MATHEMATICAL MODELLING AND SIMULATION OF A PARTIALLY SHADED PHOTOVOLTAIC MODULE … · 2016. 9. 9. · Fig. 2. Setting up a group of PV cells illuminated at 50%. These bypass diodes

MATHEMATICAL MODELLING AND SIMULATION OF A PARTIALLY SHADEDPHOTOVOLTAIC MODULE

Deli GORON1, Donatien NJOMO2Environmental Energy Technologies Laboratory (EETL), Faculty of Sciences, University ofYaoundé 1, P.O. Box 812, Yaoundé, [email protected] (corresponding author)[email protected]

AbstractPhotovoltaic installers are very much concerned with photovoltaic systems working under shadedconditions and this has led to detailed research in this domain. We show in this paper that theelectrical power produced by a partially shaded module is greatly reduced as compared to whenoperating under its optimal conditions. With the aim of having a better understanding of the impactof shading on the production of a photovoltaic module and thereby estimating the economicefficiency of a photovoltaic system, we have also worked on the modelling and simulation of apartially shaded photovoltaic module. The method used consists of first, modelling the current-voltage characteristics of the photovoltaic cells independently and then, summing them upaccording to the electrical configurations of the module. The results show that the bypass diodesreduce negative effects of shading on the production of electricity of a module. An estimation ofthe power loss is made at the maximum power point under shaded conditions.Key words: photovoltaic cells, group of PV cell, photovoltaic module partially shade, bypass diode,blocking diode, Maximum power point (MPP).

1. IntroductionIn order to promote the use of photovoltaicsystems, it is important to carefully examinethe power losses of these systems underpartially shaded conditions. Indeed, theshading of a PV module implies that PV cells,which constitute it, work in differentillumination conditions. The immediateconsequence of this is not only a significantreduction of the power generated by the PVmodule as compared to when operating atoptimal conditions but also, a risk ofdestruction of the PV module if it lacks aprotecting system.

Deli GORON, PhD student, Environmental Energy TechnologiesLaboratory (EETL), Faculty of Sciences, University of Yaoundé 1,P.O. Box 812, Yaoundé, Cameroon [email protected] Njomo, Professor, Environmental Energy TechnologiesLaboratory (EETL), Faculty of Sciences, University of Yaoundé 1,

P.O. Box 812, Yaoundé, Cameroon [email protected]

Under these real operating conditions, the PVcells are no longer identical and the I-Vcharacteristics curve is thus no longer easy tocalculate and depends on the behaviour ofeach PV cells. A detailed analysis of theelectrical behaviour of a partially shaded PVmodule therefore needs to take into accounteach cell’s I-V characteristics, protectingdiodes (bypass and blocking) and the variousexisting series and parallel connections of thecells. This complex combination is mainlycharacterized by the existence of non-linearequations which are difficult to solve. In orderto solve these equations, most authors usedthe Newton-Raphson's method [1], [2], [3],[4]. Moreover, this method presents anadvantage in that, a rapid quadraticconvergence of the initial values is obtainedwith results closed to the roots in such a way

International Journal of Scientific & Engineering Research, Volume 7, Issue 2, February-2016 ISSN 2229-5518 1187

