Modeling of Random Shading Effects in Solar Cells

Priyanka Singh and Mohammed Niamat

Department of Electrical Engineering and Computer Science

The University of Toledo Toledo, OH 43606, USA

priyanka.singh@rockets.utoledo.edu

Srinivasa Vemuru

Department of Electrical & Computer Engineering and Computer Science

Ohio Northern University Ada, OH 45810, USA s-vemuru@onu.edu

Abstract— This paper introduces a modeling scheme that takes the effects of shading patterns on the output power of a solar cell array using MATLAB. A module consisting of an array of parallel connected strings of solar cells is considered for analysis under shading conditions. The model finds the solutions of complex nonlinear equations of solar cell under random illumination conditions. The approach has been extended to special shading cases. Additionally the effect of load resistance variation on the maximum power point under different shading patterns is performed.

Keywords- Solar Cells, Renewable Energy, Shading, Modeling, Maximum Power Point

I. INTRODUCTION The aim of this study is to develop a universal code for

modeling a solar cell array under complex illumination conditions using MATLAB. The effectiveness of the algorithm lies in its ability to simulate the maximum power for random illumination across the cells in an array design. The generic approach is extended to study the effects of shading across different patterns such as uniform column wise shading, uniform row wise shading and a triangular pattern of uniform shading. All the cases are analyzed for Np parallel connected cells tied in Ns series strings. It is also possible to expand this scheme to other conventional solar cell structures such as total-cross tied, Honey-comb or Bridge link [1]. This technique can act as a predictive model to foretell the performance under varying or uniform shading conditions prior to the actual installation of solar panels.

In order to predict the performance of a solar array under shaded conditions, a computer model is essential. Studying the effects of shading on the solar cells by testing on field is expensive. This report aims at modeling the effects of varying levels of shading on the above mentioned configurations using MATLAB [2]. Moreover it is difficult to maintain the same level of shading or varying numbers of shaded and fully illuminated cells throughout the experiment [3]. Photo voltaic (PV) systems are modeled using circuit simulators such as PSPICE as they can accurately predict the behavior. However, using higher-level modeling using MATLAB has gained importance in recent

years as it provides a better system level modeling and interactions [4-8]. This facilitates a quicker solution to obtain the unique maximum power point (MPP) on its power–voltage (P–V) curve.

Partial shading of single or more cells of a solar array reduce the power output of the whole array. It is one of the main causes of overheating of shaded cells and reduced energy yield of the module. Mismatched losses in solar cells with parallel and series configurations due to shading and excessive heating have been studied by [9-10]. A readily available solar cell library in MATLAB /SIMULINK has been used by many authors in [5][6][11] to study effects of shading. However these models are not suited when it comes to integrating PV models for more complex renewable power energy systems. Instead, the modeling used in this paper is an attempt to expand the circuit analysis of a single solar cell (as a single unit) for complicated random shading patterns on different topologies of the entire solar array.

II. MODELLING OF SOLAR CELL Shading of solar cells is a critical functional and

reliability issue as the shaded cells can get reverse biased and consume power resulting in loss of output power. The power losses in the individual shaded cells would result in local heating and increase the temperature. The increase in temperature creates thermal stress on the entire module and cause hot spots and local defects which potentially results in the failure of the entire array [12].

Figure 1 is the electrical representation of a 1-D solar cell with the following parameters: the photonic current IPH, the diode current ID, the total output current IM, series resistance RS, and shunt resistance RSH [13]. The parasitic elements, RS and RSH, are caused by resistances in solder bonds, emitter and base regions, cell metallization, and cell-interconnect bus bars, and resistances in junction-box terminals. The developed models are based on Figure 1 and also have been extended for use as solar arrays and in different patterns of shading. The cell current, IM is given as: �� � � ��� � � � �� ��� �� ������� �� � �������������� � (1)

2011 21st International Conference on Systems Engineering

978-0-7695-4495-3/11 $26.00 © 2011 IEEE

DOI 10.1109/ICSEng.2011.23

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where io represents the reverse saturation current of the diode D, and VM represents the total output voltage across the cell.

