Missouri University of Science nd Technology Scholrs' Mine UMR-MEC Conference 1975 Direct AC Genertion from Solr Cell Arrys Fernndo L. Alvrdo Follow this nd dditionl works t: http://scholrsmine.mst.edu/umr-mec Prt of the Electricl nd Computer Engineering Commons, Mechnicl Engineering Commons, Mining Engineering Commons, Nucler Engineering Commons, nd the Petroleum Engineering Commons Recommended Cittion Alvrdo, Fernndo L., "Direct AC Genertion from Solr Cell Arrys" (1975). UMR-MEC Conference. 86. http://scholrsmine.mst.edu/umr-mec/86 This Article - Conference proceedings is brought to you for free nd open ccess by Scholrs' Mine. It hs been ccepted for inclusion in UMR-MEC Conference by n uthorized dministrtor of Scholrs' Mine. This work is protected by U. S. Copyright Lw. Unuthorized use including reproduction for redistribution requires the permission of the copyright holder. For more informtion, plese contct scholrsmine@mst.edu.
DIRECT AC GENERATION FROM SOLAR CELL ARRAYS Fernndo L. Alvrdo The University of Wisconsin Adel H. Eltimshy The University of Toledo Abstrct Results of the investigtion of the performnce of solr cells when directly coupled to conventionl three-phse power network re presented. This pproch dissocites the electricity production problem from the electric energy storge problem. Extensive studies of the required power inverter re performed. Preliminry simultion results indicte tht c power outputs of better thn 90% of the optimum cell power output cn be esily chieved by mens of suitbly controlled inverter, thereby justifying the elimintion of dc lods or locl dc electric energy storge devices. It is lso shown tht the controlling policy for the inverter must depend on the operting conditions of the system, such s cell temperture, solr intensity nd power system voltge vritions, otherwise the performnce of the inverter cn deteriorte quite drmticlly. INTRODUCTION It ppers likely tht the cost of solr cells will drop in the next few yers; it is, therefore, pertinent to investigte the possibility of utilizing solr cells for bulk genertion of electricity on erth-bsed fcilities. Since solr cells re inherently dc devices, three lterntives pper fesible: direct utiliztion of the dc power, storge of dc electric energy nd direct connection to the power network. The direct utiliztion of the dc power through inverters requires the selection of suitble useful dc lod [1]. As the operting conditions vry, so do the optiml lod chrcteristics. This method hs other limittions, such s the loction nd type of lod tht cn be used. Furthermore, the power vilble to the lod is of n intermittent nture. The storge of dc electric energy cn be ccomplished by vriety of mens, such s electrochemicl storge (btteries), or fuel cells. This elimintes the shortcomings due to the intermittent nture of the source. There re still limittions s to useful lod loction nd type. Moreover, the overll efficiency of the system is reduced nd its cost incresed. The third lterntive, connection to the power network through inverters offers gret mount of flexibility nd high efficiency t the expense of inverter circuit complexity. This pproch plces solr cells in the sme ctegory s "off the river" hydro plnts to the extent tht power is supplied to the network on n 297
"s vilble" bsis. The problem of energy storge is not eliminted, but it cn be studied independently of the detiled study of solr genertors/power inverters. A compnion pper [9] studies the coincidence fctor between solr insoltion nd electric demnd for specific region of the country. It is encourging to notice tht there is generlly good correltion between pek electric demnd nd solr intensity. MODELING SOLAR CELLS Voltge-current reltionships for solr cells re well-estblished from both theoreticl nd experimentl considertions [2-6]. For the studies to be undertken in this pper the following mthemticl model hs been chosen, bsed primrily on nph' tlle P^oton rte of flow per unit re for photons with n energy content greter thn the energy gp Eg in the semiconductor junction. Lrger vlues of n ^ (like those chieved by mens of concentrtors) tend to increse the importnce of the losses in the internl cell resistnce R. 1 [3,4,7]. Importnt dynmic effects pper if temperture vritions re considered. The present pper neglects therml dynmics nd ssumes constnt temperture. Higher