 Open Access
 Total Downloads : 522
 Authors : Mohamed AbdElHakeem Mohamed, Mohamed. H. Osman
 Paper ID : IJERTV3IS10415
 Volume & Issue : Volume 03, Issue 01 (January 2014)
 Published (First Online): 16012014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Evaluation of a PV Model Based on a Novel Parameter Estimation Procedure for Different Manufacturers Modules
Mohamed AbdElHakeem Mohamed,
Faculty of Engineering, Electric Eng., AlAzhar University, Qena, Egypt.
Abstract
This paper presents the evolution of the single diode five parameters model for different manufacturer's modules. Also a novel procedure is improved to estimate the parameters of a PV model. The proposed procedure proposes an easy and accurate alternative approach to predict the currentvoltage characteristics of a photovoltaic (PV) system. The proposed procedure is used the NewtonRaphson method based on simplified method to calculate the parameters of a PV system .The initial values of these parameters are estimated by using the simplified method to prevent a bad starting point which can compromise the convergence of the NewtonRaphsons method. Also the proposed equations which are used to calculate these parameters of a PV system, allow one to calculate it's without relying on the experimental IV curve to determine the parameters of a PV system as usually reported in literature. The proposed procedure takes the temperature dependence of the cell dark saturation current into consideration. The proposed procedure is used to calculate the parameter of different manufacturer panel models, which is able to predict the panel behaviour in different temperature and irradiance conditions, is built and tested.
Nomenclature
STC Standard Test Conditions (Eref =1000 W/mÂ², Tref=25 Â°C, spectrum AM1.5).
Io – Dark saturation current in STC. Rsh Panel parallel (shunt) resistance. Isc – Shortcircuit current in STC.
Vmpp – Voltage at the Maximum Power Point (MPP) in STC.
Pmpp – Power at the MPP in STC.
Kv – Temperature coefficient of the opencircuit voltage.
q Electron charge.
ns – Number of cells in series.
Iph – the photogenerated current in STC. Rs – Panel series resistance.
A – Diode quality (ideality) factor. Voc Opencircuit voltage in STC. Impp – Current at the MPP in STC.
Ki Temperature coefficient of the shortcircuit current. Vt – Junction thermal voltage.
T Cell Temperature, in Kelvin.
V The voltage appearing at the cell terminals.
Mohamed.H.Osman,
Faculty of Engineering, Electric Eng., AlAzhar University, Qena, Egypt.

Introduction
Nowadays the worldwide installed Photovoltaic power capacity shows a nearly exponential increase, despite of their still relatively high cost[1] .This, along with the research for lower cost and higher efficiency devices, motivates the research also in the control of photovoltaic inverters, to achieve higher efficiency and reliability[2,3,4]. The possibility of predicting a photovoltaic plants behavior in various irradiance, temperature and load conditions is very important for sizing the photovoltaic plant and converter, as well as for the design of the Maximum Power Point Tracking (MPPT) and control strategy. There are numerous methods for extracting the panel parameters. The majority of the methods are based on measurements of the IV curve or other characteristic of the panel [58]. Charles et al. [5] have suggested a method that analyzes the practical IV measurements. The different mathematical methods have been presented in order to estimate the parameters of the four parameters PV model and to simulate its currentvoltage and power voltage characteristics [6]. A new approach for modeling the temperature dependence of the dark saturation current and the equation parameters can be evaluated by using five data points obtained from an experimental IV curve is presented in paper [7]. El Tayyan [8] has proposed the new equation is that one doesnt rely on the experimental IV curve to determine Rsh.
Many investigations were reported above, about estimation for a model of photovoltaic panels using the NewtonRaphson method but no attention was paid to the initial estimation of PV system parameters. The initial estimation of these parameters is critical because a bad starting point can compromise the convergence of the NewtonRaphsons method. On other hand, single exponential models that neglect the shunt resistance is used in [6]. However, this assumption is not generally valid for amorphous PV systems. And also, the problems of relying on the experimental IV curve to determine of PV system parameters still unsolved. This motivates the authors to investigate the new method in order to estimate the Parameters of PV panels by using NewtonRaphson based on simplified method.
In this paper the construction of a model for a PV panel using the singlediode fiveparameter model, based exclusively on datasheet parameters. The parameters of a PV system are calculated by using the NewtonRaphson method. The initial values of these parameters are estimated by using the simplified
method. Also the proposed method, allows one to calculate the parameters PV system without relying on the experimental IV curve to determine Rsh. In this work the temperature dependence of the cell dark saturation current is taken into consideration.

