Research Article Improved Fractional Order VSS Inc-Cond MPPT …downloads.hindawi.com/journals/ijp/2014/128327.pdf · 2019. 7. 31. · Research Article Improved Fractional Order VSS

Research ArticleImproved Fractional Order VSS Inc-Cond MPPT Algorithm forPhotovoltaic Scheme

R Arulmurugan12 and N Suthanthiravanitha2

1 Department of Electrical and Electronics Engineering Anna University Regional Zone Coimbatore India2Department of Electrical and Electronics Engineering Knowledge Institute of Technology KIOT CampusNH-47 Salem to Coimbatore Road Kakapalayam Salem 637 504 India

Correspondence should be addressed to R Arulmurugan arullectyahoocom

Received 5 November 2013 Revised 7 January 2014 Accepted 7 January 2014 Published 2 March 2014

Academic Editor Ismail H Altas

Copyright copy 2014 R Arulmurugan and N Suthanthiravanitha This is an open access article distributed under the CreativeCommons Attribution License which permits unrestricted use distribution and reproduction in any medium provided theoriginal work is properly cited

Nowadays a hot topic among the research community is the harnessing energy from the free sunlight which is abundant andpollution-free The availability of cheap solar photovoltaic (PV) modules has to harvest solar energy with better efficiency Thenature of solar modules is nonlinear and therefore the proper impedance matching is essential The proper impedance matchingensures the extraction of the maximum power from solar PVmodule Maximum power point tracking (MPPT) algorithm is actingas a significant part in solar power generating system because it varies in the output power from a PV generating set for variousclimatic conditions This paper suggested a new improved work for MPPT of PV energy system by using the optimized novelimproved fractional order variable step size (FOVSS) incremental conductance (Inc-Cond) algorithmThe new proposed controllercombines the merits of both improved fractional order (FO) and variable step size (VSS) Inc-Cond which is well suitable for designcontrol and executionThe suggested controller results in attaining the desired transient reaction under changing operating pointsMATLAB simulation effort showsMPPT controller and aDC toDCLuo converter feeding a battery load is achievedThe laboratoryexperimental results demonstrate that the new proposed MPPT controller in the photovoltaic generating system is valid

1 Introduction

Renewable energy sources are considered as an importantsource of energy in the 21st century that is in use to fulfillour needs and growing demands of electricity Among allrenewable energy sources solar energy is readily availablefree of cost The production cost of solar photovoltaic basedsystem is decreased considerably The advancement in PVtechnology also causes less cost per unit and thus PVtechnology do not contribute to global warming [1] Theextraordinary diffusion of solar PV system in electricitygeneration is evident from the fact that the PV scheme isanticipated to be the largest source of electricity generationamong all the accessible nonconventional energy sourcesThey are considered feasible in residential applications andare suitable for roof top installations [2]The PVmodules areprimarily a current source device and the current is producedwhen light falls on the surface of solar device The character-istics curve of the PV module shows its nonlinear behavior

The nonlinear 119881-119868 curve of PV module has only one point ofmaximumpower extractionTherefore the energy harvestingat maximum efficiency is not simple enough The survival ofonly one unique point of maximum power requires specialtechniques to function the scheme at the point of maximumpower These operating techniques are named as MPPT[3] MPPT techniques control the power electronic interfacesuch that the source impedance is matched with the loadimpedance and hence maximum power is transferred Incontrast with the nonlinear characteristicsMPPT techniquesare vital for any solar PV system

Different methods have been reported in literature fortracking the maximum power point (MPP) Among the20 distinct methods reported by [4] the methods such asperturb and observe (PampO) incremental conductance (Inc-Cond) fractional open circuit voltage (FOCV) fractionalshort circuit current (FSCC) fuzzy logic and neural networkalgorithm are widely used by the researchers Among these

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2014 Article ID 128327 10 pageshttpdxdoiorg1011552014128327

2 International Journal of Photoenergy

methods the FOCV and FSCC are considered as offlineMPPT techniques because they isolate the PV array whenthey track the MPP and calculate the operating point forMPPT [5 6] These techniques adopt both analog as well asdigital implementations [7] However the periodic isolationof the PV array is power loss and the change in operatingpoint depends on irradiance (119866) therefore the periodicpower loss is to be avoidedwe need irradiance sensor that canmeasure the 119866 and hence PV array needs not to be isolated[8] The fuzzy logic andor neural network based MPPTtechnique have good performance under fast changing envi-ronmental circumstances and display improved performancethan the PampO method [9] However the main drawback ofthis technique is that its efficiency is extremely reliant onthe technical information of the engineer in calculating theerror and approaching up with the fuzzy rule based tableIt is importantly reliant on how a designer assembles thesystem based on his experience and skill Perturb and observealgorithm can be failure under fast varying environmentalcircumstancesThe Inc-Cond technique is constructed on theslope of the solar photovoltaic panel power curve This tech-nique has partly solved divergence of perturb and observemodel [10]

In this paperwe suggested a novel technique that will tunethe onlineMPPT techniques based on changingweather con-ditions The proposed algorithm modifies the existing con-ventional Inc-Cond controller based on improved fractionalorder variable step size which differs from the existing Thedifference is based on the datasheet of the panel on the novelcontroller and is constant for any particular PV array Theproposed algorithm is implemented intoMATLABSimulinkenvironment and it is tested and validated

The structure of the system is organized as followsSection 2 discuss the modelling of PV modules ImprovedFOVSS Inc-Cond controller and analysis of DC to DC Luoconverter Section 3 provides the simulation and experimen-tal setup hence results validate the controller performanceFinally Section 4 concludes remarks

2 Proposed System Description

The schematic circuit diagram for the suggested system isshown in Figure 1 It contains PV panel designed novelFOVSS Inc-Cond control algorithm synchronous DC to DCLuo converter and battery load The power switches of thedesigned DC to DC Luo converter are controlled by the gatedrivers programmed via a controller module The designedconverter delivers required levels of the output power to thestand alone battery load The impedance of the battery loadshould be assumed as a suitable one for subsequent analysisThe DC to DC converters are responsible for MPPT andvoltage regulations Simulation and experimental models areestablished in MATLABSimulink and controller processorenvironment

21 Modeling of PV Modules PV systems convert sunlightinto electrical energy without causing any environmentalissues Various equivalent models are available in the litera-ture for better understanding of concept of PV array Among

PV array

or panel

DC to DCboost-buck Luo

converterLoad

Improved FO VSS Inc-CondMPPT algorithm

Switch control signal

Vin

Iin

+

minus

+

minus

Io

Vo

Figure 1 The proposed optimized novel FOVSS Inc-Cond MPPTsystem

D

G

Radiation

ID

IR

Rsh

Rs

IoVo

Figure 2 Equivalent circuit model of solar cell

the models Figure 2 is considered as good which supportsaccuracy and user friendliness [11] For the constant weatherconditions the curve has only one unique point of maximumpower (MP) and the 119881-119868 characteristic of an irradiatedcell is nonlinear It depends on several factors includingthe temperature and irradiance With a varying irradiancethe short circuit current varies however the open circuitvoltage changes significantly with changes in temperatureThe varying atmospheric conditions make the MPP keepshifting around the PV curve In the PV simulation resultsshow the cumulative effect of the nonhomogenous weatherconditions on MPP The analytical expression based on thetemperature (119879) and irradiance (119866) variation can be writtenas follows

119868PV = 119896 sdot 119866 sdot 119878 (1)

where 119868PV is the photovoltaic current source119868119889 is the single exponential junction current and is given

by

119868119889 = 119868119900 sdot (119890119860119881119889 minus 1) (2)

119868 is the output current and is given by 119868 = 119868PV minus 119868119889 minus 119881119889119877sh119881 is the output voltage and is given by 119881 = 119881119889 minus 119877119904 sdot 119868

119868sc (119866 119879) = 119868sc (STC) sdot119866

1000sdot (1 + 120572119868scΔ119879) (3)

119881oc (GT) = 119881oc (STC) sdot (1 + 120573119881ocΔ119879) (4)

119875119898 (119866 119879) = 119875119898 (STC) sdot119866

1000sdot (1 + 120574120588Δ119879) (5)

120578 =119875119898

119866119860= (119875119898 (STC) sdot

(1 + 120574120588Δ119879)

