Research Article Efficient Maximum Power Point …downloads.hindawi.com/archive/2014/673840.pdfpower point keeps changing with the irradiance levels and ambient temperature. erefore,

Research ArticleEfficient Maximum Power Point Tracking Algorithm forPV Application under Rapid Changing Weather Condition

Khaled M Bataineh and Amr Hamzeh

Department of Mechanical Engineering Jordan University of Science and Technology Irbid Jordan

Correspondence should be addressed to Khaled M Bataineh batenihyahoocom

Received 10 October 2013 Accepted 28 October 2013 Published 27 March 2014

Academic Editors A Bosio and S Dai

Copyright copy 2014 K M Bataineh and A Hamzeh This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

This study presents a novel search algorithm of maximum power point tracking for photovoltaic power generation systemsThe I-Vcharacteristics and the P-V power output under specific irradiation and temperature conditions are simulated The performanceof the algorithm under fully shaded and sudden partially shaded conditions as well as variable insulations levels is investigatedThe developed algorithm performs a wide-range search in order to detect rapidly changing weather conditions and keeps thesimulated stand-alone or grid-connected systems continuously operating close to the maximum power point The performance ofthe developed algorithm under extremely changing environmental conditions is found to be superior compared to that of otherconventional algorithms The results of this study show that under uniform radiations conditions the developed algorithm takesonly half of the time required by the Perturbation and Observe algorithms to reach maximum power point MMP Furthermorewhen PV is subjected to sudden partial shading conditions the algorithm rapidly detects these changes and reaches the newMMPin less than a second

1 Introduction

It is now widely accepted that the nonrenewable sources inthe world are finite and it is only a matter of time beforereserves will essentially be consumed [1 2] It has been proventhat the use of nonrenewable energy sources has severe effecton the environment Due to environmental awareness andtechnological advancement high oil price and governmentsupport the renewable electricity generation capacity hasreached an estimated 240 gigawatts (GW) worldwide in 2007while it was 160GW in 2004 [3] The solar photovoltaic (PV)power system is attractive renewable energy source due to itsavailability and economic feasibility [4 5] Stand-alone PVsystems are found suitable for powering remote areas [4]

The power produced by a PV module depends on theoperating temperature the amount of falling solar irradianceover the PV Cells array and the load connected [5 6]The power output of PV cells depends on the nonlinearcurrent voltage (I-V) characteristics relationship Becauseof this nonlinear relationship between the current and

the voltage of the PV cell there is a unique maximum powerpoint at particular weather conditions and this maximumpower point keeps changing with the irradiance levels andambient temperature Therefore a maximum power pointtracking (MPPT) algorithm is commonly used to obtain themaximum possible power under varying weather conditionsand loads Because of the nonlinear I-V relation the powerversus voltage P-V relation has more complicated behaviorespecially when the weather conditions changeThis complexbehavior makes analytical solution very difficult and forceresearchers to develop numerous techniques for findingMPP MPPT algorithms are implemented using digital signalprocessors (DSP) or microcontrollers They control DCDCconverters to drive the PV panel to operate at their MPP

The main methods used to achieve MPPT for PV cellsare EstimationMethods HeuristicMethod and SearchAlgo-rithms Systemmodelingmethod [7ndash9] curve-fittingmethod[10 11] open circuitmethod [12 13] and short circuitmethod[14 15] are examples of Estimation Methods They run PVcells to track an EstimatedMaximumPower Point rather than

Hindawi Publishing CorporationISRN Renewable EnergyVolume 2014 Article ID 673840 13 pageshttpdxdoiorg1011552014673840

2 ISRN Renewable Energy

the Actual Maximum Power Point In general EstimationMethods depend on an approximated mathematical modelto calculate an estimated MPP PV cell current-voltage datairradiance and temperature levels are the required inputs forthese methods The main advantages of Estimation Methodsare their simple implementation and fast response On theother hand they are expensive and inaccurate require the useof many sensors demand large computational power and failunder rapidly changing atmospheric conditions

Heuristic methods are recently developed to overcomethe problem associated with the inaccuracy of the PV cellmathematical model The succesful development of thesemethods is attributed to the recent advances in nonlinearcontrol method Fuzzy Logic Control methods [16 17]Neural Network methods [18ndash22] and Genetics Algorithmmethods are examples of Heuristic Methods developed toachieve MPPT of PV cells The Fuzzy Logic Control methodeffectively tracks the MPP under various weather conditionsHowever the performance highly depends on the expertise ofthe rule-based systemdesignerwhichmight lead to the failureof the controller in tracking the MPP under partial shadingcondition The outcomes of MPPT using Neural Networkmethods are highly related to the accuracy and efficiencyof the designed algorithm the size of the training databaseand the network training quality Furthermore they requiregathered data for various conditions and multiple locationsto guarantee a better performance

Unlike estimation methods Search Algorithms trackthe actual MPP rather than an estimated MPP Howeverthey continuously search for the MPP by increasing ordecreasing the PV cell output voltage Many methods aredeveloped implementing the search algorithms conceptSome of those methods are the differentiation method [2324] the Perturbation and Observe methods or the modifiedPerturbation and Observe methods [25ndash30] the IncrementalConductance method [31] the Parasitic Capacitance method[32] the Fibonacci Search method [33 34] the Slide Controlmethod [35] and the Particle Swamp Optimization method[36 37] The main advantage of these methods can besummarized as follows No previous knowledge about thePV cell characteristics is required no or minimal use ofsensors is required to show acceptable response to rapidlychanging conditions On the other hand search algorithmswaste energy as they continuously oscillate around the MPPUnfortunately solving the oscillation problem requires com-plex computational power Furthermore the performance ofthese methods degrades significantly under partial shadingconditions and fails under sudden partial shading conditionsUnfortunately none of the developed search algorithms cansuccessfully dealwith all extremeweather conditions namelyrapidly changing partial shading and sudden partial shadingconditions

All the developed methods found in the literature stillsuffer from weak performance under extreme weather con-ditions It is the objective of this study to develop an efficientnovel search algorithm that deals with rapidly changingpartial shading and sudden partial shading conditions totrack the MPP of PV cells Minimal user interface for wider

G

T

IL

V

Rs

I

Figure 1 Simple PV equivalent circuit model

Ipv VRp

I

RL

Id

Practical PV device

Ideal PV cell

Figure 2 Single-diode model of the theoretical PV with additionalparameters for the improved PV model

adaptation to different solar panels and different environ-mental conditions is considered in developing the proposedsearch algorithm

2 PV Cells Model

The modern solar cells are fabricated from a p-n junctionand prepared in a small thickness semiconductor layerThesecells create electric current when subjected to sunlight ThePV cells act as a form of diode in which the parameters ofthis diode define the circuit model Walker [38] proposeda simple approximate circuit for the PV cells as shown inFigure 1 Hemodeled the PV cells as a constant current sourceconnected in parallel with a diode The model includes thenecessary series resistance but neglects the shunt resistanceThe characteristics equation of the current 119868 produced by thePV cell is proportional to the intensity of the radiation fallenon the PV cells [38] as follows

119868 = 119868pv minus 1198680 [119890119902(119881+119868119877

119904)119886119896119879

minus 1] (1)

where 119868pv is the current (A) generated by the photovoltaic celldue the incident light 119896 = 13806503 times 10

minus23 (JK) is theBoltzmannrsquos constant 119879 is the temperature in Kelvins (K) atthe p-n junction 119902 = 160217646 times 10

minus23 (C) is the electroncharge 119868

0is the diode saturation or leakage current (A) 119881 is

the PV cell output voltage (Volt) and 119886 is the diode idealityfactor

Villalva et al suggested adding several parameters inorder to capture the behavior of actual panels which consistof a number of connected photovoltaic cells [39] Figure 2demonstrates the equivalent circuit of a photovoltaic cell

ISRN Renewable Energy 3

Current measurement

Voltage measurement

Ramp

IpvV

Vv

Rs

I

Rs1s s

1

1

+

+

++

minusminusminus

minus

2

i

Im

Figure 3 MATLABSimulink model of improved PV panel

with the additional parameters for the improved model Theimproved I-V characteristic of a PV array is given as [39]

119868 = 119868pv minus 1198680 [119890119902(119881+119868119877

119904)119886119881119905 minus 1] minus

119881 + 119877119904119868

119877119901

(2)

where 119881119905= (119873119904119896119879119902) is the thermal voltage of the array with

119873119904cells connected in series and 119877

119904and 119877

119901are the equivalent

series and shunt resistances (Ω) of the array respectivelyTheseries resistance is the sum of several internal and structuralresistances within the device The parallel resistance modelsthe current leakage through the p-n junction

Figure 3 shows a MATLABSimulink model for theimproved PV panel mathematical model Figure 4 shows aMATLABSimulink model of the PV circuit built to obtainthe I-V characteristics according to (2) The photogeneratedcurrent is function of solar radiation and temperature of thep-n junction is given by [39] as follows

119868pv = (119868pv119899 + 119896119894Δ119879)119866

119866119899

(3)

where 119868pv119899 is the photogenerated current at the nominalconditions (25∘C 1000Wm2) Δ119879 = 119879 minus 119879

119899 119879119899is the

nominal temperature in kelvin 119866 is the radiation fallen onthe device and 119866

119899is the nominal radiation Figure 5 shows

the Simulinkmodel for calculating 119868pvThe saturation currentequation derived by [39] is given as

1198680=

119868sc119899 + 119896119894Δ119879

(119890((119881oc119899+119870VΔ119879)119886119881119905) minus 1)

(4)

where 119868sc119899 is the short circuit current at nominal conditionsand 119896

119894and 119896V are the current and voltage coefficients

respectively 119881oc 119899 is the open circuit current at nominalconditions Figure 6 shows the Simulink model used tocalculate saturation current 119868

