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Solar Photovoltaic technology is the fastest growing green energy technologies. Since year 2002, the worldwide production volume of the PV modules is increasing at a rate of 100% every 2 years.  This growing trend in the adoption of the PV technology is sustained by the continual improvement in manufacturing technologies and less expensive raw materials which leads to, more efficient and lower cost PV solutions in the market.
The cost effectiveness of a PV system largely depends on its ability to meet the varying electrical load demands under varying environmental factors. Thus, accurate PV module modeling and simulating the PV system's performance subjected to varying environmental factors are critical aspects of sizing the PV system.
Various PV models are available in the literature (citations required). These models are generally simplifications to the dual-diode model. While these model simplifications would ease system sizing calculation effort, over-simplification would result in an over- or under-sized PV system. In both cases, the PV system is not a cost effective solution.
The performance of a PV module varies significantly with temperature and solar irradiation level. The performance of PV modules connected in series and parallel configurations; PV array, gets more complicated when subjected to partial shading. Partial shading occurs when the entire PV array is not under uniform isolation. When this occurs, the output power of the PV array would demonstrate multiple peaks. Thus, reducing efficiency of the PV system as the Maximum Power Point Tracking (MPPT) technique might not be able to distinguish the global maximum power point among the multiple peaks.
The objectives of this report are thus to study the issues as discussed in the aforementioned discussions:
To evaluate and compare the effectiveness of the PV models in modeling the I-V characteristics with varying Fill-factor (FF) as well as shading effects
To study the effects of partial shading on the I-V and P-V characteristics of a PV array
Sand recourses are unlimited on surface of earth which is used to make silicon that is why PV cells are commercially manufactured from silicon. However materials like Gallium Arsenide are also considered to make PV cells these days.
Four general types of PV cells considered to compare in this study include:
Single-crystal silicon also known as monocrystalline silicon).
Polycrystalline silicon (also known as multicrystalline silicon).
Hybrid solar cells
Amorphous silicon (abbreviated as "aSi," also known as thin film silicon).
Single crystalline PV cells are most commonly used in solar applications. These cells are usually blue or black in color (Figure.1). Silicon is purified, melted and crystallized in order to produce wafers to make cells.
Figure.1: A solar cellmade from a monocrystalline silicon wafer
Typically, most of the cell has a slight positive electrical charge. A thin layer at the top has a slight negative charge.
The cell is attached to a base called a "backplane." This is usually a layer of metal used to physically reinforce the cell and to provide an electrical contact at the bottom.
Since the top of the cell must be open to sunlight, a thin grid of metal is applied to the top instead of a continuous layer. The grid must be thin enough to admit adequate amounts of sunlight, but wide enough to carry adequate amounts of electrical energy (Figure.2).
Figure.2: PV cell operation
These cells have lower efficiency as compared to monocrystalline reason of it is that a lower cost silicon is used in these. Their lower cost is reason to make them which is considered better compared to their efficiency.
Figure.3:Â Polycrystalline photovoltaic cells laminated to backing material in a module
Instead of the solid color of single crystal cells the surface of polycrystalline cells shows a random pattern of crystal borders
Amorphous or thin film silicon
The previous two types of silicon used for photovoltaic cells have a distinct structure. Amorphous silicon has no such structure. Amorphous silicon is sometimes abbreviated as "aSi" and is also called thin film silicon.
Amorphous silicon units are made by depositing very thin layers of vaporized silicon in a vacuum onto a support of glass, plastic or metal.
Amorphous silicon cells are produced in a variety of colors.(Figure.3).
Because the layers of silicon allow some light to pass through, multiple layers can be deposited. The added layers increase the amount of electricity the photovoltaic cell can produce. Each layer can be "tuned" to accept a particular band of light wavelength.
The performance of amorphous silicon cells can drop as much as 15% upon initial exposure to sunlight. This drop takes around six weeks. Manufacturers generally publish post-exposure performance data, so if the module has not been exposed to sunlight, its performance will exceed specifications at first.
The efficiency of amorphous silicon photovoltaic modules is less than half that of the other three technologies. This technology has the potential of being much less expensive to manufacture than crystalline silicon technology. For this reason, research is currently under way to improve amorphous silicon performance and manufacturing processes.