Equivalent circuit of the solar cell
without any measurement, using only the data from the product datasheet.

Starting equations
Equation (1) can be written for the three keypoints of the VI characteristic: the shortcircuit point, the maximum power point and the opencircuit point.
Mathematical descriptions of the IV characteristics of PV cells are available since many years and are
=
(3)
derived from the physics of the pn semiconductor junction.A crystalline solar cell is, in principle, a
=
+
+
(4)
largearea silicon diode. In the dark state, the IV characteristic curve of this diode corresponds to the one of a normal pn junction diode and it produces
= 0=
(5)
neither a voltage nor a current. Illumination of the PV cell creates free charge carriers, which allow current to flow through a connected load. The so called photocurrent Iph is proportional to irradiance [9]. If the circuit is open the photocurrent is shunted internally by the pn junction diode. The simplest equivalent
The above parameters are normally provided by the datasheet of the panel. An additional equation can be derived using the fact that is on the PV characteristic of the panel, at the MPP, the derivative of power with voltage is zero.
circuit of a PV cell (Fig. 1) is a current source whose
= = 0
(6)
intensity is proportional to the incident radiation, in parallel with a diode D and a shunt resistance Rsh.
=
This resistance represents the leakage current to the ground. The internal losses due to current flow and the connection between cells are modeled as a small series resistance Rs [9].
So far there are four equations available, but there are
five parameters to find, therefore a fifth equation can be derived using the fact that is on the PI characteristics of a PV system at the maximum power point, the derivative of power with respect to current is zero [8].
= = 0
(7)
=

Parameter extraction
From the expression of the current at shortcircuit and opencircuit conditions, the photogenerated current Iph and the dark saturation current Io can beexpressed:
Figure.1. Equivalent circuit of a photovoltaic cell using the
= +
(8)
single exponential module
By inserting Eq. (8) into Eq. (3), it takes the form:
The general currentvoltage characteristic of a PV
= +
(9)
panel based on the single exponential model is: The second term in the parenthesis from the above
+
= 1
+
(1)
equation can be omitted, as it has insignificant size compared to the first term. Than Eq. (9) becomes:
In the above equation, Vt is the junction thermal voltage:
= +
(10)
=
(2)
Solving the above equation for Io, results in:
It is a common practice to neglect the term 1in (1), as in silicon devices, the dark saturation current is very
=
(11)
small compared to the exponential term.
Eqs. (8) And (11) can be inserted into Eq. (4), which
will take the form