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that a good solution could be gotten in only afew iterations steps. Many authors havealready studied the behaviour of a partiallyshaded PV module [5], [6], however, in mostcases, the PV cells are either completelyilluminated or completely shaded In thispaper we address the problem of consideringthat the shadow on the module affects severalPV cells at different shading rates.The mathematical modelling and thebehaviour of a partially shaded PV module atits maximum power point (MPP) is of greatimportance. For this reason, so manyalgorithms were developed to study themaximum power point tracking (MPPT) [7],[8], [9], [10] where the converters make adynamic research so that the PV systemfunctions best at this point. In addition, theMPP is determined by searching for themaximum point on the P-V curve or bysearching for the maximum value of the IVproduct in the characteristic I-V curve. Thiswork is of great importance in that; a partiallyshaded module produces a lower poweroutput as compared to that produced by anilluminated module. It is in this context thatdifferent scenarios have been developed toshow that the power at the maximum powerpoint is sensitive to a shadow casted on amodule when some of the cells in groups areshaded. This work portraits the importance ofprotection diodes to abate the impact of theshadow on the electrical production of a PVmodule. Furthermore, according to theelectrical interconnections, twoconfigurations of the PV module are studied;one of which is that consisting of only PVcells connected in series, and the other; amixed series/parallel connection.This paper is divided into four sections:Section 2 describes the method adopted tostudy the I-V characteristics of the cells atvariable shaded rates, the grouped cellstogether with their different electrical

connections. The iterative method which isused is also presented. Section 3 analyses thebehaviour of a module with 36 cells subjectedto four different shading cases. Anotheranalysis of a module with 72 cells in a mixedconnection is also described in three differentshading cases. The last section 4 is theconclusion of this work.

2. MethodThe proposed method is based on the additionof the I-V characteristics of each PV cellcompositing the module. This process isdivided into four (04) main parts according tothe electrical interconnections (series andparallel) of the cells in the module as shownin figure1:

Fig. 1. Modelling strategy of a PV module infaulty operation.2.1. I-V characteristics of PV cells andmathematical solving methodThe I-V characteristic of an illuminated cell isdescribed by the nonlinear equation (1) [7].

( )( ) ( )1 1 0 1, 1 1, 1exp ( . ) 1 .ph cell s cell s shI I I q AkT V I R V I R Ré ù= - + - - +ë û(1)

where, Rsh is the cell shunt resistance, Rs thecell series resistance, and q is the electroncharge, k is Boltzmann constant, T is thetemperature cell, I0 is the diode reverse biassaturation current, A is the diode idealityfactor, Iph1 is the current generated by the



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incident light. The equation of the I-Vcharacteristic of a partly shaded cell,according to Bishop's model is given by therelation (2). [2, 3, 4, 11]:

( )( )( ) ( )

2 2 0 2, 2

2, 2 2, 2

exp ( ) 1

( )/ 1 1 ( )/

ph cell s

ncell s sh cell s br

I I I q AkT V I R

V I R R a V I R V-

é ù= - + - -ë ûé ù+ + - +ê úë û

(2)

where a is the Bishop's fitting coefficient ; nthe exponent of avalanche breakdown; Vbrthe cell junction breakdown voltage .Iph1 and Iph2 are the photocurrents ofilluminated and shaded PV cells,respectively. Equation (3) links these terms[5], [11]:

2 1.ph phI Ia= (3)

where a is the shading coefficient of valuebetween 0 and 1; when a= 1 the cell iscompletely illuminated and when a = 0 thecell is completely shaded.Indeed, the shading coefficient is defined asthe ratio between the solar radiation receivedby a shaded cell (module, array) (Gsha) andthat of an illuminated cell (Gill) as indicatedby (4) [4], [12]:

1 / 1 /i sha ill iG G Aa z= - = - (4)where zi is the shaded area of the cell and A,the total surface area of the cell.

2.2. Mathematical model resolutionThe I-V characteristic is obtained byimposing the current over a given range,which enables the search for thecorresponding voltage according to (5):

cell imposedI I= (5)

( ), , , 0,

cell cell i if I Vcell cell iI V

a =¾¾¾¾¾¾®where f(Icell,Vcell,i, ai) is a non-linear implicitfunction, associated with ith PV cell and a itscorresponding shading coefficient defined by(6).

