asokatechnologies@gmail.com 09347143789/09949240245

Search This Blog

Tuesday 8 December 2015

Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays


ABSTRACT:

This paper proposes a method of modeling and simulation of photovoltaic arrays. The main objective is to find the parameters of the nonlinear I–V equation by adjusting the curve at three points: open circuit, maximum power, and short circuit. Given these three points, which are provided by all commercial array datasheets, the method finds the best I–V equation for the single-diode photovoltaic (PV) model including the effect of the series and parallel resistances, and warranties that the maximum power of the model matches with the maximum power of the real array. With the parameters of the adjusted I–V equation, one can build a PV circuit model with any circuit simulator by using basic math blocks. The modeling method and the proposed circuit model are useful for power electronics designers who need a simple, fast, accurate, and easy-to-use modeling method for using in simulations of PV systems. In the first pages, the reader will find a tutorial on PV devices and will understand the parameters that compose the single-diode PV model. The modeling method is then introduced and presented in details. The model is validated with experimental data of commercial PV arrays.

KEYWORDS:
1.      Array
2.       Circuit
3.       Equivalent
4.       Model
5.      Modeling
6.      Photovoltaic (PV)
7.       Simulation.

SOFTWARE: MATLAB/SIMULINK

CIRCUIT DIAGRAM:
                    




Fig. 1. PV array model circuit with a controlled current source, equivalent resistors, and the equation of the model current (Im ).

EXPECTED SIMULATION RESULTS:

                  


Fig. 2. P V curves plotted for different values of Rs and Rp .



                     

Fig. 3. Pmax,m versus V for several values of Rs > 0.




                                    


Fig. 4. IV curves plotted for different values of Rs and Rp .


                                  
                          


Fig. 5. Pmax = f (Rs ) with I = Imp and V = Vmp.

        
                   

Fig. 6. IV curve adjusted to three remarkable points.

                        


Fig. 7. P V curve adjusted to three remarkable points.

                      



Fig. 8. IV model curves and experimental data of theKC200GT solar array at different temperatures, 1000 W/m2 .
        
                 

Fig. 9. IV model curves and experimental data of theKC200GT solar array at different irradiations, 250C.

CONCLUSION:

This paper has analyzed the development of a method for the mathematical modeling of PV arrays. The objective of the method is to fit the mathematical IV equation to the experimental remarkable points of the IV curve of the practical array. The method obtains the parameters of the IV equation by using the following nominal information from the array datasheet: open circuit voltage, short-circuit current, maximum output power, voltage and current at the MPP, and current/temperature and voltage/temperature coefficients. This paper has proposed an effective and straightforward method to fit the mathematical IV curve to the three (V, I) remarkable points without the need to guess or to estimate any other parameters except the diode constant a. This paper has proposed a closed solution for the problem of finding the parameters of the single-diode model equation of a practical PV array. Other authors have tried to propose single-diode models and methods for estimating the model parameters, but these methods always require visually fitting the mathematical curve to the IV points and/or graphically extracting the slope of the IV curve at a given point and/or successively solving and adjusting the model in a trial and error process. Some authors have proposed indirect methods to adjust the IV curve through artificial intelligence and interpolation techniques . Although interesting, such methods are not very practical and are unnecessarily complicated and require more computational effort than it would be expected for this problem. Moreover, frequently in these models Rs and Rp are neglected or treated as independent parameters, which is not true if one wishes to correctly adjust the model so that the maximum power of the model is equal to the maximum power of the practical array. An equation to express the dependence of the diode saturation current I0 on the temperature was proposed and used in the model. The results obtained in the modeling of two practical PV arrays have demonstrated that the equation is effective and permits to exactly adjust the IV curve at the open-circuit voltages at temperatures different from the nominal. Moreover, the assumption Ipv ≈ Isc used in most of previous works on PV modeling was replaced in this method by a relation between Ipv and Isc based on the series and parallel resistances. The proposed iterative method for solving the unknown parameters of the IV equation allows to determine the value of Ipv , which is different from Isc . This paper has presented in detail the equations that constitute the single-diode PV IV model and the algorithm necessary to obtain the parameters of the equation. In order to show the practical use of the proposed modeling method, this paper has presented two circuit models that can be used to simulate PV arrays with circuit simulators. This paper provides the reader with all necessary information to easily develop a single-diode PV array model for analyzing and simulating a PV array. Programs and ready-to-use circuit models are available for download at: http://sites.google.com/site/mvillalva/pvmodel.

REFERENCES:

[1] A. S. Sedra and K. C. Smith, Microelectronic Circuits. London, U.K.: Oxford Univ. Press, 2006.
[2] H. J. M¨oller, Semiconductors for Solar Cells. Norwood, MA: Artech House, 1993.
[3] A. L. Fahrenbruch and R. H. Bube, Fundamentals of Solar Cells. San Francisco, CA: Academic, 1983.
[4] F. Lasnier and T. G. Ang, Photovoltaic Engineering Handbook. New York: Adam Hilger, 1990.

[5] “Photovoltaic systems technology,” Universit¨at Kassel, Kassel, Germany, 2003.