Single diode model of PV sell
+ + +
In order to construct a model of the PV panel, which exhibits the specifications described in the datasheet,
+
= 1 (12)
using the abovementioned singlediode model, there are five parameters to be determined: Iph, Io, A, Rs, and Rsh. The goal is to find all these parameters
The above expression still contains three unknown
parameters: Rs, Rsh, and A. The derivative of the power with voltage at MPP can be written as:
=
=
= +
(13)
Rsh=),after simplification of equations (3), (4) and
=
(5) we obtain [6].
Thereby, to obtain the derivative of the power at MPP, the derivative of Eq. (12) with voltage should be
= (
) (22)
found. However, Eq. (12) is a transcendent equation, and it needs numerical methods to express Impp. Eq.
(12) can be written in the following form:
The equation at the point of maximum power at is
turned becomes:
+
= , (14)
= 1
(23)
Where , is the right side of Eq. (12) .By differentiating Eq. (14):
From this equation, we can deduce the initial value of series resistance:
= (,) + (,)
(15)
= ln 1 +
(24)
The derivative of the current with voltage results in:
=
(,)
1 (,)
(16)
By exploiting the fact that the derivative of the maximum power is zero:
= 0 = + (25)
From Eqs. (16) And (13) results:
(,)
= +
1 (,)
(17)
And using equation (20) one can find:
= (2 )
(26)
)
From the above:
+ln (1
=
=
The last parameter to be determined is the shunt
=
+
+
+ 1
resistance Rsho, from equation 5:
= ( )
(27)
=
(18)
+ 2
+
( )
1 +
here are two equations now, Eqs .(12) and (18), with three unknowns. Eq. (7) can be the used as the third equation.
5. Parameters estimation procedure of PV panel model
This section describes the NewtonRaphson based on
=
=
simplified in order to calculate the three unknown
=
1 +
+
+
parameters (Rs, A, and Rsh) of PV panel model. Then, the other parameters ( , ) are calculated
+
+ 1
= 3
(19)
directly from Eqs. (21, 22) respectively. The determination of all unknown parameters (A, Rs, Rsh,
+
I , and I ) at various temperature and irradiance
It is possible now to determine all the three unknown ph o
parameters, the Rs, A, and Rsh using Eqs. (12), (18) and (19). As these equations do not allow separating the unknowns and solving them analytically, they are solved using Newton Raphson iterative method is exploited because it converges remarkably quickly, especially if the iteration begin sufficiently near the desired root.

Expression of photo current Iph and dark saturation current Io
Parameter
KC200GT solar
module
SP75 solar
module
Maximum Power (Pmpp)
200 W
75 W
Maximum Power Voltage (Vmpp)
26.3 V
17 V
Maximum Power Current
(Impp)
7.61 A
4.4 A
Open Circuit Voltage (Voc)
32.9 V
21.7 V
Short Circuit Current (Isc)
8.21 A
4.8 A
Temperature Coefficient
of Voc(Kv)
– 0.123V/oC
– 76 mV/oC
Temperature Coefficient
of Isc (Ki)
+ 3.18 mA/oC
+ 2 mA/oC
number of cells (ns)
54
36
The first equations when constructing the model are the expressions of Io from Eq. (3) and Iph from Eq. (5), in STC.
conditions, are described in the following steps: Step1:The parameters (A, Rs, and Rsh) are determined by using NewtonRaphson method. To apply the NewtonRaphson method for obtaining these parameters, the values of (Isc, Voc, Impp, and Vmpp) are obtained from the datasheet for different manufacturers modules (SP75 solar [10] module sand KC200GT solar module [11]) at 25 C, AM1.5, and 1000 W/m2 as shown in the table1.
Table1.Shows the data obtained from the datasheet for KC200GT solar module sand SP75 solar module at 25 C, AM1.5, and 1000 W/m2.
=(
)
(20)
= +
(21)