0 The values of 119868sc119899 119896119894 119896V and

119881oc119899 are supplied by the PV panelmanufacturer Villalva et alsuggested a method to adjust the values of 119877

119904and 119877

119901based

on the fact that there is only pair 119877119904 119877119901 which makes the

simulated maximum power point 119875max119898 = 119881119898119901

times 119868119898119901 equal

to the experimental maximum power point 119875max119890 [39] Themethod yields the following equations

119875max119898 = 119881119898119901119868pv minus 1198680 [exp(

119902

119870119879

119881119898119901

+ 119877119904119868119898119901

119886119873119904

)]

minus

119881119898119901

+ 119877119904119868119898119901

119877119901

119877119901= 119881119898119901(119881119898119901

+ 119868119898119901119877119904)

times (119881119898119901119868pv minus 1198811198981199011198680 [exp(

119902

119870119879

119881119898119901

+ 119877119904119868119898119901

119886119873119904

)]

+1198811198981199011198680minus 119875max119890)

minus1

(5)

From the above equations it is obvious that output powerof a PV module depends on the solar irradiance values andambient temperature

3 Partial Shading Problem

The temperature the irradiation levels and the shadingof the system affect the performance of photovoltaic cellsPartial shading problems arise due to the existence of cloudsor building shadows This problem makes the photovoltaicpower characteristics more complicated with multiple peaksin power This reduces the efficiency of most MPPT tech-niques The effect of partial shading problem appears signifi-cantly for large arrangement of panelsUnder partially shadedcondition it has been found that the I-V curves havemultiplestairs while the P-V curves have multiple peaks [40]

4 Boost Converter Design

In this paper we utilized a boost convertor to change the PVpanel operating point to its MPP The operation of the DC-DC converters is controlled by the MPPT algorithm makingthe power output of the panel operate at its the maximumlevel The MPPT algorithms are usually implemented usingeither digital signal processors (DSP) or a microcontroller

DC-DC boost converter shown in Figure 7 transformsan unstable 119881

119868voltage source into a higher-level stable

output voltage 119881119874 Over the past years these converters

have shifted from the conventional analog control to pulsewidth modulated PWM digital control These convertersuse solid-state components including MOSFETS transistorsand diodes to operate a digital switch (on-off switching)to control the resultant output of these DC-DC convertersThese converters employ capacitive and inductance elementsto store and transfer energy and eliminate the noise (lowpassfilter) Unlike analog control methods the digital controlmethods of DC-DC converters are quite resilient and flexiblein changing the software Also they offer the advantage ofimplementing more complex control algorithms

Boost converters have two modes of operation Theclosed-switch mode starts the diode reverse bias mode


Ipv

I

V

T

Rs

Ns

1

1

1++

+minus

+minus 2

2

dividetimes

times

times

times

3

125

015 5

4

Product

Product 2

Product 1 Math function

Subtract 1SubtractConstant

Divide

Addeu

I0

Im

Vta

q(alowastKlowast )

Figure 4 MATLABSimulink model for calculating the I-V characteristics

IpvG

T

1

1 +

+

+

minus

2

2

Ipvn

times

divide

times

times

0065

298

1000

356

Product 1

Product 3

Subtract 1

Divide

Add

dT

Gn

Tn

ki

Figure 5 PV cell MATLABSimulink model for calculating 119868pv

It causes the input power source to store energy in theinductor as well as the capacitor to discharge into the storagebattery while the open-switch mode starts the diode forwardbiasmode causing higher output energy supply fromboth thepower source and the inductor to the capacitor and the loadThe equation defining the ratio between the input voltage andthe output voltage is given as

119881in119881out

=1

1 minus 119863 (6)

where119863 = 119879on(119879on+119879off ) is the duty cycle of the input PWMsignal The microcontroller sends the proper PWM signal tothe boost converter switch to reach the MPP advised by theMPPT algorithm

In order to design an appropriate boost converter thefollowing steps are carried out

(i) The boost converter specifications listed in Table 1are selected to satisfy continuous operation under allconditions

(ii) A 200 kHz switching frequency is chosen to reducethe size of the boost converter components anddecrease the power loss

Table 1

Specification Min Max UnitsInput voltage 0 30 VOutput voltage 50 51 VOutput power 0 150 WOperation frequency 1 MHzVoltage allowed output ripple 50 mV

(iii) The boost inductor value plays a key role in deter-mining the operational mode of the system In orderto have continuous operation mode the inductanceshould satisfy the following equation

119871 ge119877 times 119905119904

2times(119872 minus 1)

1198723 (7)

where 119877 is the load resistance 119871 is the inductance119872 is the maximum voltage gain which is equalto (119881out119881in) and 119905119904 is the switching periodWe chosethe closest available conductor value of 68 120583H

(iv) The maximum duty cycle is calculated according to(6) and is found to be 0846


Vocn

1

1

1

+

+

++

+

minus2

Iscn

divide

times

times

timestimes

421 0065

38705

Product 1

Product 3

Product 2

Math functionSubtract 1

Divide

Add Add 1

euI0

dT

ki

kv

kv1

Vta

Figure 6 MATLABSimulink model for calculating 1198680

VI

RL

Lc p

C

R

VOd

g

s

a

ia

Rc

iL = iC

Diode

Q1

Drive circuit

+

minus

Figure 7 Circuit diagram of boost converter

(v) The capacitance value is given by

119862 =

119868119901119896

2times 119871

2 times Δ119881 times (1198810minus 119881119894) (8)

where 119868119901119896

is given by

119868119901119896=119881119894

119871times 119863 times 119905

119904

=8

66 times 10minus6times 0846 times

1

2 times 10minus6= 05A

(9)

The allowed ripple in the output voltage is required to be50mV Hence the desired capacitance value obtained from(8) is as

119862 =052times 66

2 times 005 times (13 minus 2)= 153 120583F (10)

The equivalent series resistance needed to limit the outputripple to 5mV is calculated by

ESR =Δ1198810

Δ1198680

=005

05= 10mΩ (11)

To sooth the signal almost twice of the calculatedcapacitor value is used that is 330 120583F Using all the design

calculated and chosen specifications the Simulink model ofthe PV panel system with the boost converter is shown inFigure 8

5 Theory of the Proposed MPPT Algorithm

There are several factors to consider when developing andchoosing the techniques for performing MPPT such as theability of an algorithm to detect multiple maxima costsand convergence speed MPPT is naturally a maxima-findingprocess The proposed Maximum Power Point tracking algo-rithm implements the search algorithms conceptThe reasonsbehind this choice as mentioned previously are no previousknowledge about the PV cell characteristics is required sim-ple implementation and guaranteed convergence The maindisadvantage of search algorithms are that they waste energyas they continuously oscillate around theMPP and they showinadequate response under partial shading conditions and failunder sudden partial shading conditions

Most search algorithms model the data as a 1-D functionand go about a Brute-Force method of finding the maximaof the function These kinds of algorithms require a largeamount of processing time Other algorithms like the Shubertalgorithm [40ndash42] rely on Lipschitz continuity They useweighing parameters that emphasize on the local searchversus the global search for the optima However theseconstants may not exist or could not be easily computedespecially for optimizing nonlinear control system which isthe case in this study Also these constants are requiredto be large enough to exceed the rate of change of I-Vcurve This might lead to a large number of iterations as therate of convergence towards the optimal point slows downRegardless of these draw backs the Lipschitzmethod remainshighly attractive due to the ability to bound the rate of changeof the function thus searching algorithms can be easilyimplemented and one parameter is required to be specifiedthat is Lipschitz constant [41]

Eliminating the need to specify the constant and makingthe algorithm consider both local and global search are thecriteria for developing the new algorithm In this studywe followed Jones et al methodology [41] by utilizing


R1

C

i

i

IL

ILDiode 1

G

G

T

T

Ipv

Ipv

PV

gv

1

1

+

+

+

minus

minus

minus

To workspace 1

2

2

Pulse generator

Search

EmbeddedMATLAB function

Change pulsewidth

Connection

Connection

Level-2 M-fileS-function

Switch

port

port 1

dutyVpv

Vpv

2120583H

Figure 8 Full simulator model

the advantages of Shubert algorithm mainly the bounding ofthe rate of change Jones et al presented an algorithm calledDIRECT algorithm that is a modification of the standardLipschitzian to overcome the problems of normal Shubertrsquosalgorithm [40] (Figure 11) In order to clarify the logicaldevelopment and the features of the proposed algorithmwe begin by reviewing Shubertrsquos method and discussing itsmain drawbacks then we will present Jonesrsquos algorithm thateliminates the need to specify a Lipschitz constant Finally wepresent the newly developed algorithm

51 Lipschitzian Optimization The goal is to find the maxi-mum functional value of 119891(119909) The normal Shubert methodcan be summarized as follows

Lipschitz continuity states that a function 119891(119909) definedon the closed interval [119897 119906] is called Lipschitz continuous on[119897 119906] if there exists a positive constant the Lipschitz constantsuch that

10038161003816100381610038161003816119891 (119909) minus 119891 (119909

1015840)10038161003816100381610038161003816lt 120572

10038161003816100381610038161003816119909 minus 119909101584010038161003816100381610038161003816 forall119909 119909

1015840isin [119897 119906] (12)

Let us take a hypothetical function119891(119909) defined on [119886 119887]If we substitute 119886 and 119887 for 1199091015840 into the definition of Lipschitz-continuity we get the following two inequalities for 119891(119909)where 119909 isin [119886 119887]

119891 (119909) gt 119891 (119886) minus 120572 (119909 minus 119886)

119891 (119909) gt 119891 (119887) + 120572 (119909 minus 119887)

(13)

