2012 International Conference on Computing, Electronics and Electrical Technologies [ICCEET]

DEVELOPMENT OF MATLAB

SIMULINK MODEL FOR

PHOTOVOLTAIC ARRAYS

Jenifer .AI Newlin Nishia.R2 Rohini.G3 Jamuna. V'

Department of Electrical and Electronics Engineering, Jerusalem College of Engineering, Centre for collaborative research with Anna University, Velachery main road, Pallikkaranai, Chennai-600 100, India.

Email: jeniinbox@gmail.com, newlinnishia@yahoo.co.in

Abstract: This paper presents the mathematical

model for a photovoltaic array. It has been

developed with the help of Matlab/Simulink

software package. Since the PV module has non

linear characteristics, it is necessary to model it

for the design and simulation of maximum power

point tracking (MPPT) for PV system

applications, and to study the dynamic analysis

of converters. This model of photovoltaic array is

user-friendly. The developed model is simulated

and analyzed in conjunction with power

electronics, for a maximum power point tracker.

The parameters of the photovoltaic array model

are obtained from the information available in

the datasheet. The same is also explained in this

paper.

Keywords- photovoltaic array, equivalent model,

modeling , MAT LAB ISIMULINK

I.INTRODUCTION

In recent years, renewable sources such as solar, wave and wind are being used for the generation of electricity. Photovoltaic (PV) generation is getting increasingly important as a renewable source due to the advantages such as the absence of fuel cost, little maintenance and no noise and wear due to the absence of moving parts. With the development of solar cell technology, the price of solar modules has dropped dramatically. A recent worldwide survey shows that in the last three years, the retail price of solar modules has dropped by 16.95%. Solar cells can convert the energy of sunlight directly into electricity. The basic device of a photovoltaic system is the photovoltaic cell. Cells may be grouped to form panels or modules. Panels can be grouped to form large photovoltaic arrays. The term array is usually employed to describe a photovoltaic panel (with several cells connected in series andlor parallel) or a group of panels. Most of the time one are interested in modeling photovoltaic panels, which are

978-1-4673-0210-4112/$31.00 ©2012 IEEE 436

commercial photovoltaic devices. This paper focuses on modeling photovoltaic modules or panels composed of several basic cells. The term array, used henceforth, means any photovoltaic device composed of several basic cells[1]-[2] . Figure 1 shows the development of a PV panel from a cell. PV module represents the fundamental power conversion unit of a PV generator system. The output characteristics of a PV module depend on the solar insolation (incoming solar radiation), the cell temperature, and the output voltage of the PV module. The main contribution of this paper is the development of a PV model using MA TLAB ISIMULINK. The developed model is simulated and analyzed in conjunction with power electronics for a maximum power point tracker.

Figure 1 Photovoltaic cells, modules, panels, and array

II.PHOTOVOL TAlC MODELS

A solar cell or photovoltaic (PV) cell is a device that converts solar energy into electricity by the photovoltaic effect. A majority of the solar cells produced, are composed of Silicon (Si) which exists in sufficient quantities, and does not harm the environment.

2012 International Conference on Computing, Electronics and Electrical Technologies [ICCEET]

The doping technique is used to obtain a surplus of positi ve charge carriers (p-type) or negative carriers (n-type). When two layers of different doping are in contact, then a p-n junction is formed on the boundary. An internal electric field is built up, which then causes the separation of the charge carriers released by light. Light is composed of small packets called photons. When these photons bombard, many electrons are freed within the electric field proximity, which then pulls the electrons from the p-side to n­side. Through metal contacts, an electric charge can be taped. If the outer circuit is closed, then direct current flows as illustrated in Figure 2.

Figure 2 Operation of a PV cell

Each of these cells produces around 0.5V (for Silicon). The voltage across a solar cell is primarily dependent on the design and materials of the cell, while the electrical current depends primarily on the incident solar irradiance and the cell area.