119860) (6)

where Δ119879 = 119879119888 minus 25∘C

International Journal of Photoenergy 3

22 A New Design of Improved Fractional OrderVSS Inc-Cond Controller

221 FractionalOrderDifferentiator AFOsystemcomprisedby a fractional differential or an integral equation and sys-tems covering few equations has been deliberate in engineer-ing andphysical appliances for example active control signalprocessing and linear and nonlinear response controllerThe generally utilized approaches have been anticipated fornumerical assessment of fraction derivatives by Riemann-Lioville and Grunwald-Letnikov definition [12] It reflects acontinuous function 119891(119905) where its 120572th order derivative canbe conveyed as follows [13]

119889120572119891 (119905)

119889119905120572 = lim

ℎrarr0

1

ℎ120572

120572

sum

119903=0

(minus1)119903(120572

119903)119891 (119905 minus 119903ℎ)

120573 = (120572

119903) =

120572

119903 (120572 minus 119903)

(7)

where 120573 is the coefficient binomial and 120572 is an integerpositive order We use the guesstimate approach arising theGrunwald Letnikov definition as

119863120572

119905119891 (119905) asymp ℎ

minus120572

[119905ℎ]

sum

119903=0

(minus1)119903120573119891 (119905 minus 119903ℎ) (8)

For generalization it is suitable to adopt 119905 = 119899ℎ where ldquo119905rdquois the opinion at which the derivative is appraised and ℎ isthe discretization step We can rewrite the estimate of the 120572thderivative as follows

119863120572

119905119891 (119905) =

119889120574

119889119905120574 [119863minus(120574minus120572)

119905]

119863120572

119905119891 (119905) asymp (

119905

119899)

minus120572 119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (minus120572) Γ (119903 + 1)119891 (119905 minus 119903

119905

119899)

(9)

where 120574 is an integer satisfying 120574 minus 1 lt 120572 le 120574 Clearly theFO calculus leads to an immeasurable dimension while theintegral calculus is a finite dimension Reflect119891119898(119905) = 119905

119898119898 =

1 2 3 4 and the 120572th derivative is

119863120572

119905119905119898

asymp119905119898minus120572

Γ (minus120572)119899120572

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1)(1 minus

119903

119899)

119898

(10)

If we expand [1 minus (119903119899)]119898 by the binominal theorem [3 6]

(10) becomes

119863120572

119905119905119898

asymp119905119898minus120572

Γ (minus120572)

119898

sum

119896=0

(minus1)119896(119898

119896) 119899120572minus119896

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1)119903119896 (11)

119870 equiv

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1)119903119896 (12)

If y is an unstipulated and if 119895 is an integer positive then 119910 119895fractional is defined as

119910(119895)

= 119910 (119910 minus 1) (119910 minus 2) sdot sdot sdot (119910 minus 119895 minus 1)

Γ (119910 + 1) = 119910(119895)

Γ (119910 minus 119895 + 1)

(13)

So an integral power of 119910 can be expressed as a factorialpolynomial as

119910119896=

119896

sum

119895=1

120585119896

119895119910(119895)

=

119896

sum

119895=1

120585119896

119895

Γ (119910 minus 119895 + 1)

Γ (119910 + 1) (14)

where the 120585 is the sterling values Let 119910 = 119903 in (14) besubstituted in (12) and replace 119899 by 119899 minus 119895 and 120572 by 120572 minus 119895 then

119870 =

119896

sum

119895=1

120585119896

119895(

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1 minus 119895)) =

119896

sum

119895=1

120585119896

119895

Γ (119899 minus 120572)

Γ (119899 minus 119895)(

1

119895 minus 120572)

(15)

Equation (11) becomes

119863120572

119905119905119898

asymp119905119898minus120572

Γ (minus120572)

119898

sum

119896=0

(minus1)119896(119898

119896)

119896

sum

119895=0

120585119896

119895119899120572minus119896

Γ (119899 minus 120572)

(119895 minus 120572) Γ (119899 minus 119895)

lim119899rarrinfin

119899120572minus119896 Γ (119899 minus 120572)

Γ (119899 minus 119895)=

1 if 119895 = 119896

0 if 119895 lt 119896

(16)

where119898

sum

119896=0

(minus1)119896(119898

119896)

1

(119896 minus 120572)= 119861 (minus120572119898 + 1) (17)

A general fractional order differentiator can be expressed asfollows

119863120572

119905119905119898

asympΓ (119898 + 1)

Γ (119898 + 1 minus 120572)119905119898minus120572

(18)

For all 120572 positive negative andor zero 119898 = 0 1 2 3 4 Note the select of 120572 can be seen as selecting the spectaclesthat will be modeled By selecting 0 lt 120572 lt 1 anomalous phe-nomena such as heat conduction diffusion viscoelasticityand electrode-electrolyte polarization can be described [1]

222 Design of New Improved VSS Inc-Cond ControllerGenerally step size is fixed for the Inc-CondMPPT techniqueThe produced power from the PV panel with a higher stepsize plays to quicker dynamics but results in extreme steadystate fluctuations and subsequent poor efficiency [14] Thiscondition is inverted through the MPPT by operating witha lesser step size Thus the tracking with constant step sizemakes a suitable trade-off among the fluctuation and dynam-ics Thus the problem can be resolved with VSS restatement[15 16] Even though all the conventional methods are simpleperturb and observe method produce oscillations occurringat maximum power point and hence output power is notachieved at desired level and results in poor efficiency TheInc-Cond method is envisioned to resolve the difficulty ofthe conventional perturb and observe method under quickvarying environment circumstances [17] Hence in this paperthe performance of the FOVSS Inc-Cond method in quicklyvarying environment conditions by using voltage versus cur-rent graph [18] Condition 1 the curve power versus voltage ispositive and the indication of the altering voltage and current


Sample

Obtain dV120572= ΔV

120572= (Vz minus

d120572I = ΔI = Iz

dP120572

dP120572

=

S = Mtimes

d120572I = 0

dV120572gt 0

V(z) = V(zminus1)

V(z) = V(zminus1)

Eq (25) = Eq (26)

Eq (25) gt Eq (26) V(z) = V(zminus1) minus S

V(z) = V(zminus1) + S

V(z) = V(zminus1) minus S1V(z) = V(zminus1) + S2

dV120572gt 0

andd120572I gt 0

dV120572lt 0 and

d120572I lt 0

End

Iz rarr Izminus1

Vz rarr Vzminus1

V(z) = V(zminus1) minus S

YY

Y

Y

Y

YY

N

N

N

N

N

minus 120572Izminus1

magnitude ( d120572I)

dV120572= 0

Vzminus1)120572

V(z) I(z)

ΔV120572times ΔI

Po lt P

Figure 3 Novel improved FOVSS Inc-Cond MPPT algorithm

is the same simultaneously the algorithm recognizes that 119866is in quickly accumulative environmental circumstances andreduces the voltage Condition 2 on the other side if theslope of the power versus voltage graph is positive alteringcurrent and voltage are opposite concurrently the algorithmrecognizes that it is quickly reducing environment situationsand rises the voltage Condition 3 lately if altering 119868 and119881 are in conflicting directions the algorithm for tracingsupreme power upsurges the119881 as the Inc-Cond conventionalalgorithmThus this algorithm eludes difference from the realMPP in quickly varying environmental circumstances

In this report a VSS procedure is suggested for theimproved Inc-Cond tracking technique and is dedicated tosearch an easier and active way to increase tracking dynamicas well as correctness In every tracking application thepossible power follower is attained by joining a DC to DCconverter among the PV panel and load system [19] Thepower output of the PV is utilized for energetic control

of the DC to DC converter pulse width modulation (119863)to diminish well the complication of the structure [20]The flowchart of the FOVSS improved Inc-Cond trackingalgorithm is illustrated in Figure 3 where the power DCto DC converter PWM (119863) recapitulation step size tunedautomatically The power output of PV panel is involved toregulate the power DC to DC converter PWM (119863) donatingto a shortened control scheme where the outputs 119868 and 119881 ofthe PV array represent119881(119911) and 119868(119911) at time 119911 respectivelyTheVSS implemented to diminish the problem represented aboveis written in the equation as follows