The inequalities (13) formV-shaped formed from the twolines with slopesminus120572 and+120572with the intersection occur below119891(119909) as shown in Figure 9

The point of intersection for the two lines 1199091is easy to

calculate and is given as

1199091=(119886 + 119887)

2+(119891 (119886) minus 119891 (119887))

2120572 (14)

f(x)

Slope-120572

f1

a bx1

Slope 120572

Figure 9 An initial lower bound for 119891 using the Lipschitz constant

The initial lower bound of 119891 is denoted by 1198911and given

by

1198911=(119891 (119886) minus 119891 (119887))

2120572minus 120572 (119887 minus 119886) (15)

The Shubert algorithm uses this straightforward idea infinding the minimum or the maximum of 119891(119909) Shubertrsquosalgorithm is an iterative algorithm that continues to performthe same operation on the regions [119886 119909

1] and [119909

1 119887] elimi-

nating the higher 1198911value intervals to finally reach the global

minimum value as demonstrated by Figure 10Evaluating the function at the center of any interval rather

than the bounds of the interval is the main idea of DIRECT


f(x)

a bx1

(a)

f(x)

a bx1 x2

(b)

f(x)

a bx1 x2 x3

(c)

Figure 10 Iterations of the Shubert algorithm in dividing the intervals of minimum 1198911[41]

a bc1

c1c2 c3a1 b3b1 = a2 b2 = a3

Figure 11 Dividing strategy of DIRECT algorithm

algorithm developed by Jones et al [41] Mathematically thiscan be expressed as

119891 (119909) gt 119891 (119888) + 119870 (119909 minus 119888) for 119909 le 119888

119891 (119909) gt 119891 (119888) minus 119870 (119909 minus 119888) for 119909 ge 119888(16)

where 119888 = (119886 + 119887)2 Thus the lower bound equation hasto take into account the function value at the center of theinterval

Lower bound = 119891 (119888) minus 120572 (119887 minus 119886)

2 (17)

Figure 13 shows the interval-dividing strategy of theDIRECT algorithm when a sampling interval [119886 119887] has beenspecified Assume that the algorithm has already taken thesample 119888 at the center of [119886 119887] in the previous step This

f(c)

+ 120576|fmaxmax |f

f

max

(bj minus aj)2 (b minus a)2

Potentially optimalNonoptimal

Figure 12 Set of potentially optimal intervals

interval is then divided into three intervals [1198861 1198871] [1198862 1198872]

and [1198863 1198873] resulting in two new center points to be evaluated

1198881 1198882 The sample 119888 simply becomes the center of the new


I

OP DOP

V

(a)

V

P

POP

P998400OP

VMMP

(b)

Figure 13 Change in power under partially shaded condition identification in (a) I-V and (b) P-V

middle interval The algorithm then evaluates the threesamples to decide the next sampling interval It is clear thatonly two new samples in each dividing iterations are requiredfor evaluation Further subdivision for the potential intervalcontaining optima is carried out until the optimal point isfoundTheoretical details are found in reference [41]The factthat in convex hull functions local optima are global optimais used to select potentially optimal interval Suppose that wehave partitioned the interval [119897 119906] into intervals [119886

119894 119887119894] with

midpoints 119888119894 for 119894 = 1 119898 Let 120576 gt 0 be a positive constant

and let 119891max be the current best function value Interval 119895is said to be potentially optimal if there exists some rate-of-change constant gt 0 such that [41]

119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891 (119888

119895) +

(119887119894minus 119886119894)

2 forall119894 = 1119898

(18)

119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891min + 120576

1003816100381610038161003816119891min1003816100381610038161003816

(19)

The inequality (18) selects intervals that would improvethe current function value For intervals with the samelength the interval with the highest function value at itscenter point is chosen to be the potentially optimal interval(POI) The inequality (19) ensures that the POIs exceed thecurrent best solution by a nontrivial amount 120576|119891max| Figure 12demonstrates how convex hull sets help choose POIs thatsatisfy both (18) and (19) [41] If we construct convex hullfrom the function values at the center points the intervalsthatmake up convex hull are considered POIs Grahamrsquos Scanis efficient algorithmused to create a convex hull out of the setof center points [43] Grahamrsquos scan is a phase algorithm thatcan be summarized as follows given a set of points 119878

119901

(1) Find the point in 119878119901with the maximum value If two

or more have the same value use one with the lowest119909 coordinate Call it 119875

0

(2) Calculate the angles in radians that each of the pointsmakeswith119875

0 then sort them in increasing order and

push them onto a stack(3) If 119875

0forms a left turn with the last two points in the

stack we push 1198750onto the stack else we discard and

make the next point in the stack 1198750and repeat

(4) Repeat step number (3) until you encounter 1198750again

A simplified approach is to calculate the direction crossproduct of the two vectors formed from three points 119875

0-1198751

and 1198751-1198752 If the value is positive it is a left turn and thus

we keep the point and the interval If it is negative then wediscard the interval all together

52 Golden Section Search (for Rapidly Changing Conditions)The golden section algorithm is used to detect the envi-ronmental change by continuously oscillating around themaximum power point The Golden Section Search methodis used to find the maximum or the minimum of a unimodalfunction by calculating the function at three different pointsIn this study Golden Section Search (GSS) MPPT algorithmuses the voltage as the search variable The main advantageof GSS algorithm is its fast convergence compared to manyother MPPT algorithms The MPPT algorithm is developedwith the limiting parameters for fast convergence The mainsteps in GSS algorithm are as follows

Initialization

(1) Determine 119909119897and 119909

119906which is known to contain the

maximum of the function 119891(119909)(2) Determine two intermediate points 119909

1and 119909

2such

that

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

1199092= 1199092minusradic5 minus 1

2(119909119906minus 119909119897)

(20)


Set m = 1

[a1 b1

] = [a b]

c1 = (a1 + b1)2

Evaluate f(c1)

Set fmax = f(c1)

Set iteration counter p = 1

Identify the set S of potentiallyoptimal intervals using Grahamrsquos

scan

Select any interval j in set S

120590 = (bj minus aj)3cm+1 = cj minus 120590

cm+2 = cj + 120590

Evaluate f(cm+1) and evaluate f(cm+2)

Update fmax

In the partition add the left and right subintervals

[am+1 bm+1] = [aj aj + 120590] center point cm+1

[am+2 bm+2] = [aj + 2120590 bj] center point cm+2

[aj bj] = [aj + 120590 aj + 2120590]

m = m + 2

Is S empty

Is MPP found

Environment change happens One needs to find global OP

Ct lt 4

Ct lt 4

Ct lt 4

No environmentchange

Continueoscillating

around MPP

xu = mpp mpp = xL

xL = mpp + (xu minus mpp )062

xL = mpp + (xu minus mpp )062P(mpp ) gt P(xl )

xu = mpp mpp = xl

Ct = Ct + 1

Ct = Ct + 1

Ct = Ct + 1

P(mpp ) gt P(xu)

xL = mpp mpp = xu

xu = mpp + 062(mpp minus xL)

No

No

No

No

No

No

No

YesYes

Yes

Yes

Yes

Yes

Yes

S = S minus j

xL = mpp minus (05062) Ct = 0

GSS xu = mpp + 05

OP interval is identified and reached

Figure 14 Flowchart of the proposed search algorithm

(3) If 119891(1199091) gt 119891(119909

2) then new points 119909

119897 1199091 1199092 and 119909

119906

are updated as

119909119897= 1199092 1199092= 1199091 119909119906= 119909119906

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

(21)

(4) If 119891(1199091) lt 119891(119909

2) then the new points 119909

119897 1199091 1199092 and

119909119906are updated as

119909119897= 119909119897 119909119906= 1199091 1199091= 1199092

1199092= 119909119906+radic5 minus 1

2(119909119906minus 119909119897)

(22)

(5) If 119909119906minus 119909119871lt 120576 (a predefined condition) then the

maximum occurs at (119909119906+ 119909119871)2 stop iteration else

go to step 2The intermediate points 119909

1and 119909

2are chosen such that

the ratio of the distance from these points to the boundaries ofthe search region is equal to the golden ratioThe golden ratiowhich is equal to 161803398 makes the algorithm converge ata constant speed

53 Implementation for PV System Theoretically 119881MMP fallsbetween 0V and 119881oc max In the present study a DCDCconverter is used to vary the optimal point OP of the PVsystem Hence the duty cycle would be in the range of (0 1)


G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1

Figure 15 Masked Simulink model of PV cells

However this range can be controlled to be much smallerin practice The smaller range will increase the convergencespeedThemaximumduty cycle is calculated according to (6)and found to be 0846

As mentioned previously the I-V curves have multiplestairs while the P-V curves have multiple peaks underpartially shaded condition as shown in Figure 15 To explainthemain idea of the new algorithm assume that DIRECT hassuccessfully found the maximum power point as shown inFigure 13(a) When weather condition changes happen theOP will move to a different point due to the change of the I-Vcurve Since the duty cycle is not changed the power of the PVis decreased from 119875OP to 119875

1015840

OP as explained in Figure 13(b) Todetect environment changes on the PV arrays GSS algorithmcontinuously oscillates around the current 119881MMP The GSSis chosen due to its rapid local searching for optimal pointWhen executing the GSS algorithm within small intervalaround the current 119881MMP the GSS has the ability withinfour iterations to decide whether environment changes haveoccurred or not If OP is not found when GSS iteratedfour times DIRECT algorithm is called to search for globalOP This will increase the response time of the proposedalgorithm Figure 14 shows the simplified flowchart of theDIRECT search algorithm incorporated with GSS

6 Results

The simulation results are carried out using MATLABSimulink to validate the performance of the proposed MPPTalgorithm

