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3rd International Conference on Energy Systems and Technologies 16 – 19 Feb. 2015, Cairo, Egypt

DEDUCTION OF TWO-DIODE MODEL PARAMETERS FOR PHOTOVOLTAIC SYSTEM

Adel A. Elbaset1, Hamdi Ali2, Montaser Abd-El Sattar2

(1)Department of Electrical Engineering, Minia University, El-Minia, 61517, Egypt

E-mail: Adel.Soliman@mu.edu.eg (2)Department of Electrical and Computer Engineering, El-Minia High Institute

for Engineering and Technology, El-Minia, Egypt E-mail: hamdihesha@yahoo.com, mymn2013@yahoo.com

The paper presents a proposed two-diode model for PV module to describe I-V and P-V characteristic curves at different weather conditions such as, temperature and solar radiation. Two two-diode model parameters are estimated using Newton-Raphson method with the aid of initial values which are derived from basic equations of an equivalent circuit for two-diode model and manufacturing data sheet at standard test conditions. The two-diode model parameter represent an important role in design, manufacturing and performance of PV system at different weather conditions especially at low radiation. Newton-Raphson method is used to describe non-linear output characteristic curves of I-V and P-V. The proposed two-diode model is validated for multi-crystalline solar cell PV modules. Results are compared with the manufacturer’s data sheet curves and the proposed results of other published research works. The results of proposed model are validated with an excellent manner with respect to data sheet and other published research works. Keywords: PV modules, Seven-parameter model, Two-diode model, Single diode model.

1. INTRODUCTION

Nowadays, solar photovoltaic systems become popular and have many applications in the world that extended from remote area energy services, house appliances up to grid utilities. The rapid growth of PV system utilizations is due to many benefits and advantages such as availability everywhere which reduces costs and losses, free, abundant, and pollution free. It also represents the most important available renewable energy resources due to its permanent energy source in everywhere of the world to generate electricity on site where it is needed, which reducing CO2 emission in environment. Silicon is the basic material required for the production of solar cells based on crystalline technology. Most of solar cells are based on multi-crystalline silicon technology due to their reliability and high efficiency for manufacturing PV solar modules [1-3].

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The PV system operation depends on many physical parameters like site latitude of PV systems, weather conditions, the panel tilt and its azimuth angles, the air and surfaces surrounding temperatures and finally electrical loads. Although PV systems have many advantageous, but unfortunately, they suffered from changing of system performance due to weather variations, high cost installation and low efficiency that is hardly reached up to 20% for module. Therefore, the modeling of PV system becomes important in design, manufacturing, and operation of the PV based power systems to obtain optimization performance from such system [4-8].

PV cell is the main building block of PV module which represents the main unit of electrical solar power generation system. The PV module consists of many PV cells connected in series/ parallel manner for each module to produce I-V and P-V curves. These characteristic curves depend mainly on weather conditions such as solar radiation and cell temperature. So, it is important to model a PV module to obtain accurate manufacturing, operation, and discovering the causes of degradation of PV performance. The PV system modeling should fulfill the following criteria [9-11]:

1- It should be simple and fast. 2- It should be predicted the I-V and P-V characteristic curves with accurate manner. 3- It should be developed and has a comprehensive tool. 4- It should be validated PV system manufacturing data sheet.

Ref. [1] described an improved five-parameter which are Rs, Rsh, a, Iph and Is for single diode model that is capable of analytically describing the I-V characteristic curves of a PV module for each generic condition of operative temperature and solar radiation. The parameters of the equivalent electrical circuit parameters are solved by a system equations based on data commonly issued by manufacturers in standard test conditions with a trial and error process. Ref. [5] estimated the solar cell parameters of single diode model using the hybrid genetic algorithm and Nelder-Mead simplex search method from the given voltage - current data. Ref. [6] implemented a generalized PV model based on single diode model using Matlab/Simulink software package for PV cell, module, and array. Ref. [8] proposed a PV single diode model by Hybrid Genetic Algorithm and Particle Swarm Optimization techniques. Refs. [11-20] proposed several computational methods with different techniques for single diode model, but most of these techniques required new additional coefficients into the model equations causing increase of their computational burdens. The equivalent electric circuit of PV cell is represented by Wolf which is composed of many lumped elements such as a current source, a diode and a series resistance for each cell [21]. Wolf modeling has been simplified to a single diode model as shown in Fig. 1. The general characteristic equation of a single diode model is given as [1,6,17,25].

