The panel parameters as shown in the equivalent circuit Fig. 1 as the photon current h, the series resistance R,, the shunt ideality factor n. These data have been ...
FUZZY MODELING OF PHOTOVOLTAIC PANEL EQUIVALENT ClRCUIT **Prof.Dr.E.M.ABOU-ELZAHAB ,**Dr.A.A.T.ELKOUSY
*Dr.TH.F.ELSHATTER , *F'rof.Dr.M. T.ELHAGRY *ElectronicsResearch Institute, Doklu - Giza - Egypt
** Faculty of Eng. Cairo University ,Dokki - Giza - Egypt
ABSTRACT For simulation purposes of photovoltaic (PV) system using MA~AB and for on-line application the different parameters of the PV panel have to be known at the specific operating point. The parameters of interest are the photon current, the series and shunt resistance's, the ideality factor, and the diode reverse saturation current. Hence the different parameters have to be known at all operating condition which is practically not available in many cases. So, in this paper we will introduce a new type of data analysis that express these parameters by means of a f k z y regression model. The available PV array under consideration is defined by the manufacturer data sheet which specifies the panel under a narrow range of operating conditions. A b y model has been developed for the aforementioned PV arrays. The model has been validated using a set of data that have been obtained at our site or obtained from extrapolating data from the manufacturer data sheet.
on measurements made at Standard Test Conditions (STC) which are: . Illumination of 1 sun at spectral distribution of AMI .5. . Cell temperature of 25 OC or as otherwise specified (on curves). These data are used in developing the fuzzy regression models. The models have been validated using the measured data with the available instruments at our site.
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Fig. 1 Solar Panel Equivalent Circuit
INTRODUCTION The PV panel electrical behavior depends on the environmental conditions surrounding the system [l]. The main items are solar radiation, panel surface temperature, and the maximum power point. So, for simulation purposes of PV system the model parameters at various solar radiation's and surface temperatures must be available. That type of data may not be enough, o r h d contain errors. These errors are produced as a result of measuring system uncertainties. The existence of uncertainty, which can be described by fkzy sets, should be taken into consideration during system processing. The panel parameters as shown in the equivalent circuit Fig. 1 as the photon current h, the series resistance R,, the shunt resistance Rsh, the re erse saturation current Id and the ideality factor n. These data have been calculated using the available characteristics curves. These data are used in developing the fizzy model of the equivalent circuit. The model has been validated using different set of data. The available solar array under consideration consists of 4 panels mounted on the same structure. Each panel deliver approximately 56 W at 1000 W/m2 (1 sun) and 25 "C. The available data that can be used in the simulation purposes is obtained from the manufacturer data sheet The data are based
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0-7803-5772-8/00/$10.00 02000 IEEE
Hence, we don't have an accurate complete model that can be applied at all operating conditions or complete characteristics. Moreover, the manufacturer characteristics are insufficient for reliable operation , hence some sort of characterization is to be needed. A fuzzy model has been developed using the above mentioned data.
ANALYTICAL MODEL The I-V relation of the solar panel can be given by:
where, VT= kT/q is the thermal voltage and n is the ideality factor. From [2] the parameters are calculated using experimental data at three different points on the I-V characteristics, namely the short circuit current (O,Isc), the open circuit voltage (V,,O), and the maximum power point (Vm&J7 also the dynamic series resistance
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and
v=v,,
dynamic
shunt
resistance
Rsho = -
are obtained at the respective points. By
Min Problem
substituting the measured and obtained values from the experimental I-V characteristics , we get the required panel parameters; Rs,Rsh, n, Id, and Iph
(5)
FUZZY REGRESSION MODEL The type of data handled are standard data and data for which the output is fimy numbers (fuzzy data).
and Max Problem
Standard Data
The given data are (yi,xil,....,xi,),i = 1,..., N . m e r e y j is an output for the ith sample and x y is the jth input or jth explanatory variable for the ith sample. The vector for the explanatory variables is expressed asxi = (xil,.,.,x~)*. Since the formulation that gives us the linear possibility regression model is performed from this position. Let the linear possibility system be the model,
APPLICATION For simulation purposes of PV system using MATLAB and for on-line application the different parameters of the PV panel have to be known at the specific operating point. The main parameters affecting the equivalent circuit of the PV panel parameters are: 1. Panel surface temperature ( T,).