119863 (119911) = 119863 (119911 minus 1) plusmn 119872 times

10038161003816100381610038161003816100381610038161003816

119889119875

119889119881

10038161003816100381610038161003816100381610038161003816

(19)

In the above equation 119872 denotes the scaling factor which isadjusted at the period to regulate the step size The VSS canalso be recognized from the incline of the power versus dutycycle graph in [16] for perturb and observe tracking writtenas follows


1003816100381610038161003816100381610038161003816

Δ119875

Δ119881

1003816100381610038161003816100381610038161003816 (20)

In the above written equation Δ119863 represents the change instage 119863 at earlier sample period As illustrated in the powerversus voltage the derivative of (119889119875119889119881) of a PV panel canbe seen to be changing efficiently and is suggested in [15]as an appropriate constraint for determining the VSS of theperturb and observe method So the derivative (119889119875119889119881) isalso working herein to control the VSS for the Inc-Condtracking method The modern rule for PWM (119863) can beacquired as the following equation

119863(119911) = 119863 (119911 minus 1) plusmn 119872 times

10038161003816100381610038161003816100381610038161003816

119875 (119911) minus 119875 (119911 minus 1)

119881 (119911) minus 119881 (119911 minus 1)

10038161003816100381610038161003816100381610038161003816

(21)

The 119872 is necessarily determined by the effectiveness of thetracking structure Physical fine-tuning of this constraintis boring and resultant output may be effective only for agiven structure and operating circumstance [15] A modesttechnique is used to determine whether the 119872 is suggestedhere Initially higher step size of the maximum duty cycle(119863max) for constant step size tracking scheme was selectedBy such results the active development is best adequatebut gives poor steady state performance The stable stateassessment instead of dynamic assessment in the start-updevelopment of themagnitude119875 divided by119881 of the PVpaneloutput can be estimated under the constantVSSworkingwithmaximum duty cycle which will be selected as the superiorcontroller as VSS Inc-Cond tracking technique To confirmthe conjunction of the tracking superior rule the variable step(VS) rule should observe the following

119872 times

10038161003816100381610038161003816100381610038161003816

119889119875

119889119881

10038161003816100381610038161003816100381610038161003816fized step=Δ119863max

lt Δ119863max (22)

In the above equation |119889119875119889119881|fized step=Δ119863maxis the |119889119875119889119881|

at FSS operation of maximum duty cycle The 119872 can beobtained as follows

119872 ltΔ119863max

|119889119875119889119881|fized step=Δ119863max

(23)


In the equation above the VSS improved Inc-Cond trackingwill be operating with FSS of the early set superior controllerΔ119863max The above equation delivers an easier supervision todetermine the 119872 of the VSS Inc-Cond tracking techniqueWith the fulfillment of above calculation superior scalingfactor shows a relatively quick reaction than a minor scalingfactor The SW will become minute as derivative power tovoltage becomes very slight nearby the maximum power [21]

223 The Control Process of Improved FOVSS Inc-CondAlgorithm The 119881-119868 characteristics of a single module areresolute and enlarge to control the performance of a PV arrayas illustrated in Figure 3 It seems 119889119868119889119881 lt 0 with rising 119881

as 119868 is diminishing Based on (1)ndash(3) current and voltage arecontingent on environment and electricity transmission Theirregular singularities can be designated as FOD Thus the119889119868119889119881 can be altered as follows

119889120572119881 (119868)

119889120572119868= limΔ119881rarr0

119881120572(119868) minus 119881

120572

119900(119868 minus Δ119868)

Δ119868 (24)

119889119881120572

119889120572119868asymp

(119881 minus 119881119900)120572

119868 minus 120572119868119900

(25)

The efficiency of the weighing Δ119868 is altered as 120572 gt 0 and 120572 isan even number If 120572 = 1 then it yields to the rate of changequickness For 120572 = 2 outside the range it yields accelerationTherefore for 0 lt 120572 lt 1 the appearance can be called as thefractional rate of the alteration of operation Equation (25) isutilized to direct the FO incremental variations of the 119868 and119881

of the PV array The VSS incremental conductance load canbe modified as follows

119889120572

119889119881120572 (minus

119881119900

119868119900

)

= (minus1

119868119900

)119889120572119881120572

119900

119889120572119868+ (minus119881119900)

119889120572119868minus1

119874

119889120572119868

= (minus1

119868119900

)(Γ (2)

Γ (2 minus 120572))1198811199001minus120572

+ (minus119881119900)Γ (0)

Γ (minus120572)1198681minus120572

119874

(26)

where Res(Γ minus119911) = ((minus1)119911119911)119885 = 0 minus1 minus2 minus3 minus4 with

remainder Γ(0) = Res(Γ minus 0) = 1 Thus the procedureof improved FOVSS Inc-Cond method examines the 119881 as avariable at which the MPP has an increasing or diminishingduty cycle

Figure 3 shows the flowchart of the improved FOVSSInc-Cond control algorithm By using the radiation meterthis control technique can modify the working mode in theprogram Based on the power output of the PV module MPPvaries hence the suggested control technique increases ordiminishes the voltage output of the PV module as a similarpath and it can be traced to the MPP It regulates the 119863

by the immediate values 119868119911 and 119881119911 at existent iteration stepand their consistent values of 119868119911minus1 and 119881119911minus1 deposited at theend of the foregoing repetition step The VSS incrementalchanges in 119868 and 119881 are approached as 119889120572119868 asymp (119868119911 minus 120572119868119911minus1) =

Δ119868 and 119889119881120572

asymp (119881119911 minus 119881119911minus1)120572

= Δ119881120572 correspondingly To

evade underestimating the employed state under numerous

+

+ minus

+

minus

minus

R

Io

VL2+

minus

+

minus

L2

S2

S1

Vd

Vd L1

L c

VC2

VC1

Figure 4 DC to DC Luo converter

conditions the first voltage 119881119911 can be set to 0119881 or defaultvalues rendering to the 119879 differences Rendering to the fourconclusions the control process of improved FOVSS Inc-Cond method algorithm can be expressed as follows

Situation one if (Δ119881120572

= 0 and Δ119868 = 0) not anycontroller accomplishment is requiredSituation two if (Δ119868 = 0 and Δ119881

120572gt 0) a controller

action is required to enhance the Δ119881120572 to present

voltage 119881 with a cumulative119863 step sizeSituation three if (Δ119868 = 0 and Δ119881

120572lt 0) a controller

action is required to decrease the Δ119881120572 to present

voltage 119881 with a diminishing119863 step sizeSituation four calculated power output is equal tomultiplication of voltage and current output 119875 = 119881119868If 119875119900 lt 119875 modernize the 119881 119881119911minus1 = 119881119911 and 119868119911minus1 = 119868119911

and then dismiss the controller process

23 Analysis of Synchronous DC to DC Luo Converter Whenrecommending a MPP tracker the most important processis to choose and analyze a highly suitable converter whichis invented to function as the foremost fragment of thetracker (MPPT) Therefore switching mode power suppliesare suitable to operate with high efficiency Among allthe complete topologies existing the series of buck-boostconverters provide the opportunity to have either higheror lower output voltage compared with the input voltageThe conventional buck-boost formation is cheaper than theLuo one even though some drawbacks occur such as lessefficient weak transient reaction high peak current in powerapparatuses and discontinuous current input On the otherside the Luo converter has the highest efficiency with lowswitching losses amongst nonisolated DC to DC convertersand no negative polarity regulated output voltage comparedto the input voltage It can deliver an improved current outputcharacteristic due to the output stage inductor Thus theLuo configuration is an appropriate converter to be active indeceiving the MPPT [21]

The DC to DC Luo converter provides a positive polarityregulated output voltage with respect to the input voltagewhich is shown in Figure 4 The process of the synchronousLuo converter with ZVS and ZCS technique is for droppingthe switching loss of the primary switch In addition thefreewheeling diode is replaced by power switch to reduce


+

minus

+minus

R

Vd

VoC

C1

Mode-1

L1

+

minus

VL2

L2

(a)

+

minus

+minus

Vd

VoC

C1

Mode-2

L1

+

minus

VL2

L2

(b)

