Development Of A Solar Cell Model In Matlab For PV Based Generation System

G. Bhuvaneswari and R. Annamalai

Indian Institute of Technology Delhi, New Delhi, India

Abstract— Solar PV based electricity generation is gaining importance due to its abundant availability and improvements in materials and energy conversion technology. Global warming and fossil fuel depletion is indirectly catalyzing this transformation process. As the solar power conversion is already a low efficient conversion process, accurate and reliable modelling of solar cell is imperative to optimize the design of the solar PV system. Due to the non-linear nature of its characteristics, accurate modelling of a solar cell is still a difficult task. The existing models do suffer in a few issues while developing an integrated solar PV power conversion system. This paper compares two of the existing models for solar cell in MATLAB with a newly proposed model. To analyse and validate the results of the simulation models, I-V and P-V characteristics obtained from all the three models are compared with the experimental characteristics obtained from a 50W photovoltaic module. Finally relative merits and demerits of all the three models are discussed.

Keywords-component; Photovoltaic module, MATLAB/ SIMULINK, Solar cell modelling, Simulation, double exponential model, PV power generation

I. INTRODUCTION Energy is a basic necessity for human activity and for

economic and social development. Energy is a key driver for the betterment of human life. But due to growing population coupled with global warming and depleting fossil resources, mankind is in desperate need of alternative renewable energy technologies based on wind, solar energy etc. Further, factors like continuous technological advancements leading to reduced product costs, increase in the scale of production of renewable energy products, renewable energy friendly government policies are catalyzing the growth of renewable energy

Renewable energy resources such as wind, solar and micro-hydro for electricity production are being explored by various researchers as a way to limit the green-house gas emissions and to combat climate change and global warming menace. Energy from the sun is being utilized by mankind in different forms since time immemorial. However the growing need for sustainable development and concern for global warming has made us to relook at it with greater importance and real vigor.

Photovoltaic (PV) power generation is reliable, involves no moving parts and operation and maintenance costs are very low [1]. The PV cells/modules form the core of the solar PV power generation unit. A solar PV system uses solar cells to convert solar energy into electricity based on Photo Electric effect. PV systems directly convert solar energy into electricity. The basic

building block of a PV system is the PV cell, which is a semiconductor device that converts solar energy into direct-current (DC) electricity. PV cells are interconnected to form a PV module, typically rated up to 50-300 W. The PV modules combined with a set of additional application dependent system components form a complete PV system. PV systems are highly modular and these modules can be linked together to provide power ranging from a few watts to tens of megawatts.

The output of the solar module is in Direct Current (DC) form, and so power conditioning is necessary to convert this power into Alternating current (AC) form through power electronic circuits either for Stand alone or for grid interfaced applications. The solar PV energy conversion process itself is a low efficient one due to major losses involved in the physical process of conversion within the cell. Hence the available energy after conversion has to be dealt with utmost care to utilize it to the maximum extent.

In this context, the modelling and analysis of the solar cell is very much important and essential too. In fact, accurate and reliable modelling of solar cell is imperative to optimize the design of the solar PV system. The mathematical model of the solar cell had been developed a long time ago. But the recent spurt in the use of simulation software such as SPICE, SABER, SIMULINK/MATLAB etc., has made it essential to have accurate and reliable models for the PV array so that PV based generating system can be accurately analyzed and its performance can be studied.

Matlab is one of the more prominent simulation software used by industries and as well as the institutions due to its various advantages. To facilitate development of solar PV based power conversion systems, large numbers of simulation models developed in MATLAB are available in the literature [2-5]. Many of these models are based on non-linear equations describing the solar cell behavior, however, with a few approximations. In this paper, an attempt has been made to evaluate the accuracy of two of the existing solar cell models in MATLAB/SIMULINK and based on the single diode equations of the Photovoltaic cell a new model has also been developed as accurately as possible.

II. MATHEMATICAL DESCRIPTION OF SOLAR CELL

Solar cells consist of a p-n junction fabricated in a thin wafer or layer of a semiconductor material. In the dark, the I-V output characteristic of a solar cell has an exponential characteristic similar to that of a diode [6]. When photons

from the solar energy hits the solar cell, with energy greater than band gap energy of the semiconductor, electrons are knocked loose from the atoms in the material, creating electron-hole pairs. These carriers are swept apart under the influence of the internal electric fields of the p-n junction and create a current proportional to the incident radiation. When the cell is short circuited, this current flows in the external circuit; when open circuited, this current is shunted internally by the intrinsic p-n junction diode. The characteristics of this diode therefore set the open circuit voltage characteristics of the cell. The photovoltaic modules are made up of silicon cells. The silicon solar cells which give output voltage of around 0.7V under open circuit condition. The current rating of the modules depends on the area of the individual cells. Higher the cell area high is the current output of the cell. The double exponential equation of the solar cell derived

from the physics of the pn junction aptly describes the operation of the solar PV cell [7]. It is equivalently modeled as a current source with 2 parallel diodes, a shunt and a series resistance as shown in Fig.1.