Figure 1. A circuit representation of solar cell with parasitic resistances

In order to model the random shading pattern across cells in an array, a basic structure of Np parallel strings comprising of Ns serially connected solar cells is considered. Depending on whether IPH > IM or IPH < IM, the cell is operating in either illuminated or shaded condition. Shading results in reduced photonic interactions in the solar cells and results in reduced power output and is represented in the solar cell model with reduced photonic currents. Depending on the evaluation for the photonic current, (2) and (3) are used to determine the output voltage for illuminated and shaded cases respectively. For each of the serial strings, the output voltage VM across each cell is calculated at respective illumination and summed over to derive the total output voltage VOUT.

�� � �! � �"� � #! $%��� � � � ��& �' ( � ��� � )*��� (2)

�+, � -��%��." � � � ���& � )*��/ � ��� � )*� (3)

where �"� is the thermal voltage, �+, is the voltage across individual shaded solar cell, and �� is the voltage across individual illuminated cell. The negative sign in the first term of (3) accounts for the negative voltage that a shaded cell can generate.

A. Shading across random cells in Ns X NP array design. To generate power output of around 1000 W an analysis for a 26x45 array of solar cells with 45 parallel cells connected in 26 series string configuration is carried out. A typical scenario studied for shading across different cells in the array is shown in the Figure 2. This is a rather complex illumination pattern to analyze where the voltage and the current across each cell is different depending on the insolation received at the respective cell. The algorithm developed is a general case for studying the effects of any pattern of shading across the cells in the array configuration for user defined number of parallel and series cells. Iterative techniques used to solve the nonlinear equations of the model are based on the flowchart given in Figure 3. The model is solved to yield the solution for the individual cell current.

Figure 2. Random Shading Pattern of Solar Cells

A 1% difference in the following equation: �012 ���012 � �) is used to determine the convergence of the entire module where ) is the load resistance, VOUT is the output voltage of the array and IOUT is the output current of the array. The process is continued until convergence takes place.

The advantage of using this type of modeling is that it can be extended to any type of shading patterns such as passing cloud, shadow casted by trees, bird droppings, etc.

III. SPECIFIC SHADING PATTERNS FROM THE GENERAL MODEL.

The following three specific patterns of shading across NS X NP array of cells have been analyzed in detail.

A. Row wise shading of 26X45 cell array. The general model discussed above is used to create a

scenario where a uniform shading is applied across the first parallel string of the 26x45 array configuration and is shown in the Figure 4(a). All other cells of the array are at maximum illumination. Fixed resistive load is maintained at the output to study the degradation in the maximum power transferred. Similar structure is implemented in PSPICE and the results are compared with the model.

B. Column wise shading of 26X45 cell array. For a fixed load resistance, a second scenario with

uniform shading across the first cell of each of the 26 series strings and maximum illumination across the other cells is maintained. This is indicated in the Figure 4(b) below. An initial guess of total output voltage is provided from which is used to calculate the output current across each cell. The reduction in power obtained from the model for different levels of shading is compared with PSPICE simulations.

C. Triangular pattern of shading across 26X45 cell array In the triangular pattern of shading of the array the

assignment of the shading levels to the individual cells is made in such a way so as to shade only the lower left corner portion of the array as shown in the Figure 4(c). Fixed resistance at the output is used and degradation in power for different shading levels is noted in proposed model and PSPICE.

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IV. RESULTS AND DISCUSS

A generic code for evaluating the perforcell array/module with different levels ofrandom positions in the architectural dimplemented and applied to cases suchcolumn-wise and triangular patterns. Apatterns are modeled to observe the degpower drawn by a fixed load resistance andload values. The load resistance is varied values to observe the maximum power pointhe reduction in power transferred to resistance for different shading patterns actabulated in Table I.

For the column wise shading, the percenin the total output power from no illumillumination is 0.8% in PSPICE while thatmodel is 1%.

