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. I–V curves
plotted for different values of Rs and Rp .
Fig. 5. Pmax = f
(Rs ) with I = Imp and V =
Vmp.
Fig.
6. I–V curve adjusted to three remarkable points.
Fig. 7. P –V curve
adjusted to three remarkable points.
Fig.
8. I–V model curves and experimental data of theKC200GT solar
array at different temperatures, 1000 W/m2 .
Fig.
9. I–V 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 I–V
equation to the experimental remarkable points of the I–V curve
of the practical array. The method obtains the parameters of the I–V 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 I–V 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 I–V points and/or
graphically extracting the slope of the I–V 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 I–V 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 I–V 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 I–V 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 I–V 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.