Figure 5 Equivalent modes of converter (a) main switch on (b) main switch off

Continuous

Pv

+minus

+minus

+

+

minus

minus

+

minus

i m gS D

mg

SD

IMean

times

NOT

Mosfet1

Mosfet2

Batt lSOC

Battery

Ramp2

Relationaloperator2

Transportdelay

Transportdelay1

Clock

D initSwitch

EmbeddedMATLAB INC-Cond

fcn

i

d

inew

newdnew

Powergui

0

2

C4C2C5 L1

L2

C6

C1

Transport delay2

Figure 6 Simulation layout of the proposed FOVSS Inc-Cond system

conduction losses too The designed circuit two powersMOSFET switches are utilized to reduce switching andconduction lossesThe energy storage elements are capacitors1198621 and 1198622 and inductors 1198711 and 1198712 119877 is the load resistanceTo analyze the process of the DC to DC Luo converter thecircuit can be divided into two equivalent modes [22]

231 Modes of Operation In mode one operation when thepower switch 1198781 is turned on the inductor 1198711 is charged bythe input supply voltage 119881in At similar time the inductor1198712 absorbs the energy from input source and the primarycapacitor 1198621 The load is delivered by the capacitor 1198622 Theequivalent method of DC to DC Luo converter operatingmode 1 is shown in Figure 5(a)

In the mode 2 process when the switch is in turnedoff state the input current drawn from the source becomeszero as shown in Figure 5(b) The inductor current 1198681198711 flowsthrough the power 1198782 to charge the capacitor1198621The inductor

second current 1198681198712 flows through1198622 to load resistance circuitand the second switch 1198782 to keep it continuous

3 Simulation Results and Discussion

31 Simulation Setup The PV array is modeled and coupledwith the DC to DC Luo converter and is controlled bysuggested tracking algorithm To examine the performanceand effectiveness of suggested FOVSS Inc-Cond controller itis tested on the experimental prototype of the photovoltaicMPPT controller and the complete simulation structure of aproposed system is illustrated in Figure 6 [23] It is made upof multi and mono crystalline silicon materials of 40 watt PVarray The Table 1 shows the specifications for single 10 wattPV module [10]

32 Analysis of PV Results To confirm the enactment of thesuggested system the119881-119868 and119881-119875 characteristics of single PV


Table 1 Electrical parameters of PV module

Designation Peak maximum power Peak maximum voltage Peak maximum current Open circuit voltage Short circuit currentValue [units] 10Wp 164V 0610A 21V 0700A

08

07

06

05

04

03

02

01

0

Curr

ent (

A)

Voltage (V)Voltage (V)0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16

Voltage versus current curve Voltage versus power curve109876543210

Pow

er (W

)

Model 02KWm225∘CModel 04KWm230∘CModel 06KWm235∘C

Model 08KWm240∘CModel 1KWm245∘C



Figure 7 Simulated 119881-119868 and 119881-119875 characteristics of single PV module with variation of solar GampT which are installed on the floor of thelaboratory at GCE Salem (sponsored by IIT Bombay)

module of proposed panel are plotted for different values ofsolar insulation and cells temperature as shown in Figure 7Simulation uses the standard design method which showsthat an increased number of modules can deliver a nominallevel of operating charging current for normal range of 119866From this PV curves it was discovered that the decreasein the maximum power causes increase in temperature Thefollowing operating conditions are observed from this study(1) when increasing the load current causes drops in the PVvoltage (2) when increase in temperature causes reductionin power output due to rises of internal resistance across thecell (3) when increasing the insolation the power outputPV increases as more photons hit out electronics and furthercurrent flow causing higher recombination The variation ofpower output acts as a function of module voltage and isaffected by altered working conditions Also the output 119881

versus 119868 characteristics of the single PV module is observedunder various conditions of 119879 and 119866 [23]

33 Results for Proposed System under Dynamic WeatherConditions To distinguish the enactment of the designedimproved FOVSS Inc-Cond MPPT control algorithm whichcan automatically regulate the step size with the traditionalincremental conductance algorithm the MATLAB simu-lations are constructed under similar circumstances Thesampling period carried out for the conventional Inc-Condalgorithm was selected as 002 second Consequently thePWM duty cycle (119863) of the DC to DC Luo converteris modernized for each 002 seconds The performance ofoutput power of conventional Inc-Cond maximum trackingcontrol with a fixed size step is 002 under an irradiance stepvarious from 200Wm2 at temperature 25∘C to 800Wm2at temperature 27∘C at 05 seconds which are shown in

Figure 8(a) To differentiate the consistent photovoltaicpower output response of the designed improved FOVSS Inc-Cond maximum tracking control algorithm with allowablepossible duty size Δ119863 is 010 and is illustrated in Figure 8(b)It is observed that the fluctuations happening at steady statein conventional Inc-Cond algorithm are nearly eliminated bythe design of improved FOVSS Inc-Cond tracking algorithmAlso the dynamic enactment of the designed method isnoticeably quicker than the conventional technique by fixedsize step of 002The outcomes point out that the fluctuationsat steady state conditions are significantly reduced by usingthe designed FOVSS Inc-Cond maximum tracking controlalgorithm

The performance is compared between conventional Inc-Cond and proposed FOVSS Inc-Cond tracking algorithmand is obtained in Table 2 Compared with the conventionalincremental conductance fixed step size of Δ119863 is 010which shows good performance but results in greater steadystate fluctuation The proposed FOVSS Inc-Cond techniquesolves this problem The fluctuation at the steady state isnearly exterminated by the use of very small magnitude of(119889119875120572119889120572119868) and the resultant output power of PV array is

395W Furthermore the dynamic performance of proposedFOVSS Inc-Cond technique is quicker than conventional Inc-Cond technique which is shown in Figure 8

34 Experimental Setup and Results Theprocess of improvedFOVSS Inc-Cond maximum tracking algorithm has beenassessed by experiment The experimental test was carriedout on the laboratory test bench of the standalone PV systeminstalled on the floor of the Electrical and Electronics Engi-neering at Government College of Engineering Salem Indiasponsored by IIT Bombay A model of the suggested scheme


Table 2 Comparison of conventional and proposed tracking algorithm performance

Technique Parameter

Irradiance-200Wm2

and temperature is minus25∘CIrradiance-800Wm2

and temperature is minus27∘C Under steady stateconditionsOutput power Sampling period

in seconds Output power Sampling periodin seconds

ConventionalInc-Cond Δ119863 = 010 119875119900 129W 002 seconds 119875119900 387W 05 seconds More fluctuation

takes placeProposed FOVSSInc-Condalgorithm

119872 = 0056 119875119900 135W 002 seconds 119875119900 395W 05 seconds Eliminate thefluctuation

10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(a)

10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(b)

Figure 8 Simulated photovoltaic power output response under sudden change in GampT (a) conventional Inc-Cond algorithm (b) designedimproved FOVSS Inc-Cond tracking technique

(a) (b)

Figure 9 Photos of prototype setup (a) PV array (b) DC to DC Luo converter with improved FOVSS Inc-Cond MPPT algorithm

depicted in Figure 9 is composed of (a) photovoltaic paneland (b) DC to DC Luo converter with suggested controllingtechnique The DC to DC Luo converter specifications areselected as follows The input voltage is 21 V capacitance 1198621

and capacitance 1198622 are 220120583F inductances 1198711 and 1198712 are15mH and 2mH respectively switching frequency is 10 Khz

and 12V battery Note that these passive components aredesignated to fill design criteria distilled based on equationsIn the test there are four PV modules mounted side byside and connected in series and parallel manner Atmega8 microcontroller was used to deliver the control pulsesfor the DC to DC Luo converter The 119862 language code of


Figure 10 Initial waveforms ofMPPTwith PV array (channel-1 PVvoltage channel-2 PV current channel-3 gate pulse)

the improved FOVSS Inc-Cond controller and PWM gen-erator system is constructed debugged and executed withthe assistance of the Arr studio development tool and Proispsoftware [16 17]

