Verification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance

Verification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance

Sanika Gawhane Onkar Hule

B.Tech., Department of Electronics Engineering B.Tech., Department of Electronics Engineering Vishwakarma Institute of Technology, Vishwakarma Institute of Technology,

Pune-411037-India Pune-411037- India

Chinmoy Kulkarni Ojas Pandav

1. ech., Department of Electronics Engineering B.Tech., Department of Electronics Engineering Vishwakarma Institute of Technology, Vishwakarma Institute of Technology,

   Pune-411037-India Pune-411037- India

   AbstractWe propose a new formula to calculate the value of Series Resistance from the values of VOC, ISC, VMPP and IMPP. This formula was tested on different solar data in different conditions. The data included the values of VOC, ISC, VMPP, IMPP, Temperature, Irradiance and PMAX at different times during the

   calculate the value of Series Resistance from the values of VOC, ISC, Vmpp and Impp. This formula was tested on different solar data in different conditions. A data from January 2010 was used to calculate all the complex parameters. The data

   included the values of VOC, ISC, Vmpp, Impp, Temperature,

   day for 7 days. From the given data, two values of G and T are

   considered. Using the above atmospheric conditions and the

   Irradiance and P

   max

   at different times during the day for 7

   panel behavior at those conditions, a new formula for calculation of series resistance of the solar panel is proposed.

   KeywordsSeries; resistance; Maximum power; formula; solar irradiance; temperature

   1. INTRODUCTION

      We plan to extract the quality parameters of a Solar Panel at a location where the atmospheric conditions are known which will be used to decide the use of a particular Solar Panel. Various atmospheric conditions like Solar Irradiance, Temperature and Wind Speed affect the parameters. The various solar panel parameters include VOC (Open Circuit Voltage), ISC (Short Circuit Current), Maximum Power, Voltage and Current at Maximum power point Vmpp and Impp, Fill Factor and Efficiency. These factors vary with changing atmospheric conditions. The values of these parameters will be determined at different environmental conditions. These parameters account for the complex dependence of Solar Panel performance upon Solar Irradiance Intensity and Solar Panel Temperature. To find the above parameters, minimum data in form of the Datasheets of Solar Panels and the measured atmospheric conditions like Solar Irradiance and Panel Temperature will be required. With this data, we can predict the panel behavior by using a mathematical model representing the Panel already proposed. The mathematical model was tested on given data. All of the calculated parameters matched with the given parameters expect for the Series Resistance values which caused discrepancies in the final power values. Hence, we propose a new formula to

      days. From the given data, two values of G and T are considered. Using the formulae, values of, and are calculated. The given values of VOC, ISC are used to verify the calculated values of VOC, ISC. Also, the values of VOC, ISC, Vmpp and Impp are used in calculating the Series resistance and in turn, the Ideality Factor. Using all these complex parameters, the value of Pmax is calculated which is then com-pared with the given value of Pmax in the data to verify the results.

   2. CALACULATION OF COMPLEX PARAMETERS

      1. Calculation of

         Where ISC0=6.436

         G0=749.54 W/sq m and

         ISC1=4.201,

         G1=500 W/sq. m

         On substituting the above values we get =1.052

      2. Calculation of

         Using different values of G and T, the values of Short circuit current ISC were found. They were compared with the values of ISC in the given data and plotted with respect to time. The graph showed that the calculated and given values were almost in complete conjunction with each other with very minor deviations. This proved the method proposed to calculate the value of ISC. The graph comparing the two ISC values for a day has been plotted below.

         Where VOC0=25.54 V

         G0=749.54 W/sq m and VOC1=24.76 V

         G1=500 W/sq. m

         On substituting the above values we get =0.07

      3. Calculation of

      Where VOC0=25.54 V T0=315.126 K and VOC1=24.76 V T1=300.95 K

      On substituting the above values we get =0.07

   3. CALCULATION OF VOC AND ISC USING THE VALUES OF CALCULATED PARAMETERS

      Now, using the values of , and we can calculate the values of ISC and VOC. The values of the parameters can be substituted in the equations previously defined. Thus, the values of ISC and VOC were calculated at different values of G and T for a given data of one day which was later extended to 7 days. The values of VOC and ISC were calculated for one day first. The results were compared with the given values and then the method was extended for the data of 7 days.

      1. ISC

         Where ISCo=6.436 A

         G0=749.54 W/sq. m

         Figure 1: Comparison of given and calculated ISC for 1 day

         The same method was used to calculate the ISC for different values of G and T across 7 days. The graph showed similar results.

         Figure 2: Comparison of given and calculated ISC for 7 days

      2. VOC

      VOC0=25.54 V G0=749.54 W/sq m T0=315.126 K

      Values of G and T were substituted and the values of Open Circuit Voltage VOC were calculated.

      They were compared with the values of VOC in the given data and plotted with respect to time. The graph showed that the calculated and given values were in conjunction with each other with some deviations. Although the graph deviates from some of the values, the deviation is small. The graph is obtained with a good accuracy. This proved the method proposed to calculate the value of VOC.

      The graph comparing the two VOC values for a day has been plotted.

      Figure 3: Comparison of given and calculated VOC for 1 day

      The same method was used to calculate the VOC for different values of G and T across 7 days. The graph showed similar results.