A.Ideal photovoltaic cell

The use of equivalent electric circuits makes it

possible to model the characteristics of a PV cell. The

mathematical model for a photovoltaic cell can be

developed, using the MA TLAB package. The basic

equation from the theory of semiconductors that

mathematically describes the I-V characteristic of the

ideal photovoltaic cell is

(1)

Where, Id=lo.cell[exp(qV/akt)-l] (2)

1=lpv,cell- 10.cell[exp(qV/akt)-1] (3)

Where, Ipv.cell is the current generated by the incident light(it is directly proportional to the sun irradiation), Id is the diode equation, 10,cell is the reverse saturation or leakage current of the diode , q is the electron charge [1.60217646· 10-19C], k is the Boltzmann

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constant [1.3806503 10-23J/K], T is the temperature of the p-n junction, and 'a' is the diode ideality constant. Figure 3 shows the equivalent circuit of ideal PV cell.

ideal PV cell J ---------- ---- --- ------, , -

,

I,. �L-----+¥-P d ---7-1 _

v

, , 1-________________________ •

Figure 3 Ideal PV equivalent circuit

B. Modeling the photovoltaic array

The same technique is extended for developing the mathematical model of a PV module. Practical arrays are composed of several connected PV cells, and the observation of the characteristics at the terminals of the PV array, requires the inclusion of additional parameters (as shown in figure 4) to the basic equation:

Where 11;, = NskT<lq is the thermal voltage of the array with Ns cells connected in series. Cells connected in parallel increase the current and cells connected in series provide greater output voltages. V, I are the terminal voltage and current.

practical PV device ,-------------------------------------------------------, , I , , , , , , , , , , , , , , , , I ,

ideal PV cell :-------------------------1 I ' , ,

i Ipv t , , , , , I

, L ________________________ _

I -+

If

'---------------------------------------------------------

Figure 4 Equivalent circuit of a practical photovoltaic device including the series and parallel resistances

For a good solar cell, the series resistance, R" should be very small and the shunt (parallel) resistance, Rp, should be very large. For commercial solar cells, Rp is much greater than the forward resistance of a diode. The I-V curve is shown in Figure 5. The curve has three important points namely, open circuit voltage (V oc), short circu it current (lsc) and maximum power point. In this model single diode is considered. The J-V characteristic of the photovoltaic device shown in Figure 5 depends on the internal

2012 International Conference on Computing, Electronics and Electrical Technologies [ICCEET]

characteristics of the device and on external influences such as the irradiation level and temperature.

I (rnA)

Isc Illumination

Figure 5 I-V characteristics of a PV cell

V (Volt)

This model offers simplicity and accuracy, with the basic structure composed of a current source and a parallel diode. The simplicity of the single-diode model, with its flexibility of adjusting the parameters and scope for improving makes this model perfect for the simulation of photo voltaic devices with power converters. Manufacturers's data sheets, provide data like the nominal open-circuit voltage �c'n' the nominal short­circuit current ISC'n, the voltage at the maximum power point V;np, the current at the maximum power point Imp, the open-circuit voltage/temperature coefficient K v , the short-circuit current/temperature coefficient KJ , and the maximum experimental peak output power �nax[> Details like the light-generated current, the series and shunt resistances, the diode ideality constant, the diode reverse saturation current, and the bandgap energy of the semiconductor with reference to the nominal or standard test conditions (STC) of temperature and solar irradiation will not be provided by the manufacturer in the datasheets.

The light generated current will be equal to Isc but in this model it is determined by

(5)

Where Ipv.n is the light-generated current at the nominal condition (usually 25 °C and 1000W/m\LlT=T-Tn (being T and Tn the actual and nominal temperatures [K]), G [W/m2] is the irradiation on the device surface, and Gn is the nominal irradiation. The value of Ipv is chosen from

(6)

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The diode saturation current can be determined by

(7)

VI,n being the thermal voltage of Ns series-connected cells at the nominal temperature Tn. The value of the diode constant 'a' may be arbitrarily chosen. Usually 1 :S a :S 1.5 and the choice depends on other parameters of the I-V model. The values of Rp and Rs are selected such that Rs is chosen iteratively by starting from zero, and Rp by

III. SIMULATION OF THE PHOTO VOLTAIC ARRAY

The simulations are carried out using MA T ALB/SIMULINK package. The developed mathematical model of the PV array is used for the simulation studies. Various parameters of the PV array are determined and chosen. For the simulation work, we consider the solar panel model ND-1240Q2. The specifications of the panel ND-1240Q2 are given in Table1.

Table I Specifications of solar panel ND-1240Q2

Open circuit voltage Voe 37.5V

Short circuit current Ise 8.61A

Maximwn output power 240W

Voltage at maximum power 30.2V

Current at maximum power 7.95A

A. Selection of Rs and Rp

Rs is iteratively chosen by incrementing the values from O. Rp is chosen based on equation 8.Decreasing Rp too much will lead V oe to drop, and increasing Rs too much will lead Ise to drop.