Figure 1. Single diode circuit model of PV cell.

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The photo current is a function of temperature and solar radiation is given as follows [6,15]:

The single diode saturation current as function of working PV temperature is given as follows [6,15]:

Although single diode is more popular for PV modeling, but it has many disadvantageous such as [22]: 1- It exhibits high deficiencies when studying PV performance with temperature

variations. 2- It neglects recombination loss in PV cell depletion region. 3- Deterioration its accuracy at low radiation levels especially at open circuit .

The single diode model was based on the assumption that the recombination loss in the depletion region is absent. In a real solar cell, the recombination represents a substantial loss, which cannot be adequately modeled using a single diode. Consideration of this loss leads to a more precise model known as the two-diode model [23]. However, the inclusion of the additional diode increases the PV model parameters to seven-parameter (new parameters: , a2). Also, the two-diode model is proposed to improve the accuracy of PV module and to overcome the disadvantageous of single diode model. The main purpose now is to estimate the values of all the model parameters within a reasonable simulation time [22-27]. Ref. [22] employed a Matlab / Simulink to simulate a PV system with a two-diode model. The inputs to the simulator are information available on standard PV module datasheets. Ref. [23] estimates four-parameter of two-diode model which are short-circuit current (Isc), saturation current (Is), the series resistance, Rs and the parallel resistance, Rsh. The three other parameters of such model were simplified to Is1 = Is2 = Is and arbitrarily chosen ideality factors of diodes a1 and a2.

There were many mathematical techniques of the two-diode model in Refs. [22-27] such as, the Levenberg / Merquardt technique, an equivalent thevenin circuit technique to estimate the model parameters, and finally, the simplification technique of the two-diode current equations using iteration method. However, in all these techniques many new additional coefficients are introduced into the equations and difficulty arises in determining the initial values of the parameters. These cited methods are very sensitive to the initial conditions and, if not properly guided by an initial estimation of the parameters, lead to inconsistent results.

This paper proposed a novel seven-parameter model for PV modules to predict I-V and P-V characteristic curves based on three main points such as open circuit, maximum power and short circuit at STC which lead to accurate results. The proposed model is based on:

1- Basic equations of two-diode model and data sheets of the PV manufacturing. 2- Newton-Raphson method for estimated the seven-parameter.

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2. METHODOLOGY

The two-diode equivalent circuits based model are shown in Figs. 2 and 3 [6], for cells and modules. The equivalent circuit of the module consists of series and parallel cells with and respectively.

Figure 2. Two-diode circuit model of PV cell model.

Figure 3. Equivalent circuit model of generalized PV.

The general equation of two-diode model is given by [25]:

The seven-parameter respectively known as follow, photo current , saturation currents of two diodes series and shunt resistances and , and ideality factors of two diodes and . These seven-parameter can be arranged respectively in the following matrix form [24,28]:

The photo current is a function of temperature and solar radiation is expressed as follows [6,22]:

The two-diode saturation currents as function of working PV temperature are written as follow [6,22]:

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The current equation of module is given as [6,22]:

where:

Ns: is the number of series cells. Np: is the number of parallel cells. The derivative of output current with respect to cell voltage is given from Eq. (4) as:

To determine seven-parameter, it needs seven-equation that will be solved

simultaneously using Newton-Raphson method. The seven-equation are derived as follow:

The first equation is obtained from open circuit condition, then I=0, V=Voc and Eq. (4) becomes as:

The second equation is given from short circuit condition, then V=0, I=Isc and Eq. (4)

expressed as:

The third equation is obtained from the maximum power and Eq. (4) rewritten as:

Moreover the 4th, 5th and 6th equations are deduced from current derivative

equation at open circuit, short circuit, and maximum power points in data sheet of PV module as follow:

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where: at open circuit where and at STC.

at short circuit where and at STC.

The 7th equation is obtained from diode ideality factors for which their summation is greater than or equal to three for all PV cell types. The ideality factors of two-diode model are given as follow [6,18,20]:

(18)

The particular solution is starting by choosing suitable initial values of two-diode ideality factors and . Choose the initial value of as a partial value from to satisfy the following equation:

where: is the fractional number and is given by

is the reciprocal slope of I-V curve of cell at open circuit voltage.

The equations of diffusion saturated current of diode, D1, and recombination saturated current of diode, D2, are derived from Eqs. (12-14) and (17) as follow:

where:

Finally, the diffusion saturated current of D1, and recombination saturated current of D2, are computed as follow:

The initial value of is derived from Eq. (17) as follow:

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The final initial value of photo current is estimated from Eq. (12).