      Figure 4: Comparison of given and calculated VOC for 7 days

   4. CALCULATIONOF COMPLEX PARAMETERS RS AND IDEALITY FACTOR

      1. Calculation of Rs

         The formula proposed by Jia and Anderson to calculate Rs is

         Using this formula, the values of Rs were calculated. But when the Maximum output power Pmax was calculated using these values of Rs and compared with the given values of Pmax, deviation was observed between the two sets of values. The Pmax calculated using Jia and Andersons formula for Rs was much smaller in magnitude than expected. Hence, we derive/proposed a new formula for the calculation of Rs. Firstly, we calculated the correct or expected values of Rs (which would eventually generate the correct values of Pmax as per given data) using reverse engineering. With the help of given experimental data, the values of VOC, ISC and Pmax were substituted in the equation of Pmax.

         The only unknown in the equation was FF or the Fill Factor which is given by the equation

         In this equation, the value of FF0 remains almost equal to constant value 1 all the time. Hence, it was approximated to be constant. Substituting the other values, the expected value of Rs was calculated for all times during the day. These values of Rs would generate the expected Pmax. Now, to derive the formula for Rs using the given data which included, VOC, ISC, Vmpp and Impp we plotted the values of VOC/ISC, VMPP/IMPP against the values of epected Rs in MATLAB. Using ISC IMPP the property of Curve Fitting, we found the equation relating the above 3 terms. The equation formed is given by,

         Using this equation, the value of Rs was calculated by substituting the values in the equation. Thus, values of Rs were obtained at different times during the day. They were compared with the expected Rs values and a clear agreement was found between the two sets with very minor deviations. The plot of expected Rs vs calculated Rs using the formula showed a straight line which confirmed the agreement.

         Figure 6: Comparison of values of Rs for 1 day

         The graphs below show the comparison of Rs values for seven days using both the formulae.

         Figure 7: Comparison of values of Rs for 7 days

      2. Calculation of Ideality Factor n

      The value of Vt was calculated by substituting the value of T at different times during the day (as given in the data) in the equation

      Figure 5: Comparison of expected and calculated Rs

      The comparison of values of Rs calculated by Jia and Andersons formula and by the proposed formula with the expected value of Rs can be seen below.

      Substituting the values in the above equation, we calculate the values of Ideality factor. The values of Ideality factor for a data of 1 day was calculated which was later extended for a data of 7 days. The values of Ideality factor are around 1 for the entire duration

   5. CALCULATION OF FILL FACTOR AND MAXIMUM POWER POINT PMAX

      1. Calculaion of Fill Factor

         The value of Fill Factor is given by

         Where, FF0 is the fill factor of the ideal PV module without resistive effects; Rs is the series resistance; VOC is the normalized value of the open-circuit voltage to the thermal voltage, i.e.

         First, the values of normalized open circuit voltage VOC were calculated by substituting the value of n (Ideality Factor) found out earlier.These values were then substituted in the equation of the Ideal PV Module Fill Factor FF0. The values of the Ideal Fill Factor were found and remained almost equal to 1 as we had approximated earlier while finding the value of Rs using reverse engineering. This verified the newly obtained values of Series Resistance. Now, the values of Fill Factor were obtained by substituting the values of VOC, ISC, Rs and FF0 in the equation. The Fill Factor for different conditions was found to be between 0.7 to 0.8 as per the changes in Temperature and Irradiance which in turn resulted in different values of VOC, ISC and Rs.

      2. Calculation of Maximum Power Point PMAX

         We calculated the values of ISC, VOC and Fill Factor FF. We now substitute these values in the equation of PMAX:-

         The expanded form of the above equation is

         Substituting all the values, we calculated the power. This value of PMAX was calculated using the formula we proposed for Rs. This value was compared with the given PMAX values and the PMAX calculated using Jia and Andersons formula for Rs. This plot confirmed that the method proposed in this project gives more accurate values of PMAX as compared to

         the other methods as the curve of calculated PMAX using our method traces the curve of given PMAX with very minor deviations as compared to the other curve. The plot of PMAX comparison for 1 day and 7 days is given below

         Figure 8: Comparison of values of Pmax for 1 day

         Figure.9: Comparison of values of PMAX for 7 days

   6. CALCULATION OF PMAX FOR DIFFERENT SET OF data

      The proposed formula for Rs was tested for an altogether different solar panel data for a different day, different weather conditions and different solar panel. The same sequence of steps was followed to get the values of VOC, ISC. The value of Rs was calculated using the new formula. From this value, the values of Ideality Factor, Fill Factor and eventually PMAX were calculated. These values of PMAX were tallied with the given PMAX and an agreement was observed with minor deviations. Hence, the data calculated by our proposed formula was tested for different conditions and the results matched every time. Hence, we proposed the new formula for Rs.

      Figure 10.Comparison of values of PMAX for different data

   7. CONCLUSION

      • Using the mathematical model proposed, the values of various panel parameters were obtained.

      • After calculating the values of , , the Series resistance and open circuit voltage values were calculated. The calculated values of VOC and ISC matched with the values of VOC and ISC in the given data.

      • The values of Fill Factor and Maximum power were calculated but variations were found with these and the values in the given data because of the discrepancies in the calculated values of Series Resistance Rs.

      • Hence, a new formula was proposed to calculate the value of Rs. This formula was derived using reverse engineering and curve fitting methods.

      • Using the new formula, the calculated values of Rs were obtained. These were used to find the Fill Factor and maximum power.

      • The newly calculated values matched with the required data.

      • The same formula was tested on other data to verify the results. The calculated values matched with the given data in this case too.

      • Very minor and negligible discrepancies were found in the answers unlike the case of the earlier proposed mathematical model.

      • Hence, a new formula has been proposed to calculate the values of Series Resistance Rs using the values of VOC, ISC, VMPP and IMPP.

      • With the incident data available at a particular place, the output power of the panel at all the time during the day can be found out.

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