tempertures (often the result of lrger G ) result in reduced voltges nd powers. To illustrte the typicl reltionships obtined from (1) to (4) silicon solr cell with the following prmeters ws chosen [6] : [5] : K = 8.617 x10~5 E = 1.11 ev e g E = K e T n[l+ (Is - I)/IQ] (1) K o = 275 A = 2 x 1 0-4 r' 2 where I 0 H I = S K o T4 A exp[-eg/(kgt)] (2) K = 4.28 x10-2 R. =.4 ohm S l K A G (3) s (Note: Under the solr conditions nd 2 V = E - I R. l (4) energy gp chosen G =1 W/m corresponds E - internl light-induced cell voltge (V) I - cell current (A) T - temperture ( K) I - idel (R. = 0) cell short-circuit s 1 current (A) I2 I - mximum reverse-current (A) 0 V - cell terminl voltge (V) R. - internl series resistnce (ft) 1 2 A - cell re (m ) 2 G - energy density (W/m ) Eg - energy gp of mteril (ev) Kg, Kq nd Kg - proportionlity constnts (Kq nd Kg depend lso on mteril properties). The incident rdition is chrcterized in this model by the totl solr energy density G. For this reson the "constnt" Kg depends on the shpe of the solr spectrum density, since I depends ctully on to n ^ = 7.20 x 1 0 ^ photons/m2.) The E-I curves for this cell were obtined for vriety of incident rdition levels G nd cell temperture T combintions. The results re illustrted in Figure 1. Fig. l. Voltge-current chrcteristics of cells. Vritions in G with T = 300 K. 298
is reched by ttempting to circulte negtive current. For simultion purposes n idel controlled rectifier cn be mthemticlly modeled s follows: To if g(t) = 0 nd v(t) ^0 g(t + dt) = { (5) 1 if g(t) = 1 nd i(t) 0 g (t) = 0 =s> i (t) = 0 { ( 6 ) [g(t) = 1 =*> v (t) = 0 w / m ^. THE INVERTER This pper considers the use of controlled rectifiers to convert from c power to dc power. This technology hs been extensively studied nd developed in connection with dc power trnsmission lines [8]. The specific configurtion used in this report is the one for three-phse full-wve rectifier/inverter using six controlled rectifiers s illustrted in Figure 2. Idel controlled rectifiers re considered. The idel controlled rectifier is memory binry element with two sttes: "on" (g =1) nd "off" (g = 0). The "on" stte is reched under the presence of n pproprite control pulse p = l ; the "off" stte The model for the ctive component within the dc source (the solr cell) hs been described in the previous section. It is ssumed tht low-pss filter in the form of simple series inductor is used. The series of resistnce of the cells is combined with the inductor resistnce into n overll series resistnce R,. The model d for the dc source is lso illustrted in Figure 2. The presence of introduces dynmic eqution for 1^ nd (4) must be replced by - (Ed - v - RdId )/Ld The three-phse c system is modeled by inductive impednces in series with idel (7) sinusoidl voltge sources. The model for this system is illustrted in Figure 2 nd it cn be described mthemticlly s: Fig. 2. The cell/inverter/power system equivlent circuit. Voltges V, Vn, V&, V^ nd Vc re defined with respect to power system neutrl. p 1 299
where i = (v - e - R i )/L K = (vb * eb - R i,)/l b i = c (v e c c R i c (/L o> e = E sin (cot - 0 ) eb = o I E /2 sin E /2 sin (cot - 0 - (cot - 0-120 ) 240 ) E - effective line to neutrl voltge 0, - phse ngle c l THE SIMULATION STUDY: GENERAL The successful design nd opertion of the solr electric genertor described in the previous sections involves such considertions s the dequte design, orienttion nd loction of solr cells, the design of dequte concentrtors, the selection of circuit prmeters (inductors, etc.) nd the selection of the number of series cells nd prllel pths within n rry. One of the most fundmentl considertions, however, is the pproprite timing of the control pulses p to the controlled rectifiers. The reminder of this pper is devoted primrily to the study of controlled rectifier control policies. The following nottion is dopted for ll further discussions: - ignition dely in electricl degrees (e.g., dely between the time when conduction would strt in n uncontrolled rectifier, v > 0 nd the time when the corresponding pulse p is pplied to the rectifier). u - overlp ngle (time in electricl degrees between the beginning of conduction of given controlled rectifier nd the termintion of conduction of nother rectifier directly in prllel with it). 