a ripple, respeciely defined as: k 1 o o 1 x ( = x(, (2) T x( = x( x(. (3) p Fig. 2. PV curren, power, and power slope characerisics s. olage and he emperaure changes he open-circui olage of abou -.4 %/ C. For hese reasons, saic seings such as consan olage, consan curren, or een consan impedance, are no effecie o locae he MPP under boh ypes of ariaion. Then, in order o maximize he power exraced from he PV panels, dynamic mehods hae been largely inesigaed. In he perurbaion and obseraion mehod, he conroller perurbs he operaing poin and obseres he resuling P and V o idenify he acual operaing region. Then, he reference olage is increased or decreased according o hese measured quaniies. The implemenaion of his mehod is simple bu i does no allow he racking of rapid change in enironmenal condiions. In he incremenal inducance mehod, he MPP is racked by comparing he incremenal conducance and he insananeous conducance of he PV panels, according wih he condiion p/ = : p i i i = i = =. (1) Some arians o hese mehods hae been considered in order o improe he dynamic performance and/or o reduce undesired oscillaions around he MPP [3], [4], [5]. The proposed MPPT algorihm is based on he deerminaion of he oupu power slope of he PV panels ersus olage, i.e., he power deriaie p/. This quaniy is uilized as represenaie of he olage error, i.e., he difference beween he acual olage of he PV panels and he olage corresponding o he MPP. The qualiaie behaior of p/ is represened in Fig. 2: in he region near o i can be considered a sraigh line haing he slope k. Since he PV panels are direcly conneced o a VSI operaing in swiching mode, a swiching ripple will affec he PV oupu olage and curren, for any operaing condiion of he VSI. The ampliude of he ripple is an inerse funcion of he dc-link capacior size, C dc, and of he swiching frequency f c (PWM carrier frequency). Then, he ripple can be considered iself as an embedded dynamic es signal useful o deermine p/. A similar approach has been inroduced in [6] and [7] o Applying hese definiions o he oupu olage and power of he PV panels, and considering as period T=1/f c, leads o ( = ( (, (4) p ( p(. (5) The aerage operaing poin ( o, p o ) on he p ) characerisic, and he corresponding olage and power alernaie componens are represened in Fig. 2, according o p ( ( ) o ) = p o, o = (. (6) Assuming he cure p ) sill alid for dynamic analysis [6] and linearizing nearby he aerage operaing poin leads o a simple correlaion beween he power ripple and he olage ripple, expressed as p p( (. (7) o The power deriaie s. olage can be calculaed by (7) as a funcion of power and olage ripple for he gien operaing poin o. In [9] his power deriaie is expressed as he ime deriaie raio p / and approximaed by a sign funcion o exrac is sign only, in he same way as in he perurbaion and obseraion mehod. In his paper we propose o aoid calculaions based on insananeous alues, considering insead of (7) he moing aerage of he produc of (7) and ( ), leading o 2 p( ( p o (. (8) Then, he power deriaie can be ealuaed as he following raio p o p( ( 2 (. (9) The olage and power alernaie componens uilized in (9) can be calculaed on he basis of (3) and (2), leading o
i ( p ( HPF p ( ) p ( ( ) LPF p ( ( ) HPF 2 ( ) LPF Fig. 3. Esimaion of he PV power deriaie by using filering blocks 1 ( = ( ( T, (1) 1 p ( p(. (11) T Alernaiely, a more radiional filering approach can be adoped o deermine he power slope [7]. In paricular, highpass filers (HPF) can be used o exrac he alernaie componens insead of (1) and (11). In he same way, low-pass filers (LPF) can be used for aeraging he ripple producs insead of he inegrals in (9). The corresponding block diagram is depiced in Fig. 3. B. Volage Regulaion of he PV panels Usually, dc-link olage conrollers perform he regulaion by acing on he insananeous error beween a reference olage and he acual olage. Since he characerisic i = i() of he PV panels always has a negaie slope, he olage can be increased by decreasing he oupu curren, and ice ersa. In his