ABSTRACT PV-Photovoltaic source is one of the most significant players in the worldâs energy portfolio, and it will make one of the biggest contributions to electricity generation among all the renewable energy sources by 2040, because it is clean, emission free, and renewable electrical generation with high reliability. The research on Photovoltaic (PV) generation is extensively increasing, since it is considered as an essentially inexhaustible and broadly available source of energy. Photovoltaic systems that convert solar energy into electrical energy are divided into two categories: â¢ Stand Alone (Offline) â¢ GRID- Connected. Stand Alone system is commonly used in rural areas and more often as backup systems for situations when the Grid is unavailable due to natural disasters or human caused disruptions. Even if they are capable of providing AC power for immediate appliance power usage, they make use of energy storage devices such as large capacity batteries, where the energy stored during the day will then be used when sunlight is not available. Grid- Connected systems are installed in areas where the Grid is present and robust, and able to accept energy feeding from the above described Photovoltaic systems. Operating a renewable system in parallel with an Electric Grid requires special Inverters. In this project, simulation of solar modeling, MPPT, and synchronizing PV source with Grid will be carried out. Hardware would be developed in next phase of our project by using ARDUINO Controller. This proposed configuration can greatly reduce the existing power demand, limit the use of conventional power generation techniques and also it is the means to tackle the future power requirements. It saves the fossils fuels from depletion, limits global warming and keeps the environment clean and green. LIST OF FIGURES SR NO FIGURE NO NAME OF FIGURE PAGE NO 1 3.2 BLOCK DIAGRAM OF SOLAR GRID TIE INVERTER 6 2 4.1.1 PV PANEL 7 3 4.2 EQUIVALENT CIRCUIT OF SOLAR PV CELL 8 4 4.4 MODELLING OF PV PANEL IN MATLAB/SIMULINK 10 5 4.5.1 PV GRAPH FOR DIFFERENT INTENSITY RADIATIONS 11 6 4.5.2 PV GRAPH FOR RADIATION OF SINGLE INTENSITY 11 7 4.5.3 IV GRAPH FOR DIFFERENT INTENSITY RADIATIONS 13 8 4.5.4 IV GRAPH FOR RADIATION OF SINGLE INTENSITY 13 9 5.6 FLOWCHART OF PERTURB AND OBSERVE METHOD 17 10 6.2 SCHEMATIC DIAGRAM OF BOOST CONVERTER 19 11 6.4.1 CONTINUOUS CONDUCTION MODE OF BOOST CONVERTER 21 12 6.4.2 DISCONTINUOUS CONDUCTION MODE OF BOOST CONVERTER 21 13 6.5 SIMULATION OF BOOST CONVERTER IN MATLAB/SIMULINK 22 14 6.6 SIMULATION RESULT OF BOOST CONVERTER 23 15 6.6.1 PV GRAPH OF BOOST CONVERTER 24 16 6.6.2 IV GRAPH OF BOOST CONVERTER 24 18 7.6 UNIPOLAR SPWM IN MATLAB/SIMULINK: 28 19 7.6.1 SIMULATION RESULTS 29 20 7.7 BIPOLAR SPWM IN MATLAB/SIMULINK 30 21 7.7.1 SIMULATION RESULTS 30 22 8.1 MATLAB SIMULATION FOR SYNCHRONIZATION OF PV PANEL WITH BOOST CONVERTER 31 23 24 25 ABBREVIATIONS PV- Photovoltaic DC- Direct current AC- Alternating current CHAPTER1 INTRODUCTION Introduction Fossils fuels are playing a major role to meet the increasing growth on energy demand. At the same time it is responsible for many environmental hazards like carbon emissions and global warming. The concept of using renewable energy sources emerged from the need to search for alternate green sources of energy. In order to diminish the greenhouse Effect and slow the depletion of fossils fuel, the solar energy has been developed. PV power systems are becoming increasingly important in modern electrical grids. In the recent years, PV power systems have drawn significant research attention in modeling and simulation studies for stand-alone and grid-tied systems. Simulation based implementation is being widely popular in research, especially for large scale analysis. MPPT technique is further used to get maximum power output of PV module and also Boost converter is used to boost the constant DC voltage up to certain high voltage, which is then converted into AC using inverter. 1.2 Reason for selecting this project As the non renewable fuels and fossil fuels used for generation of electricity are depleting day by day, the need arises to generate electricity by some other means. It is discovered that potential of solar energy was 1,575-49,387 extra joules which is several times larger than the world total energy consumption. So the use solar energy to generate electricity is increasing day by day to meet the ever increasing demand and shortage of non renewable fuels. Thus instead of only generating from solar energy we can supply the generated electricity directly to the grid so that some demand can be met by solar energy and remaining by other sources, thus indirectly reducing the demand of non-renewable energy sources. 