q(V+IRse) q(V+IRse)

kT AkTph s1 s2(V+IRse)

RshI=I -I [e -1]-I [e -1]-

(1)

where Iph is the photo diode current generated by solar cell mainly depending upon irradiance and temperature; Is1 is the saturation current of diode D1 due to diffusion mechanism; Is2 is the saturation current due to recombination in space charge layer ; Rsh is the shunt resistance representing shunt current leakage to the ground; Rse is the series resistance representing contact resistances etc.; k is Boltzmann’s constant, 1.38x10-23 J/K; q is the electron charge, 1.6 x 10-19 C; Tc is the Cell working temperature; V is the terminal voltage of solar cell.

Fig. 1: Double diode Model for solar cell

However the above model can be further simplified by

omitting the current Is2, the reverse saturation current of diode D2 due to recombination of charge carrier in space charge layer is neglected as the amount of recombination is less and negligible. This assumption is very much acceptable especially under standard test conditions and induces error only at very low values of irradiation such as 100W/m2 [5]. Hence finally the generalized model of the solar cell with moderate complexity is arrived at. This model (as shown in Fig.2) is mostly used for all analytical and design purposes with moderate complexity and acceptable accuracy. The equation of the single diode model is

q (V + IR se)

A k T sep h s

sh(V + IR )I= I -I [e -1 ]- R (2)

where, I r rI p h = I s c * * [ 1 + ( T c e l l - T r e f ) * K ) ]

1 0 0 0 (3)

Fig.2 Single diode model of solar cell

III. MODELLING AND SIMULATION OF SOLAR CELL

A typical solar cell of 50W capacity (Waree WS-50) has

been chosen for modelling and analysis in this work. The details of the solar cell are presented in Table 1. For any design and development, simulation is the first step to ascertain the satisfactory working of the system before proceeding to implementation. Many solar PV cell models developed in MATLAB have been reported in various research papers [2-5, 7-10].

The inbuilt model for solar cell available in the simscape subset of Simulink/ MATLAB is based on double diode equation model [7]. This model accepts the solar irradiance and the temperature as input parameters and yields current characteristics for that particular cell voltage under defined conditions. The input and output parameters are treated as physical parameters as simscape works on physical network modelling approach. Hence in case of interface with a power conditioning systems, these physical parameters are to be converted into equivalent electrical parameters by making use of controlled sources.

Another model proposed [8] for PV electrical module is based on Shockley diode equation. The investigations in this particular model draw conclusions on variations in maximum power point with temperature and insolation. This simulation model is also based on single diode cell model. Based on solar insolation, cell temperature and operating voltage of the cell, this model gives the output in terms of current. The model parameters are processed in a Matlab script file and the output current is evaluated in terms of the input insolation and temperature. Newton Raphson method is used to solve for the cell current iteratively.

In this paper, an attempt had been made to develop a model for the solar cell using Matlab/simulink as the tool. The cell temperature and solar irradiance are given as inputs and the output is the current of the cell based on its operating voltage.

This model is based on the single diode model with moderate complexity. The model has been developed by translating the mathematical equations in to a model with the help of simulink blocks directly.

This model can be directly programmed as a single cell module or an array as per the requirements similar to the other simulink library blocks. The model can be manipulated by the user from the manufacturer’s data like open circuit voltage and short circuit current. It can be custom designed to form a solar module by specifying the number of cells in series and parallel according to the requirements. This generalized model can be directly interfaced with the simpower systems tools in Matlab/Simulink for implementation of the solar PV power conversion system. The solar cell block and its sub systems are as shown in the Figs.3 and 4 respectively.

Fig.3: Solar cell model and its port

Fig.4: Simulink Subsystem of solar cell model

IV. EXPERIMENTATION The manufacturer specifications of the solar module used

for experimentation are as given in Table1 [11]. In order to validate the results obtained from the simulation model, an experimental set up has been arranged to obtain I-V and P-V characteristics of the solar cell at various temperature and illumination conditions. Most of the specifications of the manufacturer are valid at the STC conditions. However, the

solar PV module is rarely operated at these standard conditions and this gives rise to various uncertainties in terms of its power delivering capability. Mostly the solar irradiance over the year on an average sunny day hover around 400 – 700W/m2 and temperature depends on the season and climatic conditions of the location.

