Verification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance
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1 Verificatin f Quality Parameters f a Slar Panel and Mdificatin in Frmulae f its Series Resistance Sanika Gawhane Pune India Onkar Hule Pune India Chinmy Kulkarni Pune India Ojas Pandav Pune India Abstract We prpse a new frmula t calculate the value f Series Resistance frm the values f V OC, I SC, V MPP and I MPP. This frmula was tested n different slar data in different cnditins. The data included the values f V OC, I SC, V MPP, I MPP, Temperature, Irradiance and P MAX at different times during the day fr 7 days. Frm the given data, tw values f G and T are cnsidered. Using the abve atmspheric cnditins and the panel behavir at thse cnditins, a new frmula fr calculatin f series resistance f the slar panel is prpsed. Keywrds Series; resistance; Maximum pwer; frmula; slar irradiance; temperature I. INTRODUCTION We plan t extract the quality parameters f a Slar Panel at a lcatin where the atmspheric cnditins are knwn which will be used t decide the use f a particular Slar Panel. Varius atmspheric cnditins like Slar Irradiance, Temperature and Wind Speed affect the parameters. The varius slar panel parameters include V OC (Open Circuit Vltage), I SC (Shrt Circuit Current), Maximum Pwer, Vltage and Current at Maximum pwer pint V mpp and I mpp, Fill Factr and Efficiency. These factrs vary with changing atmspheric cnditins. The values f these parameters will be determined at different envirnmental cnditins. These parameters accunt fr the cmplex dependence f Slar Panel perfrmance upn Slar Irradiance Intensity and Slar Panel Temperature. T find the abve parameters, minimum data in frm f the Datasheets f Slar Panels and the measured atmspheric cnditins like Slar Irradiance and Panel Temperature will be required. With this data, we can predict the panel behavir by using a mathematical mdel representing the Panel already prpsed. The mathematical mdel was tested n given data. All f the calculated parameters matched with the given parameters expect fr the Series Resistance values which caused discrepancies in the final pwer values. Hence, we prpse a new frmula t calculate the value f Series Resistance frm the values f V OC, I SC, V mpp and I mpp. This frmula was tested n different slar data in different cnditins. A data frm January 2010 was used t calculate all the cmplex parameters. The data included the values f V OC, I SC, V mpp, I mpp, Temperature, Irradiance and P max at different times during the day fr 7 days. Frm the given data, tw values f G and T are cnsidered. Using the frmulae, values f, and are calculated. The given values f V OC, I SC are used t verify the calculated values f V OC, I SC. Als, the values f V OC, I SC, V mpp and I mpp are used in calculating the Series resistance and in turn, the Ideality Factr. Using all these cmplex parameters, the value f P max is calculated which is then cm-pared with the given value f P max in the data t verify the results. II. CALACULATION OF COMPLEX PARAMETERS A. Calculatin f α Where I SC0 =6.436 G 0 = W/sq m and I SC1 =4.201, G 1 =500 W/sq. m On substituting the abve values we get α=
2 B. Calculatin f β Using different values f G and T, the values f Shrt circuit current I SC were fund. They were cmpared with the values f I SC in the given data and pltted with respect t time. The graph shwed that the calculated and given values were almst in cmplete cnjunctin with each ther with very minr deviatins. This prved the methd prpsed t calculate the value f I SC. The graph cmparing the tw I SC values fr a day has been pltted belw. Where V OC0 =25.54 V G 0 = W/sq m and V OC1 =24.76 V G 1 =500 W/sq. m On substituting the abve values we get β=0.07 C. Calculatin f γ Where V OC0 =25.54 V T 0 = K and V OC1 =24.76 V T 1 = K On substituting the abve values we get γ=0.07 III. CALCULATION OF V OC AND I SC USING THE VALUES OF CALCULATED PARAMETERS Figure 1: Cmparisn f given and calculated I SC fr 1 day The same methd was used t calculate the I SC fr different values f G and T acrss 7 days. The graph shwed similar results. Nw, using the values f α, β and γ we can calculate the values f I SC and V OC. The values f the parameters can be substituted in the equatins previusly defined. Thus, the values f I SC and V OC were calculated at different values f G and T fr a given data f ne day which was later extended t 7 days. The values f V OC and I SC were calculated fr ne day first. The results were cmpared with the given values and then the methd was extended fr the data f 7 days. A. I SC Figure 2: Cmparisn f given and calculated I SC fr 7 days Where I SC =6.436 A G 0 = W/sq. m 742