61 Photovoltaic Model Simulation Results The developedphotovoltaic cell Simulinkmodel built and shown inFigure 15is used to simulate the performance of PV cells underdifferent temperatures and irradiance levels Figure 16 showsthe I-V characteristic curve of a practical photovoltaic deviceunder different weather conditions It can be seen that the I-Vcharacteristics are dependent on the levels of irradiance andthe temperature of PV cell Figure 17 shows the power-voltagevariations under different weather condition It is clear thatthe P-V curve has single peak that could be easily found byconventional searching method

To investigate partial shading conditions first a maskedmodel of a single PV cell is built as shown in Figure 18 Thena model for a panel consisting of three PV cells connected inparallel is built as shown in Figure 19 Each cell is subjected to

1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35

Figure 16 I-V characteristic curves of a practical photovoltaicdevice under different weather conditions

1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)

Figure 17 P-V curves plotted for different weather conditions

different solar irradiation to allow producing different valuesof photovoltaic current 119868pv

In order to clarify the complexity associated with partialshading sample simulations are carried out and their resultsare shown in Figures 20 and 21It can be seen in Figures 20and 21 that there are two local maxima in the power-voltagecurves As mentioned previously many MPPT algorithmsare incapable of dealing with the effects of partial shadingand might mistakenly drive the system to its local maximuminstead of the desired global maximum

62 Performance under Uniform Weather Condition ThePerformance and operation of the proposed search algorithmhave been evaluated usingMATLABSimulinkThe samplingtime is chosen to be 005 s For the implemented proposedMPPT algorithms the simulation results have been obtainedduring starting up of the system The results have beenobtained for a solar irradiance value of the proposed systemthat is tested under two uniform radiation levels 1000Wm2and 2000Wm2 As shown in Figures 22 and 23 the proposedMPPT algorithm found the global maximum in a relativelyshort time that is in less than 08 seconds with small oscil-lation in steady state IT is also observed that the power lossfrom oscillation is insignificant To evaluate the effectivenessof the proposed algorithm its performance is compared withthat of the Perturbation and Observe algorithm [25ndash31] Theresult in Figure 24 shows that Perturbation and Observeneeded 19 seconds to reach the MPP


G

T

G

T

Ipv

1

1

2

Out 1

Subsystem

Figure 18 Masked Simulink model to calculate 119868pv

G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1

Figure 19 Simulink model for partial shading

Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)

Figure 20 The variation of the I-V under varying irradiance (600200 and 100Wm2)

Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)

Figure 21The variation of the P-V under partially shaded condition(600 200 and 100Wm2)

63 Proposed MPPT Algorithm under Partially Shaded Theproposed scheme for MPPT algorithm is tested underpartially shaded conditions The simulations were con-ducted with two consecutive scenarios In the first scenario

Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18

Figure 22 The simulated power curves for the 1000Wm2 25∘Cfully shaded designed algorithm

Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120

Figure 23 The simulated power curves for the 2000Wm2 25∘C

the PV panels are subjected to uniform insolation conditionThis condition is maintained for 04 s before it is changedto partially shaded condition The cells temperatures arekept constant at 25∘C Figure 25 shows that the MMPTalgorithm maintains the MPP until the radiation level variesat 04 s It can be seen from Figure 25 that the proposedalgorithm immediately detects theweather changes and starts

12 ISRN Renewable EnergyPo

wer

(W)

Time (s)

100

50

00 05 1 15 252

Figure 24 The simulated power curves for the 2000Wm2 25∘CPerturbation and Observe [25ndash31]

Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18

Figure 25 MMP tracking under partial shading (600 200 and100Wm2)

immediately searching for the newMPP As it can be seen inFigure 25 the proposedMPPT found the newMPP after 07 s

7 Conclusion

A novel algorithm of maximum power point tracking forphotovoltaic power generation system is presented A math-ematical model of the PV panel is presented based on thetheory of photovoltaic The V-I characteristics and the P-V power output under several irradiation levels and tem-perature conditions are simulated The proposed algorithmis implemented in a PV panel connected to DC-DC boostconverter with resistive loading A full Simulink MATLABmodel is built to simulate the performance of the proposedalgorithmThe proposedMPPT algorithm is evaluated underextreme weather conditions The results show that variousadvantages are gained with the proposed scheme comparedto perturbation and observe algorithmsThe response time issmaller and the oscillations around the MPP were reducedto obtain steady state maximum power output It is foundthat the proposed algorithm quickly identifies theMPP of thesolar panels under extremeweather conditions Furthermorethe MMPT algorithm sustains its performance when sub-jected to sudden changes in the insulation levels In additionit is capable of finding the globalmaximumpoints under bothfully and partially shaded conditions

Conflict of Interests

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

References

[1] K Bataineh and N Fayez ldquoThermal performance of buildingattached sunspace in Jordan climaterdquo in Proceedings of the1st International Nuclear and Renewable Energy Conference(INREC rsquo10) Amman Jordan March 2010

[2] K Bataineh ldquoNumerical simulations for average temperaturedifferential stirling enginerdquo Journal of Technology Innovations inRenewable Energy vol 2 no 3 2013

[3] K Bataineh and D Dalalah ldquoAssessment of wind energypotential for selected areas in Jordanrdquo Journal of RenewableEnergy vol 59 pp 75ndash81 2013

[4] K M Bataineh and D Dalalah ldquoOptimal configuration fordesign of stand-alone PV systemrdquo Smart Grid and RenewableEnergy vol 3 no 2 2012

[5] K Bataineh and A Hamzeh ldquoEfficient maximum power pointtracking algorithm for photovoltaic cellsrdquo in Proceedings ofthe 1st WSEAS International Conference on Industrial andManufacturing Technologies Athens Greece 2013

[6] M Adel Hamdy ldquoA new model for the current-voltage out-put characteristics of photovoltaic modulesrdquo Journal of PowerSources vol 50 no 1-2 pp 11ndash20 1994

[7] T Takashima T Tanaka M Amano and Y Ando ldquoMaximumoutput control of photovoltaic (PV) arrayrdquo in Proceedings of the35th Intersociety Energy Conversion Engineering Conference andExhibit (IECEC rsquo00) pp 380ndash383 Las Vegas Nev USA July2000

[8] N Takehara and S Kurokami ldquoPower control apparatus andmethod and power generating system using themrdquo Patent US5654883 1997

[9] K Nishioka N Sakitani K-I Kurobe et al ldquoAnalysis of thetemperature characteristics in polycrystalline Si solar cells usingmodified equivalent circuit modelrdquo Japanese Journal of AppliedPhysics vol 42 no 12 pp 7175ndash7179 2003

[10] J CH PhangD SH Chan and J R Phillips ldquoAccurate analyt-ical method for the extraction of solar cell model parametersrdquoElectronics Letters vol 20 no 10 pp 406ndash408 1984

[11] D Lafferty ldquoCoupling network for improving conversion effi-ciency of photovoltaic power sourcerdquo US 4873480 1989

[12] P Chetty ldquoMaximum power transfer system for a solar cellarrayrdquo US 4604567 1986

[13] M A S Masoum and H Dehbonei ldquoOptimal power pointtracking of photovoltaic system under all operating conditionsrdquoin Proceedings of the 17th Congress of the World Energy CouncilHouston Tex USA 1998

[14] S M Alghuwainem ldquoMatching of a dc motor to a photovoltaicgenerator using a step-up converter with a current-locked looprdquoIEEE Transactions on Energy Conversion vol 9 no 1 pp 192ndash198 1994

[15] T Noguchi S Togashi and R Nakamoto ldquoShort-currentpulse-based adaptive maximum-power-point tracking for aphotovoltaic power generation systemrdquoElectrical Engineering inJapan vol 139 no 1 pp 65ndash72 2002

[16] P Takun S Kaitwanidvilai and C Jettanasen ldquoMaximumpower point tracking using fuzzy logic control for photovoltaicsystemsrdquo in Proceedings of the International MultiConference ofEngineers and Computer Scientists (IMECS rsquo11) pp 986ndash990Hong Kong March 2011

[17] M S A Cheikh C Larbes G F T Kebir and A ZerguerrasldquoMaximum power point tracking using a fuzzy logic controlschemerdquo Revue des Energies Renouvelables vol 10 no 32 pp387ndash395 2007


[18] THiyama S Kouzuma andT Imakubo ldquoIdentification of opti-mal operating point of PV modules using neural network forreal time maximum power tracking controlrdquo IEEE Transactionson Energy Conversion vol 10 no 2 pp 360ndash367 1995

[19] K Ro and S Rahman ldquoTwo-loop controller for maximizingperformance of a grid-connected photovoltaic-fuel cell hybridpower plantrdquo IEEE Transactions on Energy Conversion vol 13no 3 pp 276ndash281 1998

[20] A Hussein K Hirasawa J Hu and J Murata ldquoThe dynamicperformance of photovoltaic supplied DC motor fed from DC-DC converter and controlled by neural networksrdquo in Proceed-ings of the International Joint Conference on Neural Networks(IJCNN rsquo02) pp 607ndash612 May 2002

[21] X Sun W Wu X Li and Q Zhao ldquoA research on photovoltaicenergy controlling system with maximum power point track-ingrdquo in Proceedings of the Power Conversion Conference pp822ndash826 2002

[22] L Zhang Y Bai and A Al-Amoudi ldquoGA-RBF neural networkbased maximum power point tracking for grid-connected pho-tovoltaic systemsrdquo in Proceedings of the International Conferenceon Power Electronics Machines and Drives pp 18ndash23 April2002

[23] L TW Bavaro ldquoPower regulation utilizing only battery currentmonitoringrdquo Patent US 4794272 1988

[24] C Hua and J R Lin ldquoDSP-based controller application in bat-tery storage of photovoltaic systemrdquo in Proceedings of the IEEE22nd International Conference on Industrial Electronics Controland Instrumentation (IECON rsquo96) pp 1705ndash1710 August 1996