Under uniform full illumination acroportion of the photonic current flows throu

Figure 3. Fl

ION rmance of a solar f shading across

design has been h as row-wise, All the shading gradation in the

d also for varying over a range of

nt. The results of the fixed load

cross the array is

ntage degradation mination to full t of the proposed

oss each cell, a ugh the diode and

maintains the necessary output voltof the current serves as the output c45x26 cell solar array, all the indivparallel strings add up to give the farray while the voltage across remains constant at the output voltacross each 45 parallel strings is voltage at the diode required to pcurrent is reduced resulting in a smand a reduced array output voltagshading is increased, the photonic diode forward biased. As a result, from the remaining 44 parallel through the diode of the shaded maintained constant which is instrcurrent values very close to tilluminated conditions. However, current from the entire array as silluminated cells is directed to the cconnected in parallel..

low Chart Used in Implementation of the Modelof Solar Cells

tage of the cell. The rest current of the cell. In the idual currents of each 45 final current for the solar each 26 parallel string

tage. When the first cell shaded, the amount of

produce the same output maller cell output voltage ge. As the percentage of

current cannot keep the a portion of the current illuminated cells flows cell and voltage is still rumental in keeping the that obtained in fully there is reduced output ome of the current from

corresponding shaded cell

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(a) (b) (c)

Figure 4. (a) Row-Wise Shading Pattern (b) Column-Wise Shading Pattern (c) Triangle Shading Pattern

TABLE I. OUTPUT POWER FOR ROW, COLUMN AND TRIANGLE SHADING PATTERN WITH A FIXED LOAD.

Column-Wise Shading Pattern Row-Wise Shading Pattern Triangle Shading Pattern Shading

(%) Output Power from

PSPICE (W) Output Power from

MATLAB (W) Output Power from

PSPICE (W) Output Power from

MATLAB (W) Output Power from

PSPICE (W) Output Power from

MATLAB (W) 0 653.6 607.2 653.69 607.2 653.6 607.9

20 653.1 606.2 653.03 603.30 649.1 603.7 40 652.7 606.5 652.01 602.43 644.5 599.5 60 651.9 600.3 649.86 600.78 640.0 595.3 80 650.6 600.2 376.57 367.51 635.5 591.1

100 648.1 601.1 51.48 47.82 631.1 587

Table I shows the degradation in the power for a case where the entire first row of the 45 parallel strings is shaded for various illumination values for fixed load resistance. When insolation level is below certain level, the photonic currents can be larger than the output current. As the shading increases, less forward current flows through the diode, resultin in reduced output voltage of the shaded cell. At certain level of shading the entire top row of cells have enough photonic current equal to the output current. Under this conditions the current flowing through the diode is zero resulting in almost no output voltage of the cell. In fact the complete array can be assumed to be devoid of the first row. Any further increase in shading causes the diode to be reverse biased. Under this condition entire top row of the module will be generating negative voltages. This implies that the entire row will start dissipating power instead of generating power. Any further increase in shading will result in a significant loss in power. This is indicated to 367 W as shading is increased from 60% to 80%. If the entire row is completely shaded, then the power developed by the module reduces to 48 W. The power deterioration from full illumination to no illumination for entire row in the array is approximately 92.1% and 92% for PSPICE and proposed model respectively.

An error of 5% - 7% in the measured values of power degradation between the proposed model and PSPICE measurements is observed in all the three shading scenarios. One source for this disparity is the condition for convergence is set to less than or equal to ±0.1 V for each

cell. When this error is compounded over the entire cells in the array, the cumulative error adds up. Simplified models are used in the proposed model as compared to those used in PSPICE. However, the advantage of the proposed model is that different shading configurations can be easily evaluated in the proposed model whereas the circuit simulation involves significant preprocessing.

B. Variation of load resistance to observe maximum power

point. The load resistance is varied ranging from 0.01 � to 3� for all the three shading patterns in order to observe the variation of power with load resistance. Figure 5(a) shows the results of output power variation against changing load resistance measured from proposed model and PSPICE simulations for random shading pattern across different cells in the 26X45 array design shown in Figure 5(b). It clearly shows that for a particular pattern of shading, for different illumination level a unique value of RL gives the maximum power point. Similarly, the load resistance was varied to study power under uniform shading levels for row, column, and triangle shading patterns. A unique value of load resistance transfers maximum power from the solar cell array to its output. The difference of maximum power corresponding to the particular load resistance value for proposed model and PSPICE is within 7% for all patterns od shading.

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V. CONCLUSIONS A general code for modeling shading effects for random

illumination across random solar cells in an array has been implemented. This can be extended to study different patterns of shading to predict the performance of solar arrays/panels prior to their installation. Moreover, load resistance variation to observe the maximum peak power for uniform/non uniform shading has been implemented for random or specific shading patterns. This can be further used to track maximum peak power under shaded conditions.