( ) ( )

( )( )( ) ( )

,

0 , ,

0 ,

, ,

( , , )

. exp ( / )( . ) 1 . / 0 1

. exp ( / )( . ) 1

. / 1 1 ( . )/ 0 1

cell i i

i ph cell i s cell i s sh i

i ph cell i s

ncell i s sh cell i s br i

f I V

I I I q AkT V I R V I R R if

I I I q AkT V I R

V I R R a V I R V if

a

a a

a

a-

=

ì é ù- + - + - - + = =ë ûïïïí é ù- + - + -ë ûïï é ù- + + - + = ¹ï ê úë ûî

(6)The value of the voltage Vcell,i across the cellindexed i for a given current (I) is obtained byusing the Newton-Raphson method, whichoffers considerable advantages over othernumerical methods. Moreover, it has theadvantage of a rapid quadratic convergence ofthe initial values near the roots so as to obtaina good solution calculated in a few iterations.The Newton-Raphson iterative methodenables an approach to the functionf(Vcell,I,ai)=0, solution to (7):

( ) ( )( ), , , , ,( ) ( 1) ( 1), , / ( 1), , /cell i cell i cell i i cell i i cell iV k V k f V k I f V k I Va a= - - - ¶ - ¶ (7)where k is the number of iterations. Thisiteration is performed once an initial value isgiven to Vcell,i(1). The iteration will stop whentwo consecutive values of the voltage satisfythe following condition:

, ,( ) ( 1)cell i cell iV k V k e- - p (8)where e is very close to zero. The derivativeof the characteristic function f (Vcell,I,ai) withrespect to the voltage Vcell is given by relation(9):

( )

( )

( )( ) ( )

( )

, ,

0 ,

0 ,

,

,

( 1), , /

( . )/( )exp ( / )( ( 1) . ) 1/ 1

( . )/( )exp ( / )( ( 1) . ) 1/

/ 1 ( ( 1) . )/

( . / ) ( ( 1) . )/ . 1 (

cell i i cell i

cell i s sh i

cell i s sh

nsh cell i s br

br cell i s sh

f V k I V

qI AkT q AkT V k I R R if

qI AkT q AkT V k I R R

a R V k I R V

an V V k I R R V

a

a

-

¶ - ¶ =

- + + =

- + + +

- - +

+ - + -( ) 1, ( 1) . )/ 1n

cell i s br ik I R V if a- -

ìïïïïíïïïï - + ¹î

(9)2.3. I-V characteristics of a group PV cellsA group of PV cells is a set of PV cells inseries (12 cells in our study) on which is



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mounted one bypass diode as shown inFigure (2) [2], [3], [13];

Fig. 2. Setting up a group of PV cellsilluminated at 50%.

These bypass diodes can help to avoid the hotspot effect which usually occurs when onecell among the series connected cells isshaded. For most manufacturers, a modulemade up of 36 cells is equipped with three(03) bypass diodes [13], that is, one diode ina series of 12 PV cells. As reported in theliterature [3], [14] a few modules also haveone (01) bypass diode for eighteen (18) cells.The number of cells protected by a bypassdiode can thus vary between different modulemanufacturers.When the bypass diode is active, it happenswhen one or more PV cells are crossed by acurrent greater than the short circuit current,the voltage at the terminals of the group iszero if the sum of the voltages of all cells isnegative. We then have the relation (10):

, ,1 1

,

,1

0

0 0

cells cells

cells

N N

cell i cell ii i

group j N

cell ii

V if VV

if V

= =

=

ì³ï

ï= íï £ïî

å å

å (10)

group bypass cell fixedI I I I= + =Figure 3 is a simplified electrical circuit of agroup of PV cells having different shadingrates.

Fig. 3. A simplified electrical circuit for agroup of PV cells shaded at different rates.

Thus, for a (01) partially illuminated cell (at50%) and eleven (11) cells completelyilluminated (see Figure 2), the I-Vcharacteristic curve for the 12 grouped PVcells is shown in Figure 4.

Fig. 4. I-V Characteristic of a group of PVcells with bypass diode.