1.3 Challenges in the project Generation of electricity and converting it to alternating source is not a major problem but the main problem is synchronizing it with grid. As the voltage and frequency of grid is constant the output from the solar energy is not constant it is changing and accordingly the output voltage and frequency also changes which is not adaptable. The overall efficiency of the project is less and there is switching losses in the inverter which further reduces the losses. Also when the power supply of the grid is cut off, the switching pulses to the Mosfet of inverter is not available and thus the solar inverter also stops working. 1.4 Utilities of the project Solar grid tie is basically an inverter that converts DC electricity into AC electricity with an ability to interface with the grid. Residences and businesses using grid tie system to generate electricity are permitted in some countries to sell their energy to utility grid. Also the entity that owns the renewable power source receives compensation from the utility but this is not applicable in India till now. Commercial complexes and educational institutions (e.g. colleges) uses grid tie inverter for reducing their electricity bill and have a reliable supply. Also in U.S.A feed-in-tariff policy is there where the producer is paid for every kilowatt hour delivered to the grid by a special tariff based on a contract with distribution company or power authority. 1.5 Objectives The main objective is to reduce the power demand on grid or power consumption, during the day when sun is available. To avoid power cut-off due to increase load demand on grid as demand can be met using solar energy. Also reliability of the power system can be increased. â CHAPTER 2 LITERATURE REVIEW 2.1 Literature Review 1. S.Chowdhury, Member, IEEE, S.P.Chowdhury, Member, IEEE, G.A.Taylor, Member, IEEE and Y.H.Song, Senior Member, IEEE”. Mathematical Modeling and Performance Evaluation of a Stand-Alone Polycrystalline PV Plant with MPPT Facility”. 2. Md. Aminul Islam, Graduate Student Member, IEEE, Adel Merabet, Member, IEEE, Rachi Beguenane and Hussein Ibrahim.” Modeling Solar Photovoltaic Cell and Simulated Performance Analysis of a 250W PV Module.” 3. Nand Kishor, Member, IEEE, Marcelo Gradella Villalva, Soumya Ranjan Mohanty, Member, IEEE, Ernesto Ruppert.” Modeling of PV Module with Consideration of Environmental Factors”. 4. Dola Sinhal, Amiya Bandhu Das, Dipak Kr. Dhak.” Equivalent Circuit Configuration for Solar PV Cell”. 5. Saurav Das, Khosru .M. Salim.” Design and Implementation of One kilowatt Capacity Single Phase Grid Tie Photovoltaic Inverter”. 6. K. Arulkumar, D.Vijayakumar, K.Palanisamy.” Efficient Control Design for Single Phase Grid Tie Inverter of PV System”. 7. Power Electronics-P.S. Bimbhra CHAPTER 3 SOLAR GRID TIE INVERTER 3.1 Introduction The inverter is the main part of the PV system and is the focus of all utility interconnection. A grid tie inverter converts direct current into alternating current with an ability to synchronize with a utility line. They are classified as: Stand Alone Type: It is like ordinary inverter which is having battery backup. Synchronous Grid Tie Inverter: This is a special type of inverter which is specially design for solar panel. This inverter is used to synchronize the output of PV panel and the utility. It can be used with the battery backup also. The grid tie inverter must synchronize its frequency with that of the grid using a local oscillator and limit the voltage to no higher than the grid voltage. Solar grid-tie inverters are designed to quickly disconnect from the grid if the utility grid goes down. This is an NEC requirement that ensures that in the event of a blackout, the grid tie inverter will shut down to prevent the energy it produces from harming any line workers who are sent to fix the power grid. 3.2 Block Diagram fig. 3.2 Block Diagram of Solar Grid Tie Inverter 3.3 Execution Process The output of PV panel is variable DC which is very small. It is fed to boost converter which boosts up the voltage up to desired level. MPPT is used to obtain maximum power point to obtain higher efficiency. The output of Boost converter is constant DC. This is fed as input to single phase inverter. The SPWM technique is used to reduce THD in output. When the inverter output is pure sinusoidal it is connected to the grid. But, to match the frequency, phase and amplitude of the grid and inverter, Modulation signals to the gating of the inverter switches. The PWM pulses are generated with the help of Arduino controller which controls the switching of MOSFET of inverter. The inverter converts DC to AC with help of SPWM gate switching pulses. Finally the synchronization of the phase and frequency of the inverter output voltage with the grid is done. CHAPTER 4 PV MODULE 4.1 Introduction to PV panel PV power generation is reliable, involves no moving parts and operation and maintenance costs are very low. 