where, fuzzy coefficient A j is symmetrical fizzy numbex (ai , ci h ,and A is a fuzzy constant. The fuzzy coefficient A j that minimizes the total width of y i is detexmined, that is, J(c)
=ZC'IX~(
2. Solar insulation ( W, ). ( T, and W sare measured data) 3. Panel maximum output voltage ( V, ). 4. Panel maximum output current ( I, ). (V, and I, arecalculatedin [6])
(3)
where c = (CI ,....,cn)t , and c'lxil is the width of yi . J(c) corresponds to the sum of errors in conventional regression analysis. This brings us to the following linea progamming (LP) problem:
I
min J(c)=c c (xi a,c
1 >
Fig. 2 shows the P , -V, characteristics at different solar insolation and temperature. The input data to the fuzzy regression model are the above four factors. The output of this fuzzy model is the panel model parameters namely : n, R,, Rsh, h, .Iph This leads us to a consideration of the mini" and m m u m problems.
(4)
[XI=
The linear possibility model can be obtained by solving the LP problem.
Fuzzy Data The given data we will use here are(yi,xi),i =l;..,N. Where yi expresses the fimy output and is expressed
[v, I, T~ our case the input data are , and the output data are the panel model parameters n, Id, Rs, RA, Iph . For simplicity, let the fuzzy coefficientbe triangular, that is L(X) = 1 - 1x1 . Using the l i n w programming method the fuzzy model coefficients ai and c (center and width) can be obtained.
Yi = (yi,ei)L. Given the fuzzy data (yi,xi), the basic idea is to find A_ and
given by:
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w,]
RESULTS Applying the manufacturer data sheet ai and c (0 I;i < 4 ) of the regression fuzzy model at specific value of 'h'. Figs. 3-7
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show the results of applying the fuzzy model to the PV panel. The obtained results of Rs R,h, n and are matched with the analytical model. The obtained resul s are matched with ,Id, different models given in the litratures. The model given in [SI discusses the variation of the parameters with illumination only and in this respect it agrees with our model, while the model given in [6] gives the variation of the shunt resistance and series resistance with the light intensity and it agrees with our model as well. The model given in [7] agrees with our model except in the dependence of the series resistance and ideality factor on the temperature and this may be due to approximationsand least square method used in [7].
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1.0 sun 0.947Sun
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Maximum V o k g e (volt)
Fig.2 Pm-Vm characteristics 0.00
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Solar insolation (sun)
Fig.5 Photogenerated Current
l.m 7
75°C
S0"C 25°C
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Fig.3 Panel Series Resistance
Fig6 Reverse Saturation Current
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Photovoltaic System", 14* European Photovoltaic Solar Energy Conference, Barcelona, Spain, 30 June4 July 1997. [5] Charles J.P.,Bordure G., and Mialhe P., Solar Cells: Continuity and Light Variation of The Parameters"
[6] L.S.Kothari, P.C.Mathur, Avinashi Kapoor, PSaxena, and R.P.Sharma,"Determinationof Optimum Load For A Solar Cell", J. AppliedPhysics, 53, No. 8, August 1982.
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[7] N.Veissid and A.M.De Andrade." The Silicon Solar Cell Characteristic Parameters Temperature Dependence. An Ex rimental Study Using The Standard Deviation Method", 10$European Photovoltaic Solar Energy Conference, Lisbon, Portugal, 8-12 April 1991. I
I
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I 0.W
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Solar lnsulatlon (sun)
Fig.7 Panel Ideality Factor CONCLUSION
The regression fuzzy model gives results as good as those obtained using the analytical models [ 2, 5-71 , while itis supperior to that model in the following points: 1. The data required is the open circuit voltage, the short circuit current and the environmental data surrounding the PV system. While the data required in the analytical model is the complete I-V characteristics. 2. Applicable for any type of PV system. 3. Applicable for on-line applications 4. Minimum running time. 5 . Requires a small memory size and can be integrated in a small microcomputer controller. With the proposed regression fuzzy model the PV parameters can be determined without running of the spice software. As it requires much more data about constants and fabrication process ( diffusion length, recombination ,....etc) , This data are not available for the commercial users. From the above results it can be shown that the proposed model agrees with the real system characteristics. REFERENCES
[l] A.Hanel & M.S.Imamura, "Improvement of PV Array Performance", llth E.C. PVSEC, 12-16 Oct., Switzerland, 1992. [2] Mohammed BSaleh, M.M.Shabana and M.R. "Environmental Study of Locally Made PV Modules in EGYPT", Project Report. [3] T.Terano, K.Asai, and MSugeno, "Fuzzy Systems Theory and Its Applications", 1992, Academic Press ,Inc., USA.
[4] TH.F.Elshatter, M.T.Elhagree, M.E.Aboueldahab and A.A.Elkousy, "Fuzzy Modelling and Simulation of
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