Research ArticleResearch on Parameter Distribution Features of PhotovoltaicArray under the Cover and Shadow Shading Conditions

Honglu Zhu12 Cao Yu23 Lingxing Lu2 Weiwei Lian2 Jianxi Yao 12 and Yang Hu 1

1State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power UniversityChangping District Beijing China2School of Renewable Energy North China Electric Power University Changping District Beijing China3China Three Gorges New Energy Co Ltd Beijing China

Correspondence should be addressed to Yang Hu hooyoungncepueducn

Received 19 April 2018 Accepted 5 July 2018 Published 6 August 2018

Academic Editor Jegadesan Subbiah

Copyright copy 2018 Honglu Zhu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The outdoor operating photovoltaic arrays have two different shading conditions shadowing and covering The shading causes adecrease in output power of photovoltaic system and may bring hot spots which causes physical damage to the array This paperstudies the electrical parameter distribution feature of photovoltaic array under different shading conditions by means of analogsimulation and empirical testing Through introducing theoretical computational method of the electrical parameters itdescribes the distribution features of the electrical parameters of photovoltaic array The results indicate that the influence oflocal shadowing on the current of array can be neglected Shadowing decreases the optimal operating voltage while coveringleads to a decrease in the optimal operating voltage and the open-circuit voltage The drop magnitude of voltage is associatedwith the number of the shaded cell strings and the string voltage The two shading types can be identified on the basis ofdistribution rules of open-circuit voltage and optimal operating voltage Simulations and experiments verify the consistency ofthe rules Relevant conclusions provide a reference for modeling online fault diagnosis and optimization design of themaximum power tracking algorithm of photovoltaic array under different shading conditions

1 Introduction

As the most important method for solar energy utilizationphotovoltaic power generation is developing rapidly Withthe world cumulative photovoltaic (PV) installed capacityof up to 390GWp in 2017 PV power generation plays anincreasingly important role in the energy supply structureIn actual operation PV arrays are usually distributed in avery large region due to their low power density Thereforeshadowing from the front and rear rows of photovoltaic arrayis often inevitable due to the restriction of floor space Mean-while photovoltaic arrays are mostly shaded by tall buildingstall trees fallen leaves and birdsrsquo droppings It is commonthat the photovoltaic arrays usually operate under differentshading conditions [1 2] The temporary shadowing of PVarrays will lead to a decrease in array efficiency increasedpower loss and more complex output characteristics Theprolonged covering can cause excessively high local

temperature hot spots and breakdown phenomenon whichadversely influence the output efficiency and service life ofthe PV modules [3 4] Therefore the good understandingof electrical parameter transfer law of PV arrays under differ-ent shading conditions is significant for the performanceassessment fault diagnosis and optimal operation of thephotovoltaic power station

At present scholars both locally and abroad are conduct-ing series of simulations and experimental studies on the out-put characteristics of the PV modulesarrays under shadingconditions In [5ndash7] MATLAB-Simulink is used to establisha simulation model of photovoltaic array under the shadow-ing condition and concluded that the output of the PV arrayexhibits a multipeak and stepped shape under the shadowcondition In [8] it is concluded that hot spots occur whenthe short-circuit current of the photovoltaic cells is smallerthan the electric current flowing through the cells based onthe simulations and experimental studies of the reverse

HindawiInternational Journal of PhotoenergyVolume 2018 Article ID 9207917 14 pageshttpsdoiorg10115520189207917

Bishop model of photovoltaic arrays In [9 10] it is con-cluded that the loss of the output power increases as the shad-ing area increases and the more the cell strings are shadedthe greater the power loss under the same area is In [11] itis pointed out that the conventional maximum power pointtracking (MPPT) algorithms (such as the conductance incre-ment method and the disturbance observation method) aresusceptible to failure due to the local extreme point underthe shadowing condition In [12ndash14] some improved MPPTalgorithms are proposed to raise the output efficiency of thephotovoltaic array under the shadowing condition In actualengineering PV arrays may be subjected to two types ofshading that is the shadow shading arising from tall build-ings and the front and rear rows of array and the cover shad-ing arising from objects such as fallen leaves and dust In theabove literature however only the output properties of pho-tovoltaic array under the shadow condition by means of sim-ulation or experiment are studied but no theoretical analysesor experimental studies are conducted on the cover shadingIt is impossible to systematically describe the distributionrules of electrical parameters of photovoltaic array in actualoperation A research on the output characteristics and therules of electrical parameter distribution of photovoltaicarray under different shading conditions is therefore has sig-nificant theoretical and engineering application

To illustrate the output characteristics and the electricalparameter distribution feature of photovoltaic array underthe shadow and cover conditions the paper first presentsmathematical description of photovoltaic cells modulesand arrays and establishes the appropriate Simulink modelDesigning simulation experiments under the two shadingconditions and discussing the theoretical maximum powerpoint voltage and current as the contrasting parameters forempirical testing were considered in this study Comparingthe theoretical results with experimental results concludesthe rules of electrical parameter distribution of the photovol-taic array under various shading conditions The simulationresults coincide with the empirical testing results

2 Mathematical Models of Photovoltaic CellsModules and Array

21 Equivalent Circuit Model of Photovoltaic Cells Photovol-taic cell converts the luminous energy into electricalenergy through the photovoltaic effect The analysis pro-cess of this paper is based on the equivalent circuit ofthe photovoltaic cell of the monolithic diode model asshown in Figure 1 where Iph is the photogenerated

current ID is diode current Ish is parallel current IL isoutput current Rsh is parallel resistance Rs is series resis-tance and RL is external load

The voltage-current equation can be expressed as follows

IL = Iph minus I0 exp q U + RsIAKT

minus 1 minusU + RsIRsh

1

where I0 is reverse saturation current of diode q is electroncharge (1 602 times 10minus19 C) A is ideal coefficient of diode andK is Boltzmann constant (1 38 times 10minus23 JK)

The photogenerated current Iph can be considered toapproximate the short-circuit current of photovoltaic cellIsc and the tail term U + RsI Rsh can be ignored hence itis much smaller than that of the short-circuit current Equa-tion (1) therefore can be rewritten as follows

IL = Isc 1 minus C1 exp UC2Uoc

minus 1 2

where C1 and C2 are the definition coefficients In case ofmaximum power point (I = Im U =Um) and open-circuitvoltage (I = 0 U =Uoc) in (2) we can obtain

C1 =Isc minus ImIsc

lowast exp minusUmC2 lowastUoc

3

C2 =UmUoc minus 1ln 1 minus ImIsc

4

External operating environment is not considered in theexternal behavioral characteristics of the photovoltaic cellsdescribed in (2) (3) and (4) However the output of the pho-tovoltaic modules is primarily influenced by solar irradianceand temperature Therefore it is necessary to consider thechanges in solar irradiance and temperature during the pro-cess of photovoltaic module simulation as below [15]

Isc = Iscref 1 + a T minus T ref sdotSSref

5

Uoc =Uocref 1 minus c T minus Tref ln e + bSSref

minus 1 6

Im = Imref 1 + a T minus Tref sdotSSref

7

Um =Umref 1 minus c T minus Tref ln e + bSSref

minus 1 8

Rs

Rsh

IshID

Iph

IL

RLUoc

Figure 1 Equivalent circuit of the photovoltaic cell

2 International Journal of Photoenergy

where S and Sref are the solar irradiance received by pho-tovoltaic cells and solar irradiance under standard condi-tions respectively T and Tref are actual temperature andtemperature of photovoltaic cells under standard condi-tions respectively and a b and c are correction coeffi-cients where a = 0 0008degC b = 0 2 and c = 0 002degC

Equations (5) (6) (7) and (8) describe the distribu-tion features of theoretical short-circuit current open-circuit voltage and voltage and current at optimal operat-ing point of photovoltaic cells under different solar irradi-ances and temperatures The electrical parameters ofphotovoltaic array under different shading conditions areanalyzed using (5) (6) (7) and (8) in the subsequentexperimental process

Based on the above mathematical model the simula-tion model is established for photovoltaic cells as shownin Figure 2 There are two inputs irradiance and temper-ature The photogenerated current Iph does not changewith the operative mode of photovoltaic cells when theirradiation intensity is constant A constant current sourceIph is therefore used for simulation The circuit alsoincludes bypass diode parallel resistance Rsh and seriesresistance Rs where R is the output load

22 Model of Photovoltaic Modules and Array The currentand voltage generated by a single photovoltaic cell arenot enough for the load Generally many photovoltaiccells are connected in series or in parallel to create a pho-tovoltaic module [16] In a photovoltaic power stationseveral modules are connected in series or in parallelThe modules and arrays might be connected in a way asshown in Figure 3

It is assumed that the number of cells in series in the pho-tovoltaic module is n and the number of cells in parallel ismThen the parameters of the photovoltaic module may beexpressed as follows

Uoc‐module = n sdotUocUm‐module = n sdotUmUmodule = n sdotU Isc‐module =m sdot IscIm‐module =m sdot ImImodule =m sdot I

9

It is assumed that the photovoltaic array comprises of Nphotovoltaic modules in series and M photovoltaic modulesin parallel Then we can obtain

Rs‐array =NM

sdot Rs‐module

Rsh‐array =NM

sdot Rsh‐module

Isc‐array =M sdot IscIarray =M sdot I

Im‐array =M sdot ImUoc‐array =N sdot Ioc‐moduleUarray =N sdot Imodule

Um‐array =N sdotUm‐module

10

The simulation model of the cells is encapsulatedand the appropriate parameters are set to obtain thesimulation model of the modules The modules are con-nected in series and parallel to create a photovoltaicarray Figure 4 presents the simulation model of a N timesM photovoltaic array A 1 times 3 photovoltaic array wasused in the simulations and experiments for the nextanalysis simplicity

23 Output Characteristics of ModulesA typical 245Wmod-ule is used for the analysis in the paper The cell connectionwithin the module and the module parameters are shownin Table 1 and Figure 5

The simulation model is established for the modulesaccording to (9) The output characteristics of the modulesunder typical temperature and light conditions are shownin Figure 6

Figure 6 shows that photovoltaic module is a nonlineardirect-current power source instead of a constant voltagesource or a constant current source Its output currentapproximates a constant one under most operating volt-ages The current declines sharply as it approaches open-circuit voltage point The red line in the figure denotesthe variation trend of the optimal operating point withchange in solar irradiance and temperature It can be seenfrom (a) and (b) that the current parameters of photovol-taic modules are directly proportional to irradiance at afixed temperature An increase in irradiance leads to anincrease in short-circuit current and current at optimaloperating point but the effect of the irradiance on the

1Radiation

Temperature2

SS

A

Bypass diode Rs

Rsh R

minus+

Iph

Iph

T3

Figure 2 Simulink model of photovoltaic cells

3International Journal of Photoenergy

open-circuit voltage and the optimal operating voltage isminimal It can be seen from (c) and (d) that the voltageand temperature parameters of the photovoltaic moduleare inversely proportional A lower temperature leads toa higher open-circuit voltage and a higher optimal

operating voltage but the effect of temperature on theshort-circuit current and the current at the optimal oper-ating point is little and insignificant The relationshipbetween various electrical parameters of photovoltaic mod-ules irradiance and temperature is specifically describedin (5) (6) (7) and (8)

3 Simulation of the Output Features ofPhotovoltaic Array under VariousShading Conditions

The shading of a photovoltaic array which working in out-door can be classified into two one is the shadow shadingarising from the surrounding buildings or the front andrear rows of the arrays Such shading moves with sunposition causing no physical damage to the photovoltaicmodules or arrays and the direct radiation received bythe shadowed cells decreases substantially but small

m

n

PV cell

(a)

Load

PV mudule

N

M

(b)

Figure 3 (a) Schematic diagram for photovoltaic module (b) Schematic diagram for photovoltaic array

S

T T

+

minus

+

minus

S

TT

SS

Radiation 1 1

PV model 1 1

Bypass diode 1 1

Bypass diode 2 1

Bypass diode N 1

PV model 2 1

Temperature 1 1

S

T T

+

minus

S

Radiation N 1

PV model N 1Temperature N 1

Temperature 2 1

Radiation 2 1

S

T T

+

minus

+

minus

+

minus

S

TT

SS

Radiation 1 2

PV model 2 3

PV model 2 2

PV model N 2

Temperature 1 2

Temperature 2 2

Radiation 2 2

Radiation N 2

Temperature N 2T T

SS

Bypass diode 1 2

Bypass diode 2 2

Bypass diode N 2 Radiation N MS S

TT

Bypass diode 1 M

Bypass diode 2 M

Bypass diode N M

R

S

T T

+

+

minus

+

minus

+

minus

S

TT

SS

Radiation 1 M

PV model 1 M

PV model 2 M

Temperature 1 M

Temperature 2 M

Temperature N MPV model N M

Radiation 2 M

Figure 4 Simulation model of photovoltaic array By entering different temperatures and irradiance we can get the IVPV curves of PVarrays under different operating conditions

Table 1 Basic parameters for the module

Parameter Variable Value

Maximum power Pm 245 (W)

Optimum operating voltage Vm 301 (V)

Optimum operating current Im 814 (A)

Open-circuit voltage Uoc 375 (V)

Short-circuit current Isc 876 (A)

Temperature coefficient of Isc α 006 (degC)

Temperature coefficient of Voc β minus031 (degC)

Specific parameters of photovoltaic module

4 International Journal of Photoenergy

amount of scattered radiation being absorbed In simula-tion the irradiation intensity of the shadowed photovoltaicmodules is set at 15 of the irradiation intensity absorbedby the unshadowed modules [17] Cover shading on theother hand refers to that arising from direct covering ofthe array surface by objects like leaves and falling prod-ucts In such a case the irradiation intensity received bythe covered cells approximates to zero Such shading hasoften a fixed position and causes permanent hot spotswhich jeopardizes the safe operation of photovoltaic arrayif not identified in time In simulation the solar irradia-tion intensity of such shading is set at zero Differentshading types and the setting of shading conditions areshown in Figure 7 and Table 2

31 Shadow Shading The simulation results under theshadow conditions are shown in Figure 8 Shadowing leadsto nonuniform irradiation received by the array and theoutput presents multiple peaks and ladder-like featuresShadows 1 2 and 4 have consistent output characteristicsSimilarly shadows 3 and 5 are consistent The output charac-teristics decrease in a ladder manner from shadow 4 toshadow 6 Table 3 lists the distribution of the electricalparameters of the array under different shadowing condi-tions The open-circuit voltage Uoc and short-circuit currentIsc change a little but the electrical parameters of the optimaloperating point vary regularly