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 panel 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 50-300W. The PV modules combined with a set of additional application dependent system components form a complete PV system. PV system 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 conversions has to be dealt with utmost care to utilize it to maximum extend. fig. 4.1.1 PV panel 4.2 Equivalent Circuit of SOLAR PV Cell fig. 4.2 Equivalent circuit of Solar PV cell I_SC=Short circuit current I_(PV cell)=PV cell current I_D=Diode current V_D=Voltage across diode R_S=Series resistance R_P=Parallel resistance V_T=Terminal voltage I_O=Diode saturation current Applying KCL, ã Iã_SC-I_D-V_D/R_P -I_PV=0 From Diode Characteristics, I_D=I_O (e^(V_D/V_T )-1) Applying KVL, V_(PV cell)=V_D-R_S I_PV 4.3 Working of PV Panel Solar cell consists of p-n junction fabricated in a thin wafer or a layer of semiconductor material. In the dark the I-V output characteristics of a solar cell has an exponential characteristics similar to that of a diode. When photons from the solar energy hits the solar cell with energy greater than band gap energy of semiconductor ,electrons are knocked loose from the atoms in the material, creating electronâ”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 photovoltaic modules are made up of silicon cells. 4.4 Flow chart for modeling of PV panel 4.5 Modeling of PV Panel in MATLAB/SIMULINK fig. 4.4 modeling of PV panel in MATLAB/SIMULINK 4.5 Simulation Results On basis of simulations we obtain P-V and V-I characteristics of solar cell On plotting graph of power vs. voltage it can be seen that as the voltage of PV panel goes on increasing the power increases only upto maximum point then it starts decreasing with increase in voltage due to exponential used in equations. The efficiency of PV panel is maximum at the maximum power point and other point efficiency reduces. Figure shows graph for different values of radiation, it can be seen that as the radiation goes on decreasing the maximum power obtained decreases and the graph shifts downwards with decrease in radiation. On plotting graph of current vs. voltage it can be concluded that as the voltage goes on increasing the current is reducing non linearly till open circuit voltage is obtained. Figure shows graph for different values of radiation as it goes on decreasing the corresponding current also decreases for same value of voltage. CHAPTER 5 MPPT (MAXIMUM POWER POINT TRACKING) 5.1 What is MPPT? Maximum power point tracking is a technique that charge controllers use for PV solar systems to maximize power output. PV solar systems exist in several different configurations. The most basic version sends from collector panels directly to the DC-AC inverter and from there directly to the electrical grid. 5.2 How does MPPT work? The power point tracker is a high frequency DC to DC converter. They take the DC input from the solar panels, change it to high frequency AC, and convert it back down to a different DC voltage and current to exactly match the panels to the batteries. MPPTâs operate at very high frequency usually in the 20-80 kHZ range. The advantage of high frequency circuits is that they can be designed with very high efficiency transformers and small components. The design of high frequency components is not very easy due to problems with broadcasting just like a radio and TV interference. So noise isolation and suppression becomes very important. There are few linear MPPTâs charge controls around us, which are much easier and cheaper to build and design than the digital ones. This MPPTâs improve efficiency but some loose their “tracking point” as for example if a cloud passed over the panel , the linear circuit searches for the next best point, but then gets too far out on the deep end to find it again when the sun comes out. The power point tracker operates by taking the DC input current ,changing it to AC through a transformer and then rectifying it to DC followed by the output regulator. As light and temperature conditions vary continuously all day long the charge controllers for solar panels need to be sensitive enough. 