6 = + u - extinction ngle. Kimbrk [8] hs performed detiled nlyticl studies of these three-phse inverters. One of the limittions of these nlyticl studies is tht for mthemticl convenience the dc source is modeled s constnt current source for ll commuttion studies, lthough slow long term vritions re llowed. ------------------------f ' i------1 ------- ----------------------------------3 ------- ------------------------- 4 t...... i---------- 5 ------------------- u----. ---- 6 () No o v e rl p (u=0) 1 2 3 --------- > I.... [ ----------5....... 6 (b) Single o v e rl p (0 u 60 ) * 4 ------- 1--- 1------ 2 I t " 1 1 1----- 3 ---- 1-------------- 4 (c) D ouble o v e rl p (u 60 ) Fig. 3. Rectifier conduction sequence (solid line denotes "on" stte of rectifier). Under idel conditions conduction in one rectifier ceses when one in prllel with it is fired. This sitution rises when L& = 0 nd implies u = 0 [8]. Figure 3 illustrtes the typicl conduction sequence under these circumstnces. voltge The wveforms for vrious ignition dely ngles for the sme cse re illustrted in Figure 4. It cn be observed tht the verge vlue of positive is positive only when > 90. This mens tht if - 90 power cnnot be delivered by the dc source but is insted bsorbed by it, n obviously undesirble sitution. Also, is further restricted 300
proper opertion. Fig. 4. wveforms, no overlp. to less thn 180, otherwise conduction in the previous vlve cnnot cese nturlly. The presence of n inductnce in the c system lters the commuttion sequence so tht three rectifiers cn be conducting t once, s illustrted in Figure 3b. This sitution occurs when L > 0 nd results in -1 u = cos (cos - Ij/I d sz -) -, where I 0 = /3E //2wL. In fct, if either L or o Z d d become sufficiently lrge or E sufficiently smll, n bnorml condition in which four rectifiers conduct t once cn develop, s illustrted in Figure 4c. This bnorml sitution is not discussed herein. A further effect due to the presence of L cl is resistive drop in the verge vlue of V,, even if R is zero. Also, 6 d must be restricted to less thn 180 for Three modes of control for controlled rectifiers re trditionlly recognized: constnt ignition ngle control (CIA), constnt current 1^ control (CCC), nd constnt extinction ngle 6 control (CEA). In the bsence of L, CIA nd CEA re equivlent. Adjusting or 6 under these conditions results in chnge in with corresponding chnge in 1^ ccording to (1) nd (4). The presence of n inductnce L c l ffects the CIA to the, extent tht V, will d become somewht current dependent. More importnt, however, is its effect on CEA, when nonzero u mens tht the rectifier must be triggered in dvnce of the desired extinction, nd this ngle must be bsed on computed predicted vlues of the current; this problem becomes more criticl when vlues of 6 close to 180 must be chosen, since 6 should never exceed 180. CCC is bsed on djustments of the ignition ngle bsed on devitions of the ctul current 1^ from desired vlue of current. Proper design of gins nd time constnts in the feedbck loop should be mde to prevent possible control loop instbilities. Rectifier/inverter systems re generlly controlled by setting the rectifier in CCC mode (current pproximtely constnt); or lterntely, the rectifier in CCC mode nd the inverter in CEA mode. The choice is usully dependent on the operting conditions. It is, hence, interesting to notice tht the solr cell chrcteristics under fixed operting conditions s illustrted in Figure 1 closely resemble the chrcteristics of three-phse rectifiers with one pproximtely constnt current segment nd one pproximtely constnt voltge segment. The simulted experimentl setup used in connection with the present reserch ws implemented in digitl computer using continuous system modeling progrm. 301
