# Matlab Based Empirical Model of PV System

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#### Matlab Based Empirical Model of PV System

JITENDRA BIKANERIA

Lecturer

Government Polytechnic College, Rajsamand jitendra.bikaneria@gmail.com

ANIL VERMA

Lecturer

Government Polytechnic College, Bhilwara verma_25dec@yahoo.co.in

#### Abstract The basic one diode & two diode model of photovoltaic has too many parameters. Evaluating values of some parameter are very difficult. This paper proposes general and specific modelling and simulation for empirical model of solar / PV cell. Studies and draw various characteristics of Photovoltaic cell as a function of temperature. The PV module is represented by the empirical model. The P-V & I-V characteristics are obtained and studied at different irradiances & temperatures. Developed model is validating by the comparison of the executed characteristics with one given by the manufacturer of PV cells. Proposed model can be extended to draw photovoltaic cell characteristics at any temperature & irradiance.

KeywordsSolar cell, PV cell, Empirical, Simulation, BPSX150.

parameters are not provided by the solar cell manufacturer & that cant easily determined by developer.

PV / solar cell manufacturers provided specification sheets include I-V curve at standard reporting conditions (SRC) or other sets of operating conditions. Manufacturers of solar cell provide some parameters on their specification sheet such as short circuit current, open circuit voltage, current at maximum power & voltage at maximum power rather than variable data used to plot characteristics curve. So our research is based to develop a model which can generate characteristic curve with manufacturers provided data sheets.

1. INTRODUCTION

The most of conventional fuel sources are used for power generation & they will be lost in future. Now the entire researcher going to work on the renewable energy conversion for meeting power demands. One of this renewable energy source photovoltaic cell is most common in uses which convert solar energy into electrical energy. The solar / PV cell is used as main power source where the transmission of electrical power is not possible or difficult

2. EMPIRICAL MODEL OF SOLAR CELL

One diode & two diode model required too many input parameters. Some parameters are known & remaining are physical constants. The empirical model is developed to simulate PV / solar cell with manufacturers provided four parameters such as short circuit current Isc, open circuit voltage Voc, current at maximum power Imp & voltage at maximum power Vmp without requirement of additional data input. The proposed model generating P-V & I-V curves by following equation:

like remote or rural area, space etc. Many PV models are

I = I

exp(

developed & PV simulation program are written in last few

sc 1

2

)[exp

2

1] …………………(5)

decades. Those model treats solar cell as an irradiance dependent current source connected in circuit. This model has four parameters & given by:

Model equation constant are denoted by C1 & C2. This model shows that required PV/solar cell module voltage is zero when current equal to Isc. Now we can determine C1 &

I = IL

I0

exp q

kTc

(V + IRs ) 1

C2 for zero current i.e. V= Voc. Equation (5) becomes

…………………(1)

0 = Isc 1[1 exp ] …………………….(6)

2

Where: – Dimensionless diode curve-fitting factor.

Rewrite the Equation (6)

I0- Reverse saturation current. q- Electrical charge.

1

= Isc

[1exp 2 ]

……………………(7)

k- Boltzmann constant.

Tc-Temperature in 0kelvin.

A new modification to this model made by connecting a

Dimensional analysis of equation (7) shows that C1 & C2 has units of current & voltage respectively. At a point maximum power current Imp & maximum power voltage Vmp, equation (5) reduces to:

shunt resistor Rsh parallel to the previously connected diode. This five parameter model developed by Lehman & Chamerlin & given by:

= Isc 1exp(

2

)[exp

1] ………(8)

2

I = I

I exp q

V + IR 1 V+IRs …………..(2)

Rewrite the Equation (8)

Isc I

L 0 kTc s

1 =

[exp

]

…………………(9)

This model has major limitations due to its parameter dependencies like Rs, Rsh, I0, IL & . These above mentioned

2 1][exp 2

It is difficult to determine C1 & C2 by analytical solution of equation (5) & (7). With the help of some product parameter (Isc, Vsc, Imp & Vmp) we can easily solve these two equations by graphical method for constant C1 & C2 where

the solution is intersection point of both two curves. We can find C1 & C2 by another way with following assumptions:

1. Assuming that Voc / C2>>1, we find that equation (7) reduces to

1 ………………..(10)

2. Assuming that Vmp/C2>>1, we find that equation (8) reduces to

Isc 1exp(

2

) …………………..(11)

Rearranging terms, we obtain

1

= Isc I

exp

2

……………………..(12)

Fig.2: Standard I-V characteristic of BPSX150 solar cell

Now substituting equation (10) into (11) & Rearranging terms, we obtain:

3. SIMULATION RESULTS

Isc I

For simulation result the empirical model of solar cell is

= exp

2

……………………..(13)

implemented in Matlab/Simulink. We use the BPSX150

After solving above equation we get

PV module. The electrical parameter for BPSX150 PV module is given by:-

2

=

ln 1

……………………..(14)

Maximum power (P

max

) =150W

The assumptions taken are valid when they fulfill equation

(10) & (12) that is approx to solution of equation (7) & (9). Plotting curve of equations (10) & (12) with equation (7) & (9). The graph shows that the solution of this two sets of equations intersecting at the same point. Thus, the assumptions cannot affect the values of C1 & C2.

Fig. 1: Characteristics behavior of C1 & C2

Voltage at Pmax (Vmp) = 34.5V

Current at Pmax (Imp) = 4.35A Warranted minimum Pmax =140W Short-circuit current (Isc) = 4.75A Open-circuit voltage (Voc) = 43.5V Maximum system voltage = 600V NOCT = 47Â±2Â°C

After the simulation process we get following characteristics:

Fig. 3: P-V characteristics for temperature 250C

Fig. 4: I-V characteristics for temperature 250C

Fig. 5: P-V characteristics for various conditions of solar radiation

Fig. 6: I-V characteristics for various conditions of

Fig. 7: P-V characteristics for temperature variation from 00C to 750C

Fig. 8: P-V characteristics for temperature variation from 00C to 750C

4. CONCLUSION

The behavior of empirical model of solar cell BPSX150 is studied in this paper. The various characteristics are drawn depending upon factors such as temperature dependence & solar radiation changes with help of the manufacturers provided data. Especially this empirical model is to be compared with tandard curve thats available on manufacturers website & found both curve matched to each other. This model is suitable to find the characteristics behavior of any solar cell with manufacturers provided data without internal knowledge of PV / solar cell.

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