[25] J H R EnslinM SWolf D B Snyman andW Swiegers ldquoInte-grated photovoltaic maximum power point tracking converterrdquoIEEE Transactions on Industrial Electronics vol 44 no 6 pp769ndash773 1997

[26] A Al-Amoudi and L Zhang ldquoOptimal control of a grid-connected PV system for maximum power point tracking andunity power factorrdquo in Proceedings of the 7th InternationalConference on Power Electronics and Variable Speed Drives pp80ndash84 September 1998

[27] N Kasa T Iida and H Iwamoto ldquoMaximum power pointtracking with capacitor identificator for photovoltaic powersystemrdquo in Proceedings of the 8th International Conferenceon Power Electronics and Variable Speed Drives pp 130ndash135September 2000

[28] L Zhang A Al-Amoudi and Y Bai ldquoReal-time maximumpower point tracking for grid-connected photovoltaic systemsrdquoin Proceedings of the 8th International Conference on PowerElectronics and Variable Speed Drives pp 124ndash129 September2000

[29] WXiaoWGDunford P R Palmer andACapel ldquoApplicationof centered differentiation and steepest descent to maximumpower point trackingrdquo IEEETransactions on Industrial Electron-ics vol 54 no 5 pp 2539ndash2549 2007

[30] J M Enrique J M Andujar and M A Bohorquez ldquoAreliable fast and low cost maximum power point tracker forphotovoltaic applicationsrdquo Solar Energy vol 84 no 1 pp 79ndash89 2010

[31] K H Hussein I Muta T Hoshino and M Osakada ldquoMax-imum photovoltaic power tracking an algorithm for rapidlychanging atmospheric conditionsrdquo IEE Proceedings vol 142 no1 pp 59ndash64 1995

[32] A Brambilla M Gambarara A Garutti and F Ronchi ldquoNewapproach to photovoltaic arrays maximum power point track-ingrdquo in Proceedings of the 30th Annual IEEE Power ElectronicsSpecialists Conference (PESC rsquo99) pp 632ndash637 July 1999

[33] M Miyatake T Kouno and M Nakano ldquoMaximum powerpoint tracking control employing fibonacci search algorithmfor photovoltaic power generation systemrdquo in Proceedings ofthe International Conference of Power Electronics (ICPE rsquo01) pp622ndash625 Seoul Republic of Korea October 2001

[34] N A Ahmed andMMiyatake ldquoA novelmaximumpower pointtracking for photovoltaic applications under partially shadedinsolation conditionsrdquo Electric Power Systems Research vol 78no 5 pp 777ndash784 2008

[35] M Zhang J Wu and H Zhao ldquoThe application of slidetechnology in PV maximum power point tracking systemrdquo inProceedings of the 5th World Congress on Intelligent Control andAutomation (WCICA rsquo04) pp 5591ndash5594 June 2004

[36] M Miyatake F Toriumi T Endo and N Fujii ldquoA novelmaximum power point tracker controlling several convertersconnected to photovoltaic arrays with particle swarm optimiza-tion techniquerdquo in Proceedings of the European Conference onPower Electronics and Applications (EPE rsquo07) September 2007

[37] S R Chowdhury andH Saha ldquoMaximumpower point trackingof partially shaded solar photovoltaic arraysrdquoRenewable Energyvol 34 no 10 pp 2093ndash2100 2009

[38] GWalker ldquoEvaluatingMPPT converter topologies using amat-lab PVmodelrdquo Journal of Electrical and Electronics EngineeringAustralia vol 21 no 1 pp 49ndash55 2001

[39] MG Villalva J R Gazoli and E Ruppert Filho ldquoModeling andcircuit-based simulation of photovoltaic arraysrdquo in Proceedingsof the Brazilian Power Electronics Conference (COBEP rsquo09) pp1244ndash1254 Mato Grosso do Sul Brazil October 2009

[40] H Patel and V Agarwal ldquoMATLAB-based modeling to studythe effects of partial shading on PV array characteristicsrdquo IEEETransactions on Energy Conversion vol 23 no 1 pp 302ndash3102008

[41] B O Shubert ldquoA sequential method seeking the global maxi-mum of a functionrdquo SIAM Journal on Numerical Analysis vol9 no 3 pp 379ndash388 1972

[42] D R Jones C D Perttunen and B E Stuckman ldquoLipschitzianoptimization without the Lipschitz constantrdquo Journal of Opti-mizationTheory andApplications vol 79 no 1 pp 157ndash181 1993

[43] E A Galperin ldquoThe cubic algorithmrdquo Journal of MathematicalAnalysis and Applications vol 112 no 2 pp 635ndash640 1985

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of


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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of


Journal of


Renewable Energy

Submit your manuscripts athttpwwwhindawicom


StructuresJournal of


RotatingMachinery


EnergyJournal of


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


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Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


the Actual Maximum Power Point In general EstimationMethods depend on an approximated mathematical modelto calculate an estimated MPP PV cell current-voltage datairradiance and temperature levels are the required inputs forthese methods The main advantages of Estimation Methodsare their simple implementation and fast response On theother hand they are expensive and inaccurate require the useof many sensors demand large computational power and failunder rapidly changing atmospheric conditions

Heuristic methods are recently developed to overcomethe problem associated with the inaccuracy of the PV cellmathematical model The succesful development of thesemethods is attributed to the recent advances in nonlinearcontrol method Fuzzy Logic Control methods [16 17]Neural Network methods [18ndash22] and Genetics Algorithmmethods are examples of Heuristic Methods developed toachieve MPPT of PV cells The Fuzzy Logic Control methodeffectively tracks the MPP under various weather conditionsHowever the performance highly depends on the expertise ofthe rule-based systemdesignerwhichmight lead to the failureof the controller in tracking the MPP under partial shadingcondition The outcomes of MPPT using Neural Networkmethods are highly related to the accuracy and efficiencyof the designed algorithm the size of the training databaseand the network training quality Furthermore they requiregathered data for various conditions and multiple locationsto guarantee a better performance

Unlike estimation methods Search Algorithms trackthe actual MPP rather than an estimated MPP Howeverthey continuously search for the MPP by increasing ordecreasing the PV cell output voltage Many methods aredeveloped implementing the search algorithms conceptSome of those methods are the differentiation method [2324] the Perturbation and Observe methods or the modifiedPerturbation and Observe methods [25ndash30] the IncrementalConductance method [31] the Parasitic Capacitance method[32] the Fibonacci Search method [33 34] the Slide Controlmethod [35] and the Particle Swamp Optimization method[36 37] The main advantage of these methods can besummarized as follows No previous knowledge about thePV cell characteristics is required no or minimal use ofsensors is required to show acceptable response to rapidlychanging conditions On the other hand search algorithmswaste energy as they continuously oscillate around the MPPUnfortunately solving the oscillation problem requires com-plex computational power Furthermore the performance ofthese methods degrades significantly under partial shadingconditions and fails under sudden partial shading conditionsUnfortunately none of the developed search algorithms cansuccessfully dealwith all extremeweather conditions namelyrapidly changing partial shading and sudden partial shadingconditions

All the developed methods found in the literature stillsuffer from weak performance under extreme weather con-ditions It is the objective of this study to develop an efficientnovel search algorithm that deals with rapidly changingpartial shading and sudden partial shading conditions totrack the MPP of PV cells Minimal user interface for wider

G

T

IL

V

Rs

I

Figure 1 Simple PV equivalent circuit model

Ipv VRp

I

RL

Id

Practical PV device

Ideal PV cell

Figure 2 Single-diode model of the theoretical PV with additionalparameters for the improved PV model

adaptation to different solar panels and different environ-mental conditions is considered in developing the proposedsearch algorithm

2 PV Cells Model

The modern solar cells are fabricated from a p-n junctionand prepared in a small thickness semiconductor layerThesecells create electric current when subjected to sunlight ThePV cells act as a form of diode in which the parameters ofthis diode define the circuit model Walker [38] proposeda simple approximate circuit for the PV cells as shown inFigure 1 Hemodeled the PV cells as a constant current sourceconnected in parallel with a diode The model includes thenecessary series resistance but neglects the shunt resistanceThe characteristics equation of the current 119868 produced by thePV cell is proportional to the intensity of the radiation fallenon the PV cells [38] as follows

119868 = 119868pv minus 1198680 [119890119902(119881+119868119877

119904)119886119896119879

minus 1] (1)

where 119868pv is the current (A) generated by the photovoltaic celldue the incident light 119896 = 13806503 times 10

minus23 (JK) is theBoltzmannrsquos constant 119879 is the temperature in Kelvins (K) atthe p-n junction 119902 = 160217646 times 10

minus23 (C) is the electroncharge 119868

0is the diode saturation or leakage current (A) 119881 is

the PV cell output voltage (Volt) and 119886 is the diode idealityfactor

Villalva et al suggested adding several parameters inorder to capture the behavior of actual panels which consistof a number of connected photovoltaic cells [39] Figure 2demonstrates the equivalent circuit of a photovoltaic cell


Current measurement

Voltage measurement

Ramp

IpvV

Vv

Rs

I

Rs1s s

1

1

+

+

++

minusminusminus

minus

2

i

Im



119868 = 119868pv minus 1198680 [119890119902(119881+119868119877

119904)119886119881119905 minus 1] minus

119881 + 119877119904119868

119877119901

(2)



119904and 119877




119868pv = (119868pv119899 + 119896119894Δ119879)119866

119866119899

(3)


119899 119879119899is the




1198680=

119868sc119899 + 119896119894Δ119879

(119890((119881oc119899+119870VΔ119879)119886119881119905) minus 1)

(4)






