Evaluation of a PV Model Based on a Novel Parameter Estimation Procedure for Different Manufacturers Modules

Evaluation of a PV Model Based on a Novel Parameter Estimation Procedure for Different Manufacturers Modules

Mohamed Abd-El-Hakeem Mohamed,

Faculty of Engineering, Electric Eng., Al-Azhar 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 current-voltage characteristics of a photovoltaic (PV) system. The proposed procedure is used the Newton-Raphson 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 Newton-Raphsons 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 I-V 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/m², Tref=25 °C, spectrum AM1.5).

Io – Dark saturation current in STC. Rsh- Panel parallel (shunt) resistance. Isc – Short-circuit 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 open-circuit voltage.

q- Electron charge.

ns – Number of cells in series.

Iph – the photo-generated current in STC. Rs – Panel series resistance.

A – Diode quality (ideality) factor. Voc -Open-circuit voltage in STC. Impp – Current at the MPP in STC.

Ki- Temperature coefficient of the short-circuit 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., Al-Azhar University, Qena, Egypt.

1. 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 I-V curve or other characteristic of the panel [5-8]. Charles et al. [5] have suggested a method that analyzes the practical I-V measurements. The different mathematical methods have been presented in order to estimate the parameters of the four parameters PV model and to simulate its current-voltage 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 I-V curve is presented in paper [7]. El Tayyan [8] has proposed the new equation is that one doesnt rely on the experimental I-V curve to determine Rsh.

   Many investigations were reported above, about estimation for a model of photovoltaic panels using the Newton-Raphson 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 Newton-Raphsons 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 I-V 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 Newton-Raphson based on simplified method.

   In this paper the construction of a model for a PV panel using the single-diode five-parameter model, based exclusively on data-sheet parameters. The parameters of a PV system are calculated by using the Newton-Raphson 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 I-V curve to determine Rsh. In this work the temperature dependence of the cell dark saturation current is taken into consideration.

2. Equivalent circuit of the solar cell

   without any measurement, using only the data from the product data-sheet.

   1. Starting equations

      Equation (1) can be written for the three key-points of the V-I characteristic: the short-circuit point, the maximum power point and the open-circuit point.

      Mathematical descriptions of the I-V characteristics of PV cells are available since many years and are

      =

      (3)

      derived from the physics of the p-n semiconductor junction.A crystalline solar cell is, in principle, a

      =

      +

      +

      (4)

      large-area silicon diode. In the dark state, the I-V characteristic curve of this diode corresponds to the one of a normal p-n 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 p-n junction diode. The simplest equivalent

      The above parameters are normally provided by the data-sheet of the panel. An additional equation can be derived using the fact that is on the P-V 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 P-I characteristics of a PV system at the maximum power point, the derivative of power with respect to current is zero [8].

      = = 0

      (7)

      =

   2. Parameter extraction

      From the expression of the current at short-circuit and open-circuit conditions, the photo-generated 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 current-voltage 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

3. 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 above-mentioned single-diode 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 Newton-Raphson 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.

   1. 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 Newton-Raphson method. To apply the Newton-Raphson 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)

4. 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 Newton-Raphsons 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 data-sheet. The temperature dependencies of the

models V-I 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=60°C

R(0)

2

2 2

f (0)

2.5

T=40°C

s

A

R Rsh

2

3

Rsh

(0)

(0)

s

(0)

(0)

f

(0)

2

1.5

T=20°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. Voltage-Current characteristics of the

shell SP75 model (mono-crystalline 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=75°C

Rsh( k 1)

Rsh( k )

Rsh( k ) 5

T=50°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=25°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. Voltage-Current 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 short-circuit current, and the open-circuit voltage are in very good agreement with the data-sheet values for SP75 (mono-crystalline silicon) solar module and KC200GT (multicrystal) solar module. The change in the open-circuit voltage and short-circuit current are in accordance with the temperature coefficients given in

the data-sheet.

To show the effect of irradiance on the performance of a module the temperature is kept fixed at25 °C and the values of irradiance are changed to different values. The variation of the current-voltage 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=60°C

2.5

2

1.5

1

0.5

G= 400 W/m2

Calculated data Experimental data

40 T=40°C

30 T=20°C

20

0

0 5 10 15 20 25

voltage(V)

Figure. 6.Voltage-Current characteristics of the shell SP75 model (mono-crystalline 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 (mono-crystalline 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=75°C

T=50°C

T=25°C

2 Calculated data

Experimental data

1

0

0 5 10 15 20 25 30 35

voltage(V)

Figure. 7.Voltage-Current 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.Voltage-Power 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 (P-V) 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 open-circuit voltage, which increases logarithmically with the irradiation. Figures (6, 7) show that, the calculated (I-V) 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 P-V characteristic, and the experimental characteristic . Also, it can be seen that the calculated (P-V) 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 (mono-crystalline 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 Newton-Raphson 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 I-V 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:-

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

2. The proposed equations which are expressed in a PV system, allow one to calculate the parameters PV system without relying on the experimental I-V curve to

   0 5 10 15 20 25 30 35

   voltage(V)

   Figure. 9.Voltage-Power characteristics of the KC200GT model (multicrystal) at different irradiation and standard temperature.

   determine Rsh.

3. 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 (I-V, P-V) curves based on proposed model are in good agreement with the experimental data at different manufacturer models shell SP75 model (mono-crystalline silicon and shell KC200GT model multicrystal).

5- The calculated (I-V, P-V) 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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   Industry Applications (INDUSCON), IEEE/IAS International Conference, 2010, PP.1-5.

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