The initial graph with improved FOVSS Inc-Cond peaktracking control algorithm is illustrated in Figure 10 Whenthe scheme attains close to the peak power the size of the stepbecomes very tiny outcoming in an excellent power graphThe power and current of the PV rises to a length due to greatstep size change at the starting An adjustable resistive loadwas straight joined with the PV panel as well to investigatethe peak power The peak power distinguishing between thePV panel could be fashioned and the modules outputs withthe suggested FOVSS Inc-Cond peak tracking technique arewithin numerous watts Thus the peak tracking efficiency ofthe suggested technique under the present situation is about9892The peak tracking efficiency variance is not clear dueto theminor step size selected for the fixed step size Inc-CondalgorithmThe reason of this paper is to advance the dynamicreaction and investigate the change in irradiance further [18ndash20] A dual switch is familiarized to series with one set ofseries assembled PV module to simulate the consequence ofthe irradiance on the PV scheme When the SW is off oron both the voltage and power output of the PV panel willhit a step variation simulating a poor operational conditionfor the maximum tracking control When the SW is off themodules of the PV altered from three to four The equivalentPV schemepower output graphswith the suggested improvedFOVSS Inc-Cond peak tracking algorithm controller areillustrated in Figure 11 while Figure 12 demonstrates individ-uals graph for the modules of the PV that suddenly variedfrom four to three The sampling periods of the improvedFOVSS Inc-Cond peak tracking algorithm are selected toachieve almost steady state accuracy From the outcome of thefigures it can be illustrated that the PV schemewith improvedVSS gets the peak power within 13 seconds to trace the peakpower when the power output of the PV is instantly variedFrom the result it is concluded that the improved FOVSS Inc-Cond peak tracking control algorithm has the best dynamicenactment

Tek Stop M Pos 2040ms

M 100msMATH 100 vv

M

Figure 11 Change in power when the number of PV modules isincreased from three to four

Tek Stop

MATH 100 vv

M

M Pos

M 100 s

minus3440 s

Figure 12 Change in power when the number of PV modules isdecreased from four to three

4 Conclusion

In this paper a novel improved fractional order variable stepsize (FOVSS) incremental conductance (Inc-Cond) trackingalgorithm is designed and verified with MATLAB simula-tion and experimental environment The major differencebetween the suggested technique and existing tracking tech-nique includes elimination of the additional PI control loopand investigates the effect of novel Improved FOVSS Inc-Cond control technique This paper includes huge contribu-tions such as how improved VSS Inc-Cond is derived basedon fractional order derivative method how DC to DC softswitching Luo converter is designed and how comparisonbetween the proposed scheme and existing system is donewith the help of simulation and experimental arrangementThe experimental and simulation results demonstrate thatthe suggested controller tracks the peak power of the pho-tovoltaic scheme in variable insulation with quick transientresponse Since current and voltage of the solar photovoltaicare utilized as input elements it has controller characteristicswith variable step size Thus fluctuations around peak powerare significantly eliminated Thus the suggested FOVSS Inc-Cond based peak tracking algorithm increase the poweroutput 475 times the conventional power output for lowload conditions Accordingly it is seen that the suggestedtechnique is favorable for quick varying climatic situation


Nomenclature

119879 Temperature119866 IrradianceMPPT Maximum power point trackingMPP Maximum power pointPV PhotovoltaicInc-Cond Incremental conductanceADC Analog to digital converterFSS Fixed step sizeFOVSS Fractional order variable step size119863 Duty cycle119860 AppendixSW SwitchVSS Variable step size119868 Current119881 VoltageMP Maximum powerFO Fractional orderFOD Fractional order derivativeZVS Zero voltage switchingZCS Zero current switching

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] C-H Lin C-H Huang Y-C Du and J-L Chen ldquoMax-imum photovoltaic power tracking for the PV array usingthe fractional-order incremental conductancemethodrdquoAppliedEnergy vol 88 no 12 pp 4840ndash4847 2011

[2] A Al Nabulsi and R Dhaouadi ldquoEfficiency optimization of aDSP-based standalone PV system using fuzzy logic and Dual-MPPT controlrdquo IEEE Transactions on Industrial Informaticsvol 8 no 3 pp 573ndash584 2012

[3] S Subiyanto A Mohamed and M A Hannan ldquoIntelligentmaximum power point tracking for PV system using Hopfieldneural network optimized fuzzy logic controllerrdquo Energy andBuildings vol 51 pp 29ndash38 2012

[4] N Patcharaprakiti S Premrudeepreechacharn and Y Sri-uthaisiriwong ldquoMaximum power point tracking using adaptivefuzzy logic control for grid-connected photovoltaic systemrdquoRenewable Energy vol 30 no 11 pp 1771ndash1788 2005

[5] T Tafticht K Agbossou M L Doumbia and A CheritildquoAn improved maximum power point tracking method forphotovoltaic systemsrdquoRenewable Energy vol 33 no 7 pp 1508ndash1516 2008

[6] A A Ghassami S M Sadeghzadeh and A Soleimani ldquoA highperformance maximum power point tracker for PV systemsrdquoElectrical Power and Energy Systems vol 53 pp 237ndash243

[7] T K Soon S Mekhilef and A Safari ldquoSimple and lowcost incremental conductance maximum power point trackingusing buck-boost converterrdquo Journal of Renewable and Sustain-able Energy vol 5 pp 023106ndash023110 2013

[8] L Guo J Y Hung and R M Nelms ldquoComparative evaluationof sliding mode fuzzy controller and PID controller for a boostconverterrdquo Electric Power Systems Research vol 81 no 1 pp 99ndash106 2011

[9] D Rekioua A Y Achour and T Rekioua ldquoTracking powerphotovoltaic system with sliding mode control strategyrdquo EnergyProcedia vol 36 pp 219ndash230 2013

[10] K Punithaa D Devaraj and S Sakthivel ldquoDevelopment andanalysis of adaptive fuzzy controllers for photovoltaic systemunder varying atmospheric and partial shading conditionrdquoApplied Soft Computing vol 13 pp 4320ndash4332 2013

[11] A I Dounis P Kofinas C Alafodimos andD Tseles ldquoAdaptivefuzzy gain scheduling PID controller formaximumpower pointtracking of photovoltaic systemrdquo Renewable Energy vol 60 pp202ndash214 2013

[12] S Lalouni andD Rekioua ldquoOptimal control of a grid connectedphotovoltaic systemwith constant switching frequencyrdquo EnergyProcedia vol 36 pp 189ndash199 2013

[13] A Safari and SMekhilef ldquoSimulation and hardware implemen-tation of incremental conductance MPPT with direct controlmethod using cuk converterrdquo IEEE Transactions on IndustrialElectronics vol 58 no 4 pp 1154ndash1161 2011

[14] F Liu S Duan F Liu B Liu and Y Kang ldquoA variable stepsize INCMPPT method for PV systemsrdquo IEEE Transactions onIndustrial Electronics vol 55 no 7 pp 2622ndash2628 2008

[15] Q Mei M Shan L Liu and J M Guerrero ldquoA novel improvedvariable step-size incremental-resistanceMPPTmethod for PVsystemsrdquo IEEETransactions on Industrial Electronics vol 58 no6 pp 2427ndash2434 2011

[16] D A R Wati W B Pramono and R D G WibowoldquoDesign and implementation of fuzzy logic controller basedon incremental conductance algorithms for photovoltaic poweroptimizationrdquo in Proceeding of the International Conference onSustainable Energy Engineering andApplication (ICSEEArsquo12) pp6ndash8 Yogyakarta Indonesia November 2012

[17] M H Taghvaee M A M Radzi S M Moosavain HHizam and M H Marhaban ldquoA current and future study onnon-isolated DC-DC converters for photovoltaic applicationsrdquoRenewable and Sustainable Energy Reviews vol 17 pp 216ndash2272013

[18] M A Al-Saffar E H Ismail and A J Sabzali ldquoFamily of ZC-ZVS converters with wide voltage range for renewable energysystemsrdquo Renewable Energy vol 56 pp 32ndash43 2013

[19] T Esram andP L Chapman ldquoComparison of photovoltaic arraymaximum power point tracking techniquesrdquo IEEE Transactionson Energy Conversion vol 22 no 2 pp 439ndash449 2007

[20] K Ishaque Z SalamM Amjad and S Mekhilef ldquoAn improvedparticle swarm optimization (PSO)-based MPPT for PV withreduced steady-state oscillationrdquo IEEE Transactions on PowerElectronics vol 27 no 8 pp 3627ndash3638 2012