B. Calculation of Io

2012 International Conference on Computing, Electronics and Electrical Technologies [ICCEET]

10 depends strongly on the temperature hence, the simulation circuit of 10 includes Kv and Ki which are the voltage and current coefficients

10=(lsc,n+kl� T)/exp[(Voc,n+Ki� T)/aVtl-l (9)

Based on equation 9 10 is calculated.

C. Calculation of Ipv

The light generated by the incident light is simulated according to equation 5 where in Ipv,n is calculated from equation 7.

D. Equivalent model

The light generated by the PV is modeled as an equivalent current source. The series and parallel resistances are connected and simulated. The various equations describing the PV array characteristics are modeled using suitable mathematical blocks from the simulink library. The simulink model is shown in Figure 6.This simulation is done for the standard test condition (STC) i.e. temperature is 25°C and Irradiation is 1000 W/m2•

1T��r� ' �,. � . . ' g l

Inputs:

B-------+G Tempasture

[I<)

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Figure 6 Photovoltaic circuit model built with MA TLAB/SIMULINK

The PV array is modeled separately and put in a MA TLAB subsystem, which contains all the equations required for modeling a PV array. This subsystem is integrated with the PV array which replaces the constant DC voltage source of the chopper. Figure 7 shows the integrated PV array with the boost converter.

•

Figure 7 Integrated PV array - boost converter circuit

IV.RESULTS AND DISCUSSION

The I-V and P-V characteristic curves of the simulated model for 800 W/m2 and 25°C are shown in Figure 8a and 8b. The simulated I-V, P-V curves at different insolation levels are shown in Figures 8, 9 and lO.The graph in Figure 8 represents the behavior of a solar cell at particular intensities of solar radiation. The point at which a curve intersects the

2012 International Conference on Computing, Electronics and Electrical Technologies [ICCEET]

vertical axis is known as the short circuit condition. It defmes how the cell operates if a wire is connected between its terminals, shorting it out. The current flow here is known as Isc. Because there is no voltage, the cell delivers no power.

;.... v :::: 0 p.

40 n------.------.------..-----� 35 30 25 20 15 10

300

250

200

150

100

50

0 0

10 20

Figure 8(a)

10 20

Figure 8(b)

30

voltage

30 40 voltage

Figure 8(a) P-Y curve 8(b) I-Y curve

40

50

The point at which a curve intersects the horizontal axis, is where the cell operates if it is unconnected. This is known as the open circuit condition, and the voltage produced is denoted as Yoc. Because the current is zero, no power is delivered.

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Current - Voltage Curve

'\ ........ \

\\ ,,\ -�:l000w/sqJn

\ \

-sj:800w/5Q.m -5l:600w/sq.m

M 15 20 25 � 35 � �

Modu!t:Voltagt

Figure 9 P-Y curves at different insolation levels

For every point on the graph, the voltage and current can be mUltiplied to calculate the power. If this power output curve is plotted on the original graph for full sunlight, the power-voltage curves can be obtained as shown in FigurelO.

Power - Voltage Curve 300 ,---------------------------

150 1--------------------------

100 I--------------r-----+-----

j � 150 r----------/---,''--------+l-----i

-sj:1000w/;,q.m

-sj:800w/sq.m

100 1-------/--r----oI''''--------\-tt---- -sj:600w/sq.m

50 r-�r7L-------------�r_--

10 15 m 25 W 35 W 45

ModuleVoltagt

Figure 10 P-Y curves at different insolation levels

The power is maximum at a single operating point. This is known as the "Maximum Power Point", or MPP. If one is to get the most out of the solar cells, it is essential to operate around the MPP. The quality of a PV cell is often rated with a characteristic, called its "Fill Factor". This is defmed as the maximum power produced (at MPP), divided by the product of Isc and Voc' The fill factor will always be less than 1. The boost converter output voltage at the STC is shown in Figure 11.

2012 International Conference on Computing, Electronics and Electrical Technologies [ICCEET]

Figure 11 Boost converter output voltage at STC

V.CONCLUSION

This paper has dealt with the development of a mathematical model for photovoltaic arrays, using the MA TLAB package. The objective of the method is to fit the mathematical J-V equation to the experimental remarkable points of the J-V curve of the practical array. This method is simple, and the same model can be developed for Ns x Np number of cells. The developed model can be used for power electronic applications.