3 B. V OC V OC0 =25.54 V G 0 = W/sq m T 0 = K Values f G and T were substituted and the values f Open Circuit Vltage V OC were calculated. Figure 4: Cmparisn f given and calculated V OC fr 7 days They were cmpared with the values f V OC in the given data and pltted with respect t time. The graph shwed that the calculated and given values were in cnjunctin with each ther with sme deviatins. Althugh the graph deviates frm sme f the values, the deviatin is small. The graph is btained with a gd accuracy. This prved the methd prpsed t calculate the value f V OC. IV. CALCULATIONOF COMPLEX PARAMETERS R S AND IDEALITY FACTOR A. Calculatin f Rs The frmula prpsed by Jia and Andersn t calculate R s is The graph cmparing the tw V OC values fr a day has been pltted. Figure 3: Cmparisn f given and calculated VOC fr 1 day The same methd was used t calculate the V OC fr different values f G and T acrss 7 days. The graph shwed similar results. Using this frmula, the values f R s were calculated. But when the Maximum utput pwer P max was calculated using these values f R s and cmpared with the given values f P max, deviatin was bserved between the tw sets f values. The P max calculated using Jia and Andersn s frmula fr R s was much smaller in magnitude than expected. Hence, we derive/prpsed a new frmula fr the calculatin f R s. Firstly, we calculated the crrect r expected values f R s (which wuld eventually generate the crrect values f P max as per given data) using reverse engineering. With the help f given experimental data, the values f V OC, I SC and P max were substituted in the equatin f P max. 743
4 The nly unknwn in the equatin was FF r the Fill Factr which is given by the equatin In this equatin, the value f FF 0 remains almst equal t cnstant value 1 all the time. Hence, it was apprximated t be cnstant. Substituting the ther values, the expected value f R s was calculated fr all times during the day. These values f R s wuld generate the expected P max. Nw, t derive the frmula fr R s using the given data which included, V OC, I SC, V mpp and I mpp we pltted the values f V OC /I SC, V MPP /I MPP against the values f expected R s in MATLAB. Using I SC I MPP the prperty f Curve Fitting, we fund the equatin relating the abve 3 terms. The equatin frmed is given by, Figure 6: Cmparisn f values f R s fr 1 day The graphs belw shw the cmparisn f R s values fr seven days using bth the frmulae. Using this equatin, the value f R s was calculated by substituting the values in the equatin. Thus, values f R s were btained at different times during the day. They were cmpared with the expected R s values and a clear agreement was fund between the tw sets with very minr deviatins. The plt f expected R s vs calculated R s using the frmula shwed a straight line which cnfirmed the agreement. Figure 7: Cmparisn f values f R s fr 7 days B. Calculatin f Ideality Factr n The value f V t was calculated by substituting the value f T at different times during the day (as given in the data) in the equatin Figure 5: Cmparisn f expected and calculated R s The cmparisn f values f R s calculated by Jia and Andersn s frmula and by the prpsed frmula with the expected value f R s can be seen belw. Substituting the values in the abve equatin, we calculate the values f Ideality factr. The values f Ideality factr fr a data f 1 day was calculated which was later extended fr a data f 7 days. The values f Ideality factr are arund 1 fr the entire duratin 744
