Modelling and Simulation of Solar Panel

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2 generate the required current and voltage. Fig.1 shows the equivalent circuit diagram of solar cell. A. Solar Cell The voltage current characteristic curve for the p n junction diode is described by the following Shockley diode equation: I = I s [e( V d /nv T) 1] Using kirchoff s current law, we get I = I sc - I 0 (e qv d /kt 1) voltage V OC when I = 0; V oc = (kt/q)ln(i sc /I 0 + 1) At 25 degree C, equation becomes. I = I sc I 0 (e 38.9V -1) V oc = ( )ln(I sc /I 0 + 1) Where, V t = kt/q I d is the diode current (A) V d is the voltage across the diode terminals (V) I 0 is the reverse saturation current (A) q is the electron charge ( C) k is Boltzmann s constant ( J/K) T is the junction temperature (K) Fig: 2. Portion of PV cells array 4. Components of Model All the models are developed individually and then integrated together so that maximum power point of the PV array can be tracked. Fig.3 shows the net circuit diagram. Fig: 1. Equivalent model of PV cell The characteristic equation for this PV model is given by I PV =I L - I 0 (e (V PV +R S I PV )/V T 1) (V PV + R S *I PV )/R P where, I PV is output current and V PV output voltage respectively. An ideal PV module is one for which R S is low and R P is very large. The output current and voltage are then as follows: I PV =I L - I 0 (e (V PV +R S I PV )/V T 1) V PV = V T ln[(i L -I PV )/I 0 + 1] B. PV Array Since a typical PV cell produces less than 2W at 0.5V approximately, the cells must be connected in series configuration on a module to produce enough high power. A PV array is a group of several PV modules which are electrically connected in series and parallel circuits to generate the required current and voltage. Fig. 2 depicts PV array. Fig. 5 and Fig. 6 shows I-V and P-V graph obtained when a variable resistor is put across PV array. Fig: 3. Net circuit diagram A. Solar Cell Model As it is stated that I-V characteristic of PV cell or array is nonlinear so their exist a maximum power point. B. Solar Panel Model The voltage across a single solar cell is very small so to get a particular amount of power we need to connect the solar cell in series and parallel connection. Fig.2 shows the PV array model. C. Maximum Power Point Tracker To make the efficiency better at different environmental conditions its necessary to track the MPP of PV curve as shown in Fig.5. Fig: 4. Power-Voltage curve of PV cell 475

3 Fig: 5. Shows the I-V character of PV cell There are many techniques to track the maximum power point of PV curve. One of the most common and widely used algorithm is P&O algorithm, which we are explaining here and are using in our modelling. 1) P&O Algorithm: The Perturb and Observe (P&O) algorithm operates perturbs the PV voltage periodically by varying the duty cycle, and observes the PV power to increase or decrease PV voltage in the next cycle. If the perturbation voltage produces an increase of the power, then the direction or slope of perturbation voltage (duty cycle) is the same as the previous cycle. On the contrary, if the perturbation voltage produces a decrease of the power, then the direction or slope of perturbation voltage (duty cycle) is the opposite from the previous cycle. Fig.7 depicts the flowchart of P&O algorithm. 4) Cuk Converter: Fig: 8 Model of PWM A convertor regulates the input voltage at the PV MPP and providing load matching for the Maximum power transfer. The output voltage magnitude can be same, larger or smaller than the input, depending on the duty cycle. In our paper we are using Cuk converter. Its relationship to the duty cycle (D) is: If 0 < D < 0.5 the output is smaller than the input. If D = 0.5 the output is the same as the input. If 0.5 < D < 1 the output is larger than the input Fig.10 depicts the Cuk converter. For our design the value of C1, C2, L1, and L2 we have taken using the following formulas: L1(min) = ((1 - D) 2 R)/2Df L2(min) = ((1 - D)R)/2f C1(min) = (V 0 D)/(Rfdv c1 ) C2(min) = (1- D)/((dv 0 /v0)8l2f 2 ) Where L1 and L2 are inductance,c1and C2 are capacitance and R is the load resistance as shown in the fig.10. The values which we used in our model are as follows: L1: 225uH L2: 225uH C1: 15uF C2: 10uF 5) Results: The full model, which was formed after integration of all the components right from PV solar cells (series and parallel connection), MPPT, Cuk converter and all other measuring equipment appears as follows: Fig: 7. Flowchart of Perturb and Observe (P&O) algo 2) Tracking Model: Here tracking is done by P&O algorithm. Fig. 8 shows the main tracking model. 3) Pulse Width Modulation Model: It is the part of MPPT model. Once the maximum power point is tracked then the signal should be converted to pulses so that it can be fed into DC to DC converter. For that we compare the output signal with a triangular wave and thus convert it into pulses. Fig.9 shows the model. Fig: 9. Cuk Converter 476