According to Table 3 from shadow 4 to shadow 6shading leads to a drop in the optimum operating voltageUm and the output power P while the open-circuit voltageUoc and the short-circuit current Isc basically remainunchanged The drop magnitude of Um is associated withthe sum of the optimum operating voltages of the sha-dowed cell strings Meanwhile the shading positions ofshadows 1 2 and 4 are in the same cell string The volt-age at the optimal operating point Um therefore decreaseswhen the area of the shadow is larger than or equal to thearea of a single cell Based on the simulation results the

parameter computation formula of a PV array under sha-dowing conditions can be obtained as follows

Iscprime = IscUocprime =UocImprime = ImUmprime =Um minus u1 sdot n1Pmprime = Imprime sdotUmprime

11

where Iscprime and Imprime are the short-circuit current and the currentat the optimal operating point of the array under the shadow-ing condition respectively Uocprime and Umprime are the open-circuitvoltage and the voltage at the optimal operating point ofthe array under the shadowing condition respectively andIsc and Im are the short-circuited current and the current atthe optimal operating point of the array in the absence ofshading respectively From (5) and (7) we can obtain Uocand Um which are the open-circuit voltage and the voltageat the optimal operating point of the array in the absence ofshading We can obtain u1 and n1 from (6) and (8) whereu1 is the optimum operating voltage of the cell string andn1 is the number of the shadowed cell strings

Based on the above analysis we can obtain the distribu-tion rules of the electrical parameters of photovoltaic arrayunder the following shadowing conditions

(1) Local shadowing does not influenceUoc and Isc of thephotovoltaic array

(2) Um drops when the area of the shadow in a cell stringis larger than or equal to the area of a single cell Thedrop intensity is proportional to the number of theshadowed cell strings and the optimum operatingvoltage of the cell tandem The output power there-fore decreases

(3) In actual application shadowing in photovoltaicarray arises from structures such as the front and rear

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

Figure 5 Internal wiring diagram for the module The module consists of 60 cells in series

5International Journal of Photoenergy

rows of the array and tall buildings The area of theshadow is generally larger than that of a single photo-voltaic cell The voltage effect on the array arisingfrom a shadow with an area less than that of a singlephotovoltaic cell can be ignored

32 Cover Shading The simulation results under the coverconditions are shown in Figure 9 The bypass diode isusually in a nonconducting state and the module outputis normally under uniform light in the absence of cover-ing The cells will have negative voltage and trigger theconduction of bypass diode when the negative voltagereaches a certain upper limit In Figure 9 the outputcharacteristics have no multiple peaks due to the factthat the covered cells with negative voltage trigger theconduction of the corresponding bypass diode Covers 1 2

and 4 have consistent output characteristics Similarly covers3 and 5 are consistent The output decreases in a ladderpattern from cover 4 to cover 6 In terms of the electricalparameters Isc and Im remain unchanged while Uoc Umand Pm decline regularly The distribution of the electricalparameters of the array under cover shading is shown inTable 4

Based on the above analysis we can obtain the distribu-tion rules of the electrical parameters of photovoltaic arrayunder cover shading as follows

(1) Cover shading does not influence Isc and Im of thephotovoltaic array

(2) Uoc and Um drop when the area of the coveredportion within the cell string is larger than or equal

0 10 20 30 40 500

2

4

6

I (A

)

8

10

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

U (V)

(a)

0 10 20 30 40 50

P (W

)

U (V)

0

50

100

150

200

250

300

350

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

(b)

0 10 20 30 40 50

I (A

)

0

2

4

6

8

10

U (V)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(c)

0 10 20 30 40 500

50

100

150

200

250

300

350

U (V)

P (W

)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(d)

Figure 6 (a) IV curve under different irradiances (b) PV curve under different irradiances (c) IV curve under different temperatures (d) PVcurve under different temperatures Describing the IV and PV curves under different operating conditions

6 International Journal of Photoenergy

to the area of a single cell The drop intensity is pro-portional to the number of the covered cell stringsand the cell string voltage The output power there-fore decreases

(3) Cover shading with an area less than that of a singlecell can be considered negligible

The computation formula of the electrical parameters ofthe array under cover shading is as follows

Iscprime = IscUocprime =Uoc minus u2 sdot n2Imprime = ImUmprime =Um minus u1 sdot n2Pmprime = Imprime sdotUmprime

12where n2 is the number of the covered cell strings under thecovering condition and u2 is the open-circuit voltage of thecell string

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

(a) Shadowcover 1

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

(b) Shadowcover 2

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

21

(c) Shadowcover 3

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

(d) Shadowcover 4

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

(e) Shadowcover 5

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

(f) Shadowcover 6

Figure 7 Setting of different shading conditions Shading one cellcell string two cellscell strings three cellscell strings respectively

Table 2 Setting of simulation conditions

Type ofshading

Solar irradiationintensity of theshaded portion

(Wm2)

Solar irradiationintensity of the

unshaded portion(Wm2)

Moduletemperature

(degC)

Shadowshading

150 1000 25

Covershading

0 1000 25

The irradiation intensity of the shadowed photovoltaic cells is set at 15 ofthe irradiation intensity absorbed by the unshadowed modules The solarirradiation intensity of cover is set at zero Temperature is 25degC

7International Journal of Photoenergy

33 Summary To illustrate the distribution features of theelectrical parameters of the photovoltaic array under dif-ferent shading conditions Figure 10 presents the IV andPV curves of the array under the two types of shadingShadow 4 shadow 5 cover 4 and cover 5 are selectedfor comparison The output features and parameter distri-bution rules of the photovoltaic array under the shadowand cover conditions are as follows

(1) The output of the array under shadowing is char-acterized by multiple peaks and ladder patternwhile cover shading has no such characteristics

(2) Shadowing and covering have no effect on Isc ofthe array

(3) When the shaded area is larger than or equal to asingle cell the shadow causes a drop in Um while

covering causes a drop in Um and Uoc The voltagedrop extent is associated with the number of theshaded cell strings and the string voltage Anyshading with an area less than that of a single cellis considered negligible

(4) The difference between shadowing and covering con-ditions is whether Uoc is falling or not It can bejudged from the distribution characteristics of Umand Uoc

4 Empirical Validation of the ElectricalProperties of Photovoltaic Array underDifferent Shading Conditions

41 Method for Empirical Validation Three modules wereconnected in series to create a photovoltaic array in theexperiment To investigate the distribution characteristicsof the electrical parameters under different shading condi-tions an opaque paperboard was used to set the shadowand covering conditions respectively as shown inFigure 7 The electrical parameters of the array underdifferent shading conditions were recorded with an IVscanner To explain the distribution rules of the electricalparameters (8) was introduced to obtain the voltage atthe maximum power point Based on (11) and (12) wecan obtain the voltage at the theoretical maximum powerpoint under different shading conditions and comparewith the experiment results The experimental platformcomprised of a photovoltaic array constituted by JinkoJKM245P modules an irradiator for measuring the solarirradiance a temperature sensor for measuring the

9

8

7

6

5

4

3

2

1

00 50 100

Shadow 1Shadow 2Shadow 3

Shadow 5Shadow 6No shadow

Shadow 4

U (V)

I (A)

150 0 50 100U (V)

150

800

700

600

500

400

300

200

100

0

P (W

)

Figure 8 Simulation result for shadowing Under the shadow conditions the output curve presents a multipeak feature

Table 3 Distribution of electrical parameters under shadowingcondition

Shadow conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74463 9193 810

Shadow 1 11730 874 66147 8051 822

Shadow 2 11724 874 66246 8112 817

Shadow 3 11710 873 58147 7195 808

Shadow 4 11603 874 65270 8104 805

Shadow 5 11468 873 58040 7077 820

Shadow 6 11334 874 48782 6195 787

The distribution of electrical parameters under different shading conditions

8 International Journal of Photoenergy

backboard temperature and an IV tester Figure 11 pre-sents the structural diagram

42 Analysis of the Empirical Testing Results As seen inFigure 12 the results indicate that the output of the arrayunder shadow is characterized by multiple peaks Shadow-ing only influences the optimal operating voltage Accord-ing to (a) and (b) shadows 1 and 2 nearly have consistentoutput characteristics Compared to the normal operatingcondition (nonshaded) the voltage at the optimal operat-ing point moves left while the open-circuit voltage remainsunchanged The voltage at the optimal operating pointfurther moves left in the case of shadow 3 compared tothat in the case of shadow 2 According to (c) and (d)with the increase of the number of shaded cell stringsthe voltage at the optimal operating point of the arraysdecreases in sequence

As seen in Figure 13 the results indicate that theoutput of the array under cover have no multiplepeaks According to (a) and (b) cover 1 and cover 2have nearly consistent output characteristics The voltageat the optimal operating point and the open-circuitvoltage move left compared to the normal operatingcondition (noncovered) The bypass diode is thus acti-vated when the area of the covering is larger than thearea of a single cell The voltage at the optimal operat-ing point and the open-circuit voltage in the case ofcover 3 move left compared with that in the case ofcover 2 At this point two bypass diodes are activatedAccording to (c) and (d) the voltage at the optimaloperating point of the array and the open-circuit volt-age decrease in sequence with the increase of the cov-ered cell strings

As seen in Figure 14 cover shading influences boththe voltage at the maximum operating point Um andthe open-circuit voltage Uoc while shadow shading onlyinfluences the voltage at the maximum operating pointUm which coincides with the simulation results

Equations (11) and (12) present the computationalformulae for the voltage at the optimal operating pointand the open-circuit voltage Uoc under the shadow andcovering conditions which will be analyzed in the fol-lowing paragraphs Under shading conditions the rela-tive error between the voltage at the theoreticaloptimal operating point and the voltage at the mea-sured optimal operating point is expressed as e1 andthe relative error between the theoretical open-circuitvoltage and the measured open-circuit voltage isexpressed as e2 as shown in (13)

9

8

7

6

5

4

3

2

1

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 1Cover 2Cover 3

Cover 5Cover 6No Cover

Cover 4

Figure 9 Simulation result for cover shading The output curve without multipeak feature under cover shading

Table 4 Distribution of electric parameters under cover shading

Covering conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74397 9111 817

Cover 1 10347 874 66092 8026 823

Cover 2 10350 874 66299 8239 805

Cover 3 8964 873 57884 7008 826

Cover 4 10344 874 65207 8190 796

Cover 5 8968 873 57456 7024 818

Cover 6 7583 869 48936 6099 802

The distribution of electrical parameters under different cover conditions

9International Journal of Photoenergy

e1 =U prime

m‐test minusU primem‐calculate

U primem‐calculate

times 100

e2 =U prime

oc‐test minusU primeoc‐calculate

U primeoc‐calculate

times 100

13

where Um‐testprime and Uoc‐testprime are the measured voltage at theoptimal operating point and the open-circuit voltage undershading conditions respectively and Um‐calculateprime and

Uoc‐calculateprime are the theoretical voltage at the optimal operatingpoint and the open-circuit voltage under the shadingconditions

Table 5 lists the distribution of the voltage at the optimaloperating point and the open-circuit voltage under differ-ent shading conditions and the relative error between themeasured shaded voltage and the computed shaded volt-age As seen in the table the maximum error betweenthe measured voltage and the computed voltage is lessthan 2 under shading conditions The empirical resultscompletely coincide with the simulation results

10

8

6

4

2

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 4Cover 5

Shadow 5Normal

Cover 4

Figure 10 Comparison between shadow and cover conditions The difference between shadow and cover is whether the open-circuit voltagedrops or not

Computer

Radiation Temperature

IV test

Data summarization

Measuring the electricalparameters

Cover 1ndashcover 6

Different shadingconditions

Theoretical calculating

Calculating the theoretical value ofelectrical parameters

Uoc Um Isc Im

Shadow 1ndashshadow 6

Figure 11 Block diagram for experimental testing By comparing the theoretical value and the measured value summarize the rules

10 International Journal of Photoenergy

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

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Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

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Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

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SpectroscopyAnalytical ChemistryInternational Journal of

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Hindawiwwwhindawicom Volume 2018

Na

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ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

where S and Sref are the solar irradiance received by pho-tovoltaic cells and solar irradiance under standard condi-tions respectively T and Tref are actual temperature andtemperature of photovoltaic cells under standard condi-tions respectively and a b and c are correction coeffi-cients where a = 0 0008degC b = 0 2 and c = 0 002degC

Equations (5) (6) (7) and (8) describe the distribu-tion features of theoretical short-circuit current open-circuit voltage and voltage and current at optimal operat-ing point of photovoltaic cells under different solar irradi-ances and temperatures The electrical parameters ofphotovoltaic array under different shading conditions areanalyzed using (5) (6) (7) and (8) in the subsequentexperimental process

Based on the above mathematical model the simula-tion model is established for photovoltaic cells as shownin Figure 2 There are two inputs irradiance and temper-ature The photogenerated current Iph does not changewith the operative mode of photovoltaic cells when theirradiation intensity is constant A constant current sourceIph is therefore used for simulation The circuit alsoincludes bypass diode parallel resistance Rsh and seriesresistance Rs where R is the output load

22 Model of Photovoltaic Modules and Array The currentand voltage generated by a single photovoltaic cell arenot enough for the load Generally many photovoltaiccells are connected in series or in parallel to create a pho-tovoltaic module [16] In a photovoltaic power stationseveral modules are connected in series or in parallelThe modules and arrays might be connected in a way asshown in Figure 3

It is assumed that the number of cells in series in the pho-tovoltaic module is n and the number of cells in parallel ismThen the parameters of the photovoltaic module may beexpressed as follows

Uoc‐module = n sdotUocUm‐module = n sdotUmUmodule = n sdotU Isc‐module =m sdot IscIm‐module =m sdot ImImodule =m sdot I

9

It is assumed that the photovoltaic array comprises of Nphotovoltaic modules in series and M photovoltaic modulesin parallel Then we can obtain

Rs‐array =NM

sdot Rs‐module

Rsh‐array =NM

sdot Rsh‐module

Isc‐array =M sdot IscIarray =M sdot I

Im‐array =M sdot ImUoc‐array =N sdot Ioc‐moduleUarray =N sdot Imodule

Um‐array =N sdotUm‐module

10

The simulation model of the cells is encapsulatedand the appropriate parameters are set to obtain thesimulation model of the modules The modules are con-nected in series and parallel to create a photovoltaicarray Figure 4 presents the simulation model of a N timesM photovoltaic array A 1 times 3 photovoltaic array wasused in the simulations and experiments for the nextanalysis simplicity