5.3 Methods of MPPT 5.3.1 OFFLINE Method There are two types of Offline methods of MPPT: Fractional Open circuit voltage Fractional Short circuit current 184.108.40.206 Open circuit voltage: This method uses the approximately linear relationship between the MPP voltage (V_MPP) and the open circuit voltage (V_OC), which varies with the irradiance and temperature: (V_MPP)=k_1 (V_OC) k_1= constant depending on the characteristics of the PV array and it has to be determined by determining the (V_MPP) and (V_OC) for different levels of irradiation and temperatures. Once the k_1 is determined, the (V_MPP) can be determined periodically by measuring (V_OC) the power converter has to be shut down momentarily so in each measurement a loss of power occurs. fig.220.127.116.11 Flow chart of Open circuit voltage method of MPPT 18.104.22.168 Short circuit current: The relationship, under varying atmosphere conditions, between the short circuit current I_sc and the MPP current, I_MPP is: I_MPP= k_2 I_sc k_2 has to be determined according to each PV array. Measuring the short circuit current while the system is operating is a problem. It usually requires adding an additional switch to the power converter to periodically short the PV array and measureI_sc. I_sc is measured by shorting PV array with an additional field-effect transistor added between the PV array and the DC link capacitor. yes Fig.22.214.171.124 Flow chart for Short circuit method 5.3.2 ONLINE Method Perturb and Observe (P&O) Incremental Conductance Current Sweep Constant Voltage 5.4 Comparison of various MPPT technique Both perturb and observe (P&O), and incremental conductance are examples of “hill climbing” method. They can find the local maximum of the power curve for the operating condition of the PV array, and so provide a true maximum point. The Perturb and Observe method can produce oscillations of power output around the maximum power point even under steady state irradiance. The incremental conductance method has the advantage over the P& O method that it can determine the maximum power point without oscillating around this value. It can perform maximum power point tracking under rapidly varying irradiation conditions with higher accuracy than the P&O method. However the incremental conductance method can produce oscillations and can perform erratically under rapidly changing atmospheric condition. The computational time is increased due to slowing down of the sampling frequency resulting from the higher complexity of the algorithm compared to the P&O method 5.5 PERTURB AND OBSERVE In this method the controller adjusts the voltage by a small amount from the array and measures power, if the power increases, further adjustments in that direction are tried until power no longer increases. This is called P&O method and is most common, although this method results in power oscillations. It is referred to as a hill climbing method, because it depends on the rise of the curve of power against voltage below the maximum power point, and the fall above that point. It is most common because of ease of implementation. P&O method may result in top; level efficiency provided that a proper predictive and adaptive hill climbing strategy or steps is adopted. COMPARING DIFFERENT MPPT METHODS WE FOUND THAT P&O METHOD IS MORE SUITABLE FOR OUR PROJECT SO WE ARE GOING TO USE P&O TECHNIQUE IN OUR PROJECT FOR OBTAINING MAXIMUM POWER POINT. 5.6 Flow Chart of PERTURB AND OBSERVE method Fig. 5.6 flow chart of Perturb and Observe method CHAPTER 6 BOOST CONVERTER 6.1 What is Boost Converter? A Boost Converter (step-up converter) is a DC-to-DC power converter with an output voltage greater than its input voltage. It is a class of SWITCHED MODE POWER SUPPLY (SMPS) containing at least two semiconductors (a diode and a transistor) and at least one energy storage element, a capacitor, inductor, or the two in combination. Filters made of capacitors (sometimes in combination with inductors) are normally added to the output of the converter to reduce output voltage ripple. 6.2 Schematic Diagram of Boost Converter V_in=input voltage V_out=voltage across load V_i= voltage across inductor R=Resistive Load I_i=current D=diode L=Inductor SW=Mosfet switch C=Capacitor 6.3 Working of Boost Converter The Boost Converter is a medium of power transmission to perform energy absorption and injection from solar panel to Grid-tied inverter. The process of energy absorption and injection in Boost Converter is performed by a combination of four components that are: Inductor, Electronic switch, diode and output capacitor. The process of energy absorption and injection will constitute a switching cycle. The average output voltage is controlled by the switching on and off time duration. At constant switching frequency, adjusting the on and off duration of the switch is called Pulse-Width â”Modulation (PWM) switching. The switching duty cycle, k is defined as the ratio of the on duration to the switching time period. The energy absorption and injection with the relative length of switching period will operate the converter in two different modes known as Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). 