4 Fig: 11. The complete model 477

5 The following graph were obtained during the simulation of the model: Fig: 14. Finally tracked output voltage References Fig: 12. The PV curve showing the MPP Fig: 13. The IV curve [1] M A Green, K Emery, Y Hishikawa, W. Warta, Solar cell efficiency tables (37), Progress in Photovoltaics: Research and Applications. 2011; 19: [2] S M Jaralikar, M. Aruna, Case Study of a Hybrid (Wind and Solar) Power Plant. TELKOMNIKA. 2011; 9(1): [3] G R Walker. Evaluating MPPT Converter Topologies Using A MATLAB PV Model. Journal of Electrical & Electronics Engineering. Australia. 2001; 21(1): [4] J V Gragger, A Haumer, M Einhorn. Averaged Model of a Buck Converter for Efficiency Analysis. Engineering Letter. 2010, 18(1) [5] S. W. Angrist, Direct Energy Conversion, Allyn and Bacon, Inc., 4th edition, 1982, [6] O. Wasynczuk, Dynamic behavior of a class of photovoltaic power systems, IEEE Transactions on Power Apparatus and Systems, PAS-102, 9, 1983, [7] Y Jiang, J A A. Qahouq, Study and evaluation of load current based MPPT control for PV solar systems. Proceedings of IEEE Energy Conversion Congress and Exposition. Arizona. 2011: [8] M A Elgendy, B Zahawi, D J. Atkinson, Assesment of Perturb and Observe MPPT Algorithm Implementation Techniques for PV Pumping Applications. IEEE Transactions on Sustainable Energy. 2012; 3(1): [9] M M Rashid, R Muhida, A H M Z Alam, H Ullah, B. Kasemi, Development of Economical Maximum Power Point Tracking System for Solar Cell. 5. Conclusion It is thus concluded that by the application of MPPT (P and O algorithm) and Cuk convertor, better efficiency and more power can be obtained from the same solar panel in different environmental conditions. By tracking the maximum power point of the PV characteristics curve better efficiency is obtained due to the controllability of the operating point of the system. 6. Acknowledgments This paper is based on the project titled "Distributed Generation of Power", which owes its commencement to Dr. Suman Bhowmick, Electrical Energy Utilisation Laboratory, Department of Electrical Engineering, Delhi Technological University. We also thank Prof. Madhusudan Singh, Head of Department (Electrical Engineering) for supporting us and making the resources of the department available to us. Australian Journal of Basic and Applied Sciences. 2011:5(5): [10] D. Saravana Selvan, Modeling and Simulation of Incremental Conductance MPPT Algorithm for Photovoltaic Applications. International Journal of Scientific Engineering and Technology, 2(7), [11] K Vijaya Bhaskar, M. Lokanadham, Incremental Conductance Based Maximum Power Point Tracking (MPPT) for Photovoltaic System. International Journal of Engineering Research and Applications (IJERA) 2(2), 2012, [12] P Takun, S Kaitwanidvilai, C. Jettanasen, Maximum Power Point Tracking using Fuzzy Logic Control for Photovoltaics Systems. Proceedings of International Multi Conference of Engineers and Computer Scientists. Hongkong [13] R I Putri, M. Rifai, Maximum Power Point Tracking Control for Photovoltaic System Using Neural Fuzzy. International Journal of Computer and Electrical Engineering. 2012; 4(1): [14] Aryuanto Soetedjo, Abraham Lomi, Yusuf Ismail Nakhoda, Awan Uji Krismanto. Modeling of Maximum Power Point Tracking Controller for Solar Power System. TELKOMNIKA, 10(3), 2012, [15] A S Samosir, T Sutikno, A B M. Yatim, Dynamic Evolution Control for Fuel Cell DC-DC Converter. TELKOMNIKA. 2011: 9(1):

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