23 Output Characteristics of ModulesA typical 245Wmod-ule is used for the analysis in the paper The cell connectionwithin the module and the module parameters are shownin Table 1 and Figure 5

The simulation model is established for the modulesaccording to (9) The output characteristics of the modulesunder typical temperature and light conditions are shownin Figure 6

Figure 6 shows that photovoltaic module is a nonlineardirect-current power source instead of a constant voltagesource or a constant current source Its output currentapproximates a constant one under most operating volt-ages The current declines sharply as it approaches open-circuit voltage point The red line in the figure denotesthe variation trend of the optimal operating point withchange in solar irradiance and temperature It can be seenfrom (a) and (b) that the current parameters of photovol-taic modules are directly proportional to irradiance at afixed temperature An increase in irradiance leads to anincrease in short-circuit current and current at optimaloperating point but the effect of the irradiance on the

1Radiation

Temperature2

SS

A

Bypass diode Rs

Rsh R

minus+

Iph

Iph

T3

Figure 2 Simulink model of photovoltaic cells

3International Journal of Photoenergy

open-circuit voltage and the optimal operating voltage isminimal It can be seen from (c) and (d) that the voltageand temperature parameters of the photovoltaic moduleare inversely proportional A lower temperature leads toa higher open-circuit voltage and a higher optimal

operating voltage but the effect of temperature on theshort-circuit current and the current at the optimal oper-ating point is little and insignificant The relationshipbetween various electrical parameters of photovoltaic mod-ules irradiance and temperature is specifically describedin (5) (6) (7) and (8)

3 Simulation of the Output Features ofPhotovoltaic Array under VariousShading Conditions

The shading of a photovoltaic array which working in out-door can be classified into two one is the shadow shadingarising from the surrounding buildings or the front andrear rows of the arrays Such shading moves with sunposition causing no physical damage to the photovoltaicmodules or arrays and the direct radiation received bythe shadowed cells decreases substantially but small

m

n

PV cell

(a)

Load

PV mudule

N

M

(b)

Figure 3 (a) Schematic diagram for photovoltaic module (b) Schematic diagram for photovoltaic array

S

T T

+

minus

+

minus

S

TT

SS

Radiation 1 1

PV model 1 1

Bypass diode 1 1

Bypass diode 2 1

Bypass diode N 1

PV model 2 1

Temperature 1 1

S

T T

+

minus

S

Radiation N 1

PV model N 1Temperature N 1

Temperature 2 1

Radiation 2 1

S

T T

+

minus

+

minus

+

minus

S

TT

SS

Radiation 1 2

PV model 2 3

PV model 2 2

PV model N 2

Temperature 1 2

Temperature 2 2

Radiation 2 2

Radiation N 2

Temperature N 2T T

SS

Bypass diode 1 2

Bypass diode 2 2

Bypass diode N 2 Radiation N MS S

TT

Bypass diode 1 M

Bypass diode 2 M

Bypass diode N M

R

S

T T

+

+

minus

+

minus

+

minus

S

TT

SS

Radiation 1 M

PV model 1 M

PV model 2 M

Temperature 1 M

Temperature 2 M

Temperature N MPV model N M

Radiation 2 M

Figure 4 Simulation model of photovoltaic array By entering different temperatures and irradiance we can get the IVPV curves of PVarrays under different operating conditions

Table 1 Basic parameters for the module

Parameter Variable Value

Maximum power Pm 245 (W)

Optimum operating voltage Vm 301 (V)

Optimum operating current Im 814 (A)

Open-circuit voltage Uoc 375 (V)

Short-circuit current Isc 876 (A)

Temperature coefficient of Isc α 006 (degC)

Temperature coefficient of Voc β minus031 (degC)

Specific parameters of photovoltaic module

4 International Journal of Photoenergy

amount of scattered radiation being absorbed In simula-tion the irradiation intensity of the shadowed photovoltaicmodules is set at 15 of the irradiation intensity absorbedby the unshadowed modules [17] Cover shading on theother hand refers to that arising from direct covering ofthe array surface by objects like leaves and falling prod-ucts In such a case the irradiation intensity received bythe covered cells approximates to zero Such shading hasoften a fixed position and causes permanent hot spotswhich jeopardizes the safe operation of photovoltaic arrayif not identified in time In simulation the solar irradia-tion intensity of such shading is set at zero Differentshading types and the setting of shading conditions areshown in Figure 7 and Table 2

31 Shadow Shading The simulation results under theshadow conditions are shown in Figure 8 Shadowing leadsto nonuniform irradiation received by the array and theoutput presents multiple peaks and ladder-like featuresShadows 1 2 and 4 have consistent output characteristicsSimilarly shadows 3 and 5 are consistent The output charac-teristics decrease in a ladder manner from shadow 4 toshadow 6 Table 3 lists the distribution of the electricalparameters of the array under different shadowing condi-tions The open-circuit voltage Uoc and short-circuit currentIsc change a little but the electrical parameters of the optimaloperating point vary regularly

According to Table 3 from shadow 4 to shadow 6shading leads to a drop in the optimum operating voltageUm and the output power P while the open-circuit voltageUoc and the short-circuit current Isc basically remainunchanged The drop magnitude of Um is associated withthe sum of the optimum operating voltages of the sha-dowed cell strings Meanwhile the shading positions ofshadows 1 2 and 4 are in the same cell string The volt-age at the optimal operating point Um therefore decreaseswhen the area of the shadow is larger than or equal to thearea of a single cell Based on the simulation results the

parameter computation formula of a PV array under sha-dowing conditions can be obtained as follows

Iscprime = IscUocprime =UocImprime = ImUmprime =Um minus u1 sdot n1Pmprime = Imprime sdotUmprime

11

where Iscprime and Imprime are the short-circuit current and the currentat the optimal operating point of the array under the shadow-ing condition respectively Uocprime and Umprime are the open-circuitvoltage and the voltage at the optimal operating point ofthe array under the shadowing condition respectively andIsc and Im are the short-circuited current and the current atthe optimal operating point of the array in the absence ofshading respectively From (5) and (7) we can obtain Uocand Um which are the open-circuit voltage and the voltageat the optimal operating point of the array in the absence ofshading We can obtain u1 and n1 from (6) and (8) whereu1 is the optimum operating voltage of the cell string andn1 is the number of the shadowed cell strings

Based on the above analysis we can obtain the distribu-tion rules of the electrical parameters of photovoltaic arrayunder the following shadowing conditions

(1) Local shadowing does not influenceUoc and Isc of thephotovoltaic array

(2) Um drops when the area of the shadow in a cell stringis larger than or equal to the area of a single cell Thedrop intensity is proportional to the number of theshadowed cell strings and the optimum operatingvoltage of the cell tandem The output power there-fore decreases

(3) In actual application shadowing in photovoltaicarray arises from structures such as the front and rear

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

Figure 5 Internal wiring diagram for the module The module consists of 60 cells in series

5International Journal of Photoenergy

rows of the array and tall buildings The area of theshadow is generally larger than that of a single photo-voltaic cell The voltage effect on the array arisingfrom a shadow with an area less than that of a singlephotovoltaic cell can be ignored

32 Cover Shading The simulation results under the coverconditions are shown in Figure 9 The bypass diode isusually in a nonconducting state and the module outputis normally under uniform light in the absence of cover-ing The cells will have negative voltage and trigger theconduction of bypass diode when the negative voltagereaches a certain upper limit In Figure 9 the outputcharacteristics have no multiple peaks due to the factthat the covered cells with negative voltage trigger theconduction of the corresponding bypass diode Covers 1 2

and 4 have consistent output characteristics Similarly covers3 and 5 are consistent The output decreases in a ladderpattern from cover 4 to cover 6 In terms of the electricalparameters Isc and Im remain unchanged while Uoc Umand Pm decline regularly The distribution of the electricalparameters of the array under cover shading is shown inTable 4

Based on the above analysis we can obtain the distribu-tion rules of the electrical parameters of photovoltaic arrayunder cover shading as follows

(1) Cover shading does not influence Isc and Im of thephotovoltaic array

(2) Uoc and Um drop when the area of the coveredportion within the cell string is larger than or equal

0 10 20 30 40 500

2

4

6

I (A

)

8

10

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

U (V)

(a)

0 10 20 30 40 50

P (W

)

U (V)

0

50

100

150

200

250

300

350

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

(b)

0 10 20 30 40 50

I (A

)

0

2

4

6

8

10

U (V)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(c)

0 10 20 30 40 500

50

100

150

200

250

300

350

U (V)

P (W

)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(d)

Figure 6 (a) IV curve under different irradiances (b) PV curve under different irradiances (c) IV curve under different temperatures (d) PVcurve under different temperatures Describing the IV and PV curves under different operating conditions

6 International Journal of Photoenergy

to the area of a single cell The drop intensity is pro-portional to the number of the covered cell stringsand the cell string voltage The output power there-fore decreases

(3) Cover shading with an area less than that of a singlecell can be considered negligible

The computation formula of the electrical parameters ofthe array under cover shading is as follows

Iscprime = IscUocprime =Uoc minus u2 sdot n2Imprime = ImUmprime =Um minus u1 sdot n2Pmprime = Imprime sdotUmprime

12where n2 is the number of the covered cell strings under thecovering condition and u2 is the open-circuit voltage of thecell string

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

(a) Shadowcover 1

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

(b) Shadowcover 2

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

21

(c) Shadowcover 3

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

(d) Shadowcover 4

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

(e) Shadowcover 5

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

(f) Shadowcover 6

Figure 7 Setting of different shading conditions Shading one cellcell string two cellscell strings three cellscell strings respectively

Table 2 Setting of simulation conditions

Type ofshading

Solar irradiationintensity of theshaded portion

(Wm2)

Solar irradiationintensity of the

unshaded portion(Wm2)

Moduletemperature

(degC)

Shadowshading

150 1000 25

Covershading

0 1000 25

The irradiation intensity of the shadowed photovoltaic cells is set at 15 ofthe irradiation intensity absorbed by the unshadowed modules The solarirradiation intensity of cover is set at zero Temperature is 25degC

7International Journal of Photoenergy

33 Summary To illustrate the distribution features of theelectrical parameters of the photovoltaic array under dif-ferent shading conditions Figure 10 presents the IV andPV curves of the array under the two types of shadingShadow 4 shadow 5 cover 4 and cover 5 are selectedfor comparison The output features and parameter distri-bution rules of the photovoltaic array under the shadowand cover conditions are as follows

(1) The output of the array under shadowing is char-acterized by multiple peaks and ladder patternwhile cover shading has no such characteristics

(2) Shadowing and covering have no effect on Isc ofthe array

(3) When the shaded area is larger than or equal to asingle cell the shadow causes a drop in Um while

covering causes a drop in Um and Uoc The voltagedrop extent is associated with the number of theshaded cell strings and the string voltage Anyshading with an area less than that of a single cellis considered negligible

(4) The difference between shadowing and covering con-ditions is whether Uoc is falling or not It can bejudged from the distribution characteristics of Umand Uoc

4 Empirical Validation of the ElectricalProperties of Photovoltaic Array underDifferent Shading Conditions

41 Method for Empirical Validation Three modules wereconnected in series to create a photovoltaic array in theexperiment To investigate the distribution characteristicsof the electrical parameters under different shading condi-tions an opaque paperboard was used to set the shadowand covering conditions respectively as shown inFigure 7 The electrical parameters of the array underdifferent shading conditions were recorded with an IVscanner To explain the distribution rules of the electricalparameters (8) was introduced to obtain the voltage atthe maximum power point Based on (11) and (12) wecan obtain the voltage at the theoretical maximum powerpoint under different shading conditions and comparewith the experiment results The experimental platformcomprised of a photovoltaic array constituted by JinkoJKM245P modules an irradiator for measuring the solarirradiance a temperature sensor for measuring the

9

8

7

6

5

4

3

2

1

00 50 100

Shadow 1Shadow 2Shadow 3

Shadow 5Shadow 6No shadow

Shadow 4

U (V)

I (A)

150 0 50 100U (V)

150

800

700

600

500

400

300

200

100

0

P (W

)

Figure 8 Simulation result for shadowing Under the shadow conditions the output curve presents a multipeak feature

Table 3 Distribution of electrical parameters under shadowingcondition

Shadow conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74463 9193 810

Shadow 1 11730 874 66147 8051 822

Shadow 2 11724 874 66246 8112 817

Shadow 3 11710 873 58147 7195 808

Shadow 4 11603 874 65270 8104 805

Shadow 5 11468 873 58040 7077 820

Shadow 6 11334 874 48782 6195 787

The distribution of electrical parameters under different shading conditions

8 International Journal of Photoenergy

backboard temperature and an IV tester Figure 11 pre-sents the structural diagram

42 Analysis of the Empirical Testing Results As seen inFigure 12 the results indicate that the output of the arrayunder shadow is characterized by multiple peaks Shadow-ing only influences the optimal operating voltage Accord-ing to (a) and (b) shadows 1 and 2 nearly have consistentoutput characteristics Compared to the normal operatingcondition (nonshaded) the voltage at the optimal operat-ing point moves left while the open-circuit voltage remainsunchanged The voltage at the optimal operating pointfurther moves left in the case of shadow 3 compared tothat in the case of shadow 2 According to (c) and (d)with the increase of the number of shaded cell stringsthe voltage at the optimal operating point of the arraysdecreases in sequence

As seen in Figure 13 the results indicate that theoutput of the array under cover have no multiplepeaks According to (a) and (b) cover 1 and cover 2have nearly consistent output characteristics The voltageat the optimal operating point and the open-circuitvoltage move left compared to the normal operatingcondition (noncovered) The bypass diode is thus acti-vated when the area of the covering is larger than thearea of a single cell The voltage at the optimal operat-ing point and the open-circuit voltage in the case ofcover 3 move left compared with that in the case ofcover 2 At this point two bypass diodes are activatedAccording to (c) and (d) the voltage at the optimaloperating point of the array and the open-circuit volt-age decrease in sequence with the increase of the cov-ered cell strings

As seen in Figure 14 cover shading influences boththe voltage at the maximum operating point Um andthe open-circuit voltage Uoc while shadow shading onlyinfluences the voltage at the maximum operating pointUm which coincides with the simulation results