119904and 119877

119901based



times 119868119898119901 equal


119875max119898 = 119881119898119901119868pv minus 1198680 [exp(

119902

119870119879

119881119898119901

+ 119877119904119868119898119901

119886119873119904

)]

minus

119881119898119901

+ 119877119904119868119898119901

119877119901

119877119901= 119881119898119901(119881119898119901

+ 119868119898119901119877119904)


119902

119870119879

119881119898119901

+ 119877119904119868119898119901

119886119873119904

)]

+1198811198981199011198680minus 119875max119890)

minus1

(5)












Ipv

I

V

T

Rs

Ns

1

1

1++

+minus

+minus 2

2

dividetimes

times

times

times

3

125

015 5

4

Product

Product 2



Divide

Addeu

I0

Im

Vta

q(alowastKlowast )


IpvG

T

1

1 +

+

+

minus

2

2

Ipvn

times

divide

times

times

0065

298

1000

356

Product 1

Product 3

Subtract 1

Divide

Add

dT

Gn

Tn

ki



119881in119881out

=1

1 minus 119863 (6)





Table 1



119871 ge119877 times 119905119904


1198723 (7)




Vocn

1

1

1

+

+

++

+

minus2

Iscn

divide

times

times

timestimes

421 0065

38705

Product 1

Product 3

Product 2


Divide

Add Add 1

euI0

dT

ki

kv

kv1

Vta


VI

RL

Lc p

C

R

VOd

g

s

a

ia

Rc

iL = iC

Diode

Q1

Drive circuit

+

minus



119862 =

119868119901119896

2times 119871


where 119868119901119896

is given by

119868119901119896=119881119894

119871times 119863 times 119905

119904

=8


1


(9)


119862 =052times 66



ESR =Δ1198810

Δ1198680

=005

05= 10mΩ (11)








R1

C

i

i

IL

ILDiode 1

G

G

T

T

Ipv

Ipv

PV

gv

1

1

+

+

+

minus

minus

minus

To workspace 1

2

2

Pulse generator

Search


Change pulsewidth

Connection

Connection


Switch

port

port 1

dutyVpv

Vpv

2120583H





10038161003816100381610038161003816119891 (119909) minus 119891 (119909

1015840)10038161003816100381610038161003816lt 120572

10038161003816100381610038161003816119909 minus 119909101584010038161003816100381610038161003816 forall119909 119909

1015840isin [119897 119906] (12)


119891 (119909) gt 119891 (119886) minus 120572 (119909 minus 119886)

119891 (119909) gt 119891 (119887) + 120572 (119909 minus 119887)

(13)




1199091=(119886 + 119887)

2+(119891 (119886) minus 119891 (119887))

2120572 (14)

f(x)

Slope-120572

f1

a bx1

Slope 120572



by

1198911=(119891 (119886) minus 119891 (119887))

2120572minus 120572 (119887 minus 119886) (15)


1] and [119909

1 119887] elimi-





f(x)

a bx1

(a)

f(x)

a bx1 x2

(b)

f(x)

a bx1 x2 x3

(c)


a bc1

c1c2 c3a1 b3b1 = a2 b2 = a3



119891 (119909) gt 119891 (119888) + 119870 (119909 minus 119888) for 119909 le 119888




2 (17)


f(c)

+ 120576|fmaxmax |f

f

max








I

OP DOP

V

(a)

V

P

POP

P998400OP

VMMP

(b)



119894 119887119894] with



119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891 (119888

119895) +

(119887119894minus 119886119894)

2 forall119894 = 1119898

(18)

119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891min + 120576

1003816100381610038161003816119891min1003816100381610038161003816

(19)


119901



0









0-1198751




Initialization

(1) Determine 119909119897and 119909



1and 119909

2such

that

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)


2(119909119906minus 119909119897)

(20)


Set m = 1

[a1 b1

] = [a b]

c1 = (a1 + b1)2

Evaluate f(c1)

Set fmax = f(c1)



scan



cm+2 = cj + 120590


Update fmax




[aj bj] = [aj + 120590 aj + 2120590]

m = m + 2

Is S empty

Is MPP found


Ct lt 4

Ct lt 4

Ct lt 4


Continueoscillating

around MPP

xu = mpp mpp = xL



xu = mpp mpp = xl

Ct = Ct + 1

Ct = Ct + 1

Ct = Ct + 1

P(mpp ) gt P(xu)

xL = mpp mpp = xu


No

No

No

No

No

No

No

YesYes

Yes

Yes

Yes

Yes

Yes

S = S minus j


GSS xu = mpp + 05



(3) If 119891(1199091) gt 119891(119909


119897 1199091 1199092 and 119909

119906

are updated as

119909119897= 1199092 1199092= 1199091 119909119906= 119909119906

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

(21)

(4) If 119891(1199091) lt 119891(119909


119897 1199091 1199092 and


119909119897= 119909119897 119909119906= 1199091 1199091= 1199092

1199092= 119909119906+radic5 minus 1

2(119909119906minus 119909119897)

(22)




1and 119909





G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1




1015840


6 Results




1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35


1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)






G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Current measurement

Voltage measurement

Ramp

IpvV

Vv

Rs

I

Rs1s s

1

1

+

+

++

minusminusminus

minus

2

i

Im



119868 = 119868pv minus 1198680 [119890119902(119881+119868119877

119904)119886119881119905 minus 1] minus

119881 + 119877119904119868

119877119901

(2)



119904and 119877




119868pv = (119868pv119899 + 119896119894Δ119879)119866

119866119899

(3)


119899 119879119899is the




1198680=

119868sc119899 + 119896119894Δ119879

(119890((119881oc119899+119870VΔ119879)119886119881119905) minus 1)

(4)






119904and 119877

119901based



times 119868119898119901 equal


119875max119898 = 119881119898119901119868pv minus 1198680 [exp(

119902

119870119879

119881119898119901

+ 119877119904119868119898119901

119886119873119904

)]

minus

119881119898119901

+ 119877119904119868119898119901

119877119901

119877119901= 119881119898119901(119881119898119901

+ 119868119898119901119877119904)


119902

119870119879

119881119898119901

+ 119877119904119868119898119901

119886119873119904

)]

+1198811198981199011198680minus 119875max119890)

minus1

(5)












Ipv

I

V

T

Rs

Ns

1

1

1++

+minus

+minus 2

2

dividetimes

times

times

times

3

125

015 5

4

Product

Product 2



Divide

Addeu

I0

Im

Vta

q(alowastKlowast )


IpvG

T

1

1 +

+

+

minus

2

2

Ipvn

times

divide

times

times

0065

298

1000

356

Product 1

Product 3

Subtract 1

Divide

Add

dT

Gn

Tn

ki



119881in119881out

=1

1 minus 119863 (6)





Table 1



119871 ge119877 times 119905119904


1198723 (7)




Vocn

1

1

1

+

+

++

+

minus2

Iscn

divide

times

times

timestimes

421 0065

38705

Product 1

Product 3

Product 2


Divide

Add Add 1

euI0

dT

ki

kv

kv1

Vta


VI

RL

Lc p

C

R

VOd

g

s

a

ia

Rc

iL = iC

Diode

Q1

Drive circuit

+

minus



119862 =

119868119901119896

2times 119871


where 119868119901119896

is given by

119868119901119896=119881119894

119871times 119863 times 119905

119904

=8


1


(9)


119862 =052times 66



ESR =Δ1198810

Δ1198680

=005

05= 10mΩ (11)








R1

C

i

i

IL

ILDiode 1

G

G

T

T

Ipv

Ipv

PV

gv

1

1

+

+

+

minus

minus

minus

To workspace 1

2

2

Pulse generator

Search


Change pulsewidth

Connection

Connection


Switch

port

port 1

dutyVpv

Vpv

2120583H





10038161003816100381610038161003816119891 (119909) minus 119891 (119909

1015840)10038161003816100381610038161003816lt 120572

10038161003816100381610038161003816119909 minus 119909101584010038161003816100381610038161003816 forall119909 119909

1015840isin [119897 119906] (12)


119891 (119909) gt 119891 (119886) minus 120572 (119909 minus 119886)

119891 (119909) gt 119891 (119887) + 120572 (119909 minus 119887)

(13)




1199091=(119886 + 119887)

2+(119891 (119886) minus 119891 (119887))

2120572 (14)

f(x)

Slope-120572

f1

a bx1

Slope 120572



by

1198911=(119891 (119886) minus 119891 (119887))

2120572minus 120572 (119887 minus 119886) (15)


1] and [119909

1 119887] elimi-





f(x)

a bx1

(a)

f(x)

a bx1 x2

(b)

f(x)

a bx1 x2 x3

(c)


a bc1

c1c2 c3a1 b3b1 = a2 b2 = a3



119891 (119909) gt 119891 (119888) + 119870 (119909 minus 119888) for 119909 le 119888




2 (17)


f(c)

+ 120576|fmaxmax |f

f

max








I

OP DOP

V

(a)

V

P

POP

P998400OP

VMMP

(b)



119894 119887119894] with



119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891 (119888

119895) +

(119887119894minus 119886119894)

2 forall119894 = 1119898

(18)

119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891min + 120576

1003816100381610038161003816119891min1003816100381610038161003816

(19)


119901



0









0-1198751




Initialization

(1) Determine 119909119897and 119909



1and 119909

2such

that

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)


2(119909119906minus 119909119897)

(20)


Set m = 1

[a1 b1

] = [a b]

c1 = (a1 + b1)2

Evaluate f(c1)