case, he reference olage is represened by he olage corresponding o he MPP for he gien enironmenal condiions (see Fig. 2). As shown in Fig. 4 (lef side), he power deriaie p/ is uilized as represenaie of he olage error =, being almos linear he relaionship beween hese wo ariables in he region around he MPP. The proporional coefficien k is inroduced in Fig. 2; i is a funcion of he solar irradiance inensiy I irr and he emperaure θ of he PV panels. Since he regulaion loop conains a regulaor (R 1 (s) in Fig. 4), a consan alue can be assumed for k. The oupu of he regulaor is he reference curren for he grid inerer. The sysem behaior can be easily described as follows: when he esimaed power deriaie is posiie, he operaing poin is on he lef of he MPP, and he regulaor should decrease he curren exraced from he PV panels. The conerse occurs when he esimaed power deriaie is negaie: he operaing poin is on he righ of he MPP, and he regulaor increases he curren exraced from he PV panels. Finally, when he power deriaie approaches zero i means ha he MPP is reached, and he oupu curren of he PV panels is kep consan by he regulaor. A correc behaior of he VSI connecing he PV panels o he grid is obained if he excursion of he dc-link olage is limied wihin a fixed range. The dc-link olage should be high enough o ensure correc power injecion ino he uiliy grid (lower limi. On he oher hand, i should saisfy he olage insulaion requiremens of he power elecronic componens (upper limi. For his reason, i is useful o esimae he reference olage and o pass i hrough a limier, as shown in he inner dashed recangle of Fig. 4. III. VSI CONTROLLER The aim of he power condiioner is o regulae he dc-link olage dc in order o rack he MPP of he PV modules, being dc = PV. The conrol is indirecly performed by regulaing he curren exraced from he PV panels and injeced ino he power grid (source curren, i S ), according o he block diagram shown in Fig. 5. In his way, all he power coming from he PV modules is ransferred o he elecric nework. In paricular, he desired ampliude of he source currens, I S, is generaed by he regulaor R(s), considering he esimaed PV power deriaie p/ as inpu ariable. Noe ha he regulaor block R(s) shown in Fig 5 include he scheme represened inside he ouer recangle of Fig. 4. The reference alue of he insananeous source curren ecor, i S, is generaed on he basis of he magniude I S, and he phase angle of he posiie sequence componen of he supply olages [2], which is represened by he uniy space ecor in Fig. 5. The proposed srucure allows he sysem o be able o compensae non-linear, reacie, pulsaing, and/or unbalanced loads [1]. In his case, he ac curren conroller requires he measuremen of boh load and inerer currens, i L and i F (see Fig. 5). The load curren is used o calculae he reference alue of he inerer curren i F, on he basis of he reference source curren i S, gien by he regulaor R(s), ( i F = is il ). ˆS 1 p f (I irr,θ) 1/k - addiional blocks o esimae he ref. olage (MPP) limier _ - R 1 (s) R(s) I S Fig. 4. Generaion of olage and curren references
S p R(s) I S ˆS 1 i S i L i F _ i F i F K F SVM VSI F Fig. 5. Proposed regulaion scheme for he VSI conroller The measuremen of he inerer curren is used o implemen he ac curren conrol loop. A hyseresis curren regulaor acing on he insananeous curren error if = if if can be employed o deermine he inerer swich saes. Alernaiely, a PWM (or SVM) curren regulaor can be used aoiding he drawbacks of hyseresis curren conrollers. In his case, he reference olage for he inerer can be calculaed by he olage equaion wrien across he ac-link inducance L ac, according wih he block diagram represened in Fig. 1. Neglecing he resisie effecs and inroducing a ariaional model, he olage equaion yields Lac F = S if. (12) The parameer L ac / in (12) can be adjused o obain he desired regulaor performance. IV. SYSTEM PERFORMANCE The proposed conrol scheme, represened in he block diagrams of Figs. 4 and 5, has been implemened considering a hree-phase, single-sage conerer, as