Equations (11) and (12) present the computationalformulae for the voltage at the optimal operating pointand the open-circuit voltage Uoc under the shadow andcovering conditions which will be analyzed in the fol-lowing paragraphs Under shading conditions the rela-tive error between the voltage at the theoreticaloptimal operating point and the voltage at the mea-sured optimal operating point is expressed as e1 andthe relative error between the theoretical open-circuitvoltage and the measured open-circuit voltage isexpressed as e2 as shown in (13)

9

8

7

6

5

4

3

2

1

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 1Cover 2Cover 3

Cover 5Cover 6No Cover

Cover 4

Figure 9 Simulation result for cover shading The output curve without multipeak feature under cover shading

Table 4 Distribution of electric parameters under cover shading

Covering conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74397 9111 817

Cover 1 10347 874 66092 8026 823

Cover 2 10350 874 66299 8239 805

Cover 3 8964 873 57884 7008 826

Cover 4 10344 874 65207 8190 796

Cover 5 8968 873 57456 7024 818

Cover 6 7583 869 48936 6099 802

The distribution of electrical parameters under different cover conditions

9International Journal of Photoenergy

e1 =U prime

m‐test minusU primem‐calculate

U primem‐calculate

times 100

e2 =U prime

oc‐test minusU primeoc‐calculate

U primeoc‐calculate

times 100

13

where Um‐testprime and Uoc‐testprime are the measured voltage at theoptimal operating point and the open-circuit voltage undershading conditions respectively and Um‐calculateprime and

Uoc‐calculateprime are the theoretical voltage at the optimal operatingpoint and the open-circuit voltage under the shadingconditions

Table 5 lists the distribution of the voltage at the optimaloperating point and the open-circuit voltage under differ-ent shading conditions and the relative error between themeasured shaded voltage and the computed shaded volt-age As seen in the table the maximum error betweenthe measured voltage and the computed voltage is lessthan 2 under shading conditions The empirical resultscompletely coincide with the simulation results

10

8

6

4

2

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 4Cover 5

Shadow 5Normal

Cover 4

Figure 10 Comparison between shadow and cover conditions The difference between shadow and cover is whether the open-circuit voltagedrops or not

Computer

Radiation Temperature

IV test

Data summarization

Measuring the electricalparameters

Cover 1ndashcover 6

Different shadingconditions

Theoretical calculating

Calculating the theoretical value ofelectrical parameters

Uoc Um Isc Im

Shadow 1ndashshadow 6

Figure 11 Block diagram for experimental testing By comparing the theoretical value and the measured value summarize the rules

10 International Journal of Photoenergy

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

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International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

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NanotechnologyHindawiwwwhindawicom Volume 2018

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Applied ChemistryJournal of

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SpectroscopyAnalytical ChemistryInternational Journal of

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Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

open-circuit voltage and the optimal operating voltage isminimal It can be seen from (c) and (d) that the voltageand temperature parameters of the photovoltaic moduleare inversely proportional A lower temperature leads toa higher open-circuit voltage and a higher optimal

operating voltage but the effect of temperature on theshort-circuit current and the current at the optimal oper-ating point is little and insignificant The relationshipbetween various electrical parameters of photovoltaic mod-ules irradiance and temperature is specifically describedin (5) (6) (7) and (8)

3 Simulation of the Output Features ofPhotovoltaic Array under VariousShading Conditions

The shading of a photovoltaic array which working in out-door can be classified into two one is the shadow shadingarising from the surrounding buildings or the front andrear rows of the arrays Such shading moves with sunposition causing no physical damage to the photovoltaicmodules or arrays and the direct radiation received bythe shadowed cells decreases substantially but small

m

n

PV cell

(a)

Load

PV mudule

N

M

(b)

Figure 3 (a) Schematic diagram for photovoltaic module (b) Schematic diagram for photovoltaic array

S

T T

+

minus

+

minus

S

TT

SS

Radiation 1 1

PV model 1 1

Bypass diode 1 1

Bypass diode 2 1

Bypass diode N 1

PV model 2 1

Temperature 1 1

S

T T

+

minus

S

Radiation N 1

PV model N 1Temperature N 1

Temperature 2 1

Radiation 2 1

S

T T

+

minus

+

minus

+

minus

S

TT

SS

Radiation 1 2

PV model 2 3

PV model 2 2

PV model N 2

Temperature 1 2

Temperature 2 2

Radiation 2 2

Radiation N 2

Temperature N 2T T

SS

Bypass diode 1 2

Bypass diode 2 2

Bypass diode N 2 Radiation N MS S

TT

Bypass diode 1 M

Bypass diode 2 M

Bypass diode N M

R

S

T T

+

+

minus

+

minus

+

minus

S

TT

SS

Radiation 1 M

PV model 1 M

PV model 2 M

Temperature 1 M

Temperature 2 M

Temperature N MPV model N M

Radiation 2 M

Figure 4 Simulation model of photovoltaic array By entering different temperatures and irradiance we can get the IVPV curves of PVarrays under different operating conditions

Table 1 Basic parameters for the module

Parameter Variable Value

Maximum power Pm 245 (W)

Optimum operating voltage Vm 301 (V)

Optimum operating current Im 814 (A)

Open-circuit voltage Uoc 375 (V)

Short-circuit current Isc 876 (A)

Temperature coefficient of Isc α 006 (degC)

Temperature coefficient of Voc β minus031 (degC)

Specific parameters of photovoltaic module

4 International Journal of Photoenergy

amount of scattered radiation being absorbed In simula-tion the irradiation intensity of the shadowed photovoltaicmodules is set at 15 of the irradiation intensity absorbedby the unshadowed modules [17] Cover shading on theother hand refers to that arising from direct covering ofthe array surface by objects like leaves and falling prod-ucts In such a case the irradiation intensity received bythe covered cells approximates to zero Such shading hasoften a fixed position and causes permanent hot spotswhich jeopardizes the safe operation of photovoltaic arrayif not identified in time In simulation the solar irradia-tion intensity of such shading is set at zero Differentshading types and the setting of shading conditions areshown in Figure 7 and Table 2

31 Shadow Shading The simulation results under theshadow conditions are shown in Figure 8 Shadowing leadsto nonuniform irradiation received by the array and theoutput presents multiple peaks and ladder-like featuresShadows 1 2 and 4 have consistent output characteristicsSimilarly shadows 3 and 5 are consistent The output charac-teristics decrease in a ladder manner from shadow 4 toshadow 6 Table 3 lists the distribution of the electricalparameters of the array under different shadowing condi-tions The open-circuit voltage Uoc and short-circuit currentIsc change a little but the electrical parameters of the optimaloperating point vary regularly

According to Table 3 from shadow 4 to shadow 6shading leads to a drop in the optimum operating voltageUm and the output power P while the open-circuit voltageUoc and the short-circuit current Isc basically remainunchanged The drop magnitude of Um is associated withthe sum of the optimum operating voltages of the sha-dowed cell strings Meanwhile the shading positions ofshadows 1 2 and 4 are in the same cell string The volt-age at the optimal operating point Um therefore decreaseswhen the area of the shadow is larger than or equal to thearea of a single cell Based on the simulation results the

parameter computation formula of a PV array under sha-dowing conditions can be obtained as follows

Iscprime = IscUocprime =UocImprime = ImUmprime =Um minus u1 sdot n1Pmprime = Imprime sdotUmprime

11

where Iscprime and Imprime are the short-circuit current and the currentat the optimal operating point of the array under the shadow-ing condition respectively Uocprime and Umprime are the open-circuitvoltage and the voltage at the optimal operating point ofthe array under the shadowing condition respectively andIsc and Im are the short-circuited current and the current atthe optimal operating point of the array in the absence ofshading respectively From (5) and (7) we can obtain Uocand Um which are the open-circuit voltage and the voltageat the optimal operating point of the array in the absence ofshading We can obtain u1 and n1 from (6) and (8) whereu1 is the optimum operating voltage of the cell string andn1 is the number of the shadowed cell strings

Based on the above analysis we can obtain the distribu-tion rules of the electrical parameters of photovoltaic arrayunder the following shadowing conditions

(1) Local shadowing does not influenceUoc and Isc of thephotovoltaic array

(2) Um drops when the area of the shadow in a cell stringis larger than or equal to the area of a single cell Thedrop intensity is proportional to the number of theshadowed cell strings and the optimum operatingvoltage of the cell tandem The output power there-fore decreases

(3) In actual application shadowing in photovoltaicarray arises from structures such as the front and rear

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

Figure 5 Internal wiring diagram for the module The module consists of 60 cells in series

5International Journal of Photoenergy

rows of the array and tall buildings The area of theshadow is generally larger than that of a single photo-voltaic cell The voltage effect on the array arisingfrom a shadow with an area less than that of a singlephotovoltaic cell can be ignored

32 Cover Shading The simulation results under the coverconditions are shown in Figure 9 The bypass diode isusually in a nonconducting state and the module outputis normally under uniform light in the absence of cover-ing The cells will have negative voltage and trigger theconduction of bypass diode when the negative voltagereaches a certain upper limit In Figure 9 the outputcharacteristics have no multiple peaks due to the factthat the covered cells with negative voltage trigger theconduction of the corresponding bypass diode Covers 1 2

and 4 have consistent output characteristics Similarly covers3 and 5 are consistent The output decreases in a ladderpattern from cover 4 to cover 6 In terms of the electricalparameters Isc and Im remain unchanged while Uoc Umand Pm decline regularly The distribution of the electricalparameters of the array under cover shading is shown inTable 4

Based on the above analysis we can obtain the distribu-tion rules of the electrical parameters of photovoltaic arrayunder cover shading as follows

(1) Cover shading does not influence Isc and Im of thephotovoltaic array

(2) Uoc and Um drop when the area of the coveredportion within the cell string is larger than or equal

0 10 20 30 40 500

2

4

6

I (A

)

8

10

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

U (V)

(a)

0 10 20 30 40 50

P (W

)

U (V)

0

50

100

150

200

250

300

350

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

(b)

0 10 20 30 40 50

I (A

)

0

2

4

6

8

10

U (V)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(c)

0 10 20 30 40 500

50

100

150

200

250

300

350

U (V)

P (W

)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(d)

Figure 6 (a) IV curve under different irradiances (b) PV curve under different irradiances (c) IV curve under different temperatures (d) PVcurve under different temperatures Describing the IV and PV curves under different operating conditions

6 International Journal of Photoenergy

to the area of a single cell The drop intensity is pro-portional to the number of the covered cell stringsand the cell string voltage The output power there-fore decreases

(3) Cover shading with an area less than that of a singlecell can be considered negligible

The computation formula of the electrical parameters ofthe array under cover shading is as follows

Iscprime = IscUocprime =Uoc minus u2 sdot n2Imprime = ImUmprime =Um minus u1 sdot n2Pmprime = Imprime sdotUmprime

12where n2 is the number of the covered cell strings under thecovering condition and u2 is the open-circuit voltage of thecell string

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

(a) Shadowcover 1

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

(b) Shadowcover 2

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

21

(c) Shadowcover 3

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

(d) Shadowcover 4

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

(e) Shadowcover 5

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

(f) Shadowcover 6

Figure 7 Setting of different shading conditions Shading one cellcell string two cellscell strings three cellscell strings respectively

Table 2 Setting of simulation conditions

Type ofshading

Solar irradiationintensity of theshaded portion

(Wm2)

Solar irradiationintensity of the

unshaded portion(Wm2)

Moduletemperature

(degC)

Shadowshading

150 1000 25

Covershading

0 1000 25

The irradiation intensity of the shadowed photovoltaic cells is set at 15 ofthe irradiation intensity absorbed by the unshadowed modules The solarirradiation intensity of cover is set at zero Temperature is 25degC

7International Journal of Photoenergy

33 Summary To illustrate the distribution features of theelectrical parameters of the photovoltaic array under dif-ferent shading conditions Figure 10 presents the IV andPV curves of the array under the two types of shadingShadow 4 shadow 5 cover 4 and cover 5 are selectedfor comparison The output features and parameter distri-bution rules of the photovoltaic array under the shadowand cover conditions are as follows

(1) The output of the array under shadowing is char-acterized by multiple peaks and ladder patternwhile cover shading has no such characteristics

(2) Shadowing and covering have no effect on Isc ofthe array

(3) When the shaded area is larger than or equal to asingle cell the shadow causes a drop in Um while

covering causes a drop in Um and Uoc The voltagedrop extent is associated with the number of theshaded cell strings and the string voltage Anyshading with an area less than that of a single cellis considered negligible

(4) The difference between shadowing and covering con-ditions is whether Uoc is falling or not It can bejudged from the distribution characteristics of Umand Uoc

4 Empirical Validation of the ElectricalProperties of Photovoltaic Array underDifferent Shading Conditions

41 Method for Empirical Validation Three modules wereconnected in series to create a photovoltaic array in theexperiment To investigate the distribution characteristicsof the electrical parameters under different shading condi-tions an opaque paperboard was used to set the shadowand covering conditions respectively as shown inFigure 7 The electrical parameters of the array underdifferent shading conditions were recorded with an IVscanner To explain the distribution rules of the electricalparameters (8) was introduced to obtain the voltage atthe maximum power point Based on (11) and (12) wecan obtain the voltage at the theoretical maximum powerpoint under different shading conditions and comparewith the experiment results The experimental platformcomprised of a photovoltaic array constituted by JinkoJKM245P modules an irradiator for measuring the solarirradiance a temperature sensor for measuring the

9

8

7

6

5

4

3

2

1

00 50 100

Shadow 1Shadow 2Shadow 3

Shadow 5Shadow 6No shadow

Shadow 4

U (V)

I (A)

150 0 50 100U (V)

150

800

700

600

500

400

300

200

100

0

P (W

)

Figure 8 Simulation result for shadowing Under the shadow conditions the output curve presents a multipeak feature

Table 3 Distribution of electrical parameters under shadowingcondition

Shadow conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74463 9193 810

Shadow 1 11730 874 66147 8051 822

Shadow 2 11724 874 66246 8112 817

Shadow 3 11710 873 58147 7195 808

Shadow 4 11603 874 65270 8104 805

Shadow 5 11468 873 58040 7077 820

Shadow 6 11334 874 48782 6195 787

The distribution of electrical parameters under different shading conditions

8 International Journal of Photoenergy

backboard temperature and an IV tester Figure 11 pre-sents the structural diagram