Figure 4: Performance Test of Flexible Amorphous Thin-film Photovoltaic Module Trial Unit
Hybrid Solar cells
Hybrid solar cells combine advantages of both organic and inorganic semiconductors. Hybrid photovoltaic's have organic materials that consist of conjugated polymers that absorb light as the donor and transport holes .Inorganic materials in hybrid cell are used as the acceptor and electron transporter in the structure. The hybrid photovoltaic devices have a significant.
Figure.5: A hybrid solar cell
Figure.6 A Performance wise Comparison of four cells
2. PV Cell Modeling
Effectiveness of Monocrystalline, Polycrystalline, Hybrid and Amorphous cells on three PV models i.e. single diode model with series resistance, single diode model with series and parallel resistance and dual diode model.
In order to study how different PV models work for four types of cells under consideration following method is used: The parameters of each of the models are derived by curve-fitting model equations to the actual I-V characteristic curve obtained in the datasheet. The curve-fitting algorithm used inÂ this process is the Levenberg-Marquardt algorithm.The derived model parameters from the curve fitting process were inserted into the corresponding PV model for simulation (Figures.7 and 8).
Figure.7 Diagrams of three diode models used
Equations used to obtain single diode model (1), single diode model with series resistance only (2) with series and parallel résistance and dual diode model (3).
Diode equations as shown above were used to create three simulink blocks as shown in Figures.7, 8, 9 and 10 where Figure.7 shown includes all three diode models shown in Figures. 8,9 and 10.
Figure.8: Simulation Block of Simulink used to study effects of Three PV Models
Figure.9: Simulink Model for single diode model with series resistance only
Figure.10: Simulink Model for single diode model with series and parallel resistance
Figure11: Simulink Model for dual diode model
Figures.12 and 13 show simulation results of mono-crystalline cell used for three models.VI characteristics of results show that all three models work properly for mono-crystalline cells with single diode model working just as good as actual curve for both insulation levels considered i.e. 400 and 1000 W/m^2.
Figure.12: VI characteristics of a mono crystalline with 600 W/m^2 irradiation
Figure.13: VI characteristics of a Mono with 1000 W/m^2 irradiation
Figures.14 and 15 show simulation results of polycrystalline cell used for three models.VI characteristics of results show that all three models work properly for poly crystalline cells with all three model working just as good as actual curve for both insolation 1000 W/m^2 insolation level as shown in Figure.15 but not for insolation level of 600 W/m^2 as shown in Figure.14.
Figure.14: VI characteristics of a Polycrystalline with 600 W/m^2 irradiation
Figure.15: VI characteristics of polycrystalline with 1000 W/m^2 irradiation
Figures.16 and 17 show simulation results of amorphous cell used for three models.VI characteristics of results show that none of models used work properly for this type of cell with 400 W/M^2 irradiation (Figure.16).While for irradiation of 1000 W/m^2 dual diode model diode works just as good as actual curve(Figure.17).
Figure.16: VI Characteristics of a Amorphous PV Module with 400 W/m^2 irradiation
Figure.17: VI characteristics of a Amorphous Module with 1000 Irradiation
Figures.18 and 19 show simulation results of hybrid cell used for three models.VI characteristics of results show that two of models used i.e. single diode model with series resistance and single diode model with both series and parallel resistance doesn't work for 600 W/m^2 irradiation but they work exactly same as actual for 1000 W/m^2 irradiation. The VI characteristics for dual diode model are not included as the procedure followed here didn't work for hybrid model implementation on dual diode
Figure18: VI characteristics of a hybrid cell with 400 W/m^2 irradiation
Figure19: VI characteristics of a hybrid cell with 1000 W/m^2 irradiation
Figure.20: VI characteristics of a Hybrid 1000 W/m^2 irradiation
3. Study of Shading Effects on Different PV Cell Configurations
To study the effects of shading on a PV modules in series, a Simulink model of four modules have been created as shown in Figure.22.Irradiation Is gradually decreased to see effects of shading.
Figure.21: Simulink Block for PV Modules in series
In Figure.22 below it is shown how shading affects VI characteristics of whole panel in series as different modules of cells come one after the other under shading. Irradiation level is decreased from standard value of 1000 W/m^2 to 200.Where as Figure.23 next to it shows PI characteristics under shading of same four modules in series.