2.4. Series connection of several groups ofPV cellsIn order to increase the voltage at theterminals of the PV module, several groups ofcells are connected in series. These seriesconnection form the modules we most oftenencounter. Thus, the current flowing in amodule is the same as the one that circulatesin the various groups; while the sum of thevoltages across the different group of cellsprovides the voltage of the module asdepicted in Figure 5 and (11):

module groupI I= (11)

1 2 3 121110

-20 -15 -10 -5 0 5 100

1

2

3

4

Voltage (V)

Cur

rent

(A)

I-V characteristic of 11 PV cells completely illuminated I-V characteristic of 1 PV cell partially shaded at 50% I-V characteristic of a PV group without by-pass diode I-V characteristic of a PV group with an active by-pass diode



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mod ,1

groupN

ule group ii

V V=

= å

Fig. 5. An implicit power circuit of amodule.

Figure (6) shows how the I-V characteristiccurves of different PV cells groups aresummed up to give the I-V characteristic of aPV module.

Fig. 6. IV characteristic of a PV modulemade of 3 groups with one in a poor

condition.

2.5. Parallel PV cellsSome PV modules have mixedinterconnections (series-parallel). Thus, inorder to increase the current of a moduleseveral strings (of cells) can be mounted inparallel in the module. A blocking diode isconnected in series in the string with the roleto protect the group of PV cells against thenegative currents that may be generatedduring different connections in parallelstrings. A module of 72 PV cells may forexample, be mounted in two (02) parallelstrings of 36 cells each as shown in Figure 7.

Fig. 7. Implicit electrical circuit for amodule with two strings.

When some of the PV cells are shaded, thegenerated currents and voltages at theterminals of each string connected in parallelno longer have the same values. Howeversince the voltages across the string when putin parallel must be equal; then, the current ineach string must be constant. To solve thisproblem, we proceed as follows:

-We will fix the module voltage value:

mod ule fixedV V= (12)

- The value of the current of the string k afterthe parallel connection, may be obtained froman interpolation of the I-V characteristic ofthe string (Istring,k, Vstring, k) to the expectedvalue of the voltage of the module, satisfyingthe constraint that the voltage should be thesame for each string [3], [4]:

Istring,k=interpolation(Vmodule,Istring,k,Vstring,k) (13)The blocking diode crashes when the voltageof the string k becomes lower than the voltageof the module:

, , mod0string k string k uleI for V V= £ (14)

The expression of the module current is thengiven by (15):

(15)

0 5 10 15 20 25 300

1

2

3

4

Voltage (V)

Cur

rent

(A)

Group of partialliy shaded PV cells (gp1)2 groups of completely illuminated PV cells (gp2+gp3)Resultant PV module: gp1+gp2+gp3

I2

I1 I1+I2

String 1

String 2

V2

V1

Blocking diodes

1 2 1211 13 14 2423 25 26 3635

PV Module

37 38 4847 49 50 6059 61 62 7271

module ,1=

= åbrancheN

string kk

I I



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Figure 8 shows how 2 strings connected inparallel are influenced by a blocking diode.

Fig. 8. I-V characteristic of a PV moduleprotected by a blocking diode.

3. Results and Discussion.In this section, different scenarios aredeveloped according to the geometrical shapeof the shadow on the module. We willconsider a module made of 3 groups, eachcomprising of 12 PV cells.The module used is a Solarex MSX-60 whosenecessary characteristics for our simulationare listed in Table 1.

Table. 1. Useful parameters for simulation.

Parameters ValuesNumber of cells 36Number of bypass diodes 3Iph (A) 3.8119Io (A) 1.859.10-7A 1.360Rs(Ω) 0.180Rsh (Ω) 360.002A 0.1N 3Vbr (V) -20

Scenario 1: A single cell is non-illuminatedFigure 9 is a module that consists of 36 PVcells divided into 3 groups each having abypass diode shunt: Group 1 contains the PVcells numbered from 1 to 12; Group 2contains the cells numbered from 13 to 24;Group 3 contains the cells numbered from 25to 36.