3. NEWTON-RAPHSON METHOD [28-30]

3.1. Estimation of Seven-parameter

Newton-Raphson method is a numerical technique established using seven previous equations for estimation seven-parameter of two-diode model in the form of , where is array of the seven-parameter as in Eq.(5). and the Jacobian matrices

are derived from previous seven-equation as follow:

=

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The main steps of computer algorithm for estimation the PV model parameters as shown in flowchart of Fig. 4 are summarized as follow:

1- Computing the initial values of PV module parameters. 2- Forming both matrices and of PV system parameters. 3- Computing seven-parameter values using Newton-Raphson iteration method.

The iterative process is repeated up to the difference between and reaches an acceptably small value.

STCT ocV mpI mpVscI, ,, ,

≤

Figure 4. Flowchart for estimation PV module parameters using Newton-Raphson method

3.2. Establishing I-V and P-V Characteristic Curves

I-V and P-V characteristic curves are established the model parameters of Eqs. (4,9) using Newton-Raphson method.

where n denotes the nth iteration, and

The flowchart of computer program is shown in Fig. 5.

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phIsR1sI, ,, ,2sI shR , 1a 2a,

phI

≤

Figure 5. Flowchart for establishing I-V and P-V curves.

4. VERIFICATION AND RESULTS

4.1. Comparing Results with Manufacturing Data Sheet

The proposed two-diode model is validated by estimated parameters of multi-crystalline of two different modules, MSX-60 and KC-200GT which have data sheet as shown in Table 1. Table 2 shows the seven-parameter values of both MSX-60 and KC-200GT multi-crystalline modules as compared with the results of Ref. [22]. The results have reasonable values as compared with previous research work and the differences are due to assumption of = in Ref. [22].

Fig. 6 shows I-V and P-V characteristic curves of the proposed two-diode model using Newton-Raphson numerical iteration method as compared with data sheet at STC for previous two modules of multi-crystalline. This figure shows an excellent matching between manufacturer curves and computed results at STC. Tables 3-4 show matching points for short circuit current, open circuit voltage and maximum values for current, voltage and power. These tables show excellent results between data sheet and the proposed model. The percentage deviation between theses values are due to measuring process of manufacturer which normally has accuracy within determined range.

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Table 1. Data sheet parameters of multi-crystalline modules. Multi-Crystalline solar cells Data sheet

parameter Kyocera [22] KC-200GT

BP Solar [22] MSX-60

8.2100 3.8000 32.9000 21.1000 7.6100 3.5000 26.3000 17.1000

-123×10-3 -80×10-3 3.1800×10-3 3×10-3

54 36 1 1 Np

Table 2. MSX-60 and KC-200GT parameters as compared with results of reference [22].

Multi-Crystalline Kyocera KC-200GT

BP Solar MSX-60

Model parameter

Results of reference

[22]

Computed results using Newton-Raphson

method

Results of reference

[22]

Computed results using Newton-

Raphson method

8.2100 8.2237 3.8000 3.8084 4.2180×10-10 4.1437×10-10 4.7040×10-10 4.8723×10-10 4.2180×10-10 1.9032×10-6 4.7040×10-10 6.1528×10-10

0.3200 0.3305 0.3500 0.3692 160.5000 196.5000 176.4000 169.0471 1.0000 1.0003 1.0000 1.0003

≥1.2000 1.9997 ≥1.2000 1.9997

a) I-V curve b) P-V curve

Figure 6. Comparison between manufacturing data sheet and two-diode model using Newton-Raphson method.

0 5 10 15 20 25 30 350

1

2

3

4

5

6

7

8

9

PV voltage in volt

Cur

rent

[A

]

X: 26.1Y: 7.646

V = 21.06 V , I = 0 A

V = 0 V , I = 8.21 A

V = 0 V, I = 3.8 A

V = 26.1 V I = 7.646 A

V = 32.85 V I = 0 A

V = 17.1 V I = 3.493

X: 0Y: 8.21

X: 0Y: 3.8 X: 17.1

Y: 3.493

Solar KC-200GT module

Newton Raphson methodManufacturing data

Solar MSX-60 module

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Table 3. Matching points of data sheet and two-diode model for MSX-60 module.