[21] D P Hohm and M E Ropp ldquoComparative study of maximumpower point tracking algorithmsrdquo Progress in PhotovoltaicsResearch and Applications vol 11 no 1 pp 47ndash62 2003

[22] R Arulmurugan and N V Suthanthira ldquoIntelligent fuzzyMPPT controller using analysis of DC to DC novel Buckconverter for photovoltaic energy system applicationsrdquo in Pro-ceedings of the International Conference on Pattern RecognitionInformatics andMobile Engineering pp 225ndash231 February 2013

[23] R Rahmani R Yusof and M Seyedmahmoudian ldquoHybridtechnique of ant colony and particle swarm optimization forshort term wind energy forecastingrdquo Journal of Wind Engineer-ing and Industrial Aerodynamics vol 123 part A pp 163ndash1702013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


methods the FOCV and FSCC are considered as offlineMPPT techniques because they isolate the PV array whenthey track the MPP and calculate the operating point forMPPT [5 6] These techniques adopt both analog as well asdigital implementations [7] However the periodic isolationof the PV array is power loss and the change in operatingpoint depends on irradiance (119866) therefore the periodicpower loss is to be avoidedwe need irradiance sensor that canmeasure the 119866 and hence PV array needs not to be isolated[8] The fuzzy logic andor neural network based MPPTtechnique have good performance under fast changing envi-ronmental circumstances and display improved performancethan the PampO method [9] However the main drawback ofthis technique is that its efficiency is extremely reliant onthe technical information of the engineer in calculating theerror and approaching up with the fuzzy rule based tableIt is importantly reliant on how a designer assembles thesystem based on his experience and skill Perturb and observealgorithm can be failure under fast varying environmentalcircumstancesThe Inc-Cond technique is constructed on theslope of the solar photovoltaic panel power curve This tech-nique has partly solved divergence of perturb and observemodel [10]

In this paperwe suggested a novel technique that will tunethe onlineMPPT techniques based on changingweather con-ditions The proposed algorithm modifies the existing con-ventional Inc-Cond controller based on improved fractionalorder variable step size which differs from the existing Thedifference is based on the datasheet of the panel on the novelcontroller and is constant for any particular PV array Theproposed algorithm is implemented intoMATLABSimulinkenvironment and it is tested and validated

The structure of the system is organized as followsSection 2 discuss the modelling of PV modules ImprovedFOVSS Inc-Cond controller and analysis of DC to DC Luoconverter Section 3 provides the simulation and experimen-tal setup hence results validate the controller performanceFinally Section 4 concludes remarks

2 Proposed System Description

The schematic circuit diagram for the suggested system isshown in Figure 1 It contains PV panel designed novelFOVSS Inc-Cond control algorithm synchronous DC to DCLuo converter and battery load The power switches of thedesigned DC to DC Luo converter are controlled by the gatedrivers programmed via a controller module The designedconverter delivers required levels of the output power to thestand alone battery load The impedance of the battery loadshould be assumed as a suitable one for subsequent analysisThe DC to DC converters are responsible for MPPT andvoltage regulations Simulation and experimental models areestablished in MATLABSimulink and controller processorenvironment

21 Modeling of PV Modules PV systems convert sunlightinto electrical energy without causing any environmentalissues Various equivalent models are available in the litera-ture for better understanding of concept of PV array Among

PV array

or panel

DC to DCboost-buck Luo

converterLoad

Improved FO VSS Inc-CondMPPT algorithm

Switch control signal

Vin

Iin

+

minus

+

minus

Io

Vo

Figure 1 The proposed optimized novel FOVSS Inc-Cond MPPTsystem

D

G

Radiation

ID

IR

Rsh

Rs

IoVo

Figure 2 Equivalent circuit model of solar cell

the models Figure 2 is considered as good which supportsaccuracy and user friendliness [11] For the constant weatherconditions the curve has only one unique point of maximumpower (MP) and the 119881-119868 characteristic of an irradiatedcell is nonlinear It depends on several factors includingthe temperature and irradiance With a varying irradiancethe short circuit current varies however the open circuitvoltage changes significantly with changes in temperatureThe varying atmospheric conditions make the MPP keepshifting around the PV curve In the PV simulation resultsshow the cumulative effect of the nonhomogenous weatherconditions on MPP The analytical expression based on thetemperature (119879) and irradiance (119866) variation can be writtenas follows

119868PV = 119896 sdot 119866 sdot 119878 (1)

where 119868PV is the photovoltaic current source119868119889 is the single exponential junction current and is given

by

119868119889 = 119868119900 sdot (119890119860119881119889 minus 1) (2)

119868 is the output current and is given by 119868 = 119868PV minus 119868119889 minus 119881119889119877sh119881 is the output voltage and is given by 119881 = 119881119889 minus 119877119904 sdot 119868

119868sc (119866 119879) = 119868sc (STC) sdot119866

1000sdot (1 + 120572119868scΔ119879) (3)

119881oc (GT) = 119881oc (STC) sdot (1 + 120573119881ocΔ119879) (4)

119875119898 (119866 119879) = 119875119898 (STC) sdot119866

1000sdot (1 + 120574120588Δ119879) (5)

120578 =119875119898

119866119860= (119875119898 (STC) sdot

(1 + 120574120588Δ119879)

119860) (6)

where Δ119879 = 119879119888 minus 25∘C




119889120572119891 (119905)

119889119905120572 = lim

ℎrarr0

1

ℎ120572

120572

sum

119903=0

(minus1)119903(120572

119903)119891 (119905 minus 119903ℎ)

120573 = (120572

119903) =

120572

119903 (120572 minus 119903)

(7)


119863120572

119905119891 (119905) asymp ℎ

minus120572

[119905ℎ]

sum

119903=0

(minus1)119903120573119891 (119905 minus 119903ℎ) (8)


119863120572

119905119891 (119905) =

119889120574

119889119905120574 [119863minus(120574minus120572)

119905]

119863120572

119905119891 (119905) asymp (

119905

119899)


sum

119903=0

Γ (119903 minus 120572)

Γ (minus120572) Γ (119903 + 1)119891 (119905 minus 119903

119905

119899)

(9)


119898119898 =


119863120572

119905119905119898

asymp119905119898minus120572

Γ (minus120572)119899120572

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1)(1 minus

119903

119899)

119898

(10)


(10) becomes

119863120572

119905119905119898

asymp119905119898minus120572

Γ (minus120572)

119898

sum

119896=0

(minus1)119896(119898

119896) 119899120572minus119896

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1)119903119896 (11)

119870 equiv

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1)119903119896 (12)


119910(119895)


Γ (119910 + 1) = 119910(119895)

Γ (119910 minus 119895 + 1)

(13)


119910119896=

119896

sum

119895=1

120585119896

119895119910(119895)

=

119896

sum

119895=1

120585119896

119895

Γ (119910 minus 119895 + 1)

Γ (119910 + 1) (14)


119870 =

119896

sum

119895=1

120585119896

119895(

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1 minus 119895)) =

119896

sum

119895=1

120585119896

119895

Γ (119899 minus 120572)

Γ (119899 minus 119895)(

1

119895 minus 120572)

(15)


119863120572

119905119905119898

asymp119905119898minus120572

Γ (minus120572)

119898

sum

119896=0

(minus1)119896(119898

119896)

119896

sum

119895=0

120585119896

119895119899120572minus119896

Γ (119899 minus 120572)

(119895 minus 120572) Γ (119899 minus 119895)

lim119899rarrinfin

119899120572minus119896 Γ (119899 minus 120572)

Γ (119899 minus 119895)=

1 if 119895 = 119896

0 if 119895 lt 119896

(16)

where119898

sum

119896=0

(minus1)119896(119898

119896)

1

(119896 minus 120572)= 119861 (minus120572119898 + 1) (17)


119863120572

119905119905119898

asympΓ (119898 + 1)

Γ (119898 + 1 minus 120572)119905119898minus120572

(18)




Sample


120572= (Vz minus

d120572I = ΔI = Iz

dP120572

dP120572

=

S = Mtimes

d120572I = 0

dV120572gt 0

V(z) = V(zminus1)

V(z) = V(zminus1)

Eq (25) = Eq (26)




dV120572gt 0

andd120572I gt 0

dV120572lt 0 and

d120572I lt 0

End

Iz rarr Izminus1

Vz rarr Vzminus1


YY

Y

Y

Y

YY

N

N

N

N

N



dV120572= 0

Vzminus1)120572

V(z) I(z)