6.4 Waveforms fig 6.4.1 Continuous Conduction Mode Fig.6.4.2 Discontinuous Conduction Mode 6.5 Simulation of Boost Converter in MATLAB/SIMULINK fig. 6.5 Simulation of Boost Converter in MATLAB/SIMULINK 6.6 Simulation result of Boost Converter fig. 6.6 Simulation result of Boost Converter CHAPTER 7 SPWM (SINUSOIDAL PULSE WIDTH MODULATION) 7.1 What is SPWM? SPWM is the most popular method for producing a controlled output for inverters. Fig.7.1.1SPWM waveform Figure 7.1.1 shows the simplest method of producing the PWM pulses. Here the sine wave is compared with a triangular wave. When the magnitude of sine wave is more than triangular wave then will get a high pulse in PWM wave When the magnitude of sine wave is less than triangular wave then we will get a” low pulse” in PWM wave. Instead of maintaining the width of all pulses of same as in case of multiple pulse width modulation, the width of all pulses of same as in case of multiple pulse width modulation, the width of each pulse is varied in proportion to the amplitude of a sine wave evaluated at the centre of the same pulse. The distortion factor and lower order harmonics are reduced significantly. The gating signals are generated by comparing a sinusoidal reference signal with a triangular carrier wave of frequency Fc. The frequency of reference signal Fr, determines the inverter output frequency and its peak amplitude Ar, controls the modulation index M, and RMS output voltage Vo. The number of pulses per half cycle depends on carrier frequency 7.2 Why SPWM is used? The output voltage control is easier with PWM than any other schemes. Lower order harmonics are either minimized or eliminated altogether. The filtering requirements are minimized as lower order harmonics are eliminated and higher order harmonics are filtered easily. Very low power consumption. The entire control circuit can be digitized which reduces the susceptibility of the circuit to interference. 7.3 SPWM switching techniques: UNIPOLAR SWITCHING BIPOLAR SWITCHING 7.4 UNIPOLAR Switching: In this scheme, the triangular carrier waveform is compared with two reference signals which are positive and negative signal. The basic idea to produce SPWM with unipolar voltage switching is shown in Fig. 4. The different between the Bipolar SPWM generators is that the generator uses another comparator to compare between the inverse reference waveformâ’Vr . The process of comparing these two signals to produce the unipolar voltage switching signal. The switching pattern and output waveform is as follows in Fig. 5. In Unipolar voltage switching the output voltage switches between 0 and Vdc, or switching event is halved in the unipolar case from 2Vdc to Vdc. The effective switching frequency is seen by the load is doubled and the voltage pulse amplitude is halved. Due to this, the harmonic content of the output voltage waveform is reduced compared to bipolar switching. In Unipolar voltage switching scheme also, the amplitude of the significant harmonics and its sidebands is much lower for all modulation indexes thus making filtering easier, and with its size being significantly smaller between 0 and â’ Vdc. This is in contrast to the bipolar switching strategy in which the output swings between Vdc and â”Vdc. 7.5 BIPOLAR Switching: The basic idea to produce PWM Bipolar voltage switching signal comprises of a comparator used to compare between the reference voltage waveform Vr with the triangular carrier signal Vc and produces the bipolar switching signal. If this scheme is applied to the full bridge single phase inverter as shown in Fig., all the switch S11, S21, S12and 22 are turned on and off at the same time. The output of leg A is equal and opposite to the output of leg B. The output voltage is determined by comparing the reference signal,Vr and the triangular carrier signal, Vc and S12, S22 are turned on or turned off at the same time. The output of leg A is equal and opposite to the output of leg B. The output voltage is determined by comparing the control signal, Vr and the triangular signal, Vc. 7.6 UNIPOLAR SPWM in MATLAB/SIMULINK Fig.7.6 Unipolar SPWM in MATLAB/SIMULINK 7.6.1) SIMULATION RESULTS: fig.7.6.1 Unipolar SPWM 7.7 BIPOLAR SPWM in MATLAB/SIMULINK: Fig.7.7 Bipolar SPWM in MATLAB/SIMULINK 7.7.1 Simulation results fig.7.7.1 Bipolar SPWM CHAPTER 8 MATLAB SIMULATION