Equtions (1) - (3) nd (5) - (9) were used in ddition to ll the necessry binry logic for the control of the rectifiers. A block digrm for ech of the two possible operting configurtions (two rectifiers conducting or three rectifiers conducting) ws implemented s illustrted in Figure 5. Other portions of the model, not illustrted in Figure 5, re used to control the trnsition between model configurtions nd to re-evlute model prmeters t the pproprite intervls. The ignition pulses cn be controlled by either one of the three control modes lredy described, or by fourth mode, constnt rtio control (CRC). Another portion of the model is used to simulte the behvior of the ignition timing controller. Only simple integrl-error feedbck controllers were considered in this study, lthough some nonliner gins were used in n ttempt to linerize the effect of control signl errors. The equtions tht describe the dynmics of the ignition dely ngle ech of the four control modes re: Constnt = Constnt = Ignition Angle: set Extinction Angle: -1 cos (cos «set + V Is2> (10) ( I D Constnt Current Control: () When two rectifiers conduct. Fig. 5. Block digrm of model. Prmeter vlues depend on which rectifiers re conducting. = 0 if L > I set nd cos - I,/I 1 d s2 K c (1,-1 d set )/sin otherwise Constnt Rtio Control: where = (o if Ro _set. > V,/I d d, nd cos I,/I - 1 d s2 K (R. - V,/I,)/sin r set d d I s2 = /3 E //2 cos L V = 3/6 E /ti o The purpose of the Constnt Rtio Control mode is to provide n esily implemented control mode such tht the inverter efficiency is less sensitive to errors in the (12) determintion of the operting conditions, s illustrted in this next section. A possible modifiction to CEA control tht could be of prcticl interest involves the use of feedbck error signl from the desired 6 to djust rther thn the predictive formul (13). The (13) error signl, however, could be determined 302
only t discrete intervls. Other likely strightforwrd modifictions include the use of predictive term in (11) nd of more complex dynmic chrcteristics in (12) nd (13). Another feture of the simulted model is its cpbility of mesuring efficiencies. Three different efficiencies re defined nd evluted: * p* ncell = GA where: GA * ncell ncell ^inv V d ncell " GA (14) (15) _ ncell ninv n* (16) cell is the mximum power tht the solr cell rry cn deliver under the given conditions of temperture nd incident rdition. This number is clculted by the model vi Newton itertions represents the totl incident power represents the mximum efficiency tht the solr cell rry is cpble of operting t. represents the ctul efficiency under the conditions nd control policies used represents the efficiency due to performnce devition from the optiml by the presence of the inverter circuitry. This is the number tht mesures the effectiveness of the inverter. THE SIMULATION STUDY: AN EXAMPLE The digitl model described in the previous section cn be used to nswer vriety of questions bout the performnce of ny prticulr solr cell rry under vrious operting conditions nd control modes. This section outlines some of the most importnt experiments tht hve been performed with this model or with some vritions of it, nd presents the results of few of these experiments s performed for specific solr cell rry. These experiments include: the determintion of the stedy stte wveforms for the vrious currents nd voltges for specific sets of prmeters, operting conditions nd control modes; the determintion of the instntneous nd verge inverter efficiencies under stedy stte conditions; the determintion of the effect of vritions of the inverter control prmeter ( set' Sset' Iset or Rset> s wel1 s vritions of the operting conditions (G, E nd T) on the inverter efficiency. These studies cn be useful in selecting optiml control prmeter settings nd predicting the performnce degrdtion in cse of erroneous determintion of the operting conditions for the vrious control modes. The determintion of the effect of prmeter vritions (L., L, N, d p N ) on the performnce of the system under s CRC mode ws lso undertken, s well s the study of the rnsient behvior of the system under sudden vritions of the operting conditions. An rry of the sme cells described erlier in this pper ws used. The following dditionl system prmeters were chosen for the simultion. System Prmeters: Rd = 26.1 ohm Ld = 1 henry R =.3 ohm L =.3 henry = 4 n p Ns = 260 <oi) = 377 rd/sec (60 Hz) Control Prmeters: set = 137 ^set 6set = 144 R. set = 45.5 ma = 3000 ohm Operting Conditions (bsic study): T = 300 K G =1350 w/m2 E = 49 volts Figure 6 illustrtes some of the stedy- stte wveforms obtined. The comprtively lrge vritions in E^ for smll 303