ΔV120572times ΔI

Po lt P






10038161003816100381610038161003816100381610038161003816

119889119875

119889119881

10038161003816100381610038161003816100381610038161003816

(19)



1003816100381610038161003816100381610038161003816

Δ119875

Δ119881

1003816100381610038161003816100381610038161003816 (20)



10038161003816100381610038161003816100381610038161003816

119875 (119911) minus 119875 (119911 minus 1)

119881 (119911) minus 119881 (119911 minus 1)

10038161003816100381610038161003816100381610038161003816

(21)


119872 times

10038161003816100381610038161003816100381610038161003816

119889119875

119889119881

10038161003816100381610038161003816100381610038161003816fized step=Δ119863max

lt Δ119863max (22)



119872 ltΔ119863max

|119889119875119889119881|fized step=Δ119863max

(23)





119889120572119881 (119868)

119889120572119868= limΔ119881rarr0

119881120572(119868) minus 119881

120572

119900(119868 minus Δ119868)

Δ119868 (24)

119889119881120572

119889120572119868asymp

(119881 minus 119881119900)120572

119868 minus 120572119868119900

(25)



119889120572

119889119881120572 (minus

119881119900

119868119900

)

= (minus1

119868119900

)119889120572119881120572

119900

119889120572119868+ (minus119881119900)

119889120572119868minus1

119874

119889120572119868

= (minus1

119868119900

)(Γ (2)

Γ (2 minus 120572))1198811199001minus120572

+ (minus119881119900)Γ (0)

Γ (minus120572)1198681minus120572

119874

(26)





Δ119868 and 119889119881120572




+

+ minus

+

minus

minus

R

Io

VL2+

minus

+

minus

L2

S2

S1

Vd

Vd L1

L c

VC2

VC1















+

minus

+minus

R

Vd

VoC

C1

Mode-1

L1

+

minus

VL2

L2

(a)

+

minus

+minus

Vd

VoC

C1

Mode-2

L1

+

minus

VL2

L2

(b)


Continuous

Pv

+minus

+minus

+

+

minus

minus

+

minus

i m gS D

mg

SD

IMean

times

NOT

Mosfet1

Mosfet2

Batt lSOC

Battery

Ramp2

Relationaloperator2

Transportdelay

Transportdelay1

Clock

D initSwitch


fcn

i

d

inew

newdnew

Powergui

0

2

C4C2C5 L1

L2

C6

C1

Transport delay2












08

07

06

05

04

03

02

01

0

Curr

ent (

A)



Pow

er (W

)















Technique Parameter

Irradiance-200Wm2







10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(a)

10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(b)


(a) (b)










M 100msMATH 100 vv

M


Tek Stop

MATH 100 vv

M

M Pos

M 100 s

minus3440 s


4 Conclusion



Nomenclature




References

































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




119889120572119891 (119905)

119889119905120572 = lim

ℎrarr0

1

ℎ120572

120572

sum

119903=0

(minus1)119903(120572

119903)119891 (119905 minus 119903ℎ)

120573 = (120572

119903) =

120572

119903 (120572 minus 119903)

(7)


119863120572

119905119891 (119905) asymp ℎ

minus120572

[119905ℎ]

sum

119903=0

(minus1)119903120573119891 (119905 minus 119903ℎ) (8)


119863120572

119905119891 (119905) =

119889120574

119889119905120574 [119863minus(120574minus120572)

119905]

119863120572

119905119891 (119905) asymp (

119905

119899)


sum

119903=0

Γ (119903 minus 120572)

Γ (minus120572) Γ (119903 + 1)119891 (119905 minus 119903

119905

119899)

(9)


119898119898 =


119863120572

119905119905119898

asymp119905119898minus120572

Γ (minus120572)119899120572

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1)(1 minus

119903

119899)

119898

(10)


(10) becomes

119863120572

119905119905119898

asymp119905119898minus120572

Γ (minus120572)

119898

sum

119896=0

(minus1)119896(119898

119896) 119899120572minus119896

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1)119903119896 (11)

119870 equiv

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1)119903119896 (12)


119910(119895)


Γ (119910 + 1) = 119910(119895)

Γ (119910 minus 119895 + 1)

(13)


119910119896=

119896

sum

119895=1

120585119896

119895119910(119895)

=

119896

sum

119895=1

120585119896

119895

Γ (119910 minus 119895 + 1)

Γ (119910 + 1) (14)


119870 =

119896

sum

119895=1

120585119896

119895(

119899minus1

sum

119903=0

Γ (119903 minus 120572)

Γ (119903 + 1 minus 119895)) =

119896

sum

119895=1

120585119896

119895

Γ (119899 minus 120572)

Γ (119899 minus 119895)(

1

119895 minus 120572)

(15)


119863120572

119905119905119898

asymp119905119898minus120572

Γ (minus120572)

119898

sum

119896=0

(minus1)119896(119898

119896)

119896

sum

119895=0

120585119896

119895119899120572minus119896

Γ (119899 minus 120572)

(119895 minus 120572) Γ (119899 minus 119895)

lim119899rarrinfin

119899120572minus119896 Γ (119899 minus 120572)

Γ (119899 minus 119895)=

1 if 119895 = 119896

0 if 119895 lt 119896

(16)

where119898

sum

119896=0

(minus1)119896(119898

119896)

1

(119896 minus 120572)= 119861 (minus120572119898 + 1) (17)


119863120572

119905119905119898

asympΓ (119898 + 1)

Γ (119898 + 1 minus 120572)119905119898minus120572

(18)




Sample


120572= (Vz minus

d120572I = ΔI = Iz

dP120572

dP120572

=

S = Mtimes

d120572I = 0

dV120572gt 0

V(z) = V(zminus1)

V(z) = V(zminus1)

Eq (25) = Eq (26)




dV120572gt 0

andd120572I gt 0

dV120572lt 0 and

d120572I lt 0

End

Iz rarr Izminus1

Vz rarr Vzminus1


YY

Y

Y

Y

YY

N

N

N

N

N



dV120572= 0

Vzminus1)120572

V(z) I(z)

ΔV120572times ΔI

Po lt P






10038161003816100381610038161003816100381610038161003816

119889119875

119889119881

10038161003816100381610038161003816100381610038161003816

(19)



1003816100381610038161003816100381610038161003816

Δ119875

Δ119881

1003816100381610038161003816100381610038161003816 (20)



10038161003816100381610038161003816100381610038161003816

119875 (119911) minus 119875 (119911 minus 1)

119881 (119911) minus 119881 (119911 minus 1)

10038161003816100381610038161003816100381610038161003816

(21)


119872 times

10038161003816100381610038161003816100381610038161003816

119889119875

119889119881

10038161003816100381610038161003816100381610038161003816fized step=Δ119863max

lt Δ119863max (22)



119872 ltΔ119863max

|119889119875119889119881|fized step=Δ119863max

(23)





119889120572119881 (119868)

119889120572119868= limΔ119881rarr0

119881120572(119868) minus 119881

120572

119900(119868 minus Δ119868)

Δ119868 (24)

119889119881120572

119889120572119868asymp

(119881 minus 119881119900)120572

119868 minus 120572119868119900

(25)



119889120572

119889119881120572 (minus

119881119900

119868119900

)

= (minus1

119868119900

)119889120572119881120572

119900

119889120572119868+ (minus119881119900)

119889120572119868minus1

119874

119889120572119868

= (minus1

119868119900

)(Γ (2)

Γ (2 minus 120572))1198811199001minus120572

+ (minus119881119900)Γ (0)

Γ (minus120572)1198681minus120572

119874

(26)





Δ119868 and 119889119881120572




+

+ minus

+

minus

minus

R

Io

VL2+

minus

+

minus

L2

S2

S1

Vd

Vd L1

L c

VC2

VC1















+

minus

+minus

R

Vd

VoC

C1

Mode-1

L1

+

minus

VL2

L2

(a)

+

minus

+minus

Vd

VoC

C1

Mode-2

L1

+

minus

VL2

L2

(b)