As soon as a PV cell comes under shading its current decreases linearly due to irradiance while voltage decreases logarithmically, as result VI characteristics show decrease of current more evidently rather than voltage as irradiance is decreased for each module. Once a module would go under shading, due to decrease in level of current in that specific module it would go in reverse bias. This reverse biased current would in effect decrease the overall current to the level which is equivalent to level of current in revere biased module. At this point the module would start operating in forward biased condition and would contribute in the overall voltage of series array as can be seen in Figure.22.Since irradiance level of all the modules is changed by a same value of 200 W/m^2, current drops to same level in all cases, which as a result shows same maximum power point for all cases considered here (Figure.22).
Figure.22: Four Modules in series under shading VI characteristics
Figure.23: Four Modules in series under shading PI characteristics
Then to study the effects of shading on a PV modules in parallel, a Simulink model of four modules have been created as shown in Figure.24 below. Irradiation is gradually decreased to see effects of shading.
Figure.24: Simulink Block for PV Modules in parallel
In Figure.25 it is shown how shading affects VI characteristics of whole panel in parallel with one cell of each parallel string under shading. If one cell in one of modules in parallel comes under shading VI characteristics of cell remain same as is shown in case of VI characteristics of series cells with one cell under shading(Figure.22 and 25 green lines ).When one cell of next module parallel to it becomes under shading it would show same behavior. Due to added affect of these two parallel modules VI characteristics of overall series parallel array would drop down to level shown in Figure.25(red line).The same effect continues to add up as corner cells of modules parallel to each other come under shading one by one(Figure 25) .
Figure.25: Four Modules in parallel under shading VI characteristics
Figure.26: Four Cells in parallel under shading PI characteristics
A Comparison of two:
By comparison of two PI curves for series cells under shading and the second case of making one corner cell of adjacent parallel modules under shading one by one ,it can be seen that affect of shading is severe in case of single cells coming under shade in adjacent parallel modulesFigure28). it is evident that in case of series modules(Figure27), maximum power point (at knee of curves) doesn't change with increasing effect of shading(Figure 23) whereas in case of shading of one cell in each of adjacent parallel modules ,maximum power point decreases as shading increases(Figure 26). So to reduce affect of shading on PV array PV array should be planted at a location in such a way that shading occurs on that side of array where adjacent cells of array are connected in series rather than that side where cells adjacent to each other are in parallel. 
Figure.27: Series cells under shading in an array
Figure.28: Single (corner ones) cells in modules parallel to each other under shading in an PV array
4. Study of Shading Effects on PV Array
To study affects of shading on a whole PV array a GUI (Figure.30) is developed which uses the Simulink Block as shown in Figure.29. It is programmed such that by clicking on a single button of GUI (which represents a PV module) corresponding module comes under shading of 200 W/m^2 as compared to standard irradiation of 1000 w/m^2.
Figure.29 a : Simulink Model used to make a GUI
Figure29 b: Inside Block of Subsystems in Figure 29 a
Figure 29 c: Inside block of subsystems in Figure 29 b
Figure.30: GUI used to study affects of shading on different areas of an PV array
Resulting waveforms are produced for one PV module under shading, four PV modules under shading, nine PV modules under shading and the results are compared to whole PV array of 16 modules without shading as shown in Figures.31 and 32.
Figure.31: VI Characteristics of different Modules under shading
Figure.32: PV characteristics of different modules under shading
To analyze the performance of various PV cells it is essential to take into consideration what kind of a PV model would give exactly same characteristics of a specific PV cell. As it is seen in this report some PV cells work exactly the same as that single diode model with series resistance operation for a specific level of irradiation whereas the others work better with the single diode model with series and parallel resistances and dual diode model for some other value of irradiance .Second part of report shows that in order to design a and plant PV array it is not only essential to carefully configure series and parallel no of modules but to place them in some specific way in order to reduce the effects of shading.
V and I - Array Voltage and Array current respectively
Rs and Rp - Series and Shunt resistances in the equivalent circuit of the module
Io - Diode reverse saturation current in the equivalent circuit of the module
Vt - Thermal voltage (= nkT/q)
n - Diode ideality factor (1<n<2 for a single solar cell)
k - Boltzmann's constant ( = 1.381Ã-10-23 J/K)
q - Electron charge ( =1.602Ã-10-19 C )
T - Temperature in Kelvin
Io - Diode reverse saturation current in the equivalent circuit of the module
Iph - Photo current respectively
Isc - The current generation by absorption of photons at short circuit