FOR SYNCHRONIZATION OF PV PANEL WITH BOOST CONVERTER Fig.8 MATLAB simulation for synchronization of PV panel with Boost Converter 8.1 SIMULATION RESULTS: CHAPTER 9 WORK PROGRESS Study and analysis of SOLAR-GRID TIE Inverter. Learning MATLAB/SIMULINK. Modeling of PV-PANEL. MPPT techniques and its programming. Simulation of BOOST CONVERTER. Studied SPWM techniques. Circuit diagram and working of single phase Inverter. CHAPTER 10 FUTURE SCOPE The main purpose of our project is to obtain continuous power supply and meet the increasing demand of fossil fuels by using renewable energy source. In the present scenario of solar grid tie inverter, when the grid is cut off, the grid tie inverter stops receiving gate pulses which are directly fed from the grid. So research can be made for solar grid tie inverter to act as a STAND ALONE inverter during the grid failure. In order to attain this objective we require storage batteries of very large capacity which makes the system too expensive. Hence researches are going on to make the system more efficient and economical. Looking towards the increasing use of the solar energy and the depletion of the conventional sources, it may be possible that only renewable energy resources may meet the demand of electricity in future. It may be possible in the future that the efficiency of solar grid tie inverter is increased such that whole of the solar energy can be converted into electrical energy. CHAPTER 11 CONCLUSION From our project we can draw the conclusion that we can develop a new model for solar PV cell in Matlab/Simulink environment and also can evaluate the accuracy and simplicity of the newly developed model and comparing it with the existing models. The characteristics obtained from the models have been cross verified with those obtained from an actual solar cell module. The models are compared in terms of their complexity, flexibility, ease of programming, ease of interfacing with power conditioning systems and the PV and IV characteristics generated from the model. Each model has its own advantages and disadvantages based on computations time, capability to be interfaced with Simpowersystems blocks and accuracy of the output characteristics. Also the model is robust, efficient and of low computational time while running the simulation. We can determine resistances of PV cell with adjustment of characteristics that corresponds to Maximum Power Point. The influential environmental factors that affect the PV module performance were considered in the study. Finally with simulation of Boost converter and designing of inverter, we can synchronioze it with grid using Arduino controller. CHAPTER 12 BIBILOGRAPHY &REFERENCE  R. Akkaya and A.A. Kulaksiz “A microcontroller based stand alone photovoltaic power system for residential appliances” Applied Energy, 2004, vol. 78, issue 4, pages 419-431. Michael Jensen, Russell louie, Mehdi Etezadi and M.Sami fadali, “Model and Simulation of 75kW PV Solar Array”, IEEE Transmission and Distribution Conference and Exposition, April 2010, New Orleans, LA, USA.  Chowdhury, S.; Taylor, G.A., Chowdhury, S.P. Saha, A.K, Song Y.H, “Modeling, simulation and performance analysis of a PV array in an embedded environment”, 42nd International Universities Power Engineering Conference, UPEC 2007, 4-6 September.  Richard W. WIES, Ron A. Johnson, Ashish N. Agarwal and TYLER j. Chubb, “Simulink Model for Economic Analysis and Environmental Impacts of a PV with Diesel-Battery System for Remote Villages”,IEEE Transactions on Power Systems, Vol. 20, pp.692-700, May, 2005.  Engin Karatepe, Mutlu Boztepe, Metin Colak, “Development of a suitable model for characterizing Photovoltaic Arrays with shaded solar cells”, Science Direct, Solar Energy 81(2007) 977-992  A. Gow and C.D. Manning, “Development of a Photovoltaic Array Model for use in power electronics simulation studies”, IEE Proc. Elect. Power Appl., vol. 146, no. 2,pp. 193-200, 1999.  Alan L. Fahrenbruch and Richard H. Bube, “Fundamentals of Solar: Photo voltaic Solar Energy conversion. Academic press”, Inc, New York, NY, 1983.  J. D. Mondol, Y. G. Yohanis, and B. Norton, “Comparison of measured and predicted long term performance of Grid connected photovoltaic system”, Energy Conversion and Management, vol 48, pp. 1065-1080, 2007.  Y. Jiang, J. A. A. Qahouq and I. Batarseh, “Improved Solar PV cell Matlab simulation model and comparision”, Proc. of 2010 IEEE International Symposium on Circuits and Systems, pp. 2770-2773, 2010.  Mao Mei-Qing, Yu Shi-Jie, and Su Jian-Hui, “Versatile MATLAB Simulation model for Photovoltaic array with MPPT function”, Journal of SystemSimulation, vol. 17, pp. 1248-1251, 2005.