In the diagram below, only one cell is shadedand the rest are completely illuminated. ThePV cell in bad working conditions is shadedin proportions of 0%, 25%, 50% and 75%.

Fig. 9. Geometric location of shade on a PVmodule.

Figure 10 below shows a module’s I-V and P-V characteristic curves for the differentshading percentages.

Fig. 10. I-V (a) and P-V (b) characteristiccurves for a shaded module in the

configuration of figure 9.

In Table 2, we present the optimal power atMPP for different values of the shadingcoefficient and the power loss resulting fromthe production of a perfectly illuminatedmodule. We notice here that one shaded PV

0 2 4 6 8 10 12 14 16 18 20 22-2

0

2

4

6

8

Cur

rent

(A)

Voltage (V)

I-V curve string 1 I-V curve string 2 I-V curve for the module

Without a blocking diode

With a blocking diode

0 5 10 15 20 250

1

2

3

4

Voltage (V)

Curre

nt(A

)

a)-

3/4 cell is shaded

1/2 cell is shaded

1/4 cell is shaded

0 5 10 15 20 250

20

40

60

Voltage (V)

Pow

er(W

)

b)-

3/4 cell is shaded

1/2 cell is shaded

1/4 cell is shaded



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cell can reduce the electrical power of amodule to more than 30%. This can beexplained by the fact that the currentcirculating in a group of cells is greatlyinfluenced by the shaded cell (see figure 4).This “defective” group placed in series withtwo illuminated groups considerably reducesthe current of the PV module for a givenvoltage (see figure 6).

Table. 2. Power losses of a module at MPPfor shaded PV cell at different percentages.

Shadingcoefficient

Power atMPP (W)

Power loss(%)

0.25 37.5822 30.670.50 37.5822 30.670.75 49.1520 9.32

1 54.2048 0

Scenario 2: Shadow of 5 PV cells withdifferent shading factorsThe results of the geometric distribution ofthe shadow on the module of Figure 11 are asfollows: Group1: one (01) PV cell shaded at95% (cell No. 5), two (02) PV cells shaded at50% (No. 4 and 5) and nine (09) perfectlyilluminated cells; Group 2: one (01) PV cellshaded at 50% (No. 14) and eleven (11)perfectly illuminated cells; Group 3: one (01)shaded cell to 75% (No. 32) and eleven (11)perfectly illuminated cells.

Fig. 11. Location of shade on a PV module.

The I-V and P-V characteristic curves of thismodule are given in Figure 12. Since thegroups of PV cells are shaded, their resultant

gives a faulty module whose power at theMPP is 12.3323 W compared to 56.3733 Wfor a perfectly illuminated module. Thepower loss at this point is of the order of 78%.In this case, the electrical power produced bythe PV module can reduce to more than 80%.This power loss can be explained by the factthat; the three groups of cells are stronglyinfluenced by the number and the I-Vcharacteristic of the shaded cells.



Scenario 3: shadow of a larger range on themoduleIn this example, the shadow extend is greaterand the distribution of 9 PV cells are asfollows (Figure13):- Group1: four (04) cells completely shaded(No 8, 9, 10 and 11), two (02) PV cellspartially shaded to 50% (N° 7 and 12) and six(06) perfectly illuminated PV cells;- Group 2: twelve (12) perfectly illuminatedcells;- Group 3: three (03) PV cells illuminated at50% and nine (09) illuminated cells.

11 8 29 26

12 7 30 25

13 6 31 24

14 5 32 23

15 4 33 22

16 3 34 21

17 2 35 20

10 9 28 27

18 1 36 19

0 5 10 15 20 250

1

2

3

4

Voltage (V)C

urre

nt(A

)

a)-

Group 1

Group 3

Module completely illuminated

Shaded module : sum of groups 1,2 & 3

Group 2

0 5 10 15 20 250

20

40

60

Voltage (V)

Pow

er(W

)

b)-

Shaded module

Module completely illuminated



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Fig. 13. Location of shade on a PV module.