Set fmax = f(c1)



scan



cm+2 = cj + 120590


Update fmax




[aj bj] = [aj + 120590 aj + 2120590]

m = m + 2

Is S empty

Is MPP found


Ct lt 4

Ct lt 4

Ct lt 4


Continueoscillating

around MPP

xu = mpp mpp = xL



xu = mpp mpp = xl

Ct = Ct + 1

Ct = Ct + 1

Ct = Ct + 1

P(mpp ) gt P(xu)

xL = mpp mpp = xu


No

No

No

No

No

No

No

YesYes

Yes

Yes

Yes

Yes

Yes

S = S minus j


GSS xu = mpp + 05



(3) If 119891(1199091) gt 119891(119909


119897 1199091 1199092 and 119909

119906

are updated as

119909119897= 1199092 1199092= 1199091 119909119906= 119909119906

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

(21)

(4) If 119891(1199091) lt 119891(119909


119897 1199091 1199092 and


119909119897= 119909119897 119909119906= 1199091 1199091= 1199092

1199092= 119909119906+radic5 minus 1

2(119909119906minus 119909119897)

(22)




1and 119909





G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1




1015840


6 Results




1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35


1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)






G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Ipv

I

V

T

Rs

Ns

1

1

1++

+minus

+minus 2

2

dividetimes

times

times

times

3

125

015 5

4

Product

Product 2



Divide

Addeu

I0

Im

Vta

q(alowastKlowast )


IpvG

T

1

1 +

+

+

minus

2

2

Ipvn

times

divide

times

times

0065

298

1000

356

Product 1

Product 3

Subtract 1

Divide

Add

dT

Gn

Tn

ki



119881in119881out

=1

1 minus 119863 (6)





Table 1



119871 ge119877 times 119905119904


1198723 (7)




Vocn

1

1

1

+

+

++

+

minus2

Iscn

divide

times

times

timestimes

421 0065

38705

Product 1

Product 3

Product 2


Divide

Add Add 1

euI0

dT

ki

kv

kv1

Vta


VI

RL

Lc p

C

R

VOd

g

s

a

ia

Rc

iL = iC

Diode

Q1

Drive circuit

+

minus



119862 =

119868119901119896

2times 119871


where 119868119901119896

is given by

119868119901119896=119881119894

119871times 119863 times 119905

119904

=8


1


(9)


119862 =052times 66



ESR =Δ1198810

Δ1198680

=005

05= 10mΩ (11)








R1

C

i

i

IL

ILDiode 1

G

G

T

T

Ipv

Ipv

PV

gv

1

1

+

+

+

minus

minus

minus

To workspace 1

2

2

Pulse generator

Search


Change pulsewidth

Connection

Connection


Switch

port

port 1

dutyVpv

Vpv

2120583H





10038161003816100381610038161003816119891 (119909) minus 119891 (119909

1015840)10038161003816100381610038161003816lt 120572

10038161003816100381610038161003816119909 minus 119909101584010038161003816100381610038161003816 forall119909 119909

1015840isin [119897 119906] (12)


119891 (119909) gt 119891 (119886) minus 120572 (119909 minus 119886)

119891 (119909) gt 119891 (119887) + 120572 (119909 minus 119887)

(13)




1199091=(119886 + 119887)

2+(119891 (119886) minus 119891 (119887))

2120572 (14)

f(x)

Slope-120572

f1

a bx1

Slope 120572



by

1198911=(119891 (119886) minus 119891 (119887))

2120572minus 120572 (119887 minus 119886) (15)


1] and [119909

1 119887] elimi-





f(x)

a bx1

(a)

f(x)

a bx1 x2

(b)

f(x)

a bx1 x2 x3

(c)


a bc1

c1c2 c3a1 b3b1 = a2 b2 = a3



119891 (119909) gt 119891 (119888) + 119870 (119909 minus 119888) for 119909 le 119888




2 (17)


f(c)

+ 120576|fmaxmax |f

f

max








I

OP DOP

V

(a)

V

P

POP

P998400OP

VMMP

(b)



119894 119887119894] with



119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891 (119888

119895) +

(119887119894minus 119886119894)

2 forall119894 = 1119898

(18)

119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891min + 120576

1003816100381610038161003816119891min1003816100381610038161003816

(19)


119901



0









0-1198751




Initialization

(1) Determine 119909119897and 119909



1and 119909

2such

that

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)


2(119909119906minus 119909119897)

(20)


Set m = 1

[a1 b1

] = [a b]

c1 = (a1 + b1)2

Evaluate f(c1)

Set fmax = f(c1)



scan



cm+2 = cj + 120590


Update fmax




[aj bj] = [aj + 120590 aj + 2120590]

m = m + 2

Is S empty

Is MPP found


Ct lt 4

Ct lt 4

Ct lt 4


Continueoscillating

around MPP

xu = mpp mpp = xL



xu = mpp mpp = xl

Ct = Ct + 1

Ct = Ct + 1

Ct = Ct + 1

P(mpp ) gt P(xu)

xL = mpp mpp = xu


No

No

No

No

No

No

No

YesYes

Yes

Yes

Yes

Yes

Yes

S = S minus j


GSS xu = mpp + 05



(3) If 119891(1199091) gt 119891(119909


119897 1199091 1199092 and 119909

119906

are updated as

119909119897= 1199092 1199092= 1199091 119909119906= 119909119906

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

(21)

(4) If 119891(1199091) lt 119891(119909


119897 1199091 1199092 and


119909119897= 119909119897 119909119906= 1199091 1199091= 1199092

1199092= 119909119906+radic5 minus 1

2(119909119906minus 119909119897)

(22)




1and 119909





G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1




1015840


6 Results




1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35


1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)






G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Vocn

1

1

1

+

+

++

+

minus2

Iscn

divide

times

times

timestimes

421 0065

38705

Product 1

Product 3

Product 2


Divide

Add Add 1

euI0

dT

ki

kv

kv1

Vta


VI

RL

Lc p

C

R

VOd

g

s

a

ia

Rc

iL = iC

Diode

Q1

Drive circuit

+

minus



119862 =

119868119901119896

2times 119871


where 119868119901119896

is given by

119868119901119896=119881119894

119871times 119863 times 119905

119904

=8


1


(9)


119862 =052times 66



ESR =Δ1198810

Δ1198680

=005

05= 10mΩ (11)








R1

C

i

i

IL

ILDiode 1

G

G

T

T

Ipv

Ipv

PV

gv

1

1

+

+

+

minus

minus

minus

To workspace 1

2

2

Pulse generator

Search


Change pulsewidth

Connection

Connection


Switch

port

port 1

dutyVpv

Vpv

2120583H





10038161003816100381610038161003816119891 (119909) minus 119891 (119909

1015840)10038161003816100381610038161003816lt 120572

10038161003816100381610038161003816119909 minus 119909101584010038161003816100381610038161003816 forall119909 119909

1015840isin [119897 119906] (12)


119891 (119909) gt 119891 (119886) minus 120572 (119909 minus 119886)

119891 (119909) gt 119891 (119887) + 120572 (119909 minus 119887)

(13)




1199091=(119886 + 119887)

2+(119891 (119886) minus 119891 (119887))

2120572 (14)

f(x)

Slope-120572

f1

a bx1

Slope 120572



by

1198911=(119891 (119886) minus 119891 (119887))

2120572minus 120572 (119887 minus 119886) (15)


1] and [119909

1 119887] elimi-





f(x)

a bx1

(a)

f(x)

a bx1 x2

(b)

f(x)

a bx1 x2 x3

(c)


a bc1

c1c2 c3a1 b3b1 = a2 b2 = a3



119891 (119909) gt 119891 (119888) + 119870 (119909 minus 119888) for 119909 le 119888




2 (17)


f(c)

+ 120576|fmaxmax |f

f

max








I

OP DOP

V

(a)

V

P

POP

P998400OP

VMMP

(b)



119894 119887119894] with



119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891 (119888

119895) +

(119887119894minus 119886119894)

2 forall119894 = 1119898

(18)

119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891min + 120576

1003816100381610038161003816119891min1003816100381610038161003816

(19)


119901



0









0-1198751




Initialization

(1) Determine 119909119897and 119909



1and 119909

2such

that

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)


2(119909119906minus 119909119897)

(20)


Set m = 1

[a1 b1

] = [a b]

c1 = (a1 + b1)2

Evaluate f(c1)

Set fmax = f(c1)



scan



cm+2 = cj + 120590


Update fmax




[aj bj] = [aj + 120590 aj + 2120590]

m = m + 2

Is S empty

Is MPP found


Ct lt 4

Ct lt 4

Ct lt 4


Continueoscillating

around MPP

xu = mpp mpp = xL



xu = mpp mpp = xl

Ct = Ct + 1

Ct = Ct + 1

Ct = Ct + 1

P(mpp ) gt P(xu)

xL = mpp mpp = xu


No

No

No

No

No

No

No

YesYes

Yes

Yes

Yes

Yes

Yes

S = S minus j


GSS xu = mpp + 05



(3) If 119891(1199091) gt 119891(119909


119897 1199091 1199092 and 119909

119906

are updated as

119909119897= 1199092 1199092= 1199091 119909119906= 119909119906

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

(21)

(4) If 119891(1199091) lt 119891(119909


119897 1199091 1199092 and


119909119897= 119909119897 119909119906= 1199091 1199091= 1199092

1199092= 119909119906+radic5 minus 1

2(119909119906minus 119909119897)

(22)




1and 119909





G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1




1015840


6 Results




1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35


1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)






G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















R1

C

i

i

IL

ILDiode 1

G

G

T

T

Ipv

Ipv

PV

gv

1

1

+

+

+

minus

minus

minus

To workspace 1

2

2

Pulse generator

Search


Change pulsewidth

Connection

Connection


Switch

port

port 1

dutyVpv

Vpv

2120583H





10038161003816100381610038161003816119891 (119909) minus 119891 (119909

1015840)10038161003816100381610038161003816lt 120572

10038161003816100381610038161003816119909 minus 119909101584010038161003816100381610038161003816 forall119909 119909