represened in Fig. 1. The whole power conersion sysem has been numerically simulaed by he Simulink enironmen of Malab. The PV panels hae been elecrically represened by he well-known single-exponenial model [1], fied on he I-V characerisic of a series/parallel arrangemen of Solar Shell SP15 modules. The main characerisics of he PV generaion sysem are summarized in Table I. The performance of he power condiioning sysem conneced o he PV array has been ealuaed boh in seady sae and ransien operaing condiions deermined by sar-up and solar irradiance ariaions. Figs. 6 and 7 show he ime behaior of he power and olage alernaie componens, p and, which are ealuaed in he MPPT algorihm and are used in compuaion of he power deriaie. In paricular, Fig. 6 is referred o an operaing poin on he lef of he MPP, i.e., dc <. Noe ha in his case and p are in phase agreemen. Fig 7 is referred o an operaing poin on he righ of he MPP, i.e., for dc >. Noe ha in his case and p are in phase opposiion. For all he operaing condiions he frequency of oscillaion of and p is always relaed o he swiching frequency (f sw = 1 khz). Fig. 8 shows he seady-sae waeforms of source olage and source curren (uiliy grid). As expeced, he source curren is sinusoidal and in phase agreemen wih he corresponding line o neural olage. Fig. 9 shows he ime behaior of he signal represening he calculaed power deriaie p/ around he maximum power poin. This figure is aken by arying he dc-link olage reference in he range ± 7V, wih a consan slope. As prediced for his operaing region, he calculaed p/ is linear and equals o zero exacly in he poin of maximum power ( dc = ). Figs. 1-12 show he performance of he PV generaion sysem in racking he maximum power poin of he PV panels during a ransien of solar irradiance. From he saring operaing poin, he sysem reaches he MPP in. Then, as a consequence of a 5% reducion in he solar irradiance, he operaing poin moes o he new MPP in. Fig. 1 and 11 represen he sysem characerisics respeciely on he I-V and P-V diagram. Fig. 12 shows he ime behaior of he PV olage and curren during he seeking of he new MPP. I can be obsered ha he ime employed by he MPPT algorihm o reach he new maximum power poin is abou 5 ms. Once he new MPP is reached, only ery small oscillaions persis around he MPP. Fig. 13 shows he waeforms of he source olage and curren, during he ransien of solar irradiance. Afer he irradiance change, he source curren rapidly changes is ampliude and remains sinusoidal and in phase agreemen wih he corresponding line o neural source olage. TABLE I MAIN CHARACTERISTICS OF THE PV GENERATION SYSTEM Raed power of he PV sysem P PV =3 kw MPPT high pass filers: firs order Dc-link capaciance C dc = 2 mf MPPT low pass filer: firs order PWM carrier frequency f sw = 1 khz Dc-link olage conroller: PI ype Line inducor Line o line uiliy olage R ac =.5 Ω L ac = 1 mh V ac = 38 V f = 5 Hz Panels ype (series/parallel arrangemen Shor circui curren (1 W/m 2, 4 C) K HPF = 1 τ HPF =.5 s K LPF = 1 τ LPF =.5 s K P = 5 K I = 5 Solar Shell SP15 i sc = 48 A Dc-link iniial reference olage = 74 V Open circui olage (1 W/m 2, 4 C) oc = 76 V
.15 p.1.4.5 p.2 -.5 -.1 -.2 -.4 -.15.7429.743.7431.7432.7433.7434.7435.7436.7437.7438 -.6.1949.1949.195.195.1951.1951.1952.1952 Fig. 6. Volage and power alernaie componens for < Fig. 7. Volage and power alernaie componens for > 4 3 2 source olage [V] PV olage [V] 7 68 66 =667 V 1 64.3.35.4.45 ime [s] 5-1 -2 dp/d -3 source curren [A] -4.6.7.8.9.1.11.12.13.14.15.16 Time [s] Fig. 8. Source olage and curren in seady-sae condiion -5.3.35.4.45 ime [s] Fig. 9. PV panel olage and compued power deriaie p/ around he maximum power operaing poin 5 45 4 35 4 x 14 3.5 3 PV curren [A] 3 25 2 15 1 PV power [W] 2.5 2 1.5 1 5.5 1 2 3 4 5 6 7 8 9 1 PV olage [V] Fig. 1. Effec of a -5% solar irradiance ransien on he I-V diagram 1 2 3 4 5 6 7 8 9 1 PV olage [V] Fig. 11. Effec of a -5% solar irradiance ransien on he P-V diagram