Figure 14 shows the module’s characteristiccurves I-V and P-V. The power loss at MPPis about 60% for a calculated power 22.7487W for the faulty module.It is noticed that despite the range of theshadow on this module, the power loss islower compared to scenario 2 (78%). This isexplained by the fact that the shadow on themodule of scenario 2 affects all of the 3groups of PV cells. For scenario 3, two (2)groups of the PV cells are in poor conditionsand one (01) in good condition. It is the lattergroup that reduces the losses.



Scenario 4: the influence of shadow on agroup of a module

In this example, 3 PV cells are completelyshaded (a=0) as shown in the followingconfigurations:- each of the three (3) groups has one (01)shaded PV cell (see Figure 15-a);- one of the groups contains the three (03)shaded PV cells (see Figure 15-b);- two (02) groups contain the shaded cells andthe third group is completely illuminated (seeFigure 15-c).

Fig. 15. Location of a PV module with 3shaded PV cells: the 3 PV cells are divided

into 3 groups (a); 3 PV cells belong to asingle group (b); 3 PV cells belong to 2

groups (c).Figure 16 describes the appearance of themodule’s I-V and P-V characteristic curves inthe 3 configurations.We note that, when each of the 3 groups hasa shaded PV cell, the maximum power pointis very low. In this case, the power loss isabout 99% against 66.7% and 33.3% whenthe three cells are distributed on two groupsof cells, and one cell groups respectively. Wecan thus retain that any shadow casted on aPV module reduces more of the electricalpower produced when it shades many groupsof cells.

11 8 29 26

12 7 30 25

13 6 31 24

14 5 32 23

15 4 33 22

16 3 34 21

17 2 35 20

10 9 28 27

18 1 36 19

0 5 10 15 20 250

1

2

3

4

Voltage (V)

Curre

nt(A

)

Group 2

a)-

Group 1

Group 3

Shaded module: sum of groups 1,2 & 3

illuminated module

0 5 10 15 20 250

20

40

60

Voltage (V)

Pow

er(W

)

b)-

Shaded module

Illuminated module

11 8 29 26

12 7 30 25

13 6 31 24

14 5 32 23

15 4 33 22

16 3 34 21

17 2 35 20

10 9 28 27

18 1 36 19

11 8 29 26

12 7 30 25

13 6 31 24

14 5 32 23

15 4 33 22

16 3 34 21

17 2 35 20

10 9 28 27

18 1 36 19

11 8 29 26

12 7 30 25

13 6 31 24

14 5 32 23

15 4 33 22

16 3 34 21

17 2 35 20

10 9 28 27

18 1 36 19

a b c



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Fig. 16. The characteristic curve I-V (a) andP-V (b) for a faulty module in the


Scenario 5: Module with 2 strings inparallel, one containing a shaded PV cell.Consider a PV module consisting of 2 stringsof 36 cells each mounted in parallel. On eachstring is mounted a blocking diode. Only onecell is shaded (see Figure 17).

Fig. 17. A module with 2 parallel strings,containing one shaded PV cell.

By varying the shading rate of the shaded cell,we obtained I-V and P-V characteristics ofthe module as shown in figure18.

Fig. 18. I-V (a) and P-V (b) characteristiccurves for a shaded PV module in the


We notice here that for shadow casted on acell, the electrical power of the module canreduce to about 27.5%. This power lossslightly smaller than that of scenario 1 can beexplained not only by a larger number of PVcells but also by the introduction of a blockingdiode which prevents the current comingfrom the faulty string to go through the otherstrings.The energy balance of this module, themaximum power point is given in Table 3.

Table. 3. Energy balance of a module with 2strings in parallel and one shaded cell.