switching instnts cn be observed. This wveform cn be compred with Figure 4c. The short "trnsition intervls" visible in Figure 6b re due to the nonzero commu ttion ngle. The effect tht vritions of the control prmeters set> Iget, 6 set, nd R set,) under their respective control modes (CIA, CCC, CEA nd CRC) hve on the inverter efficiency cn be observed in Tble I. (Due to numericl errors nd finite settling times ll efficiencies subject to bout 2% errors.) It cn be observed from this tble tht, under the proper circumstnces, ll control modes cn result in commuttion filure or t lest chnge in mode to prevent one. The reltively wide rnge of settings tht result in cceptble opertion in the CRC mode cn be observed, s well s the rnge of settings cceptble in the CCC mode under similr conditions. vritions in 1^ when ttempting to operte t high inverter efficiency (89% in this cse) cn be observed. Also, the brupt vritions in (Figure 6c) t the Tbles II through IV illustrte the effect of vritions in the system voltge E, temperture T nd solr intensity G in ech of the control modes under the bsic prmeter settings (shown underlined in Tble I. Mode set CIA ninv Inverter efficiency vs. control prmeter setting (fixed operting conditions). (deg) (%) 108 < 40 Prmeter Setting/Efficiency 130 77 137 89 144 96 151 99 156 * CCC Iset (ra) 44 44.5 45 45.5 46 47 ^inv (%). t 99 95 93 85 < 40 CEA ^set ^inv (deg) 108 136 144 151 158 180 < 40 80 88 94 99 * CRC Rset («) 1000 1500 2000 2360 2560 3000 ^inv (%) 55 75 94 98 99 * Commuttion filure results (unless mode cn be chnged). 304
Tble II. Mode Tble III. Tble IV. Chnge in inverter efficiency vs. system voltge level Voltge 45 Level 49 E (Volts) 53 CIA -8 0 + 6 CCC -5 0-4 CEA -9 0 + 7 CRC -6 0-1 Chnge in inverter v s. temperture Temperture efficiency ( K) Mode 300 330 CIA 0 +11 CCC 0-12 CEA 0 +13 CRC 0 + 5 Inverter efficiency intensity v s. solr Mode 1200 1350 1500 CIA -10 0-1 CCC < -50 0 * CEA 0 0-1 CRC -12 0-1 * _ Commuttion filure results Tble I). The overll observtion from these tbles is tht (t lest under the conditions given) the CCC mode is fr too sensitive to vritions in solr intensity to be of prcticl importnce. The CIA nd CEA mode re simple, yet they offer somewht wider rnge with cceptble performnce; CEA is generlly preferble for its reduced likelihood of misopertion. It my be observed tht both these modes were somewht sensitive to vritions in E nd T. The CRC mode resulted in the best overll stedy stte opertion due to its reltive insensitivity to errors. Both the CCC nd CRC modes, however, require creful selection of the feedbck gins to prevent feedbck loop instbilities nd provide dequte settling times. SUMMARY This pper hs demonstrted by mens of digitl model tht high inverter efficiencies cn be chieved by direct three phse inversion of power from solr cell rrys. This suggests tht this pproch could become the primry utiliztion mode for solr cells should they become competitive with the ever-incresing costs of other forms of electric genertion. This study hs lso emphzized the importnce of dequte design nd control of the inverter nd relted hrdwre. The controlling policy for the inverter must be dependent on the operting conditions, nd the chrcteristics of four different controlling policies hve been evluted under vriety of conditions. Additionl questions tht deserve further investigtion re the fesibility of rel-time self-optimizing inverter controllers, the study of inverter filure modes, the nlysis of filtering requirements, nd the evlution of the impct of lrge mounts of intermittent power genertors on the power system. REFERENCES 1. A. Bhskr Ro nd G. R. Pdmnbhn, A Method for Estimting the Optimum Lod Resistnce of Silicon Solr Cell Used in Terrestril Power Applictions. Solr Energy 1J5, pp. 171-177 (1973). 2. J. J. Loferski, Recent Reserch on Photovoltic Solr Energy Converters. Proc. IEEE 51, pp. 667-674 (1963). 3. E. L. Rlph, Use of Concentrted Sunlight with Solr Cells for Terrestril Applictions. Solr Energy 1_0, p p. 67-71 (1966). 305
4. P. A. Bermn, Design of Solr Cells for Terrestril Use. Solr Energy 1_1 pp. 180-185 (1966). 5. S. W. Angrist, Direct Energy Conversion. Allyn nd Bcon, Boston (1965) 6. M. Altmn, Elements of Solid-Stte Energy Conversion, Vn Nostrnd- Reinhold, New York (1969). 7. M. Wolf nd H. Ruschenbch, Series Resistnce Effects on Solr Cell Mesurements. Advnced Energy Conver sion, pp. 455-479, Pergmon Press, Gret Britin (1963). 8. E. W. Kimbrk, Direct Current Trnsmission, Vol. I. Wiley, New York (1971). 9. A. H. Eltimshy, F. L. Alvrdo, T. W Boyd, The Impct of Direct Coupling of Solr Cell Arrys to Electric Power Networks. UMR-MEC Conference on Energy, October 7-9, 1975.