PV olage [V] 7 68 66 64 62 6.15.155.16.165.17.175.18.185.19.195.2 ime [s] PV curren [A] olage [V] curren [A] 5 4 3 2 1.15.155.16.165.17.175.18.185.19.195.2 ime [s] 8 6 4 2-2 Fig. 12. Effec of a -5% solar irradiance ransien a) PV olage s. ime b) PV curren s. ime -4.8.9.1.11.12.13.14 1 5-5 source curren dc-link olage load curren -1.8.9.1.11.12.13.14 ime [s] Fig. 14. Effec of a load swiching-on a) PV olage and source olage b) source curren and load curren a) b) source olage Fig. 14 shows he behaior of he sysem during he swiching-on of a load (P L = 7.5 kw, cosϕ =.8). Afer he load inserion, he source curren i SA rapidly changes is ampliude and remains sinusoidal and in phase agreemen wih he corresponding line o neural source olage. V. CONCLUSION The relaiely low olage excursion of he maximum power poin corresponding o differen enironmenal condiions, make i possible o consider he effecieness a direc coupling of PV panels and grid inerer. This simplified configuraion aoids he use of an inermediae dc chopper, reducing he losses and improing he reliabiliy of he whole sysem. In order o maximize he conersion efficiency, an improed MPPT algorihm is proposed in his paper, based on an analogue processing of curren and olage ripple of he PV panels caused by he inerer PWM swiching operaion. The MPPT algorihm is based on he regulaion of he dc-link olage wihin a safey excursion range. The PWM-VSI acs as a power acie filer, conribuing o he power qualiy requiremen of he uiliy grid. A complee se of realisic numerical 4 3 2 1-1 -2-3 source olage [V] source curren [A] -4.16.17.18.19.2.21.22 Time [s] Fig. 13. Effec of a -5% solar irradiance ransien on he source curren simulaions has been presened in he paper, wih reference o seady-sae and dynamic operaing condiions. The resuls show he good performance of he conrol sysem and confirm he effecieness of he proposed PV generaion sysem. VI. REFERENCES [1] D. Casadei, G. Grandi, U. Reggiani, G. Serra, Analysis of a Power Condiioning Sysem for Superconducing Magneic Energy Sorage, Proc. of IEEE Inernaional Symposium on Indusrial Elecronics, ISIE, Preoria (SA), July 7-1, 1998 [2] D. Casadei, G. Grandi, C. Rossi, Effecs of Supply Volage non-idealiies on he Behaior of an Acie Power Condiioner for Cogeneraion Sysems, Proc. of IEEE Power Elecronic Specialis Conference, PESC, Galway (Ireland), 18-23 June, 2 [3] Y.C. Kuo, T.J. Liang, J.F. Chen, Noel maximum-power-poin-racking conroller for phooolaic energy conersion sysem, IEEE Trans. on Indusrial Elecronics, Vol. 48 No. 3, June 21, pp. 594-61 [4] T.Y. Kim, H.G. Ahn, S.K. Park, Y.K. Lee, A noel maximum power poin racking conrol for phooolaic power sysem under rapidly changing solar radiaion, Proc. of IEEE Inernaional Symposium on Indusrial Elecronics, ISIE 21, Pusan, Korea, Vol. 2, pp. 111-114 [5] J.A. Gow, C.D. Manning, Conroller arrangemen for boos conerer sysems sourced from solar phooolaic arrays or oher maximum power sources, IEE Proceedings of Elecric Power Applicaions, Vol. 147, No. 1, Jan. 2, pp. 15-2 [6] P. Midya, P.T. Krein, R.J. Turnbull, R. Reppa, J. Kimball, Dynamic maximum power poin racker for phooolaic applicaions, Proc. of 27 h Annual IEEE Power Elecronics Specialiss Conference, PESC 1996, Vol. 2, pp. 171-1716 [7] A. Brambilla, M. Gambarara, A. Garui, F. Ronchi, New approach o phooolaic arrays maximum power poin racking, Proc. of 3 h Annual IEEE Power Elecronics Specialiss Conference, PESC 1999, Vol. 2, pp. 632-637 [8] D.L. Logue, P.T. Krein, Opimizaion of power elecronic sysems using ripple correlaion conrol: a dynamic programming approach, Proc. of IEEE 32 nd Annual Power Elecronics Specialiss Conference, PESC 21, Vol. 2, pp. 459-464 [9] Y.H. Lim, D.C. Hamill, Synhesis, simulaion and experimenal erificaion of a maximum power poin racker from nonlinear dynamics, Proc. of IEEE 32 nd Annual Power Elecronics Specialiss Conference, PESC 21, Vol. 1, pp. 199-24 [1] M.A. de Blas, J.L. Torres, E. Prieo, A. García: Selecing a suiable model for characerizing phooolaic deices, Renewable Energy Journal, Vol. 25, No. 3, March 22, pp. 371-38.5