VI.REFERENCES

[1] Muhammad H. Rashid, "Power Electronics Handbook Circuits, Devices, And Applications« ,Second Edition. [2] G. N. Tiwari and Swapnil Dubey, "Fundamentals of Photovoltaic Modules and Their Applications" RSC Energy Series No. 2. [3]J.A. Gow and C.D.Manning "Development of a model for photovoltaic arrays suitable for use in simulation studies of solar energy conversion systems'Power Electronics and Variable Speed Drives, Conference Publication No. 429. [4]www.sharpusa.com/solar [5] H. Patel and V. Agarwal. MA TLAB-based modeling to study the effects of partial shading on PV array characteristics.lEEE Transactions on

Energy Conversion, 23(1):302-310, 2008. [6] Weidong Xiao, W. G. Dunford, and A. Capel. A novel modeling method for photovoltaic cells. In Proc. IEEE 35th Annual Power Electronics

Specialists Conference, PESC, v. 3, p. 1950-1956, 2004. [7] Y. Yusof, S. H. Sayuti, M. Abdul Latif, and M. Z. C.Wanik. Modeling and simulation of maximum power point tracker for photo voltaic system. In Proc.

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National Power and Energy Conference, PECon, p. 88-93, 2004. [8] D. Sera, R. Teodorescu, and P. Rodriguez. PV panel model based on datasheet values. In Proc.

IEEE International Symposium on Industrial

Electronics, ISlE, p.2392-2396, 2007. [9]A. Kajihara and A. T. Harakawa. Model of photovoltaic cell circuits under partial shading. In Proc. IEEE International Conference on Industrial

Technology, ICIT, p. 866-870, 2005. [10] N. D. Benavides and P. L. Chapman. Modeling the effect of voltage ripple on the power output of photovoltaic modules. IEEE Transactions on

Industrial Electronics, 55(7):2638-2643, 2008. [11] W. De Soto, S. A. Klein, and W. A. Beckman. Improvement and validation of a model for photovoltaic array performance. Solar Energy,

80(1):78-88, January 2006. [12]France Lasnier and Tony Gan Ang. Photovoltaic

engineering handbook. Adam Hilger, 1990. [13] K. Khouzam, C. Khoon Ly, C.and Koh, and Poo Yong Ng. Simulation and real-time modelling of space photovoltaic systems. In IEEE 1st World

Conference on Photovoltaic Energy Conversion,

Conference Record of the 24th IEEE Photovoltaic

Specialists Conference, v. 2, p. 2038-2041, 1994. [14] M. C. Glass. Improved solar array power point model with SPICE realization. In Proc. 31st

Intersociety Energy Conversion Engineering

Conference, IECEC, v. 1, p. 286-291, August 1996

Jenifer.A is currently pursuing her M.E(power electronics and drives) in Jerusalem college of engineering, Anna university, Chennai. She has completed her B.E in Electrical and Electronics engineering in the year 2010 in Tagore Engineering college, Anna university Chennai.

Newlin Nishia.R is currently pursuing her M.E(power electronics and drives) in Jerusalem college of engineering, Anna university, Chennai. She has completed her B.E in Electricaland Electronics

engineering in the year 2010 in Tagore Engineering college, Anna university , Chennai.

2012 International Conference on Computing, Electronics and Electrical Technologies [ICCEET]

G.Rohini is Assistant Professor in Electrical and Electronics Engineering Department, Jerusalem College of Engineering, Chennai, India. She received her B.E. degree in Electrical & Electronics Engineering from IR TT Erode.

M.E. degree in Power Electronics and Drives from CEG Anna University, Chennai, and currently pursuing her ph.D. She has more than 10 years of teaching experience.

V.Jamuna is Associate Professor in Electrical and Electronics Engineering Department, Jerusalem College of Engineering, Chennai, India. She received her B.E. degree in Electrical & Electronics Engineering from St.Peter's Engineering

College, Madras University, Chennai, India in 1999, M.E. degree in Power Electronics and Drives from Anna University, Chennai, India in 2005, Ph.D from Anna university in 2010. She has secured fifth university rank in her P.G degree. She has 12 years of teaching experience. She has published over 15 technical papers in national and international conferences proceedings / journals. She is life member of Indian Society for Technical Education. She is a member of Institution of Electrical and Electronics Engineers. Her research interests include Induction Motor Drives and Neural Network controller for drives.

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