Initial estimation of PV parameters by using simplified explicit method
The initial estimation of PV parameters is critical because a bad starting point can compromise the convergence of the NewtonRaphsons method. The initial values of these parameters are estimated by using the simplified method. In this method some of approximations are applied as (Isc=Iph, and
Step2: The elements of the resulting Jacobian matrix
= , + ln(
) + (29)
(J) are obtained by differentiating equations (12), (18) and (19) with respect to the diode quality (ideality)
At the last the variations of the current and voltage at the maximum power point are described by:
factor (A), panel series resistance (Rs) and panel parallel (shunt) resistance (Rsh), and are collected into
= ,
+ (30)
portioned vector matrix forms, as:
= , + ln(
p>
) + (31)
f1
A
f1
Rs
f1
Rsh A
f
Step 8: The above steps are repeated at different manufacturer data sheets in table1.
f2
A
f2
Rs
f2
Rsh
Rs
1
2
f
6. Results and discussion
The previous section describes the construction of a
f
f3 f3 f3 Rsh
3
PV panel model. This model has been implemented in Matlab, in order to verify it in different
A Rs Rsh
Jacobian
correction
mismatches
temperature and irradiance conditions. The proposed model was tested using different manufacturer data sheets in table.
Step 3: The initial mismatch vector and the inverse of
Jacobian matrix are calculated corresponding to the initial values of A, Rs, and Rsh which are calculated in Eqs. (24, 26, 27) and are used for obtaining initial correction vector as follows:
The results have been compared to the characteristics and values provided by the product datasheet. The temperature dependencies of the
models VI curve have been verified by plotting the characteristics for three different temperatures.
f
1
A
(0)
f (0)
1
1
R
f
1
Rsh
(0)1
5
4.5
4
Calculated data
(0)
s f (0)
current(A)
3
3.5
Experimental data
A
f
(0)
f (0)
f (0)
T=60Â°C
R(0)
2
2 2
f (0)
2.5
T=40Â°C
s
A
R Rsh
2
3
Rsh
(0)
(0)
s
(0)
(0)
f
(0)
2
1.5
T=20Â°C
3
f
A
f3
Rs
f3
Rsh
1
0.5
0
0 5 10 15 20 25
voltage(V)
Step 4: The initial corrections ( A, , Rs and Rsh) are added to initial estimated values of A, , Rs and Rsh to obtain their new values first iteration, the general form can be written as:
Figure.2. VoltageCurrent characteristics of the
shell SP75 model (monocrystalline silicon)at three different temperatures and standard irradiation.
9
A( k 1) A( k )
A( k )
8
Calculated data
7 Experimental data
Rs ( k 1) Rs
( k ) Rs
( k )
current(A)
6 T=75Â°C
Rsh( k 1)
Rsh( k )
Rsh( k ) 5
T=50Â°C
Step 5: The process of iteration is repeated until the 4
values of these correction are minimized. 3
Step 6: the last two parameters (Io, and Iph) of five 2
1
PV parameters model are calculated directly from Eqs. (21, 22) respectively.
T=25Â°C
Step 7:The above steps are considered in STC. To include the effects of the environment, e.g. temperature and irradiance, these equations has to be completed with the corresponding terms.
For the short circuit current and open circuit voltage:
0
0 5 10 15 20 25 30 35
voltage(V)
Figure.3. VoltageCurrent characteristics of the KC200GT model (multicrystal) at three different temperatures and standard irradiation.
= ,
+ (28)
It can be seen on the above figures (2, 3) that the shortcircuit current, and the opencircuit voltage are in very good agreement with the datasheet values for SP75 (monocrystalline silicon) solar module and KC200GT (multicrystal) solar module. The change in the opencircuit voltage and shortcircuit current are in accordance with the temperature coefficients given in
the datasheet.
To show the effect of irradiance on the performance of a module the temperature is kept fixed at25 Â°C and the values of irradiance are changed to different values. The variation of the currentvoltage characteristics with irradiance are shown in Figure (6, 7).
5.5
The calculated and experimental variations of power with voltage for the shell SP75 model and the KC200GT model, at three different temperatures and standard irradiation are illustrated in figures (4, 5).
5
4.5
4
current(A)
3.5
3
G= 1000 W/m2
G= 800 W/m2
G= 600 W/m2
80
70 Calculated data
Experimental data
60
power(W)
50
T=60Â°C
2.5
2
1.5
1
0.5
G= 400 W/m2
Calculated data Experimental data
40 T=40Â°C
30 T=20Â°C
20
0
0 5 10 15 20 25
voltage(V)