Shadingcoefficient

Power atMPP (W)

Power lossat the MPP(W)

0 79.9565 27.58490.25 79.9565 27.58490.50 87.9530 20.34270.75 103.9821 5.82541 101.4142 0

Scenario 6: Shadow rate on 5 PV cells onthe same string of a PV module at differentshading factors.

0 5 10 15 20 250

1

2

3

4

Cur

rent

(A)

Voltage (V)

a)-

Module with 3 partially shaded groups


Module with 1partially shaded group

Completely illuminated module

0 5 10 15 20 250

20

40

60

Voltage(V)

Pow

er(W

)

b)-


Module with 1partially shaded group



0 5 10 15 20 250

2

4

6

8

Voltage (V)

Cur

rent

(A)

a)-

Module of which 1 cell is completely shaded

Module of which 3/4 cell is shaded

Module of which 1/2 cell is shadedModule of which 1/4 cell is shaded

illuminated module

0 5 10 15 20 250

50

100

150

Voltage (V)

Pow

er(W

)

b)-

Module of which 1/4 cell is shadedModule of which 2/4 cell is shadedModule of which 1/2 cell is shadedModule of which 1 cell is completely shaded

illuminated module



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One of the 2 parallel strings comprises of five(05) shaded PV cells as described in Scenario2, and the other string is completelyilluminated (see Figure 19).

Fig. 19. A 2 strings module of which 1contains 5 shaded cells.

The I-V and P-V characteristic curves of thismodule are given in Figure 20.



This shadow on the module causes powerlosses of about 50% at MPP. Here, theelectrical power losses are higher than thosein scenario 5 (27.5%) because one of thestrings contains shaded cells in all of itsgroups. As compared to scenario 2 where theelectrical power loss is about 80%, thenumber of cells and the presence of a

blocking diode explains the power reductionin scenario 6.

Scenario 7: Shading rate on 20 PV cellssymmetrically distributed in a module with2 parallel strings

The 20 PV cells of a module are shaded atdifferent rates according to the followingshading distributions: the first group of PVcells has 6 shaded PV cells in which 4 arecompletely shaded and 2 shaded at a rate of50%; the second group contains 4 shaded PVcells at a rate of 50%; the third group iscompletely illuminated. These shaded celldistributions are the same for the two stringsas shown in Figure 21.

Fig. 21. Shading of 20 PV cells on a 2stringed module.

The I-V and P-V characteristic curves of thismodule are given in Figure 22.For this scenario, the power losses at MPPhave been evaluated to be around 60%. Thepower losses are greater than those ofscenario 6 because the shadow casted on amodule is not only large in size but alsobecause it shades both strings.

0 5 10 15 20 250

2

4

6

8

Voltage (V)

Cur

rent

(A)

Partially shaded module


0 5 10 15 20 250

20

40

60

80

100

120

Voltage (V)

Pow

er(W

)

b)-





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4. ConclusionIn this paper, a mathematical modeling and adescription of the behavior of a PV module indifferent scenarios operating under partiallyshaded conditions are examined. It isobserved from this study that a PV modulesubjected to shading phenomenon, no matterhow small it could be, causes a considerabledecrease of the power produced even in thepresence of protecting diodes that reduce theshading effects. Power losses observed atMPP helped us to notice the aforementionedphenomenon. It is also observed that when ashadow casted on a PV module shades a largenumber of groups of cells protected by a by-pass diode, the electrical power loss isgreater. Likewise, the electrical power loss isless when, less strings are shaded by theshadow casted on a module. This is becausethe I-V characteristic (or P-V) of a singlyshaded PV cell considerably influences thatof the whole group, it will thus beadvantageous to increase the numbers ofgroups of cells as well as a mixed electrical

interconnection to limit the impact of theshaded cells on the other illuminated cells.Since the losses are significant at the level ofa partially shaded module, we plan to extendthis study to a photovoltaic array and considera more dense shadow. Such a study will behelpful to have a better understanding of theshading problem and thus increase theeconomic efficiency of PV systems, which isthe main concern of PV installers.