Data sheet

parameter

BP Solar MSX-60 Data sheet measuring

results

Newton-Raphson results of Fig. 6

Percentage of deviation

, A 3.8000 3.8000 zero

21.1000 21.0600 -0.1896%

3.5000 3.4930 -0.2000%

17.1000 17.1000 zero

60.0000 59.7200 -0.4667%

Table 4. Matching Points of data sheet and two-diode model for KC-200GT module. Data sheet

parameter

Multi-Crystalline Kyocera KC-200GT Data sheet measuring

results

Newton-Raphson results of Fig. 6

Percentage of deviation

8.2100 8.2100 zero

32.9000 32.8500 -0.1520%

7.6100 7.6460 0.4731%

26.3000 26.1000 -0.7605%

200.0000 199.6000 -0.2000%

4.2 Comparing Results of MSX-60 Module with Single Diode Model

Fig. 7 shows computed curves of MSX-60 module as compared with single diode model of Ref. [18] at different radiation levels and constant temperature. Figs. 8 indicate computed curves of MSX-60 module at different temperatures and constant radiation as compared with manufacturing curves and a single diode model. From these figures, it can be seen that inaccuracies and inefficiencies of single diode as compared with two-diode results at different radiation and temperature levels.

a) I-V curve b) P-V curve

Figure 7. Comparing between single diode of reference [18] and calculated (new model) using

Newton-Raphson method at different radiation levels.

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a) I-V curve b) P-V curve

Figure 8. Comparing between single diode of reference [18] and calculated (new model) using Newton-Raphson method at various temperatures and 1000 W/m2.

4.3. Comparing Results of KC-200GT Module with Manufacturing Data Sheet

In Figs. 9-10, the I-V and P-V computed curves with seven-parameter are compared with the characteristic curves issued by manufacturer of KC-200GT module at different radiation and temperature levels. These figures indicate a good agreement between the provided and calculated data at different radiation and temperature levels especially at low radiation for Newton-Raphson method.

a) I-V curve b) P-V curve Figure 9. Comparing between calculated (new model) using Newton-Raphson method and manufacturing curves at different radiation levels and temperature 250 C.

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a) I-V curve b) P-V curve Figure 10. Comparing between calculated (new model) using Newton-Raphson method and

manufacturing curves at different temperatures and radiation 1000 W/m2.

CONCLUSION

An accurate two-diode model of PV module is proposed using Matlab software with the aid of Newton-Raphson method. The two-diode model uses only data commonly provided by manufacturers, which numerically solved exactly to determine I-V and P-V curves, for different radiation and temperature levels. The results obtained are in good agreement with those published previously. The accuracy of the proposed model is verified using practical data from various manufacturers of multi-crystalline two different PV modules. The results of two-diode model are compared to the popular single diode model results. It is deduced in all comparing that the proposed model is superior than single diode model when subjected to different radiation and temperature levels, particularly at lower radiation conditions. The proposed model is powerful and accurate for using solar PV modules. This paper gives an accurate representation of the I-V and P-V characteristic curves of PV module, which will serve as a proposed model for researches in the field of PV modeling.

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APPENDIX a diode ideality factor for single diode model a1,a2 diode ideality factors for two-diode model Rs series resistance (Ω) Rso reciprocal slope of the I-V characteristic for V=Voc and I=0, (Ω) Rsh shunt resistance (Ω) Rsho reciprocal slope of the I-V characteristic for V=0 and I=Isc , (Ω) VT thermal voltage (V) (VT = kT/q) G solar radiation (kW/m2) GSTC solar radiation at standard test conditions (STC)

[GSTC=1kW/m2] Iph at STC photo current at standard test conditions (A) Ki short circuit current coefficient (A/C°) TSTC temperature of PV cell at standard test conditions Eg band gap energy of semiconductor (eV) Ns number of series cells Np number of parallel cells X array of seven-parameter

fractional number

Nomenclature

PV Photovoltaic

I output or load current of PV model (A) V output or load voltage of PV model (V) Iph photo current (A) Imp current at the maximum power point (A) Isc short circuit current of the module (A) Vmp voltage at the maximum power point (V) Voc open circuit voltage of the module (V)

Is cell reverse saturation current (A) cell reverse saturation current (A) at standard test conditions (STC)

Is1 diffusion saturated current of D1 (A) Is2 recombination saturated current of D2 (A)

diffusion saturated current of D1 (A) at standard test conditions (STC) recombination saturated current of D2 (A) at

standard test conditions (STC) q electron charge (1.6 * 10-19C) k Boltzmann constant (1.38 * 10-23J/K) T cell working temperature (K)