Hence in this study, initially the experimental data was obtained in the actual existing conditions and the same has been verified with the simulation models. The solar irradiance was measured with a high accuracy pyranometer to minimise the errors in the experimentation and the I-V curve is plotted. The same parameters (irradiance and temperature) that prevailed during the time of the experimentation process have been used in all three Matlab simulation models and the I-V and P-V characteristics are plotted on the same graph.

TABLE 1: TECHNICAL SPECS. OF SOLAR MODULE WS – 50

Parameter @ STC Variable Specs.

Maximum power in watts Pm 50 Open circuit voltage in Volts Voc 21.0 Short Circuit current in Amps Isc 3.17 Voltage @ max. power Vmp 17.0 Current @ max. power Imp 2.94

Temperature Coefficients Voltage -0.123 V/˚K Current +4.4 mA/˚K

Type of cell Mono crystalline silicon

V. RESULTS AND DISCUSSION The Current - Voltage (I-V) characteristics and Power-

Voltage (P-V) characteristics of the solar cell at various irradiance and temperature have been obtained experimentally as well as from the three simulation models. Figs.4a and 4b show the I-V and P-V characteristics of all the three simulation models for solar irradiance of 1000W/m2 and 25°C temperature (Standard Test Condition). The curves are almost matching with each other and are in line with the manufacturer’s data sheet.

Fig. 4a: I-V curve at STC (1000W/m2; 25 ˚C)

Fig. 4b: PV curve at STC (1000W/m2; 25 ˚C)

The experimental results are obtained at a

temperature of 23°C and with an irradiance of 500 W/m2. Simulations were carried out for all the three models with 23°C temperature and irradiance of 500 W/m2. Figs. 5 and 6 show the I-V and P-V characteristics of all the three simulation models and experimental results. Even though all the I-V and P-V characteristics are fairly coinciding with each other, it is very clear that I-V characteristics obtained from the experimental set-up has a slight droop in the constant voltage region which is not there in the simulated characteristics. This is actually due the omission of the series resistance Rse during the simulation whereas in actual conditions the resistance is very much present although it is a small value. However, the error due to omission of Rse is very marginal. Another notable thing is the slightly lower actual power output as compared to the simulation results in the constant current region due to omission of the shunt resistance Rsh. But this is almost negligible as compared to the discrepancy caused by the series resistance. Hence in most of the cases the shunt resistance can be grossly neglected and series resistance can be included for having an appropriate model. Also, the omission of the Saturation diode D2 affects the output from the simulation at lower solar irradiance. The P-V and I-V characteristics have also been obtained for the experimental setup at different temperatures and the same have been simulated with all the simulation models. The results are found to match fairly well.

Fig. 5: IV curve at real time condition (500W/m2)

Fig. 6: PV curve at real time condition (500W/m2)

Model 1 which is based on two diodes as shown in

Fig.1 is more complex than Model 2 and the proposed simulink model. Model 1 is built using Simscape that deals with physical signals and hence this is not directly compatible with power electronic modules in SimPowerSystems toolbox. In view of this, the output of model 1 in Simscape which is in the form of numbers has to be converted into equivalent electrical signals by making use of controlled voltage / current sources. The developed simulink model is a simplified version and hence the number of PV cells connected in series and parallel can be directly fed to obtain the required voltage and current whereas this feature is missing in Model 1. Further, model 1 being more complex also takes longer duration for simulation while connecting many units in series and parallel. The solution for Model 2 is based on the iterative technique Newton-Raphson method. Due to this iterative procedure involved, the computation time is much more than the other two models. In view of all these, Model 3 proposed in this paper seems to be a better option as compared to the other two existing models.

TABLE 2: SUMMARY OF SOLAR CELL MODELS

Description Model 1 Model 2 Simulink Model 3

Complexity Most complex Moderate Moderate

Accuracy High Reasonably acceptable

Reasonably acceptable

Flexibility in programming Low Moderate High

Interface with power conversion blocks Difficult Easy Very Easy

Simulation time Large Medium Less Dynamic performance Good Good Very Good

VI. CONCLUSION An attempt has been made to develop a new model for solar

PV cell in Matlab/ Simulink environment and also to evaluate the accuracy and simplicity of the newly developed model and compare it with the existing models. The characteristics obtained from the models have been cross verified with those

obtained from an actual solar cell module of 50 W rating under STC conditions as well as other real time operating conditions. The models are compared in terms of their complexity, flexibility, ease of programming, ease of interfacing with power conditioning systems and the P-V and I-V characteristics generated from the model. Each model has its own advantages and disadvantages based on computation time, capability to be interfaced with Simpowersystem blocks and accuracy of the output characteristics. The model proposed in this paper using simulink building blocks performs well for developing solar PV systems models as it combines features like ease of interface with power conversion systems, faster dynamic response and reasonable accuracy with moderate complexity.

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