Figure. 6.VoltageCurrent characteristics of the shell SP75 model (monocrystalline silicon) at different irradiation and standard temperature.
10 9
G= 1000 W/m2
0 8
0 5 10 15 20 25
voltage(V)
7
6
Figure. 4.Voltage Power characteristics of the shell
current(A)
SP75 model (monocrystalline silicon) at three different
temperatures and standard irradiation. 5
G= 800 W/m2
G= 600 W/m2
200
180
Calculated data Experimental data
4 G= 400 W/m2
3
160
power(W)
140
120
100
80
T=75Â°C
T=50Â°C
T=25Â°C
2 Calculated data
Experimental data
1
0
0 5 10 15 20 25 30 35
voltage(V)
Figure. 7.VoltageCurrent characteristics of the
60 KC200GT model (multicrystal) at different irradiation
40 and standard temperature.
20
0
0 5 10 15 20 25 30 35
voltage(V)
Figure.5.VoltagePower characteristics of the KC200GT model (multicrystal) at three different temperatures and standard irradiation.
Figures (4, 5) provide a clear view on how the curves vary with temperature. There is significant reduction in the power output of the photovoltaic system as cell temperature increases. And also, the calculated (PV) curves at different temperatures are in good agreement with the experimental data for different models (SP75 and KC200GT).
From the figures (6, 7) it can be noted that, according to the theory, the short circuit current shows a linear dependence with the irradiation, unlike the opencircuit voltage, which increases logarithmically with the irradiation. Figures (6, 7) show that, the calculated (IV) curves at different irradiation are in good agreement with the experimental data for different models (SP75 and KC200GT).
90
80
Calculated data
Experimental data
70
power(W)
60
50
40
30
20
10
G= 1000 W/m2
G=800 W/m2
G=600 W/m2
G=400 W/m2
In the same way, Figs.( 8,9) shows the comparison between the calculated PV characteristic, and the experimental characteristic . Also, it can be seen that the calculated (PV) curves at different irradiation are in good agreement with the experimental data for different models (SP75 and KC200GT).
8. Conclusion
A model for photovoltaic panels, based exclusively on datasheet parameters has been developed and implemented. The method for extracting the panel
0
0 5 10 15 20 25
voltage(V)
Figure. 8.Voltage Power characteristics of the shell SP75 model (monocrystalline silicon) at different irradiation and standard temperature.
220
parameters from datasheet values has been presented, and the obtained values have been used in the implemented model. The parameters of a PV system are calculated by using the NewtonRaphson method. The initia values of these parameters are estimated by using the simplified method, Also A new equation dP/dI=0 at the maximum power point is introduced. This new equation replaces the equation, usually used in
200
180
160
power(W)
140
120
100
80
60
40
20
0
Calculated data Experimental data
G= 1000 W/m2
G=800 W/m2
G=600 W/m2
G=400 W/m2
literature, determined from the slope of the IV curve at the short circuit current, namely, dI/dV=1/Rsh. In this work the temperature dependence of the cell dark saturation current is taken into consideration. From the present analysis, one can draw the following main conclusions:

By using the simplified method to estimate the parameters of a PV system the iteration begins sufficiently near the desired and the NewtonRaphson iterative method converges remarkably quickly.

The proposed equations which are expressed in a PV system, allow one to calculate the parameters PV system without relying on the experimental IV curve to
0 5 10 15 20 25 30 35
voltage(V)
Figure. 9.VoltagePower characteristics of the KC200GT model (multicrystal) at different irradiation and standard temperature.
determine Rsh.

The temperature dependence of the cell dark saturation current is expressed with an alternative formula, which gives better correlation with the datasheet values of the power temperature dependence. 4 The calculated (IV, PV) curves based on proposed model are in good agreement with the experimental data at different manufacturer models shell SP75 model (monocrystalline silicon and shell KC200GT model multicrystal).
5 The calculated (IV, PV) curves based on proposed model are in good agreement with the experimental data for different effects of the environment (temperature and irradiance).
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