ACKNOWLEDGMENTS This work was supported in part by NSF under awards 0958298 and 0958355.

REFERENCES [1] D. Picault, B. Raison, S. Bacha, J. Aguilera, J. De La Casa,

“Photovoltaic array interconnections to reduce mismatch losses: a case study”, Int. Conf. on Env. and Elec. Engr., Prague, 2010.

[2] Matlab, www.mathworks.com. [3] Ramaprabha Ramabadran, Badrilal Mathur, “Effects of shading on

series and parallel connected Solar PV modules” Modern Applied Science,Vol.3, no.10, October 2009, pp. 32-41.

[4] Volker Quaschningt and Rolf Hanitscht, “Numerical simulation of current-voltage characteristics of photovoltaic systems with shaded solar cells,” Solar Energy Vol. 56, no. 6, 1996, pp. 513-520.

[5] Huan-Liang Tsai, “Insolation oriented model of PV module using matlab”, Solar Energy 84 ,2010, pp. 1318–1326.

[6] V. Di Dio , D. La Cascia, R. Miceli, C. Rando , “A mathematical model to determine electrical energy production in photovoltaic fields under mismatch effect”, Clean Electrical Power 2009.

[7] M.C. Alonso-Garc�´aa, J.M. Ruizb, W. Herrmann, “Computer simulation of shading effects in photovoltaics arrays”, Renewable Energy, vol. 31, 2006, pp 1986–1993.

[8] Engin Karatepe, Mutle Boztepe and Metin Colak, “Development of suitable model for characterizing photovoltaic arrays with shaded solar cells”, Solar Energy, vol. 81, 2007, pp.977-992.

[9] N.D.Kaushik, Anil K Rai, “An investigation of mismatch losses in solar photovoltaic cell networks”, Energy, Vol.32-Issue5, May 2007, pp. 755-759

[10] Nguyen, D.D., Lehman B, “Modelling and simulation of solar PV array under changing illumination condition”, Computers in Power Electronics, 2006, pp. 295-299.

[11] Tony Maine, Stewart Martin,John Bell, “Minimization of power loss from partially shaded solar cells arrays”, Proceedings of ISES World Congress 2007 (Vol. I – Vol. V), 2009, pp. 1551-1555.

[12] R. E. Hanitsch, Detlef Schulz and Udo Siegfried, “Shading Effects on Output Power of Grid Connected Photovoltaic Generator Systems”, Rev. Energy. Ren. : Power Engineering, 2001, pp. 93-99.

[13] M.C. Alonso-Garcia, J.M. Ruiz, “Analysis and modelling the reverse characteristic of photovoltaic cells”, Solar Energy Materials and Solar Cells, Vol 90, no. 7-8, May 2006, pp. 1195-1120.

[14] D. Picault, B. Raison, S. Bacha, J. Aguilera, “Forecasting photovoltaic array power production subject to mismatch losses”, Solar Energy 84, 2010, pp.1301-1309.

(a) (b)

Figure 5. (a) Output Power vs Load Resistance for random shading pattern with random illumination of cells (b) Random Shading pattern on random cells

TABLE II. VARIATION OF LOAD RESISTANCE FOR ROW-WISE SHADING PATTERN ACROSS 26X45 ARRAY.

Column-wise shading pattern Row-wise shading pattern Triangle shading pattern PSPICE MATLAB PSPICE MATLAB PSPICE MATLAB

Shading (%) RL(�) POUT (W) RL(�) POUT (W) RL(�) POUT (W) RL(�) POUT (W) RL(�) POUT (W) RL(�) POUT (W) 0 0.87 1021.6 0.86 1010.8 0.87 1021.6 0.86 1012.2 0.87 1021.6 0.86 1009.1

20 0.86 1007.5 0.85 997.71 0.85 996.3 0.84 988.1 0.85 1000.8 0.84 989.62 40 0.84 983.09 0.83 972.75 0.78 915.1 0.77 909.4 0.81 958.6 0.80 940.87 60 0.80 943.41 0.79 933.66 0.61 722.3 0.61 722.1 0.75 883.4 0.75 877.5 80 0.76 897.14 0.75 887.25 0.35 413.7 0.35 417.2 0.67 792.0 0.66 780 100 0.72 850.93 0.71 841.57 0.005 6.5 0.0014 1.6 0.59 693.6 0.58 682.5

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