42 Analysis of the Empirical Testing Results As seen inFigure 12 the results indicate that the output of the arrayunder shadow is characterized by multiple peaks Shadow-ing only influences the optimal operating voltage Accord-ing to (a) and (b) shadows 1 and 2 nearly have consistentoutput characteristics Compared to the normal operatingcondition (nonshaded) the voltage at the optimal operat-ing point moves left while the open-circuit voltage remainsunchanged The voltage at the optimal operating pointfurther moves left in the case of shadow 3 compared tothat in the case of shadow 2 According to (c) and (d)with the increase of the number of shaded cell stringsthe voltage at the optimal operating point of the arraysdecreases in sequence

As seen in Figure 13 the results indicate that theoutput of the array under cover have no multiplepeaks According to (a) and (b) cover 1 and cover 2have nearly consistent output characteristics The voltageat the optimal operating point and the open-circuitvoltage move left compared to the normal operatingcondition (noncovered) The bypass diode is thus acti-vated when the area of the covering is larger than thearea of a single cell The voltage at the optimal operat-ing point and the open-circuit voltage in the case ofcover 3 move left compared with that in the case ofcover 2 At this point two bypass diodes are activatedAccording to (c) and (d) the voltage at the optimaloperating point of the array and the open-circuit volt-age decrease in sequence with the increase of the cov-ered cell strings

As seen in Figure 14 cover shading influences boththe voltage at the maximum operating point Um andthe open-circuit voltage Uoc while shadow shading onlyinfluences the voltage at the maximum operating pointUm which coincides with the simulation results

Equations (11) and (12) present the computationalformulae for the voltage at the optimal operating pointand the open-circuit voltage Uoc under the shadow andcovering conditions which will be analyzed in the fol-lowing paragraphs Under shading conditions the rela-tive error between the voltage at the theoreticaloptimal operating point and the voltage at the mea-sured optimal operating point is expressed as e1 andthe relative error between the theoretical open-circuitvoltage and the measured open-circuit voltage isexpressed as e2 as shown in (13)

9

8

7

6

5

4

3

2

1

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 1Cover 2Cover 3

Cover 5Cover 6No Cover

Cover 4

Figure 9 Simulation result for cover shading The output curve without multipeak feature under cover shading

Table 4 Distribution of electric parameters under cover shading

Covering conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74397 9111 817

Cover 1 10347 874 66092 8026 823

Cover 2 10350 874 66299 8239 805

Cover 3 8964 873 57884 7008 826

Cover 4 10344 874 65207 8190 796

Cover 5 8968 873 57456 7024 818

Cover 6 7583 869 48936 6099 802

The distribution of electrical parameters under different cover conditions

9International Journal of Photoenergy

e1 =U prime

m‐test minusU primem‐calculate

U primem‐calculate

times 100

e2 =U prime

oc‐test minusU primeoc‐calculate

U primeoc‐calculate

times 100

13

where Um‐testprime and Uoc‐testprime are the measured voltage at theoptimal operating point and the open-circuit voltage undershading conditions respectively and Um‐calculateprime and

Uoc‐calculateprime are the theoretical voltage at the optimal operatingpoint and the open-circuit voltage under the shadingconditions

Table 5 lists the distribution of the voltage at the optimaloperating point and the open-circuit voltage under differ-ent shading conditions and the relative error between themeasured shaded voltage and the computed shaded volt-age As seen in the table the maximum error betweenthe measured voltage and the computed voltage is lessthan 2 under shading conditions The empirical resultscompletely coincide with the simulation results

10

8

6

4

2

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 4Cover 5

Shadow 5Normal

Cover 4

Figure 10 Comparison between shadow and cover conditions The difference between shadow and cover is whether the open-circuit voltagedrops or not

Computer

Radiation Temperature

IV test

Data summarization

Measuring the electricalparameters

Cover 1ndashcover 6

Different shadingconditions

Theoretical calculating

Calculating the theoretical value ofelectrical parameters

Uoc Um Isc Im

Shadow 1ndashshadow 6

Figure 11 Block diagram for experimental testing By comparing the theoretical value and the measured value summarize the rules

10 International Journal of Photoenergy

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

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NanotechnologyHindawiwwwhindawicom Volume 2018

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Applied ChemistryJournal of

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SpectroscopyAnalytical ChemistryInternational Journal of

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Hindawiwwwhindawicom Volume 2018

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ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

amount of scattered radiation being absorbed In simula-tion the irradiation intensity of the shadowed photovoltaicmodules is set at 15 of the irradiation intensity absorbedby the unshadowed modules [17] Cover shading on theother hand refers to that arising from direct covering ofthe array surface by objects like leaves and falling prod-ucts In such a case the irradiation intensity received bythe covered cells approximates to zero Such shading hasoften a fixed position and causes permanent hot spotswhich jeopardizes the safe operation of photovoltaic arrayif not identified in time In simulation the solar irradia-tion intensity of such shading is set at zero Differentshading types and the setting of shading conditions areshown in Figure 7 and Table 2

31 Shadow Shading The simulation results under theshadow conditions are shown in Figure 8 Shadowing leadsto nonuniform irradiation received by the array and theoutput presents multiple peaks and ladder-like featuresShadows 1 2 and 4 have consistent output characteristicsSimilarly shadows 3 and 5 are consistent The output charac-teristics decrease in a ladder manner from shadow 4 toshadow 6 Table 3 lists the distribution of the electricalparameters of the array under different shadowing condi-tions The open-circuit voltage Uoc and short-circuit currentIsc change a little but the electrical parameters of the optimaloperating point vary regularly

According to Table 3 from shadow 4 to shadow 6shading leads to a drop in the optimum operating voltageUm and the output power P while the open-circuit voltageUoc and the short-circuit current Isc basically remainunchanged The drop magnitude of Um is associated withthe sum of the optimum operating voltages of the sha-dowed cell strings Meanwhile the shading positions ofshadows 1 2 and 4 are in the same cell string The volt-age at the optimal operating point Um therefore decreaseswhen the area of the shadow is larger than or equal to thearea of a single cell Based on the simulation results the

parameter computation formula of a PV array under sha-dowing conditions can be obtained as follows

Iscprime = IscUocprime =UocImprime = ImUmprime =Um minus u1 sdot n1Pmprime = Imprime sdotUmprime

11

where Iscprime and Imprime are the short-circuit current and the currentat the optimal operating point of the array under the shadow-ing condition respectively Uocprime and Umprime are the open-circuitvoltage and the voltage at the optimal operating point ofthe array under the shadowing condition respectively andIsc and Im are the short-circuited current and the current atthe optimal operating point of the array in the absence ofshading respectively From (5) and (7) we can obtain Uocand Um which are the open-circuit voltage and the voltageat the optimal operating point of the array in the absence ofshading We can obtain u1 and n1 from (6) and (8) whereu1 is the optimum operating voltage of the cell string andn1 is the number of the shadowed cell strings

Based on the above analysis we can obtain the distribu-tion rules of the electrical parameters of photovoltaic arrayunder the following shadowing conditions

(1) Local shadowing does not influenceUoc and Isc of thephotovoltaic array

(2) Um drops when the area of the shadow in a cell stringis larger than or equal to the area of a single cell Thedrop intensity is proportional to the number of theshadowed cell strings and the optimum operatingvoltage of the cell tandem The output power there-fore decreases

(3) In actual application shadowing in photovoltaicarray arises from structures such as the front and rear

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

Figure 5 Internal wiring diagram for the module The module consists of 60 cells in series

5International Journal of Photoenergy

rows of the array and tall buildings The area of theshadow is generally larger than that of a single photo-voltaic cell The voltage effect on the array arisingfrom a shadow with an area less than that of a singlephotovoltaic cell can be ignored

32 Cover Shading The simulation results under the coverconditions are shown in Figure 9 The bypass diode isusually in a nonconducting state and the module outputis normally under uniform light in the absence of cover-ing The cells will have negative voltage and trigger theconduction of bypass diode when the negative voltagereaches a certain upper limit In Figure 9 the outputcharacteristics have no multiple peaks due to the factthat the covered cells with negative voltage trigger theconduction of the corresponding bypass diode Covers 1 2

and 4 have consistent output characteristics Similarly covers3 and 5 are consistent The output decreases in a ladderpattern from cover 4 to cover 6 In terms of the electricalparameters Isc and Im remain unchanged while Uoc Umand Pm decline regularly The distribution of the electricalparameters of the array under cover shading is shown inTable 4

Based on the above analysis we can obtain the distribu-tion rules of the electrical parameters of photovoltaic arrayunder cover shading as follows

(1) Cover shading does not influence Isc and Im of thephotovoltaic array

(2) Uoc and Um drop when the area of the coveredportion within the cell string is larger than or equal

0 10 20 30 40 500

2

4

6

I (A

)

8

10

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

U (V)

(a)

0 10 20 30 40 50

P (W

)

U (V)

0

50

100

150

200

250

300

350

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

(b)

0 10 20 30 40 50

I (A

)

0

2

4

6

8

10

U (V)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(c)

0 10 20 30 40 500

50

100

150

200

250

300

350

U (V)

P (W

)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(d)

Figure 6 (a) IV curve under different irradiances (b) PV curve under different irradiances (c) IV curve under different temperatures (d) PVcurve under different temperatures Describing the IV and PV curves under different operating conditions

6 International Journal of Photoenergy

to the area of a single cell The drop intensity is pro-portional to the number of the covered cell stringsand the cell string voltage The output power there-fore decreases

(3) Cover shading with an area less than that of a singlecell can be considered negligible

The computation formula of the electrical parameters ofthe array under cover shading is as follows

Iscprime = IscUocprime =Uoc minus u2 sdot n2Imprime = ImUmprime =Um minus u1 sdot n2Pmprime = Imprime sdotUmprime

12where n2 is the number of the covered cell strings under thecovering condition and u2 is the open-circuit voltage of thecell string

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

(a) Shadowcover 1

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

(b) Shadowcover 2

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

21

(c) Shadowcover 3

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

(d) Shadowcover 4

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

(e) Shadowcover 5

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

(f) Shadowcover 6

Figure 7 Setting of different shading conditions Shading one cellcell string two cellscell strings three cellscell strings respectively

Table 2 Setting of simulation conditions

Type ofshading

Solar irradiationintensity of theshaded portion

(Wm2)

Solar irradiationintensity of the

unshaded portion(Wm2)

Moduletemperature

(degC)

Shadowshading

150 1000 25

Covershading

0 1000 25

The irradiation intensity of the shadowed photovoltaic cells is set at 15 ofthe irradiation intensity absorbed by the unshadowed modules The solarirradiation intensity of cover is set at zero Temperature is 25degC

7International Journal of Photoenergy

33 Summary To illustrate the distribution features of theelectrical parameters of the photovoltaic array under dif-ferent shading conditions Figure 10 presents the IV andPV curves of the array under the two types of shadingShadow 4 shadow 5 cover 4 and cover 5 are selectedfor comparison The output features and parameter distri-bution rules of the photovoltaic array under the shadowand cover conditions are as follows

(1) The output of the array under shadowing is char-acterized by multiple peaks and ladder patternwhile cover shading has no such characteristics

(2) Shadowing and covering have no effect on Isc ofthe array

(3) When the shaded area is larger than or equal to asingle cell the shadow causes a drop in Um while

covering causes a drop in Um and Uoc The voltagedrop extent is associated with the number of theshaded cell strings and the string voltage Anyshading with an area less than that of a single cellis considered negligible

(4) The difference between shadowing and covering con-ditions is whether Uoc is falling or not It can bejudged from the distribution characteristics of Umand Uoc

4 Empirical Validation of the ElectricalProperties of Photovoltaic Array underDifferent Shading Conditions

41 Method for Empirical Validation Three modules wereconnected in series to create a photovoltaic array in theexperiment To investigate the distribution characteristicsof the electrical parameters under different shading condi-tions an opaque paperboard was used to set the shadowand covering conditions respectively as shown inFigure 7 The electrical parameters of the array underdifferent shading conditions were recorded with an IVscanner To explain the distribution rules of the electricalparameters (8) was introduced to obtain the voltage atthe maximum power point Based on (11) and (12) wecan obtain the voltage at the theoretical maximum powerpoint under different shading conditions and comparewith the experiment results The experimental platformcomprised of a photovoltaic array constituted by JinkoJKM245P modules an irradiator for measuring the solarirradiance a temperature sensor for measuring the

9

8

7

6

5

4

3

2

1

00 50 100

Shadow 1Shadow 2Shadow 3

Shadow 5Shadow 6No shadow

Shadow 4

U (V)

I (A)

150 0 50 100U (V)

150

800

700

600

500

400

300

200

100

0

P (W

)

Figure 8 Simulation result for shadowing Under the shadow conditions the output curve presents a multipeak feature

Table 3 Distribution of electrical parameters under shadowingcondition

Shadow conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74463 9193 810

Shadow 1 11730 874 66147 8051 822

Shadow 2 11724 874 66246 8112 817

Shadow 3 11710 873 58147 7195 808

Shadow 4 11603 874 65270 8104 805

Shadow 5 11468 873 58040 7077 820

Shadow 6 11334 874 48782 6195 787

The distribution of electrical parameters under different shading conditions

8 International Journal of Photoenergy

backboard temperature and an IV tester Figure 11 pre-sents the structural diagram

42 Analysis of the Empirical Testing Results As seen inFigure 12 the results indicate that the output of the arrayunder shadow is characterized by multiple peaks Shadow-ing only influences the optimal operating voltage Accord-ing to (a) and (b) shadows 1 and 2 nearly have consistentoutput characteristics Compared to the normal operatingcondition (nonshaded) the voltage at the optimal operat-ing point moves left while the open-circuit voltage remainsunchanged The voltage at the optimal operating pointfurther moves left in the case of shadow 3 compared tothat in the case of shadow 2 According to (c) and (d)with the increase of the number of shaded cell stringsthe voltage at the optimal operating point of the arraysdecreases in sequence

As seen in Figure 13 the results indicate that theoutput of the array under cover have no multiplepeaks According to (a) and (b) cover 1 and cover 2have nearly consistent output characteristics The voltageat the optimal operating point and the open-circuitvoltage move left compared to the normal operatingcondition (noncovered) The bypass diode is thus acti-vated when the area of the covering is larger than thearea of a single cell The voltage at the optimal operat-ing point and the open-circuit voltage in the case ofcover 3 move left compared with that in the case ofcover 2 At this point two bypass diodes are activatedAccording to (c) and (d) the voltage at the optimaloperating point of the array and the open-circuit volt-age decrease in sequence with the increase of the cov-ered cell strings