1015840isin [119897 119906] (12)


119891 (119909) gt 119891 (119886) minus 120572 (119909 minus 119886)

119891 (119909) gt 119891 (119887) + 120572 (119909 minus 119887)

(13)




1199091=(119886 + 119887)

2+(119891 (119886) minus 119891 (119887))

2120572 (14)

f(x)

Slope-120572

f1

a bx1

Slope 120572



by

1198911=(119891 (119886) minus 119891 (119887))

2120572minus 120572 (119887 minus 119886) (15)


1] and [119909

1 119887] elimi-





f(x)

a bx1

(a)

f(x)

a bx1 x2

(b)

f(x)

a bx1 x2 x3

(c)


a bc1

c1c2 c3a1 b3b1 = a2 b2 = a3



119891 (119909) gt 119891 (119888) + 119870 (119909 minus 119888) for 119909 le 119888




2 (17)


f(c)

+ 120576|fmaxmax |f

f

max








I

OP DOP

V

(a)

V

P

POP

P998400OP

VMMP

(b)



119894 119887119894] with



119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891 (119888

119895) +

(119887119894minus 119886119894)

2 forall119894 = 1119898

(18)

119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891min + 120576

1003816100381610038161003816119891min1003816100381610038161003816

(19)


119901



0









0-1198751




Initialization

(1) Determine 119909119897and 119909



1and 119909

2such

that

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)


2(119909119906minus 119909119897)

(20)


Set m = 1

[a1 b1

] = [a b]

c1 = (a1 + b1)2

Evaluate f(c1)

Set fmax = f(c1)



scan



cm+2 = cj + 120590


Update fmax




[aj bj] = [aj + 120590 aj + 2120590]

m = m + 2

Is S empty

Is MPP found


Ct lt 4

Ct lt 4

Ct lt 4


Continueoscillating

around MPP

xu = mpp mpp = xL



xu = mpp mpp = xl

Ct = Ct + 1

Ct = Ct + 1

Ct = Ct + 1

P(mpp ) gt P(xu)

xL = mpp mpp = xu


No

No

No

No

No

No

No

YesYes

Yes

Yes

Yes

Yes

Yes

S = S minus j


GSS xu = mpp + 05



(3) If 119891(1199091) gt 119891(119909


119897 1199091 1199092 and 119909

119906

are updated as

119909119897= 1199092 1199092= 1199091 119909119906= 119909119906

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

(21)

(4) If 119891(1199091) lt 119891(119909


119897 1199091 1199092 and


119909119897= 119909119897 119909119906= 1199091 1199091= 1199092

1199092= 119909119906+radic5 minus 1

2(119909119906minus 119909119897)

(22)




1and 119909





G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1




1015840


6 Results




1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35


1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)






G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















f(x)

a bx1

(a)

f(x)

a bx1 x2

(b)

f(x)

a bx1 x2 x3

(c)


a bc1

c1c2 c3a1 b3b1 = a2 b2 = a3



119891 (119909) gt 119891 (119888) + 119870 (119909 minus 119888) for 119909 le 119888




2 (17)


f(c)

+ 120576|fmaxmax |f

f

max








I

OP DOP

V

(a)

V

P

POP

P998400OP

VMMP

(b)



119894 119887119894] with



119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891 (119888

119895) +

(119887119894minus 119886119894)

2 forall119894 = 1119898

(18)

119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891min + 120576

1003816100381610038161003816119891min1003816100381610038161003816

(19)


119901



0









0-1198751




Initialization

(1) Determine 119909119897and 119909



1and 119909

2such

that

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)


2(119909119906minus 119909119897)

(20)


Set m = 1

[a1 b1

] = [a b]

c1 = (a1 + b1)2

Evaluate f(c1)

Set fmax = f(c1)



scan



cm+2 = cj + 120590


Update fmax




[aj bj] = [aj + 120590 aj + 2120590]

m = m + 2

Is S empty

Is MPP found


Ct lt 4

Ct lt 4

Ct lt 4


Continueoscillating

around MPP

xu = mpp mpp = xL



xu = mpp mpp = xl

Ct = Ct + 1

Ct = Ct + 1

Ct = Ct + 1

P(mpp ) gt P(xu)

xL = mpp mpp = xu


No

No

No

No

No

No

No

YesYes

Yes

Yes

Yes

Yes

Yes

S = S minus j


GSS xu = mpp + 05



(3) If 119891(1199091) gt 119891(119909


119897 1199091 1199092 and 119909

119906

are updated as

119909119897= 1199092 1199092= 1199091 119909119906= 119909119906

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

(21)

(4) If 119891(1199091) lt 119891(119909


119897 1199091 1199092 and


119909119897= 119909119897 119909119906= 1199091 1199091= 1199092

1199092= 119909119906+radic5 minus 1

2(119909119906minus 119909119897)

(22)




1and 119909





G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1




1015840


6 Results




1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35


1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)






G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















I

OP DOP

V

(a)

V

P

POP

P998400OP

VMMP

(b)



119894 119887119894] with



119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891 (119888

119895) +

(119887119894minus 119886119894)

2 forall119894 = 1119898

(18)

119891 (119888119895) +

(119887119895minus 119886119895)

2ge 119891min + 120576

1003816100381610038161003816119891min1003816100381610038161003816

(19)


119901



0









0-1198751




Initialization

(1) Determine 119909119897and 119909



1and 119909

2such

that

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)


2(119909119906minus 119909119897)

(20)


Set m = 1

[a1 b1

] = [a b]

c1 = (a1 + b1)2

Evaluate f(c1)

Set fmax = f(c1)



scan



cm+2 = cj + 120590


Update fmax




[aj bj] = [aj + 120590 aj + 2120590]

m = m + 2

Is S empty

Is MPP found


Ct lt 4

Ct lt 4

Ct lt 4


Continueoscillating

around MPP

xu = mpp mpp = xL



xu = mpp mpp = xl

Ct = Ct + 1

Ct = Ct + 1

Ct = Ct + 1

P(mpp ) gt P(xu)

xL = mpp mpp = xu


No

No

No

No

No

No

No

YesYes

Yes

Yes

Yes

Yes

Yes

S = S minus j


GSS xu = mpp + 05



(3) If 119891(1199091) gt 119891(119909


119897 1199091 1199092 and 119909

119906

are updated as

119909119897= 1199092 1199092= 1199091 119909119906= 119909119906

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

(21)

(4) If 119891(1199091) lt 119891(119909


119897 1199091 1199092 and


119909119897= 119909119897 119909119906= 1199091 1199091= 1199092

1199092= 119909119906+radic5 minus 1

2(119909119906minus 119909119897)

(22)




1and 119909





G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1




1015840


6 Results




1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35


1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)






G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















Set m = 1

[a1 b1

] = [a b]

c1 = (a1 + b1)2

Evaluate f(c1)

Set fmax = f(c1)



scan



cm+2 = cj + 120590


Update fmax




[aj bj] = [aj + 120590 aj + 2120590]

m = m + 2

Is S empty

Is MPP found


Ct lt 4

Ct lt 4

Ct lt 4


Continueoscillating

around MPP

xu = mpp mpp = xL



xu = mpp mpp = xl

Ct = Ct + 1

Ct = Ct + 1

Ct = Ct + 1

P(mpp ) gt P(xu)

xL = mpp mpp = xu


No

No

No

No

No

No

No

YesYes

Yes

Yes

Yes

Yes

Yes

S = S minus j


GSS xu = mpp + 05



(3) If 119891(1199091) gt 119891(119909


119897 1199091 1199092 and 119909

119906

are updated as

119909119897= 1199092 1199092= 1199091 119909119906= 119909119906

1199091= 119909119897+radic5 minus 1

2(119909119906minus 119909119897)

(21)

(4) If 119891(1199091) lt 119891(119909


119897 1199091 1199092 and


119909119897= 119909119897 119909119906= 1199091 1199091= 1199092

1199092= 119909119906+radic5 minus 1

2(119909119906minus 119909119897)

(22)




1and 119909





G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1




1015840


6 Results




1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35


1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)






G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















G G

TT 1

1

+

minus2

2

Connection

Subsystemport

Connection port 1




1015840


6 Results




1000Wm2 25∘C1000Wm2 60∘C

1000Wm2 40∘C1500Wm2 25∘C

Curr

ent (

A)

Voltage (V)

6

4

2

00 5 10 15 20 25 30 35


1000Wm2 25∘C2000Wm2 25∘C

Pow

er (W

)

120

100

80

60

40

20

00 5 10 15 20 25 30

Voltage (V)






G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















G

T

G

T

Ipv

1

1

2

Out 1

Subsystem


G

T

G

G

G1

G2

T

T

G

T

Ipv

Ipv1

Ipv3

Ipv2

1

1

2

3

4

++

++

Out 1

Out 1Add

Add 1

Subsystem

Subsystem 1

Subsystem 2

Out 1


Pow

er (W

)

00

1

2

3

35

25

15

05

5 10 15 20 25

Voltage (V)


Pow

er (W

)

00

20

40

60

50

30

10

5 10 15 20 25

Voltage (V)



Pow

er (W

)

Time (s)

60

50

40

30

20

10

00 02 04 06 08 1 12 14 16 18


Pow

er (W

)

Time (s)

1008060402000 02 04 06 08 1 12

120




wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of


















wer

(W)

Time (s)

100

50

00 05 1 15 252


Pow

er (W

)

Time (s)

1201008060402000 02 04 06 08 1 212 14 16 18



7 Conclusion




References

















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of
















































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of





















FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of

















Documents

Research Article Efficient Maximum Power Point …downloads.hindawi.com/archive/2014/673840.pdfpower point keeps changing with the irradiance levels and ambient temperature. erefore,