5 V. CALCULATION OF FILL FACTOR AND MAX IMUM POWER POINT P MAX A. Calculain f Fill Factr The value f Fill Factr is given by the ther methds as the curve f calculated P MAX using ur methd traces the curve f given P MAX with very minr deviatins as cmpared t the ther curve. The plt f P MAX cmparisn fr 1 day and 7 days is given belw Where, FF 0 is the fill factr f the ideal PV mdule withut resistive effects; R s is the series resistance; V OC is the nrmalized value f the pen-circuit vltage t the thermal vltage, i.e. Figure 8: Cmparisn f values f P max fr 1 day First, the values f nrmalized pen circuit vltage V OC were calculated by substituting the value f n (Ideality Factr) fund ut earlier.these values were then substituted in the equatin f the Ideal PV Mdule Fill Factr FF 0. The values f the Ideal Fill Factr were fund and remained almst equal t 1 as we had apprximated earlier while finding the value f R s using reverse engineering. This verified the newly btained values f Series Resistance. Nw, the values f Fill Factr were btained by substituting the values f V OC, I SC, R s and FF 0 in the equatin. The Fill Factr fr different cnditins was fund t be between 0.7 t 0.8 as per the changes in Temperature and Irradiance which in turn resulted in different values f V OC, I SC and R s. B. Calculatin f Maximum Pwer Pint P MAX We calculated the values f I SC, V OC and Fill Factr FF. We nw substitute these values in the equatin f P MAX :- Figure.9: Cmparisn f values f P MAX fr 7 days VI. CALCULATION OF P MAX FOR DIFFERENT SET OF data The expanded frm f the abve equatin is Substituting all the values, we calculated the pwer. This value f P MAX was calculated using the frmula we prpsed fr R s. This value was cmpared with the given P MAX values and the P MAX calculated using Jia and Andersn s frmula fr R s. This plt cnfirmed that the methd prpsed in this prject gives mre accurate values f P MAX as cmpared t The prpsed frmula fr R s was tested fr an altgether different slar panel data fr a different day, different weather cnditins and different slar panel. The same sequence f steps was fllwed t get the values f V OC, I SC. The value f R s was calculated using the new frmula. Frm this value, the values f Ideality Factr, Fill Factr and eventually P MAX were calculated. These values f P MAX were tallied with the given P MAX and an agreement was bserved with minr deviatins. Hence, the data calculated by ur prpsed frmula was tested fr different cnditins and the results matched every time. Hence, we prpsed the new frmula fr R s. 745
6 VIII. BIBLIOGRAPHY Figure 10.Cmparisn f values f P MAX fr different data VII. CONCLUSION Using the mathematical mdel prpsed, the values f varius panel parameters were btained. After calculating the values f α, β, γ the Series resistance and pen circuit vltage values were calculated. The calculated values f V OC and I SC matched with the values f V OC and I SC in the given data. The values f Fill Factr and Maximum pwer were calculated but variatins were fund with these and the values in the given data because f the di sc repancies in the calculated values f Series Resistance R s. Hence, a new frmula was prpsed t calculate the value f R s. This frmula was derived using reverse engineering and curve fitting methds. Using the new frmula, the calculated values f R s were btained. These were used t find the Fill Factr and maximum pwer. The newly calculated values matched with the required data. The same frmula was tested n ther data t verify the results. The calculated values matched with the given data in this case t. Very minr and negligible di sc repancies were fund in the answers unlike the case f the earlier prpsed mathematical mdel. Hence, a new frmula has been prpsed t calculate the values f Series Resistance R s using the values f V OC, I SC, V MPP and I MPP. With the incident data available at a particular place, the utput pwer f the panel at all the time during the day can be fund ut. [1] Wei Zhu, Hngxing Yang, Zhahng Fang, A nvel mdel fr phtvltaic array perfrmance predictin, SC ience Direct, Applied Energy 84(2007); [2] D.COTFAS, P.COTFAS, S.KAPLANIS, D.URSUTIU, Results n series and shunt resistances in a c-si PV cell. Cmparisn using existing methds and a new ne, JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS Vl. 10, N. 11, Nvember 2008, [3] Kerr MJ, Cuevas A. Generalized analysis f the illuminatin intensity vs. pen-circuit vltage f PV mdules. Sl Energy 2003; 76:2637. [4] [5] Evans DL. Simplified methd fr predicting phtvltaic array utput. Slar Energy 1981; 27: [6] Jia QZ, Andersn WA. A nvel apprach fr evaluating the series resistance f slar cells, Sl cells 1988; 25:3118 [7] Van Dyk EE et al. Lng-term mnitring f phtvltaic devices. Renew Energy 2002; 22:18397 [8] Newprt Experience and Slutins, Slar Simulatin [9] Bird, R.E. and R.L. Hulstrm, L.J. Lewis, Terrestrial Slar Spectral Data Sets, Slar Energy 746
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