As seen in Figure 14 cover shading influences boththe voltage at the maximum operating point Um andthe open-circuit voltage Uoc while shadow shading onlyinfluences the voltage at the maximum operating pointUm which coincides with the simulation results

Equations (11) and (12) present the computationalformulae for the voltage at the optimal operating pointand the open-circuit voltage Uoc under the shadow andcovering conditions which will be analyzed in the fol-lowing paragraphs Under shading conditions the rela-tive error between the voltage at the theoreticaloptimal operating point and the voltage at the mea-sured optimal operating point is expressed as e1 andthe relative error between the theoretical open-circuitvoltage and the measured open-circuit voltage isexpressed as e2 as shown in (13)

9

8

7

6

5

4

3

2

1

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 1Cover 2Cover 3

Cover 5Cover 6No Cover

Cover 4

Figure 9 Simulation result for cover shading The output curve without multipeak feature under cover shading

Table 4 Distribution of electric parameters under cover shading

Covering conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74397 9111 817

Cover 1 10347 874 66092 8026 823

Cover 2 10350 874 66299 8239 805

Cover 3 8964 873 57884 7008 826

Cover 4 10344 874 65207 8190 796

Cover 5 8968 873 57456 7024 818

Cover 6 7583 869 48936 6099 802

The distribution of electrical parameters under different cover conditions

9International Journal of Photoenergy

e1 =U prime

m‐test minusU primem‐calculate

U primem‐calculate

times 100

e2 =U prime

oc‐test minusU primeoc‐calculate

U primeoc‐calculate

times 100

13

where Um‐testprime and Uoc‐testprime are the measured voltage at theoptimal operating point and the open-circuit voltage undershading conditions respectively and Um‐calculateprime and

Uoc‐calculateprime are the theoretical voltage at the optimal operatingpoint and the open-circuit voltage under the shadingconditions

Table 5 lists the distribution of the voltage at the optimaloperating point and the open-circuit voltage under differ-ent shading conditions and the relative error between themeasured shaded voltage and the computed shaded volt-age As seen in the table the maximum error betweenthe measured voltage and the computed voltage is lessthan 2 under shading conditions The empirical resultscompletely coincide with the simulation results

10

8

6

4

2

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 4Cover 5

Shadow 5Normal

Cover 4

Figure 10 Comparison between shadow and cover conditions The difference between shadow and cover is whether the open-circuit voltagedrops or not

Computer

Radiation Temperature

IV test

Data summarization

Measuring the electricalparameters

Cover 1ndashcover 6

Different shadingconditions

Theoretical calculating

Calculating the theoretical value ofelectrical parameters

Uoc Um Isc Im

Shadow 1ndashshadow 6

Figure 11 Block diagram for experimental testing By comparing the theoretical value and the measured value summarize the rules

10 International Journal of Photoenergy

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

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International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

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NanotechnologyHindawiwwwhindawicom Volume 2018

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Applied ChemistryJournal of

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Biochemistry Research International

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Enzyme Research

Hindawiwwwhindawicom Volume 2018

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SpectroscopyAnalytical ChemistryInternational Journal of

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MaterialsJournal of

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Hindawiwwwhindawicom Volume 2018

Na

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ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

rows of the array and tall buildings The area of theshadow is generally larger than that of a single photo-voltaic cell The voltage effect on the array arisingfrom a shadow with an area less than that of a singlephotovoltaic cell can be ignored

32 Cover Shading The simulation results under the coverconditions are shown in Figure 9 The bypass diode isusually in a nonconducting state and the module outputis normally under uniform light in the absence of cover-ing The cells will have negative voltage and trigger theconduction of bypass diode when the negative voltagereaches a certain upper limit In Figure 9 the outputcharacteristics have no multiple peaks due to the factthat the covered cells with negative voltage trigger theconduction of the corresponding bypass diode Covers 1 2

and 4 have consistent output characteristics Similarly covers3 and 5 are consistent The output decreases in a ladderpattern from cover 4 to cover 6 In terms of the electricalparameters Isc and Im remain unchanged while Uoc Umand Pm decline regularly The distribution of the electricalparameters of the array under cover shading is shown inTable 4

Based on the above analysis we can obtain the distribu-tion rules of the electrical parameters of photovoltaic arrayunder cover shading as follows

(1) Cover shading does not influence Isc and Im of thephotovoltaic array

(2) Uoc and Um drop when the area of the coveredportion within the cell string is larger than or equal

0 10 20 30 40 500

2

4

6

I (A

)

8

10

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

U (V)

(a)

0 10 20 30 40 50

P (W

)

U (V)

0

50

100

150

200

250

300

350

1000 Wm2

900 Wm2

800 Wm2

700 Wm2

600 Wm2

500 Wm2

(b)

0 10 20 30 40 50

I (A

)

0

2

4

6

8

10

U (V)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(c)

0 10 20 30 40 500

50

100

150

200

250

300

350

U (V)

P (W

)

5ordmC15ordmC25ordmC

35ordmC45ordmC55ordmC

(d)

Figure 6 (a) IV curve under different irradiances (b) PV curve under different irradiances (c) IV curve under different temperatures (d) PVcurve under different temperatures Describing the IV and PV curves under different operating conditions

6 International Journal of Photoenergy

to the area of a single cell The drop intensity is pro-portional to the number of the covered cell stringsand the cell string voltage The output power there-fore decreases

(3) Cover shading with an area less than that of a singlecell can be considered negligible

The computation formula of the electrical parameters ofthe array under cover shading is as follows

Iscprime = IscUocprime =Uoc minus u2 sdot n2Imprime = ImUmprime =Um minus u1 sdot n2Pmprime = Imprime sdotUmprime

12where n2 is the number of the covered cell strings under thecovering condition and u2 is the open-circuit voltage of thecell string

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

(a) Shadowcover 1

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

(b) Shadowcover 2

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

21

(c) Shadowcover 3

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

(d) Shadowcover 4

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

(e) Shadowcover 5

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

(f) Shadowcover 6

Figure 7 Setting of different shading conditions Shading one cellcell string two cellscell strings three cellscell strings respectively

Table 2 Setting of simulation conditions

Type ofshading

Solar irradiationintensity of theshaded portion

(Wm2)

Solar irradiationintensity of the

unshaded portion(Wm2)

Moduletemperature

(degC)

Shadowshading

150 1000 25

Covershading

0 1000 25

The irradiation intensity of the shadowed photovoltaic cells is set at 15 ofthe irradiation intensity absorbed by the unshadowed modules The solarirradiation intensity of cover is set at zero Temperature is 25degC

7International Journal of Photoenergy

33 Summary To illustrate the distribution features of theelectrical parameters of the photovoltaic array under dif-ferent shading conditions Figure 10 presents the IV andPV curves of the array under the two types of shadingShadow 4 shadow 5 cover 4 and cover 5 are selectedfor comparison The output features and parameter distri-bution rules of the photovoltaic array under the shadowand cover conditions are as follows

(1) The output of the array under shadowing is char-acterized by multiple peaks and ladder patternwhile cover shading has no such characteristics

(2) Shadowing and covering have no effect on Isc ofthe array

(3) When the shaded area is larger than or equal to asingle cell the shadow causes a drop in Um while

covering causes a drop in Um and Uoc The voltagedrop extent is associated with the number of theshaded cell strings and the string voltage Anyshading with an area less than that of a single cellis considered negligible

(4) The difference between shadowing and covering con-ditions is whether Uoc is falling or not It can bejudged from the distribution characteristics of Umand Uoc

4 Empirical Validation of the ElectricalProperties of Photovoltaic Array underDifferent Shading Conditions

41 Method for Empirical Validation Three modules wereconnected in series to create a photovoltaic array in theexperiment To investigate the distribution characteristicsof the electrical parameters under different shading condi-tions an opaque paperboard was used to set the shadowand covering conditions respectively as shown inFigure 7 The electrical parameters of the array underdifferent shading conditions were recorded with an IVscanner To explain the distribution rules of the electricalparameters (8) was introduced to obtain the voltage atthe maximum power point Based on (11) and (12) wecan obtain the voltage at the theoretical maximum powerpoint under different shading conditions and comparewith the experiment results The experimental platformcomprised of a photovoltaic array constituted by JinkoJKM245P modules an irradiator for measuring the solarirradiance a temperature sensor for measuring the

9

8

7

6

5

4

3

2

1

00 50 100

Shadow 1Shadow 2Shadow 3

Shadow 5Shadow 6No shadow

Shadow 4

U (V)

I (A)

150 0 50 100U (V)

150

800

700

600

500

400

300

200

100

0

P (W

)

Figure 8 Simulation result for shadowing Under the shadow conditions the output curve presents a multipeak feature

Table 3 Distribution of electrical parameters under shadowingcondition

Shadow conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74463 9193 810

Shadow 1 11730 874 66147 8051 822

Shadow 2 11724 874 66246 8112 817

Shadow 3 11710 873 58147 7195 808

Shadow 4 11603 874 65270 8104 805

Shadow 5 11468 873 58040 7077 820

Shadow 6 11334 874 48782 6195 787

The distribution of electrical parameters under different shading conditions

8 International Journal of Photoenergy

backboard temperature and an IV tester Figure 11 pre-sents the structural diagram

42 Analysis of the Empirical Testing Results As seen inFigure 12 the results indicate that the output of the arrayunder shadow is characterized by multiple peaks Shadow-ing only influences the optimal operating voltage Accord-ing to (a) and (b) shadows 1 and 2 nearly have consistentoutput characteristics Compared to the normal operatingcondition (nonshaded) the voltage at the optimal operat-ing point moves left while the open-circuit voltage remainsunchanged The voltage at the optimal operating pointfurther moves left in the case of shadow 3 compared tothat in the case of shadow 2 According to (c) and (d)with the increase of the number of shaded cell stringsthe voltage at the optimal operating point of the arraysdecreases in sequence

As seen in Figure 13 the results indicate that theoutput of the array under cover have no multiplepeaks According to (a) and (b) cover 1 and cover 2have nearly consistent output characteristics The voltageat the optimal operating point and the open-circuitvoltage move left compared to the normal operatingcondition (noncovered) The bypass diode is thus acti-vated when the area of the covering is larger than thearea of a single cell The voltage at the optimal operat-ing point and the open-circuit voltage in the case ofcover 3 move left compared with that in the case ofcover 2 At this point two bypass diodes are activatedAccording to (c) and (d) the voltage at the optimaloperating point of the array and the open-circuit volt-age decrease in sequence with the increase of the cov-ered cell strings

As seen in Figure 14 cover shading influences boththe voltage at the maximum operating point Um andthe open-circuit voltage Uoc while shadow shading onlyinfluences the voltage at the maximum operating pointUm which coincides with the simulation results

Equations (11) and (12) present the computationalformulae for the voltage at the optimal operating pointand the open-circuit voltage Uoc under the shadow andcovering conditions which will be analyzed in the fol-lowing paragraphs Under shading conditions the rela-tive error between the voltage at the theoreticaloptimal operating point and the voltage at the mea-sured optimal operating point is expressed as e1 andthe relative error between the theoretical open-circuitvoltage and the measured open-circuit voltage isexpressed as e2 as shown in (13)

9

8

7

6

5

4

3

2

1

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 1Cover 2Cover 3

Cover 5Cover 6No Cover

Cover 4

Figure 9 Simulation result for cover shading The output curve without multipeak feature under cover shading

Table 4 Distribution of electric parameters under cover shading

Covering conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74397 9111 817

Cover 1 10347 874 66092 8026 823

Cover 2 10350 874 66299 8239 805

Cover 3 8964 873 57884 7008 826

Cover 4 10344 874 65207 8190 796

Cover 5 8968 873 57456 7024 818

Cover 6 7583 869 48936 6099 802

The distribution of electrical parameters under different cover conditions

9International Journal of Photoenergy

e1 =U prime

m‐test minusU primem‐calculate

U primem‐calculate

times 100

e2 =U prime

oc‐test minusU primeoc‐calculate

U primeoc‐calculate

times 100

13

where Um‐testprime and Uoc‐testprime are the measured voltage at theoptimal operating point and the open-circuit voltage undershading conditions respectively and Um‐calculateprime and

Uoc‐calculateprime are the theoretical voltage at the optimal operatingpoint and the open-circuit voltage under the shadingconditions

Table 5 lists the distribution of the voltage at the optimaloperating point and the open-circuit voltage under differ-ent shading conditions and the relative error between themeasured shaded voltage and the computed shaded volt-age As seen in the table the maximum error betweenthe measured voltage and the computed voltage is lessthan 2 under shading conditions The empirical resultscompletely coincide with the simulation results

10

8

6

4

2

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 4Cover 5

Shadow 5Normal

Cover 4

Figure 10 Comparison between shadow and cover conditions The difference between shadow and cover is whether the open-circuit voltagedrops or not

Computer

Radiation Temperature

IV test

Data summarization

Measuring the electricalparameters

Cover 1ndashcover 6

Different shadingconditions

Theoretical calculating

Calculating the theoretical value ofelectrical parameters

Uoc Um Isc Im

Shadow 1ndashshadow 6

Figure 11 Block diagram for experimental testing By comparing the theoretical value and the measured value summarize the rules

10 International Journal of Photoenergy

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

to the area of a single cell The drop intensity is pro-portional to the number of the covered cell stringsand the cell string voltage The output power there-fore decreases

(3) Cover shading with an area less than that of a singlecell can be considered negligible

The computation formula of the electrical parameters ofthe array under cover shading is as follows

Iscprime = IscUocprime =Uoc minus u2 sdot n2Imprime = ImUmprime =Um minus u1 sdot n2Pmprime = Imprime sdotUmprime

12where n2 is the number of the covered cell strings under thecovering condition and u2 is the open-circuit voltage of thecell string

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

(a) Shadowcover 1

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

(b) Shadowcover 2

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1

20

21

(c) Shadowcover 3

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

(d) Shadowcover 4

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

(e) Shadowcover 5

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

1 2 3 4 5 6 7 8 9 10

20 19 18 17 16 15 14 13 12 11

21 22 23 24 25 26 27 28 29 30

40 39 38 37 36 35 34 33 32 31

41 42 43 44 45 46 47 48 49 50

60 59 58 57 56 55 54 53 52 51

(f) Shadowcover 6

Figure 7 Setting of different shading conditions Shading one cellcell string two cellscell strings three cellscell strings respectively

Table 2 Setting of simulation conditions

Type ofshading

Solar irradiationintensity of theshaded portion

(Wm2)

Solar irradiationintensity of the

unshaded portion(Wm2)