Continuous

Pv

+minus

+minus

+

+

minus

minus

+

minus

i m gS D

mg

SD

IMean

times

NOT

Mosfet1

Mosfet2

Batt lSOC

Battery

Ramp2

Relationaloperator2

Transportdelay

Transportdelay1

Clock

D initSwitch


fcn

i

d

inew

newdnew

Powergui

0

2

C4C2C5 L1

L2

C6

C1

Transport delay2












08

07

06

05

04

03

02

01

0

Curr

ent (

A)



Pow

er (W

)















Technique Parameter

Irradiance-200Wm2







10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(a)

10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(b)


(a) (b)










M 100msMATH 100 vv

M


Tek Stop

MATH 100 vv

M

M Pos

M 100 s

minus3440 s


4 Conclusion



Nomenclature




References

































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Sample


120572= (Vz minus

d120572I = ΔI = Iz

dP120572

dP120572

=

S = Mtimes

d120572I = 0

dV120572gt 0

V(z) = V(zminus1)

V(z) = V(zminus1)

Eq (25) = Eq (26)




dV120572gt 0

andd120572I gt 0

dV120572lt 0 and

d120572I lt 0

End

Iz rarr Izminus1

Vz rarr Vzminus1


YY

Y

Y

Y

YY

N

N

N

N

N



dV120572= 0

Vzminus1)120572

V(z) I(z)

ΔV120572times ΔI

Po lt P






10038161003816100381610038161003816100381610038161003816

119889119875

119889119881

10038161003816100381610038161003816100381610038161003816

(19)



1003816100381610038161003816100381610038161003816

Δ119875

Δ119881

1003816100381610038161003816100381610038161003816 (20)



10038161003816100381610038161003816100381610038161003816

119875 (119911) minus 119875 (119911 minus 1)

119881 (119911) minus 119881 (119911 minus 1)

10038161003816100381610038161003816100381610038161003816

(21)


119872 times

10038161003816100381610038161003816100381610038161003816

119889119875

119889119881

10038161003816100381610038161003816100381610038161003816fized step=Δ119863max

lt Δ119863max (22)



119872 ltΔ119863max

|119889119875119889119881|fized step=Δ119863max

(23)





119889120572119881 (119868)

119889120572119868= limΔ119881rarr0

119881120572(119868) minus 119881

120572

119900(119868 minus Δ119868)

Δ119868 (24)

119889119881120572

119889120572119868asymp

(119881 minus 119881119900)120572

119868 minus 120572119868119900

(25)



119889120572

119889119881120572 (minus

119881119900

119868119900

)

= (minus1

119868119900

)119889120572119881120572

119900

119889120572119868+ (minus119881119900)

119889120572119868minus1

119874

119889120572119868

= (minus1

119868119900

)(Γ (2)

Γ (2 minus 120572))1198811199001minus120572

+ (minus119881119900)Γ (0)

Γ (minus120572)1198681minus120572

119874

(26)





Δ119868 and 119889119881120572




+

+ minus

+

minus

minus

R

Io

VL2+

minus

+

minus

L2

S2

S1

Vd

Vd L1

L c

VC2

VC1















+

minus

+minus

R

Vd

VoC

C1

Mode-1

L1

+

minus

VL2

L2

(a)

+

minus

+minus

Vd

VoC

C1

Mode-2

L1

+

minus

VL2

L2

(b)


Continuous

Pv

+minus

+minus

+

+

minus

minus

+

minus

i m gS D

mg

SD

IMean

times

NOT

Mosfet1

Mosfet2

Batt lSOC

Battery

Ramp2

Relationaloperator2

Transportdelay

Transportdelay1

Clock

D initSwitch


fcn

i

d

inew

newdnew

Powergui

0

2

C4C2C5 L1

L2

C6

C1

Transport delay2












08

07

06

05

04

03

02

01

0

Curr

ent (

A)



Pow

er (W

)















Technique Parameter

Irradiance-200Wm2







10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(a)

10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(b)


(a) (b)










M 100msMATH 100 vv

M


Tek Stop

MATH 100 vv

M

M Pos

M 100 s

minus3440 s


4 Conclusion



Nomenclature




References

































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





119889120572119881 (119868)

119889120572119868= limΔ119881rarr0

119881120572(119868) minus 119881

120572

119900(119868 minus Δ119868)

Δ119868 (24)

119889119881120572

119889120572119868asymp

(119881 minus 119881119900)120572

119868 minus 120572119868119900

(25)



119889120572

119889119881120572 (minus

119881119900

119868119900

)

= (minus1

119868119900

)119889120572119881120572

119900

119889120572119868+ (minus119881119900)

119889120572119868minus1

119874

119889120572119868

= (minus1

119868119900

)(Γ (2)

Γ (2 minus 120572))1198811199001minus120572

+ (minus119881119900)Γ (0)

Γ (minus120572)1198681minus120572

119874

(26)





Δ119868 and 119889119881120572




+

+ minus

+

minus

minus

R

Io

VL2+

minus

+

minus

L2

S2

S1

Vd

Vd L1

L c

VC2

VC1















+

minus

+minus

R

Vd

VoC

C1

Mode-1

L1

+

minus

VL2

L2

(a)

+

minus

+minus

Vd

VoC

C1

Mode-2

L1

+

minus

VL2

L2

(b)


Continuous

Pv

+minus

+minus

+

+

minus

minus

+

minus

i m gS D

mg

SD

IMean

times

NOT

Mosfet1

Mosfet2

Batt lSOC

Battery

Ramp2

Relationaloperator2

Transportdelay

Transportdelay1

Clock

D initSwitch


fcn

i

d

inew

newdnew

Powergui

0

2

C4C2C5 L1

L2

C6

C1

Transport delay2












08

07

06

05

04

03

02

01

0

Curr

ent (

A)



Pow

er (W

)















Technique Parameter

Irradiance-200Wm2







10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(a)

10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(b)


(a) (b)










M 100msMATH 100 vv

M


Tek Stop

MATH 100 vv

M

M Pos

M 100 s

minus3440 s


4 Conclusion



Nomenclature




References

































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


+

minus

+minus

R

Vd

VoC

C1

Mode-1

L1

+

minus

VL2

L2

(a)

+

minus

+minus

Vd

VoC

C1

Mode-2

L1

+

minus

VL2

L2

(b)


Continuous

Pv

+minus

+minus

+

+

minus

minus

+

minus

i m gS D

mg

SD

IMean

times

NOT

Mosfet1

Mosfet2

Batt lSOC

Battery

Ramp2

Relationaloperator2

Transportdelay

Transportdelay1

Clock

D initSwitch


fcn

i

d

inew

newdnew

Powergui

0

2

C4C2C5 L1

L2

C6

C1

Transport delay2












08

07

06

05

04

03

02

01

0

Curr

ent (

A)



Pow

er (W

)















Technique Parameter

Irradiance-200Wm2







10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(a)

10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(b)


(a) (b)










M 100msMATH 100 vv

M


Tek Stop

MATH 100 vv

M

M Pos

M 100 s

minus3440 s


4 Conclusion



Nomenclature




References

































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




08

07

06

05

04

03

02

01

0

Curr

ent (

A)



Pow

er (W

)















Technique Parameter

Irradiance-200Wm2







10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(a)

10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(b)


(a) (b)










M 100msMATH 100 vv

M


Tek Stop

MATH 100 vv

M

M Pos

M 100 s

minus3440 s


4 Conclusion



Nomenclature




References

































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



Technique Parameter

Irradiance-200Wm2







10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(a)

10

20

30

40

030 040 050 060

Times (s)

Out

put p

ower

(W)

850Wm2 27∘C

200Wm2 25∘C

850Wm2 27∘C

200Wm2 25∘C

(b)


(a) (b)










M 100msMATH 100 vv

M


Tek Stop

MATH 100 vv

M

M Pos

M 100 s

minus3440 s


4 Conclusion



Nomenclature




References

































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of






M 100msMATH 100 vv

M


Tek Stop

MATH 100 vv

M

M Pos

M 100 s

minus3440 s


4 Conclusion



Nomenclature




References

































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Nomenclature




References

































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Documents

Research Article Improved Fractional Order VSS Inc-Cond MPPT …downloads.hindawi.com/journals/ijp/2014/128327.pdf · 2019. 7. 31. · Research Article Improved Fractional Order VSS