Conflict of InterestsThe authors declare that there is no conflict ofinterests regarding the publication of thispaper.

References[1] V. QUASCHNING and R. HANITSCH,Numerical simulation of photovoltaicgenerators with shaded cells, 30thUniversities Power Engineering Conference,Greenwich, Sept. 5-7, (1995), pp. 583-586.

[2] G. NOTTON, I. CALUIANU, I. COLDAet S. CALUIANU, Influence d’un ombragepartiel sur la production électrique d’unmodule photovoltaïque en siliciummonocristallin, Revue des EnergiesRenouvelables Vol. 13 N°1 (2010) pp. 49 -62.

[3] L. BUN, Détection et localisation dedéfauts dans un système photovoltaïque,thèse de l’université de Grenoble, France,2011.

[4] E. DIAZ-DORADO, J. CIDRAS et C.CARRILLO, Discrete I–V model for partiallyshaded PV-arrays, Solar Energy 103 (2014)96–107.

[5] S. SILVESTRE et A. CHOUDER, Effectsof Shadowing on Photovoltaic ModulePerformance progress in photovoltaics:research and applications, research shortcommunication Prog. Photovolt: Res. Appl.(2007).

0 5 10 15 20 250

2

4

6

8

Voltage (V)

Cur

rent

(A)

a)-



0 5 10 15 20 250

50

100

150

Voltage (V)

Pow

er(W

)

b)- Completely illuminated module

Partialy shaded module



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[6] A. GUENOUNOU , A. MAHRANE, Z.SMARA and F. CHEKIRED, Simulation ofthe electrical behavior of a partially shadedPV module in Matlab/Simulink, Revue desEnergies Renouvelables ICESD’11 Adrar(2011) 53 – 61 53.

[7] Mohammad Mehdi SeyedMAHMOUDIAN , Saad MEKHILEF,Rasoul RAHMANI, Rubiyah YUSOF andEhsan TASLIMI RENANI, AnalyticalModeling of Partially Shaded PhotovoltaicSystems, Energies 2013, 6, 128-144.

[8]Tey Kok SOON and Saad MEKHILEF, AFast-Converging MPPT Technique forPhotovoltaic System Under Fast-VaryingSolar Irradiation and Load Resistance, IEEEtransactions on industrial informatics, VOL.11, N°. 1, February 2015.

[9] Tey Kok SOON and Saad MEKHILEF,Modified incremental conductance MPPTalgorithm to mitigate inaccurate responsesunder fast-changing solar irradiation level,Science DirectSolar Energy 101 (2014) 333–342.

[10] Tey Kok SOON and Saad MEKHILEF,Modified Incremental ConductanceAlgorithm for Photovoltaic System UnderPartial Shading Conditions and LoadVariation, IEEE transactions on industrialelectronics, VOL. 61, N°. 10, October 2014

[11] G. VENKATESWARLU, P. RAJU,Simulink Based Model of Photovoltaic Cell,International Journal of Modern EngineeringResearch (IJMER) Vol.2, Issue.4, pp-2668-2671, July-Aug. 2012.

[12] Mamien PICAULD, reduction ofmismatch losses in grid-connectedphotovoltaic systems using alternativetopologies, PhD thesis, university ofGrenoble, France, 2010.

[13] Sylvain BRIGAND, Installationssolaires photovoltaïques, Editions LEMONITEUR, 2011.

[14] Anne LABOURET et Michel VILLOZ,Energie solaire photovoltaïque, Le Moniteur,Dunod, 2009.



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Documents

MATHEMATICAL MODELLING AND SIMULATION OF A PARTIALLY SHADED PHOTOVOLTAIC MODULE … · 2016. 9. 9. · Fig. 2. Setting up a group of PV cells illuminated at 50%. These bypass diodes