Moduletemperature

(degC)

Shadowshading

150 1000 25

Covershading

0 1000 25

The irradiation intensity of the shadowed photovoltaic cells is set at 15 ofthe irradiation intensity absorbed by the unshadowed modules The solarirradiation intensity of cover is set at zero Temperature is 25degC

7International Journal of Photoenergy

33 Summary To illustrate the distribution features of theelectrical parameters of the photovoltaic array under dif-ferent shading conditions Figure 10 presents the IV andPV curves of the array under the two types of shadingShadow 4 shadow 5 cover 4 and cover 5 are selectedfor comparison The output features and parameter distri-bution rules of the photovoltaic array under the shadowand cover conditions are as follows

(1) The output of the array under shadowing is char-acterized by multiple peaks and ladder patternwhile cover shading has no such characteristics

(2) Shadowing and covering have no effect on Isc ofthe array

(3) When the shaded area is larger than or equal to asingle cell the shadow causes a drop in Um while

covering causes a drop in Um and Uoc The voltagedrop extent is associated with the number of theshaded cell strings and the string voltage Anyshading with an area less than that of a single cellis considered negligible

(4) The difference between shadowing and covering con-ditions is whether Uoc is falling or not It can bejudged from the distribution characteristics of Umand Uoc

4 Empirical Validation of the ElectricalProperties of Photovoltaic Array underDifferent Shading Conditions

41 Method for Empirical Validation Three modules wereconnected in series to create a photovoltaic array in theexperiment To investigate the distribution characteristicsof the electrical parameters under different shading condi-tions an opaque paperboard was used to set the shadowand covering conditions respectively as shown inFigure 7 The electrical parameters of the array underdifferent shading conditions were recorded with an IVscanner To explain the distribution rules of the electricalparameters (8) was introduced to obtain the voltage atthe maximum power point Based on (11) and (12) wecan obtain the voltage at the theoretical maximum powerpoint under different shading conditions and comparewith the experiment results The experimental platformcomprised of a photovoltaic array constituted by JinkoJKM245P modules an irradiator for measuring the solarirradiance a temperature sensor for measuring the

9

8

7

6

5

4

3

2

1

00 50 100

Shadow 1Shadow 2Shadow 3

Shadow 5Shadow 6No shadow

Shadow 4

U (V)

I (A)

150 0 50 100U (V)

150

800

700

600

500

400

300

200

100

0

P (W

)

Figure 8 Simulation result for shadowing Under the shadow conditions the output curve presents a multipeak feature

Table 3 Distribution of electrical parameters under shadowingcondition

Shadow conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74463 9193 810

Shadow 1 11730 874 66147 8051 822

Shadow 2 11724 874 66246 8112 817

Shadow 3 11710 873 58147 7195 808

Shadow 4 11603 874 65270 8104 805

Shadow 5 11468 873 58040 7077 820

Shadow 6 11334 874 48782 6195 787

The distribution of electrical parameters under different shading conditions

8 International Journal of Photoenergy

backboard temperature and an IV tester Figure 11 pre-sents the structural diagram

42 Analysis of the Empirical Testing Results As seen inFigure 12 the results indicate that the output of the arrayunder shadow is characterized by multiple peaks Shadow-ing only influences the optimal operating voltage Accord-ing to (a) and (b) shadows 1 and 2 nearly have consistentoutput characteristics Compared to the normal operatingcondition (nonshaded) the voltage at the optimal operat-ing point moves left while the open-circuit voltage remainsunchanged The voltage at the optimal operating pointfurther moves left in the case of shadow 3 compared tothat in the case of shadow 2 According to (c) and (d)with the increase of the number of shaded cell stringsthe voltage at the optimal operating point of the arraysdecreases in sequence

As seen in Figure 13 the results indicate that theoutput of the array under cover have no multiplepeaks According to (a) and (b) cover 1 and cover 2have nearly consistent output characteristics The voltageat the optimal operating point and the open-circuitvoltage move left compared to the normal operatingcondition (noncovered) The bypass diode is thus acti-vated when the area of the covering is larger than thearea of a single cell The voltage at the optimal operat-ing point and the open-circuit voltage in the case ofcover 3 move left compared with that in the case ofcover 2 At this point two bypass diodes are activatedAccording to (c) and (d) the voltage at the optimaloperating point of the array and the open-circuit volt-age decrease in sequence with the increase of the cov-ered cell strings

As seen in Figure 14 cover shading influences boththe voltage at the maximum operating point Um andthe open-circuit voltage Uoc while shadow shading onlyinfluences the voltage at the maximum operating pointUm which coincides with the simulation results

Equations (11) and (12) present the computationalformulae for the voltage at the optimal operating pointand the open-circuit voltage Uoc under the shadow andcovering conditions which will be analyzed in the fol-lowing paragraphs Under shading conditions the rela-tive error between the voltage at the theoreticaloptimal operating point and the voltage at the mea-sured optimal operating point is expressed as e1 andthe relative error between the theoretical open-circuitvoltage and the measured open-circuit voltage isexpressed as e2 as shown in (13)

9

8

7

6

5

4

3

2

1

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 1Cover 2Cover 3

Cover 5Cover 6No Cover

Cover 4

Figure 9 Simulation result for cover shading The output curve without multipeak feature under cover shading

Table 4 Distribution of electric parameters under cover shading

Covering conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74397 9111 817

Cover 1 10347 874 66092 8026 823

Cover 2 10350 874 66299 8239 805

Cover 3 8964 873 57884 7008 826

Cover 4 10344 874 65207 8190 796

Cover 5 8968 873 57456 7024 818

Cover 6 7583 869 48936 6099 802

The distribution of electrical parameters under different cover conditions

9International Journal of Photoenergy

e1 =U prime

m‐test minusU primem‐calculate

U primem‐calculate

times 100

e2 =U prime

oc‐test minusU primeoc‐calculate

U primeoc‐calculate

times 100

13

where Um‐testprime and Uoc‐testprime are the measured voltage at theoptimal operating point and the open-circuit voltage undershading conditions respectively and Um‐calculateprime and

Uoc‐calculateprime are the theoretical voltage at the optimal operatingpoint and the open-circuit voltage under the shadingconditions

Table 5 lists the distribution of the voltage at the optimaloperating point and the open-circuit voltage under differ-ent shading conditions and the relative error between themeasured shaded voltage and the computed shaded volt-age As seen in the table the maximum error betweenthe measured voltage and the computed voltage is lessthan 2 under shading conditions The empirical resultscompletely coincide with the simulation results

10

8

6

4

2

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 4Cover 5

Shadow 5Normal

Cover 4

Figure 10 Comparison between shadow and cover conditions The difference between shadow and cover is whether the open-circuit voltagedrops or not

Computer

Radiation Temperature

IV test

Data summarization

Measuring the electricalparameters

Cover 1ndashcover 6

Different shadingconditions

Theoretical calculating

Calculating the theoretical value ofelectrical parameters

Uoc Um Isc Im

Shadow 1ndashshadow 6

Figure 11 Block diagram for experimental testing By comparing the theoretical value and the measured value summarize the rules

10 International Journal of Photoenergy

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

33 Summary To illustrate the distribution features of theelectrical parameters of the photovoltaic array under dif-ferent shading conditions Figure 10 presents the IV andPV curves of the array under the two types of shadingShadow 4 shadow 5 cover 4 and cover 5 are selectedfor comparison The output features and parameter distri-bution rules of the photovoltaic array under the shadowand cover conditions are as follows

(1) The output of the array under shadowing is char-acterized by multiple peaks and ladder patternwhile cover shading has no such characteristics

(2) Shadowing and covering have no effect on Isc ofthe array

(3) When the shaded area is larger than or equal to asingle cell the shadow causes a drop in Um while

covering causes a drop in Um and Uoc The voltagedrop extent is associated with the number of theshaded cell strings and the string voltage Anyshading with an area less than that of a single cellis considered negligible

(4) The difference between shadowing and covering con-ditions is whether Uoc is falling or not It can bejudged from the distribution characteristics of Umand Uoc

4 Empirical Validation of the ElectricalProperties of Photovoltaic Array underDifferent Shading Conditions

41 Method for Empirical Validation Three modules wereconnected in series to create a photovoltaic array in theexperiment To investigate the distribution characteristicsof the electrical parameters under different shading condi-tions an opaque paperboard was used to set the shadowand covering conditions respectively as shown inFigure 7 The electrical parameters of the array underdifferent shading conditions were recorded with an IVscanner To explain the distribution rules of the electricalparameters (8) was introduced to obtain the voltage atthe maximum power point Based on (11) and (12) wecan obtain the voltage at the theoretical maximum powerpoint under different shading conditions and comparewith the experiment results The experimental platformcomprised of a photovoltaic array constituted by JinkoJKM245P modules an irradiator for measuring the solarirradiance a temperature sensor for measuring the

9

8

7

6

5

4

3

2

1

00 50 100

Shadow 1Shadow 2Shadow 3

Shadow 5Shadow 6No shadow

Shadow 4

U (V)

I (A)

150 0 50 100U (V)

150

800

700

600

500

400

300

200

100

0

P (W

)

Figure 8 Simulation result for shadowing Under the shadow conditions the output curve presents a multipeak feature

Table 3 Distribution of electrical parameters under shadowingcondition

Shadow conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74463 9193 810

Shadow 1 11730 874 66147 8051 822

Shadow 2 11724 874 66246 8112 817

Shadow 3 11710 873 58147 7195 808

Shadow 4 11603 874 65270 8104 805

Shadow 5 11468 873 58040 7077 820

Shadow 6 11334 874 48782 6195 787

The distribution of electrical parameters under different shading conditions

8 International Journal of Photoenergy

backboard temperature and an IV tester Figure 11 pre-sents the structural diagram

42 Analysis of the Empirical Testing Results As seen inFigure 12 the results indicate that the output of the arrayunder shadow is characterized by multiple peaks Shadow-ing only influences the optimal operating voltage Accord-ing to (a) and (b) shadows 1 and 2 nearly have consistentoutput characteristics Compared to the normal operatingcondition (nonshaded) the voltage at the optimal operat-ing point moves left while the open-circuit voltage remainsunchanged The voltage at the optimal operating pointfurther moves left in the case of shadow 3 compared tothat in the case of shadow 2 According to (c) and (d)with the increase of the number of shaded cell stringsthe voltage at the optimal operating point of the arraysdecreases in sequence

As seen in Figure 13 the results indicate that theoutput of the array under cover have no multiplepeaks According to (a) and (b) cover 1 and cover 2have nearly consistent output characteristics The voltageat the optimal operating point and the open-circuitvoltage move left compared to the normal operatingcondition (noncovered) The bypass diode is thus acti-vated when the area of the covering is larger than thearea of a single cell The voltage at the optimal operat-ing point and the open-circuit voltage in the case ofcover 3 move left compared with that in the case ofcover 2 At this point two bypass diodes are activatedAccording to (c) and (d) the voltage at the optimaloperating point of the array and the open-circuit volt-age decrease in sequence with the increase of the cov-ered cell strings

As seen in Figure 14 cover shading influences boththe voltage at the maximum operating point Um andthe open-circuit voltage Uoc while shadow shading onlyinfluences the voltage at the maximum operating pointUm which coincides with the simulation results

Equations (11) and (12) present the computationalformulae for the voltage at the optimal operating pointand the open-circuit voltage Uoc under the shadow andcovering conditions which will be analyzed in the fol-lowing paragraphs Under shading conditions the rela-tive error between the voltage at the theoreticaloptimal operating point and the voltage at the mea-sured optimal operating point is expressed as e1 andthe relative error between the theoretical open-circuitvoltage and the measured open-circuit voltage isexpressed as e2 as shown in (13)

9

8

7

6

5

4

3

2

1

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 1Cover 2Cover 3

Cover 5Cover 6No Cover

Cover 4

Figure 9 Simulation result for cover shading The output curve without multipeak feature under cover shading

Table 4 Distribution of electric parameters under cover shading

Covering conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74397 9111 817

Cover 1 10347 874 66092 8026 823

Cover 2 10350 874 66299 8239 805

Cover 3 8964 873 57884 7008 826

Cover 4 10344 874 65207 8190 796

Cover 5 8968 873 57456 7024 818

Cover 6 7583 869 48936 6099 802

The distribution of electrical parameters under different cover conditions

9International Journal of Photoenergy

e1 =U prime

m‐test minusU primem‐calculate

U primem‐calculate

times 100

e2 =U prime

oc‐test minusU primeoc‐calculate

U primeoc‐calculate

times 100

13

where Um‐testprime and Uoc‐testprime are the measured voltage at theoptimal operating point and the open-circuit voltage undershading conditions respectively and Um‐calculateprime and

Uoc‐calculateprime are the theoretical voltage at the optimal operatingpoint and the open-circuit voltage under the shadingconditions

Table 5 lists the distribution of the voltage at the optimaloperating point and the open-circuit voltage under differ-ent shading conditions and the relative error between themeasured shaded voltage and the computed shaded volt-age As seen in the table the maximum error betweenthe measured voltage and the computed voltage is lessthan 2 under shading conditions The empirical resultscompletely coincide with the simulation results

10

8

6

4

2

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 4Cover 5

Shadow 5Normal

Cover 4

Figure 10 Comparison between shadow and cover conditions The difference between shadow and cover is whether the open-circuit voltagedrops or not

Computer

Radiation Temperature

IV test

Data summarization

Measuring the electricalparameters

Cover 1ndashcover 6

Different shadingconditions

Theoretical calculating

Calculating the theoretical value ofelectrical parameters

Uoc Um Isc Im

Shadow 1ndashshadow 6

Figure 11 Block diagram for experimental testing By comparing the theoretical value and the measured value summarize the rules

10 International Journal of Photoenergy

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

backboard temperature and an IV tester Figure 11 pre-sents the structural diagram

42 Analysis of the Empirical Testing Results As seen inFigure 12 the results indicate that the output of the arrayunder shadow is characterized by multiple peaks Shadow-ing only influences the optimal operating voltage Accord-ing to (a) and (b) shadows 1 and 2 nearly have consistentoutput characteristics Compared to the normal operatingcondition (nonshaded) the voltage at the optimal operat-ing point moves left while the open-circuit voltage remainsunchanged The voltage at the optimal operating pointfurther moves left in the case of shadow 3 compared tothat in the case of shadow 2 According to (c) and (d)with the increase of the number of shaded cell stringsthe voltage at the optimal operating point of the arraysdecreases in sequence

As seen in Figure 13 the results indicate that theoutput of the array under cover have no multiplepeaks According to (a) and (b) cover 1 and cover 2have nearly consistent output characteristics The voltageat the optimal operating point and the open-circuitvoltage move left compared to the normal operatingcondition (noncovered) The bypass diode is thus acti-vated when the area of the covering is larger than thearea of a single cell The voltage at the optimal operat-ing point and the open-circuit voltage in the case ofcover 3 move left compared with that in the case ofcover 2 At this point two bypass diodes are activatedAccording to (c) and (d) the voltage at the optimaloperating point of the array and the open-circuit volt-age decrease in sequence with the increase of the cov-ered cell strings

As seen in Figure 14 cover shading influences boththe voltage at the maximum operating point Um andthe open-circuit voltage Uoc while shadow shading onlyinfluences the voltage at the maximum operating pointUm which coincides with the simulation results

Equations (11) and (12) present the computationalformulae for the voltage at the optimal operating pointand the open-circuit voltage Uoc under the shadow andcovering conditions which will be analyzed in the fol-lowing paragraphs Under shading conditions the rela-tive error between the voltage at the theoreticaloptimal operating point and the voltage at the mea-sured optimal operating point is expressed as e1 andthe relative error between the theoretical open-circuitvoltage and the measured open-circuit voltage isexpressed as e2 as shown in (13)

9

8

7

6

5

4

3

2

1

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 1Cover 2Cover 3

Cover 5Cover 6No Cover

Cover 4

Figure 9 Simulation result for cover shading The output curve without multipeak feature under cover shading

Table 4 Distribution of electric parameters under cover shading

Covering conditions Uoc (V) Isc (A) P (W) Um (V) Im (A)

Normal 11737 875 74397 9111 817

Cover 1 10347 874 66092 8026 823

Cover 2 10350 874 66299 8239 805

Cover 3 8964 873 57884 7008 826

Cover 4 10344 874 65207 8190 796

Cover 5 8968 873 57456 7024 818

Cover 6 7583 869 48936 6099 802

The distribution of electrical parameters under different cover conditions

9International Journal of Photoenergy

e1 =U prime

m‐test minusU primem‐calculate

U primem‐calculate

times 100

e2 =U prime

oc‐test minusU primeoc‐calculate

U primeoc‐calculate

times 100

13

where Um‐testprime and Uoc‐testprime are the measured voltage at theoptimal operating point and the open-circuit voltage undershading conditions respectively and Um‐calculateprime and

Uoc‐calculateprime are the theoretical voltage at the optimal operatingpoint and the open-circuit voltage under the shadingconditions

Table 5 lists the distribution of the voltage at the optimaloperating point and the open-circuit voltage under differ-ent shading conditions and the relative error between themeasured shaded voltage and the computed shaded volt-age As seen in the table the maximum error betweenthe measured voltage and the computed voltage is lessthan 2 under shading conditions The empirical resultscompletely coincide with the simulation results

10

8

6

4

2

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 4Cover 5

Shadow 5Normal

Cover 4

Figure 10 Comparison between shadow and cover conditions The difference between shadow and cover is whether the open-circuit voltagedrops or not

Computer

Radiation Temperature

IV test

Data summarization

Measuring the electricalparameters

Cover 1ndashcover 6

Different shadingconditions

Theoretical calculating

Calculating the theoretical value ofelectrical parameters

Uoc Um Isc Im

Shadow 1ndashshadow 6

Figure 11 Block diagram for experimental testing By comparing the theoretical value and the measured value summarize the rules

10 International Journal of Photoenergy

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

e1 =U prime

m‐test minusU primem‐calculate

U primem‐calculate

times 100

e2 =U prime

oc‐test minusU primeoc‐calculate

U primeoc‐calculate

times 100

13

where Um‐testprime and Uoc‐testprime are the measured voltage at theoptimal operating point and the open-circuit voltage undershading conditions respectively and Um‐calculateprime and

Uoc‐calculateprime are the theoretical voltage at the optimal operatingpoint and the open-circuit voltage under the shadingconditions

Table 5 lists the distribution of the voltage at the optimaloperating point and the open-circuit voltage under differ-ent shading conditions and the relative error between themeasured shaded voltage and the computed shaded volt-age As seen in the table the maximum error betweenthe measured voltage and the computed voltage is lessthan 2 under shading conditions The empirical resultscompletely coincide with the simulation results

10

8

6

4

2

00 50 100

U (V)

I (A)

800

700

600

500

400

300

200

100

0

P (W

)

150 0 50 100U (V)

150

Cover 4Cover 5

Shadow 5Normal

Cover 4

Figure 10 Comparison between shadow and cover conditions The difference between shadow and cover is whether the open-circuit voltagedrops or not

Computer

Radiation Temperature

IV test

Data summarization

Measuring the electricalparameters

Cover 1ndashcover 6

Different shadingconditions

Theoretical calculating

Calculating the theoretical value ofelectrical parameters

Uoc Um Isc Im

Shadow 1ndashshadow 6

Figure 11 Block diagram for experimental testing By comparing the theoretical value and the measured value summarize the rules

10 International Journal of Photoenergy

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

Based on Table 5 it can be concluded that

(1) the computation results of the electrical parame-ters of the theoretical optimal operating pointunder the shading conditions are accurate andapplicable

(2) the number of the shaded modules can be knownfrom the voltage at the theoretical optimal operat-ing point and the voltage at the measured optimaloperating point The computation formula is asfollows

n3 =U prime

m‐calculate minusU primem‐test

u 14

where u is the optimum operating voltage of a cell string andn3 is the number of the shaded modules

5 Conclusion

The paper illustrates the distribution rules of the electricalparameters of photovoltaic array under two types ofshading conditions shadow and cover shadings both bysimulation and empirical testing drawing several conclu-sions as below

(1) Shadow and cover shadings have different effects onphotovoltaic array in actual engineering This modelaccurately reflects the output properties of the photo-voltaic array under different shading conditions

(2) Shadowing only influences the voltage at the optimaloperating point of the array while covering influencesboth the open-circuit voltage and the voltage at theoptimal operating point The type of shading thatis the shadow and cover can be judged from the dis-tribution of the open-circuit voltage and the voltageat the optimal operating point Shading does notinfluence the current of the array

8

6

4

2

I (A

)

0

NormalShadow 1

Shadow 2Shadow 3

0 20 40U (V)

60 80 100 120

(a)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShadow 1

Shadow 2Shadow 3

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(c)

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

NormalShade 4

Shade 5Shade 6

(d)

Figure 12 Results for the shadowing experiment The curves are coincide with the simulation results

11International Journal of Photoenergy

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

(a)

NormalCover 1

Cover 2Cover 3

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(b)

8

6

4

2

I (A

)

00 20 40

U (V)60 80 100 120

NormalCover 4

Cover 5Cover 6

(c)

NormalCover 4

Cover 5Cover 6

600

400

200

P (W

)

00 20 40

U (V)60 80 100 120

(d)

Figure 13 Results for the cover shading experiment The curves are coincide with the simulation results

8 500

450

400

350

300

250

200

150

100

50

0

7

6

5

4

3

2

1

I (A

)

P (W

)

00 20 40

U (V)60 80 100 120 0 20 40

U (V)60 80 100 120

NormalCover 1

Cover 2Cover 3

Figure 14 Comparison of the results of the shadow and the cover shading experiments The difference between shadow and cover is whetherthe open-circuit voltage drops or not

12 International Journal of Photoenergy

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

(3) A drop occurs in voltage when the area of shadingin a cell string is larger than or equal to that of asingle cell The magnitude of the drop is propor-tional to the number of the shaded strings andthe string voltage

(4) The number of the shaded modules can be effectivelyjudged from the computed results of the theoreticalmaximum power point and the measured results

Data Availability

The data used to support the findings of this study are avail-able from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities (2016MS52 2016MS31)and China Three Gorges New Energy Co Ltd

References

[1] P Guerriero F Di Napoli F Cominale V dAlessandro andS Daliento ldquoAccurate analysis of small shadows effects onphotovoltaic systems yieldrdquo in 2014 International Symposiumon Power Electronics Electrical Drives Automation andMotion pp 987ndash992 Ischia Italy June 2014

[2] J Qi X Zhang Y Zhang and W Zhou ldquoStudy on simulationalgorithm of PV array considering shade effectrdquo Proceedings ofthe CSEE vol 32 pp 131ndash138 2012

[3] C H Wu D Q Zhou and Z H Li ldquoHot spot detection andfuzzy optimization control method of PV modulerdquo Proceed-ings of the CSEE vol 33 pp 50ndash61 2013

[4] Y Haoyuan Y Shuo S-C Tan and S Y R Hui ldquoDynamicmodeling of partial shading on photovoltaic arraysrdquo in 2015

IEEE Energy Conversion Congress and Exposition (ECCE)pp 6616ndash6621 Montreal QC Canada September 2015

[5] K Ding X G Bian and H H Liu ldquoMatlab-Simulink basedmodeling to study the influence of nonuniform insolationphotovoltaic arrayrdquo in 2011 Asia-Pacific Power and EnergyEngineering Conference pp 1ndash4 Wuhan China March 2011

[6] P Burns andNAnani ldquoModelling and simulation of photovol-taic arrays under varying conditionsrdquo in 2014 9th InternationalSymposium on Communication Systems Networks amp DigitalSign (CSNDSP) pp 831ndash834 Manchester UK July 2014

[7] G Celsa and G M Tina ldquoMatlabSimulink model of photo-voltaic modulesstrings under uneven distribution of irradi-ance and temperaturerdquo in IRECrsquo2015 The SixthInternational Renewable Energy Congress pp 1ndash6 SousseTunisia March 2015

[8] Q Tian Z Zhao Y Deng L Yuan and F He ldquoSimulation andexperimental study about reverse model of photovoltaic cellsrdquoProceedings of the CSEE vol 31 no 23 pp 121ndash128 2011

[9] A Kumar R K Pachauri and Y K Chauhan ldquoExperimentalanalysis of SPTCT PV array configurations under partialshading conditionsrdquo in 2016 IEEE 1st International Conferenceon Power Electronics Intelligent Control and Energy Systems(ICPEICES) pp 1ndash6 Delhi India July 2016

[10] F Zhicheng W Yahui and W Lulu ldquoExperimental studyon characteristics of PV module under partially shaded con-ditionsrdquo Acta Energiae Solaris Sinica vol 36 no 2pp 392ndash398 2015

[11] T P Zhou and W Sun ldquoMaximum power point tracking ofphotovoltaic array under nonuniform shadow conditionsrdquoAutomation of Electric Power Systems vol 39 no 10 pp 42ndash49 2015

[12] Y P Wang X B Ruan and Y Li ldquoA rapid tracking method ofmaximum power point for solar units in series under unevensolar irradiancerdquo Proceedings of the Chinese Society for Electri-cal Engineering vol 35 pp 4870ndash4878 2015

[13] Y W Zhu X C Shi Y Q Dan et al ldquoApplication of PSOalgorithm in global MPPT for PV arrayrdquo Proceedings of theCSEE vol 32 pp 42ndash48 2012

[14] X Yuan D Yang and H Liu ldquoMPPT of PV system under par-tial shading condition based on adaptive inertia weight particle

Table 5 Error analysis for computation result

Shading type U primem‐test (V) U prime

oc‐test (V) U primem‐calculate (V) U prime

oc‐calculate (V) e1 () e2 () S (Wm2) T (degC)

Normal 870 1084 882 1098 13 13 982 36

Shadow 1 774 1086 781 1090 08 10 932 35

Shadow 2 772 1085 781 1093 11 11 936 35

Shadow 3 691 1088 683 1103 11 11 945 34

Shadow 4 765 1084 779 1096 17 10 931 36

Shadow 5 667 1083 679 1093 18 10 939 36

Shadow 6 574 1083 579 1091 08 11 936 36

Cover 1 771 974 781 9781 13 04 973 36

Cover 2 776 961 783 9803 09 19 973 35

Cover 3 681 871 684 8608 03 11 952 34

Cover 4 778 983 785 9823 08 01 942 33

Cover 5 679 838 683 8525 05 17 963 35

Cover 6 586 742 581 7369 09 06 959 36

The data of shading voltage under different conditions and the relative error between the measured occlusion voltage and the theoretical occlusion voltage

13International Journal of Photoenergy

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

swarm optimization algorithmrdquo in 2015 IEEE InternationalConference on Cyber Technology in Automation Control andIntelligent Systems (CYBER) pp 729ndash733 Shenyang ChinaJune 2015

[15] X Liu F Zhuo Y Chen and L Xiong ldquoDevelopment of fastsimulation models for photovoltaic generation system basedon Simulinkrdquo in 2015 IEEE Energy Conversion Congress andExposition (ECCE) pp 3265ndash3270 Montreal QC CanadaSeptember 2015

[16] Y J Wang and S S Lin ldquoAnalysis of a partially shadedPV array considering different module connection schemesand effects of bypass diodesrdquo in 2011 International Confer-ence amp Utility Exhibition on Power and Energy SystemsIssues and Prospects for Asia (ICUE) pp 1ndash7 Pattaya CityThailand September 2011

[17] D Q Zhou C H Wu Z H Li L Fu and Y Z Wang ldquoSim-ulation and experimental study of the photovoltaic modelunder partial shadingrdquo Acta Energiae Solaris Sinica vol 35pp 2098ndash2105 2014

14 International Journal of Photoenergy

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom

TribologyAdvances in

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

International Journal ofInternational Journal ofPhotoenergy

Hindawiwwwhindawicom Volume 2018

Journal of

Chemistry

Hindawiwwwhindawicom Volume 2018

Advances inPhysical Chemistry

Hindawiwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2018

Bioinorganic Chemistry and ApplicationsHindawiwwwhindawicom Volume 2018

SpectroscopyInternational Journal of

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Medicinal ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

NanotechnologyHindawiwwwhindawicom Volume 2018

Journal of

Applied ChemistryJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Biochemistry Research International

Hindawiwwwhindawicom Volume 2018

Enzyme Research

Hindawiwwwhindawicom Volume 2018

Journal of

SpectroscopyAnalytical ChemistryInternational Journal of

Hindawiwwwhindawicom Volume 2018

MaterialsJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

BioMed Research International Electrochemistry

International Journal of

Hindawiwwwhindawicom Volume 2018

Na

nom

ate

ria

ls

Hindawiwwwhindawicom Volume 2018

Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom