Research Article BICO MPPT: A Faster Maximum Power Point ...downloads.hindawi.com/journals/ijp/2014/586503.pdf · power point Array current, Irradiance I Terminal voltage, V F : -

Research ArticleBICO MPPT A Faster Maximum Power Point Tracker andIts Application for Photovoltaic Panels

Hadi Malek1 and YangQuan Chen2

1 Electrical amp Computer Engineering Department Utah State University Logan UT 84321 USA2MESA Lab School of Engineering University of CA Merced California 95343 USA

Correspondence should be addressed to Hadi Malek hadimalekaggiemailusuedu

Received 29 May 2013 Accepted 3 January 2014 Published 27 February 2014

Academic Editor Ismail H Altas

Copyright copy 2014 H Malek and Y Chen This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper develops a maximum power point tracking (MPPT) algorithm to optimize photovoltaic (PV) array performance andmake it more compatible to rapidly varying weather conditions In particular a novel extremum seeking controller (ESC) whichuses a Bode ideal cutoff (BICO) filter in its structure is designed and tested on a simulated PV arrayThe new algorithm is comparedagainst the commonly used ESCMPPT algorithmwith first-order filtersThe BICO extremum seeking controller achieves transientrise to the MPP faster than the common extremum seeking MPPT which is the faster and more robust method among all othermethodsThis claim has been discussed and proved mathematically in this paper in addition to simulation illustrationsThis fasterextremum seeking algorithm enables PV systems to detect rapid variations in the environmental conditions like irradiation andtemperature changes

1 Introduction

The PV cells exhibit a nonlinear119881-119868 characteristics as shownin Figure 1 and their power output mainly depends on thenature of the connected load Since connecting the loaddirectly to the PV system results in a poor overall efficiency tominimize the life cycle cost of any PV system increasing theefficiency by changing the operating point of the systemusingan intermediate maximum power point tracker (MPPT) isdesirable

MPPT controls the output current and voltage andconsequently output power of the PV panel adaptively tomaintain maximum efficiency and better performance inthe presence of environmental variations Typically MPPTalgorithms are implemented on a solar array using a switchingpower converter for instance in a grid-tied inverter the solararray charges a capacitor and then the current is switched outof the capacitor at an optimal varying duty cycle in order toextract maximum power from the PV array

A number of solar power converter architectures withMPPT are discussed in the literature [1 2] As discussed inthese works convergence speed is one of the most important

features among all different MPPT algorithms Brunton et alhave pointed out in their paper that ldquoas irradiance decreasesrapidly the IV curve shrinks and theMPV andMPI decreaseIf theMPPT algorithmdoes not track fast enough the controlcurrent or voltage will fall off the IV curverdquo [3] Consequentlyany improvement in the rise time of MPPT improves thereliability of the system and increases the power extractionand efficiency of the whole system

11 Maximum Power Point Tracking Algorithms There aremany different maximum power point tracking techniquesfor photovoltaic systems which are well established in theliterature [4ndash11] These techniques vary in many aspects assimplicity convergence speed digital or analogical imple-mentation sensors required cost range of effectiveness andother aspects In analog world short current (SC) openvoltage (OV) and CV are good options for MPPT otherwisewith digital circuits that require the use of microcontrollerPerturb and Observe (PampO) Incremental Conductance (IC)and temperature methods are easy to implement [12] Table 1and Figure 2 present the comparison among different MPPT

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2014 Article ID 586503 9 pageshttpdxdoiorg1011552014586503

2 International Journal of Photoenergy

Maximumpowerpoint

Irra

dian

ce

Arr

ay cu

rren

tI

Terminal voltage V

Figure 1 119868-119881 curves at various solar irradiances [3]

Ener

gy g

ener

ated

()

100

90

80

Low Medium High

P and Ob

P and Oa ICa

ICb

OV

TP

TGSC

P and Oc

CV

Cost

Figure 2 Comparison of the MPPT methods [12]

methods considering the costs of sensors microcontrollerand additional power components and also their efficienciesIn this table A means absence L means low M meansmedium and H means high

Currently the most popular and workhorse MPPT algo-rithm is PampO because of its balance between performanceand simplicity However it suffers from the lack of speedand adaptability which is necessary for tracking the fast tran-sients under varying environmental conditions [3] Recentlyanother adaptive algorithm called extremum seeking con-trol has been developed [13] to overcome these weaknesses

12 Extremum Seeking Control A promising new robustMPPT algorithm is the method of extremum seeking (ES)control which carries all PampOrsquos benefits like simplicity andperformance and in addition improves its weaknesses [3]Figures 3 and 4 present the comparison between ESC andPampO where the inverter controls the current and voltage

60005000400030002000

0 500 1000 1500

Pow

er (W

)

Time (s)

60005000400030002000

0 500 1000 1500

Pow

er (W

)

Time (s)

(a)

Curr

ent (

A) 15

10

50 500 1000 1500

Time (s)

(b)

MPPES

PO

400

350

300

Volta

ge (V

)

0 500 1000 1500

Time (s)

(c)

Figure 3 Comparison of current controlled PampO and ESC MPPTcontroller [3]

60005000400030002000

0 500 1000 1500

Pow

er (W

)

Time (s)

(a)

Curr

ent (

A)

15

10

50 500 1000 1500

Time (s)

(b)

MPPES

PO

400

350

300

Volta

ge (V

)

0 500 1000 1500

Time (s)

(c)

Figure 4 Comparison of voltage controlled PampO and ESC MPPTcontroller [3]

International Journal of Photoenergy 3

Table 1 MPPT methods comparison [12]

MPPT algorithm Additional components Sensors Micro-Controller TotalCV A L AL LSC H M AL MOV H LM AL LMP and Oa A M L LMP and Ob A M L LMP and Oc A M M MIC A M M MTG A MH M MHTP A H MH H

according to the set-points which are provided by these twoMPPT algorithms

The power current and voltage are plotted versus timefor the ESC and PampO algorithms as well as the truemaximumpower of the system

PampO and ESC methods oscillate closely around the realmaximum power voltage as seen in the power versus timeplot Obviously the ESC method rises to the MPP orders ofmagnitude more rapidly than the PampO

ESC MPPT has some advantages from hardware imple-mentation point of view Brunton et al have mentioned intheir paper that ldquothe ripple-based ES algorithm has goodMPPT performance over a range of inverter capacitor sizesTypically the choice of capacitor is expensive because it mustbe well characterized and large enough to maintain a smallripple However because the ES control signal exploits thenatural inverter ripple a smaller capacitor allows the trackingof rapid irradiance changesrdquo

ESC for peak power point tracking method has beensuccessfully applied to biochemical reactors [14 15] ABScontrol in automotive brakes [16] variable cam timing engineoperation [17] electromechanical valves [18] axial compres-sors [19] mobile robots [20] mobile sensor networks [21 22]optical fibre amplifiers [23] and so on A good survey of theliterature on this topic prior to 1980 can be found in [24]and a more recent overview can be found in [25] Astromand Wittenmark rated extremum seeking as one of the mostpromising adaptive control methods [26]

Since extremum seeking control has better features andperformance compare to PampO which is the best knownMPPT algorithm in this paper the improvement of betterthan the best MPPT algorithm has been investigated

2 Basic Regular Extremum Seeking Algorithm

As shown in Figure 5 ESC algorithm employs a slow periodicperturbation sin(120596119905) which is added to the estimated signal120579 If the perturbation is slow enough the plant appears as astatic map 119910 = 119891(120579) and its dynamics do not interfere withthe peak seeking scheme [13] If 120579 is on either side of 120579lowast whichis the optimal point the perturbation signal 119886 sin(120596119905) willcreate a periodic response of 119910 which is either in phase orout of phase with 119886 sin(120596119905)The high-pass filter eliminates theldquoDC componentrdquo of 119910Thus 119886 sin(120596119905) and high-pass filter will

Non linear map

Lawpassfilter

Highpassfilter

120574

s

120594

120579

sin(120596t)120596t)

J

y = f(120579)

asin(

120592

Figure 5 Extremum seeking algorithm scheme

be approximately two sinusoids which are in phase if 120579 lt 120579lowast

or out of phase if 120579 gt 120579lowast

The integrator 120579 = (120574119904)120594 approximates the gradientupdate law

120579 = 119896(1198862

2)(119891)1015840

(120579) which tunes 120579 to 120579lowast [13]

System of Figure 5 can be summarized in mathematicalequations as follows

119910 = 119891 (120579 + 119886 sin (120596119905))

120579 = minus120574120594

120594 = 120592 lowast Lminus1

HLPF (119904)

120592 = [119910 lowast Lminus1

HHPF (119904)] sin (120596119905)

(1)

where lowast is the convolution operator and Lminus1 is the inverseLaplace transform operator The transfer functions for HHPFand HLPF in the regular SISO ESC scheme are 119904(119904 + 120596

ℎ) and

120596119897(119904 + 120596

119897) respectively where 120596

119897lt 120596 lt 120596

ℎ[25] This model

will be used for stability analysis in this paperIn the following sections after introducing BICO filter

[27 28] the advantages of using this filter in the ESCalgorithm from the stability and robustness point of view willbe discussed

3 BICO Extremum Seeking Control MPPT

In this section we are going to introduce a filter which wasstrongly favored by Bode [29] called Bodersquos ideal cutoff


minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

10

Gai

n (d

B)

Frequency (rads)

HP BICO filter gain HP filter gain

0

10minus1 100 101 102

Figure 6 High-pass BICO and regular high-pass filters

characteristic (BICO) filter [27 28] The general transferfunction of low-pass BICO filter is

119866LP-BICO (119904) =119896

(119904120596119888+ radic1 + (119904120596

119888)2

)

119903 119903 isin R

+

(2)

Its corresponding time response in the special case (120596119888=

1 rads) was derived byOberhettinger and Baddi [30] but thetime response of (2) is presented as

119892BICOLP(119905) = 119896

119903119869119903(120596119888119905)

120596119888119905

(3)

where 119869119903is the 119903th order Bessel function

By replacing 119904 by 1119904 high-pass BICO filter is obtainedFigure 6 compares the frequency response of high-pass BICOfilter and regular high-pass filter (119904(119904 + 120596

119888)) with the same

cutoff frequency of 120596119888= 10 rads

As seen in this figure BICO filter has a sharp edgein its cutoff frequency This great feature causes almostno attenuation for frequencies higher than 120596

119888and a large

attenuation in the lower frequencies Therefore the behaviorof this filter is close to an ldquoidealrdquo filter This sharp edgepresents in the low-pass BICO filter By combining high-passand low-pass BICO filters the band-pass BICO filter withsharp edges in both sides can be obtained as well

4 Stability Analysis of ExtremumSeeking Control

41 Mathematical Modeling of ESC Scheme The stabilityanalysis of ESC algorithmhas been investigated in [13 31ndash34]In these literatures traditional extremum seeking control withregular first-order filters has been considered In this paperwe have considered the similar stability analysis approach as[34] to compare the stability and robustness of BICO-ESC

and regular SISO ESC The difference between this work and[34] is that in this paper the stability analysis has been doneby considering both low-pass and high-pass filters in the ESCstructure but in [34] authors have investigated the stability ofsimplified ESC with only low-pass filter in its structure

According to the previous discussion the nonlinear mapin the ESC scheme is considered to be concave and is assumedto have only one extremum point Since in the PV systemapplicationsMPPT is employed to extractmaximumamountof power from PV panels therefore extremum point in thiscase is maximum point (120579lowast) where at this point 120597119891(120579lowast)120597120579 =0 and also 1205972119891(120579lowast)1205971205792 lt 0 In ESC algorithm the output ofthe nonlinear map is

119910 = 119891 (120579 + 119886 sin (120596119905)) (4)

where 119886 and 120596 are the amplitude and angular frequency ofperturbation signal Since the perturbation signal assumes tobe small therefore the Taylor expansion of (4) is

119910 = 119891 (120579) +

119889119891 (120579)

119889120579

119886 sin (120596119905) +HOT (5)

where HOT stands for higher order terms and 120579 is theapproximation of 120579lowast The high-pass filtered signal will be

119869 ≃ Lminus1

119904

119904 + 120596ℎ

lowast 119891 (120579)

+ Lminus1

119904

119904 + 120596ℎ

lowast

119889119891 (120579)

119889120579

119886 sin (120596119905)

(6)

High-pass filter acts as a derivative opereator in serieswith a low-pass filter (119904(1(119904 + 120596

ℎ))) By multiplying the

modulation signal to the resulted signal from the high-passfilter and passing the modulated signal through the low-passfilter and since 120596

119897lt 120596ℎ the output signal of integrator will be

120579 ≃119886120574

2Lminus1

1

119904 lowast L

minus1

120596119897

119904 + 120596119897

lowast 119889

119889119905(

119889119891 (120579)

119889120579

)

(7)

Under the assumptions that the amplitude of the sinu-soidal perturbation is small and the harmonics of high-passfilter are attenuated by low-pass filter output of low-pass filteris proportional to the gradient of the nonlinear map withrespect to its input and time Therefore in the neighborhoodof the extremum point the amplitude of the estimated signalis small since the gradient is small It can be seen that thisamplitude depends on 120574 and 119886

42 Stability Analysis of Averaged ESC Scheme Theaveragingmethod is typically used to analyze the periodic steady statesolutions of weakly nonlinear systems Since the amplitude ofperturbation in the ESC scheme is small this system can be


evaluated by its averaged model The averaged form of signal119909(119905) is

119909 (119905) =1

119879int

119879

0

119909 (119905) 119889119905 (8)

where 119879 = 2120587120596 Therefore the averaged model of ESCscheme is

120579 = 120579

119910 = 119891(120579) = 119891(120579) = 119891 (120579)

120579 =120574119886

2

119889

119889119905(

119889119891 (120579)

119889120579

) lowast Lminus1

HLPF lowast Lminus1

1

119904

(9)

On the other hand in the neighborhood of the extremumpoint 119910(119905) can be approximated as

119910 ≃ 119891 (120579lowast

) +119889119891 (120579)

119889120579

10038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)

+1

2

1198892

119891 (120579)

119889120579

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)2

(10)

If the difference between the extremum point and aver-aged point is defined by 120579 = 120579minus120579

lowast and since 119889119891(120579)119889120579|120579=120579lowast =

0 thus

119910 ≃1

2

1198892

119891(120579)

1198891205792

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast1205792

(11)

By defining (12)(1198892

119891(120579)1198891205792

)|120579=120579lowast = 119870 then

(119889119891(120579)119889120579)|120579=120579lowast = 2119870120579 Therefore (119889119889119905)(119889119891(120579)119889120579)|

120579=120579lowast =

2(119889119870119889119905)120579lowast Substituting this relationship in (9) gives

120579 = (120574119886120579lowast119889119870

119889119905) lowast L

minus1

HLPF lowast Lminus1

1

119904 (12)

Without loss of generality and by assuming that 119889119870119889119905is the output signal from a high-pass filter H

119867119875119865 which its

cutoff frequency is higher than cutoff frequency of the low-pass filter H

119871119875119865 then (12) can be rewritten as

120579 = (120574119886120579lowast

119870)Lminus1

HHPF lowast Lminus1

HLPF lowast Lminus1

1

119904 (13)

This system can be considered as a feedback systemas shown in Figure 7 which 119870 can be considered as aperturbation The loop gain of this system depends on thedemodulation gain 119886 the integral gain 120574 and the curvatureof nonlinear map119870 This result completely matches with theresults obtained from other analysis method in the simplifiedcase [13 31ndash33]

K120574a

1

sHLP (s) HHP(s)

Figure 7 Averaged BICO-ESC scheme

5 Analysis of ESC MPPT on PV Panels

51 PV Cell Model The PV cell 119881-119868 curve V = 119891(119894 119866) ismodeled using the light emitting diode equations [3]

119868 = 119868119871minus 119868OS (exp(

119902

119860119896119861119879) (119881 + 119877119868) minus 1)

119868OS = 119868OR (119879

119879119877

) exp(119902119864119866

119860119896119861

(1

119879119877

minus1

119877))

119868119871=

119866

1000(119868SC + 119870119879119868 (119879 minus 119879

119877))

119881 =119860119896119861119879

119902ln(119868119871 minus 119868

119868OS+ 1) minus 119877119868

(14)

Values and definitions for further simulations are shownin Table 2

52 BICO ESC vsersus Regular SISO ESC In order tocompare the qualitative behavior of BICO MPPT with theregular SISO ESC MPPT the Root-Locus (RL) analysis hasbeen chosen Clearly other stability analysis methods areapplicable at this point

Since Root-Locus (RL) method is serving for linearsystems it is important to point out that the curvatureconstant 119870 is an uncertain parameter which depends ondifferent factors like the PV panel manufacturer and weatherconditions According to [33] 119870 isin [minus05 minus5]

As seen in Figure 7 the characteristic polynomial ofaveraged ESC system is 1 + 119886120574119870HHPFHLPF and to analyzethe behavior of this system Root-Locus (RL) analysismethodcan be employed Since there is no command in MATLABto plot Root-Locus (RL) for BICO transfer function thisequation has been solved for different 119886120574 and the roots havebeen plotted To compare the behavior of regular SISO ESCwith BICO ESC the roots for this system has been plottedwith the same method instead of using ldquorlocusrdquo command

Figure 8 shows the comparison between the root locusof averaged ESC using BICO and regular first-order filtersIn this root locus plot the constant gain is assumed to be119886120574120579lowast

= 1 and cutoff frequencies in both filters are assumedto be 120596

119888= 10 rads Clearly by using first-order filters in

the averaged ESC scheme for some values of 119870 system hascomplex poles which cause an oscillatory behavior in theresponse of the system On the other side by using BICOfilters roots of the characteristic polynomial (system poles)are always real numbers for any value of119870


Table 2 Values of the considered PV model [3]

119879119877

298 Reference temperature119868OR 225119890 minus 6 Reverse saturation curent at 119879 = 119879

119877

119868SC 32 Short circuit current119864119866

138119890 minus 19 Silicon band gap119860 16 Ideality factor119896119861

138119890 minus 23 Boltzmanrsquos constant119902 16119890 minus 19 Electron charge119877 001 Resistance119870119879119868

08 119868SC Temperature coefficient

0

0

1

2

3

4

Real

Imag

e 0

0

2

BICO ESCo Regular ESC

minus1

minus2

minus2

minus3

minus4

minus4

minus350 minus300 minus250 minus200 minus150 minus100 minus50

minus10minus20

Figure 8 Root locus of the averaged BICO and the regular first-order low-pass filters

Besides the location of the poles as can be seen in thisfigure for the same value of 119870 BICO filter has farther poleswith respect to the origin compared to the first-order filtercase Therefore the bandwidth of BICO filter is higher thanthe first-order filter with similar cutoff frequency Higherbandwidth means faster response for BICO ESCThis featureis justifiable by looking at the frequency response of bothfilters Since the bandwidth of BICO is close to the bandwidthof an ideal filter BICO ESC becomes the fastest achievableMPPT algorithm

6 Simulation Illustrations

Figures 9 and 10 show the maximum power point of aPV panel with the defined parameters in Table 2 As canbe seen in these figures environmental conditions andespecially variations in the sun irradiation will change thenonlinear behavior of PV panels Shadows cloudy or dustyweather and temperature variations cause moving of optimaloperating point in PV systems When temperature increasesthe maximum output power of PV panels decreases and vice

0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

= 30∘C= 25∘C

= 20∘CTT

T

Figure 9 119875-119881 chart of considered PV model for different tempera-tures (irradiation = 1000Wm2)

versa In Figure 9 the variations of optimal operating point bychanging the environmental temperature from 20∘C to 30∘Care illustrated As Figure 10 presents variation of peak outputpower happens in the wider range when sun irradiationchanges Generally in PV panels when sun irradiationincreases the output power increases but when temperatureincreases the maximum extractable power reduces

To compare the proposed MPPT method which is calledBICO MPPT with the ESC MPPT the working conditionsof both algorithms have been defined to be same Forall simulations the ambient temperature is 25∘C and theirradiation is assumed to be 1000Wm2 Also the cutofffrequency of high-pass filters is 120596

ℎ= 100 rads and for

low-pass filter this frequency is 120596119897

= 50 rads Underthese conditions from Figure 9 the maximum amount ofpower which can be extracted from the simulated PV panelis 48 Watts and this maximum happens around 17 VoltsTo implement the BICO MPPT the discrete approxima-tion of this filter in MathWorks Incrsquos website has beenused

Figure 11 shows the outputs of extremum seeking algo-rithms resulted from two different MPPTmethods Figure 12


0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

G = 1100Wm2

G = 1000Wm2G = 900Wm2

Figure 10 119875-119881 chart of considered PV model for different irradia-tions (temperature = 25∘C)

0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT

Figure 11 Comparison of power tracking in BICOMPPT and ESCMPPT

represents the maximum voltage tracking in BICO MPPTalgorithm and ESC with first-order filters As expected andproved before BICO MPPT converges to the peak powerpoint two times faster than the regular ESCMPPT algorithmFaster convergence speed is due to the higher bandwidth ofthe averaged BICO system

Figures 13 and 14 show the performance of the proposedMPPT approach compare to the ESC in the presence of whitenoise As can be seen in these figures in the presences ofa white noise (noise power = 004) which is consideredas the variations in the nonlinear map behavior 119870 BICO

0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Volta

ge (V

) and

curr

ent (

A)

ESC voltageBICO voltage

Figure 12 Comparison of voltage tracking in BICOMPPT and ESCMPPT

0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT

Figure 13 Performance of BICO MPPT and ESC MPPT in thepresence of a white noise with noise power 004

MPPTpreforms better than ESCMPPT from attenuation andtracking point of view

Another parameter which is considered in these simula-tions is the robustness of these two methods to the variationsof the system gain Figures 15(a) and 15(b) illustrate theperformance of BICO MPPT and regular ESC MPPT to thegain variations respectively From these figures it can beconcluded that BICOMPPT tolerates higher gain variationsbut by increasing the gain of the integrator in ESC MPPT itstarts oscillating


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Volta

ge (V

) and

curr

ent (

A)


Figure 14 Voltage tracking of BICO MPPT and ESC MPPT in thepresence of a white noise with noise power 004

7 Conclusions

The ubiquity of usingMPPT in the renewable energy systemshas stimulated the persistent development of various MPPTalgorithms According to the comparison in this paper oneof the most popular methods of maximum power trackingmethod is the PampO method However this method fails inthose situations when there is a need to track the MPPsrapidly

ESC is a new robust MPPT algorithm which carries allPampOrsquos benefits and improves its weaknesses In this paper anovel ES algorithm has been presented which is called BICOMPPTThis algorithm employs BICO filter in its structure toimprove the ESC rise time response even further BICO filteris a forgotten part of Bodersquos research that for the first time inthis paper was used for PV applications

BICO filter is the closest filter to the ideal filter andthis feature of BICO improves the performance of ESCalgorithm Also the advantages of BICO has been discussedin this paper As discussed in this paper using BICO in theESC structure increases the bandwidth of the system whichimproves the system response

In addition applying BICO filter to the ESC algorithmmoves all the roots of characteristic polynomial of averagedBICO ESC system to the real axis Consequently this systemhas no pole with imaginary part and therefore theoreticallythe system has no oscillatory response by increasing itsintegrator gain These poles however can have imaginarypart by increasing the gain of the system in the regular ESCThis feature increases the robustness of the BICO MPPTcompared to regular ESC

As can be seen in the results BICO MPPT not only canfollow themaximumpower point faster than regular ESC butalso it shows more robustness in the presence of disturbancein the system or gain variations

0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30Gain = 55

Gain = 75

Gain = 95

(a)

0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30

Gain = 55

Gain = 75

(b)

Figure 15 Sensitivity of BICO MPPT and ESC MPPT to the gainvariation of integrator

Conflict of Interests

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

References

[1] B Bose P Szczesny and R Steigerwald ldquoMicrocomputer con-trol of a residential photovoltaic power conditioning systemrdquoIEEE Transactions on Industry Applications vol 21 no 5 pp1182ndash11191 1985

[2] R A Mastromauro M Liserre T Kerekes and A DellrsquoAquilaldquoA single-phase voltage-controlled grid-connected photovoltaicsystem with power quality conditioner functionalityrdquo IEEE


Transactions on Industrial Electronics vol 56 no 11 pp 4436ndash4444 2009

[3] S L Brunton C W Rowley S R Kulkarni and C ClarksonldquoMaximum power point tracking for photovoltaic optimizationusing ripple-based extremum seeking controlrdquo IEEE Transac-tions on Power Electronics vol 25 no 10 pp 2531ndash2540 2010

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

[5] J JNedumgatt K B Jayakrishnan SUmashankarDVijayaku-mar and D P Kothari ldquoPerturb and observe MPPT algorithmfor solar PV systems-modeling and simulationrdquo in Proceedingsof the Annual IEEE India Conference Engineering SustainableSolutions (INDICON rsquo11) pp 1ndash6 December 2011

[6] R Alonso P Ibanez V Martınez E Roman and A Sanz ldquoAninnovative perturb observe and check algorithm for partiallyshaded PV systemsrdquo in Proceedings of the 13th European Con-ference on Power Electronics and Applications (EPE rsquo09) pp 1ndash8September 2009

[7] N Femia G Petrone G Spagnuolo and M Vitelli ldquoOptimiza-tion of perturb and observe maximum power point trackingmethodrdquo IEEE Transactions on Power Electronics vol 20 no4 pp 963ndash973 2005

[8] G J Kish J J Lee and P W Lehn ldquoModelling and controlof photovoltaic panels utilising the incremental conductancemethod for maximum power point trackingrdquo IET RenewablePower Generation vol 6 no 4 pp 259ndash266

[9] 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

[10] H Malek S Dadras Y Q Chen R Burt and J Cook ldquoMaxi-mum power point tracking techniques for efficient photovoltaicmicrosatellite power supply systemrdquo in Proceeding of the SmallSatellite Conference Logan Utah USA 2012

[11] H Malek S Dadras and Y Q Chen ldquoA fractional order max-imum power point tracker Stability analysis and experimentsrdquoin Proceeding of the IEEE 51st Annual Conference on DecisionandControl (CDC rsquo12) pp 6861ndash6866MauiHawaii USA 2012

[12] R Faranda and S Leva ldquoEnergy comparison of MPPT tech-niques for PV systemsrdquoWSEAS Transactions on Power Systemsvol 3 no 6 pp 1ndash6 2008

[13] M Krstic and H-H Wang ldquoStability of extremum seekingfeedback for general nonlinear dynamic systemsrdquo Automaticavol 36 no 4 pp 595ndash601 2000

[14] M Guay D Dochain and M Perrier ldquoAdaptive extremumseeking control of continuous stirred tank bioreactors withunknown growth kineticsrdquo Automatica vol 40 no 5 pp 881ndash888 2004

[15] G Bastin D Nesic Y Tan and I Mareels ldquoOn extremumseeking in bioprocesses with multivalued cost functionsrdquoBiotechnology Progress vol 25 no 3 pp 683ndash689 2009

[16] S Drakunov U Ozguner P Dix and B Ashrafi ldquoABS controlusing optimum search via sliding modesrdquo IEEE Transactions onControl Systems Technology vol 3 no 1 pp 79ndash85 1995

[17] D Popovic M Jankovic S Magner and A Teel ldquoExtremumseekingmethods for optimization of variable cam timing engineoperationrdquo in Proceeding of the American Control Conferencepp 3136ndash3141 Denver Colo USA June 2003

[18] K S Peterson and A G Stefanopoulou ldquoExtremum seekingcontrol for soft landing of an electromechanical valve actuatorrdquoAutomatica vol 40 no 6 pp 1063ndash1069 2004

[19] H-H Wang S Yeung and M Krstic ldquoExperimental applica-tion of extremum seeking on an axial-flow compressorrdquo IEEETransactions on Control Systems Technology vol 8 no 2 pp300ndash309 2000

[20] C G Mayhew R G Sanfelice and A R Teel ldquoRobustsource-seeking hybrid controllers for autonomous vehiclesrdquo inProceedings of the American Control Conference (ACC rsquo07) pp1185ndash1190 New York NY USA July 2007

[21] E Biyik and M Arcak ldquoGradient climbing in formation viaextremum seeking and passivity-based coordination rulesrdquo inProceedings of the 46th IEEEConference onDecision and Control(CDC rsquo07) pp 3133ndash3138 New Orleans La USA December2007

[22] P Ogren E Fiorelli and N E Leonard ldquoCooperative controlof mobile sensor networks adaptive gradient climbing ina distributed environmentrdquo IEEE Transactions on AutomaticControl vol 49 no 8 pp 1292ndash1302 2004

[23] P M Dower P M Farrell and D Nesic ldquoExtremum seekingcontrol of cascaded Raman optical amplifiersrdquo IEEE Transac-tions on Control Systems Technology vol 16 no 3 pp 396ndash4072008

[24] J Sternby ldquoExtremum control systems an area for adaptivecontrolrdquo in Proceedings of the International Symposium onAdaptive Systems vol 24 pp 151ndash160 San Francisco Calif USA1980

[25] K B Ariyur and M Krstic Real-Time Optimization byExtremum-Seeking Control Wiley-Interscience 2003

[26] K J Astrom and B Wittenmark Adaptive Control Addison-Wesley 2nd edition 1995

[27] Y Luo T Zhang B Lee C Kang and Y Q Chen ldquoDisturbanceobserver designwith bodersquos ideal cut-offfilter in hard-disc-driveservo systemrdquoMechatronics vol 23 no 7 pp 856ndash862 2013

[28] L E Olivier I K Craig and Y Q Chen ldquoFractional orderand BICO disturbance observers for a run-of-mine ore millingcircuitrdquo Journal of Process Control vol 22 no 1 pp 3ndash10 2012

[29] T T Hartley and C F Lorenzo ldquoOptimal fractional-orderdampingrdquo in Proceedings of the ASME Design EngineeringTechnical Conferences and Computers and Information in Engi-neering Conference pp 737ndash743 Chicago Ill USA September2003

[30] Oberhettinger and Baddi Tables of Laplace TransformsSpringer Berlin Germany 1973

[31] Y Tan D Nesic and I Mareels ldquoOn stability properties of asimple extremum seeking schemerdquo in Proceedings of the 45thIEEE Conference on Decision and Control (CDC rsquo06) pp 2807ndash2812 December 2006

[32] Y Tan D Nesic and I Mareels ldquoOn non-local stabilityproperties of extremum seeking controlrdquo Automatica vol 42no 6 pp 889ndash903 2006

[33] R Leyva C Olalla H Zazo et al ldquoMppt based on sinusoidalextremum-seeking control in pv generationrdquo International Jour-nal of Photoenergy vol 98 no 4 pp 529ndash542 2011

[34] R Leyva P Artillan C Cabal B Estibals and C AlonsoldquoDynamic performance of maximum power point trackingcircuits using sinusoidal extremum seeking control for photo-voltaic generationrdquo International Journal of Electronics vol 98no 4 pp 529ndash542 2011

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


Maximumpowerpoint

Irra

dian

ce

Arr

ay cu

rren

tI

Terminal voltage V

Figure 1 119868-119881 curves at various solar irradiances [3]

Ener

gy g

ener

ated

()

100

90

80

Low Medium High

P and Ob

P and Oa ICa

ICb

OV

TP

TGSC

P and Oc

CV

Cost

Figure 2 Comparison of the MPPT methods [12]

methods considering the costs of sensors microcontrollerand additional power components and also their efficienciesIn this table A means absence L means low M meansmedium and H means high

Currently the most popular and workhorse MPPT algo-rithm is PampO because of its balance between performanceand simplicity However it suffers from the lack of speedand adaptability which is necessary for tracking the fast tran-sients under varying environmental conditions [3] Recentlyanother adaptive algorithm called extremum seeking con-trol has been developed [13] to overcome these weaknesses

12 Extremum Seeking Control A promising new robustMPPT algorithm is the method of extremum seeking (ES)control which carries all PampOrsquos benefits like simplicity andperformance and in addition improves its weaknesses [3]Figures 3 and 4 present the comparison between ESC andPampO where the inverter controls the current and voltage

60005000400030002000

0 500 1000 1500

Pow

er (W

)

Time (s)

60005000400030002000

0 500 1000 1500

Pow

er (W

)

Time (s)

(a)

Curr

ent (

A) 15

10

50 500 1000 1500

Time (s)

(b)

MPPES

PO

400

350

300

Volta

ge (V

)

0 500 1000 1500

Time (s)

(c)

Figure 3 Comparison of current controlled PampO and ESC MPPTcontroller [3]

60005000400030002000

0 500 1000 1500

Pow

er (W

)

Time (s)

(a)

Curr

ent (

A)

15

10

50 500 1000 1500

Time (s)

(b)

MPPES

PO

400

350

300

Volta

ge (V

)

0 500 1000 1500

Time (s)

(c)

Figure 4 Comparison of voltage controlled PampO and ESC MPPTcontroller [3]












Non linear map

Lawpassfilter

Highpassfilter

120574

s

120594

120579

sin(120596t)120596t)

J

y = f(120579)

asin(

120592





120579 = 119896(1198862

2)(119891)1015840



119910 = 119891 (120579 + 119886 sin (120596119905))

120579 = minus120574120594


HLPF (119904)

120592 = [119910 lowast Lminus1

HHPF (119904)] sin (120596119905)

(1)


ℎ) and

120596119897(119904 + 120596


119897lt 120596 lt 120596

ℎ[25] This model






minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

10

Gai

n (d

B)

Frequency (rads)


0

10minus1 100 101 102



119866LP-BICO (119904) =119896

(119904120596119888+ radic1 + (119904120596

119888)2

)

119903 119903 isin R

+

(2)



119892BICOLP(119905) = 119896

119903119869119903(120596119888119905)

120596119888119905

(3)






119888and a large






119910 = 119891 (120579 + 119886 sin (120596119905)) (4)


119910 = 119891 (120579) +

119889119891 (120579)

119889120579

119886 sin (120596119905) +HOT (5)


119869 ≃ Lminus1

119904

119904 + 120596ℎ

lowast 119891 (120579)

+ Lminus1

119904

119904 + 120596ℎ

lowast

119889119891 (120579)

119889120579

119886 sin (120596119905)

(6)





120579 ≃119886120574

2Lminus1

1

119904 lowast L

minus1

120596119897

119904 + 120596119897

lowast 119889

119889119905(

119889119891 (120579)

119889120579

)

(7)





119909 (119905) =1

119879int

119879

0

119909 (119905) 119889119905 (8)


120579 = 120579

119910 = 119891(120579) = 119891(120579) = 119891 (120579)

120579 =120574119886

2

119889

119889119905(

119889119891 (120579)

119889120579

) lowast Lminus1

HLPF lowast Lminus1

1

119904

(9)


119910 ≃ 119891 (120579lowast

) +119889119891 (120579)

119889120579

10038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)

+1

2

1198892

119891 (120579)

119889120579

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)2

(10)



0 thus

119910 ≃1

2

1198892

119891(120579)

1198891205792

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast1205792

(11)


119891(120579)1198891205792

)|120579=120579lowast = 119870 then


120579=120579lowast =


120579 = (120574119886120579lowast119889119870

119889119905) lowast L

minus1

HLPF lowast Lminus1

1

119904 (12)


119867119875119865 which its



120579 = (120574119886120579lowast

119870)Lminus1

HHPF lowast Lminus1

HLPF lowast Lminus1

1

119904 (13)


K120574a

1

sHLP (s) HHP(s)




119868 = 119868119871minus 119868OS (exp(

119902

119860119896119861119879) (119881 + 119877119868) minus 1)

119868OS = 119868OR (119879

119879119877

) exp(119902119864119866

119860119896119861

(1

119879119877

minus1

119877))

119868119871=

119866

1000(119868SC + 119870119879119868 (119879 minus 119879

119877))

119881 =119860119896119861119879

119902ln(119868119871 minus 119868

119868OS+ 1) minus 119877119868

(14)











119879119877


119877





0

0

1

2

3

4

Real

Imag

e 0

0

2


minus1

minus2

minus2

minus3

minus4

minus4


minus10minus20





0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

= 30∘C= 25∘C

= 20∘CTT

T









0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

G = 1100Wm2

G = 1000Wm2G = 900Wm2


0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT




0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Volta

ge (V

) and

curr

ent (

A)



0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Volta

ge (V

) and

curr

ent (

A)



7 Conclusions






0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30Gain = 55

Gain = 75

Gain = 95

(a)

0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30

Gain = 55

Gain = 75

(b)




References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of












Non linear map

Lawpassfilter

Highpassfilter

120574

s

120594

120579

sin(120596t)120596t)

J

y = f(120579)

asin(

120592





120579 = 119896(1198862

2)(119891)1015840



119910 = 119891 (120579 + 119886 sin (120596119905))

120579 = minus120574120594


HLPF (119904)

120592 = [119910 lowast Lminus1

HHPF (119904)] sin (120596119905)

(1)


ℎ) and

120596119897(119904 + 120596


119897lt 120596 lt 120596

ℎ[25] This model






minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

10

Gai

n (d

B)

Frequency (rads)


0

10minus1 100 101 102



119866LP-BICO (119904) =119896

(119904120596119888+ radic1 + (119904120596

119888)2

)

119903 119903 isin R

+

(2)



119892BICOLP(119905) = 119896

119903119869119903(120596119888119905)

120596119888119905

(3)






119888and a large






119910 = 119891 (120579 + 119886 sin (120596119905)) (4)


119910 = 119891 (120579) +

119889119891 (120579)

119889120579

119886 sin (120596119905) +HOT (5)


119869 ≃ Lminus1

119904

119904 + 120596ℎ

lowast 119891 (120579)

+ Lminus1

119904

119904 + 120596ℎ

lowast

119889119891 (120579)

119889120579

119886 sin (120596119905)

(6)





120579 ≃119886120574

2Lminus1

1

119904 lowast L

minus1

120596119897

119904 + 120596119897

lowast 119889

119889119905(

119889119891 (120579)

119889120579

)

(7)





119909 (119905) =1

119879int

119879

0

119909 (119905) 119889119905 (8)


120579 = 120579

119910 = 119891(120579) = 119891(120579) = 119891 (120579)

120579 =120574119886

2

119889

119889119905(

119889119891 (120579)

119889120579

) lowast Lminus1

HLPF lowast Lminus1

1

119904

(9)


119910 ≃ 119891 (120579lowast

) +119889119891 (120579)

119889120579

10038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)

+1

2

1198892

119891 (120579)

119889120579

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)2

(10)



0 thus

119910 ≃1

2

1198892

119891(120579)

1198891205792

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast1205792

(11)


119891(120579)1198891205792

)|120579=120579lowast = 119870 then


120579=120579lowast =


120579 = (120574119886120579lowast119889119870

119889119905) lowast L

minus1

HLPF lowast Lminus1

1

119904 (12)


119867119875119865 which its



120579 = (120574119886120579lowast

119870)Lminus1

HHPF lowast Lminus1

HLPF lowast Lminus1

1

119904 (13)


K120574a

1

sHLP (s) HHP(s)




119868 = 119868119871minus 119868OS (exp(

119902

119860119896119861119879) (119881 + 119877119868) minus 1)

119868OS = 119868OR (119879

119879119877

) exp(119902119864119866

119860119896119861

(1

119879119877

minus1

119877))

119868119871=

119866

1000(119868SC + 119870119879119868 (119879 minus 119879

119877))

119881 =119860119896119861119879

119902ln(119868119871 minus 119868

119868OS+ 1) minus 119877119868

(14)











119879119877


119877





0

0

1

2

3

4

Real

Imag

e 0

0

2


minus1

minus2

minus2

minus3

minus4

minus4


minus10minus20





0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

= 30∘C= 25∘C

= 20∘CTT

T









0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

G = 1100Wm2

G = 1000Wm2G = 900Wm2


0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT




0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Volta

ge (V

) and

curr

ent (

A)



0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Volta

ge (V

) and

curr

ent (

A)



7 Conclusions






0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30Gain = 55

Gain = 75

Gain = 95

(a)

0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30

Gain = 55

Gain = 75

(b)




References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


minus80

minus70

minus60

minus50

minus40

minus30

minus20

minus10

10

Gai

n (d

B)

Frequency (rads)


0

10minus1 100 101 102



119866LP-BICO (119904) =119896

(119904120596119888+ radic1 + (119904120596

119888)2

)

119903 119903 isin R

+

(2)



119892BICOLP(119905) = 119896

119903119869119903(120596119888119905)

120596119888119905

(3)






119888and a large






119910 = 119891 (120579 + 119886 sin (120596119905)) (4)


119910 = 119891 (120579) +

119889119891 (120579)

119889120579

119886 sin (120596119905) +HOT (5)


119869 ≃ Lminus1

119904

119904 + 120596ℎ

lowast 119891 (120579)

+ Lminus1

119904

119904 + 120596ℎ

lowast

119889119891 (120579)

119889120579

119886 sin (120596119905)

(6)





120579 ≃119886120574

2Lminus1

1

119904 lowast L

minus1

120596119897

119904 + 120596119897

lowast 119889

119889119905(

119889119891 (120579)

119889120579

)

(7)





119909 (119905) =1

119879int

119879

0

119909 (119905) 119889119905 (8)


120579 = 120579

119910 = 119891(120579) = 119891(120579) = 119891 (120579)

120579 =120574119886

2

119889

119889119905(

119889119891 (120579)

119889120579

) lowast Lminus1

HLPF lowast Lminus1

1

119904

(9)


119910 ≃ 119891 (120579lowast

) +119889119891 (120579)

119889120579

10038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)

+1

2

1198892

119891 (120579)

119889120579

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)2

(10)



0 thus

119910 ≃1

2

1198892

119891(120579)

1198891205792

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast1205792

(11)


119891(120579)1198891205792

)|120579=120579lowast = 119870 then


120579=120579lowast =


120579 = (120574119886120579lowast119889119870

119889119905) lowast L

minus1

HLPF lowast Lminus1

1

119904 (12)


119867119875119865 which its



120579 = (120574119886120579lowast

119870)Lminus1

HHPF lowast Lminus1

HLPF lowast Lminus1

1

119904 (13)


K120574a

1

sHLP (s) HHP(s)




119868 = 119868119871minus 119868OS (exp(

119902

119860119896119861119879) (119881 + 119877119868) minus 1)

119868OS = 119868OR (119879

119879119877

) exp(119902119864119866

119860119896119861

(1

119879119877

minus1

119877))

119868119871=

119866

1000(119868SC + 119870119879119868 (119879 minus 119879

119877))

119881 =119860119896119861119879

119902ln(119868119871 minus 119868

119868OS+ 1) minus 119877119868

(14)











119879119877


119877





0

0

1

2

3

4

Real

Imag

e 0

0

2


minus1

minus2

minus2

minus3

minus4

minus4


minus10minus20





0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

= 30∘C= 25∘C

= 20∘CTT

T









0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

G = 1100Wm2

G = 1000Wm2G = 900Wm2


0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT




0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Volta

ge (V

) and

curr

ent (

A)



0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Volta

ge (V

) and

curr

ent (

A)



7 Conclusions






0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30Gain = 55

Gain = 75

Gain = 95

(a)

0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30

Gain = 55

Gain = 75

(b)




References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119909 (119905) =1

119879int

119879

0

119909 (119905) 119889119905 (8)


120579 = 120579

119910 = 119891(120579) = 119891(120579) = 119891 (120579)

120579 =120574119886

2

119889

119889119905(

119889119891 (120579)

119889120579

) lowast Lminus1

HLPF lowast Lminus1

1

119904

(9)


119910 ≃ 119891 (120579lowast

) +119889119891 (120579)

119889120579

10038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)

+1

2

1198892

119891 (120579)

119889120579

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast(120579 minus 120579

lowast

)2

(10)



0 thus

119910 ≃1

2

1198892

119891(120579)

1198891205792

100381610038161003816100381610038161003816100381610038161003816120579=120579lowast1205792

(11)


119891(120579)1198891205792

)|120579=120579lowast = 119870 then


120579=120579lowast =


120579 = (120574119886120579lowast119889119870

119889119905) lowast L

minus1

HLPF lowast Lminus1

1

119904 (12)


119867119875119865 which its



120579 = (120574119886120579lowast

119870)Lminus1

HHPF lowast Lminus1

HLPF lowast Lminus1

1

119904 (13)


K120574a

1

sHLP (s) HHP(s)




119868 = 119868119871minus 119868OS (exp(

119902

119860119896119861119879) (119881 + 119877119868) minus 1)

119868OS = 119868OR (119879

119879119877

) exp(119902119864119866

119860119896119861

(1

119879119877

minus1

119877))

119868119871=

119866

1000(119868SC + 119870119879119868 (119879 minus 119879

119877))

119881 =119860119896119861119879

119902ln(119868119871 minus 119868

119868OS+ 1) minus 119877119868

(14)











119879119877


119877





0

0

1

2

3

4

Real

Imag

e 0

0

2


minus1

minus2

minus2

minus3

minus4

minus4


minus10minus20





0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

= 30∘C= 25∘C

= 20∘CTT

T









0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

G = 1100Wm2

G = 1000Wm2G = 900Wm2


0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT




0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Volta

ge (V

) and

curr

ent (

A)



0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Volta

ge (V

) and

curr

ent (

A)



7 Conclusions






0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30Gain = 55

Gain = 75

Gain = 95

(a)

0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30

Gain = 55

Gain = 75

(b)




References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119879119877


119877





0

0

1

2

3

4

Real

Imag

e 0

0

2


minus1

minus2

minus2

minus3

minus4

minus4


minus10minus20





0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

= 30∘C= 25∘C

= 20∘CTT

T









0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

G = 1100Wm2

G = 1000Wm2G = 900Wm2


0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT




0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Volta

ge (V

) and

curr

ent (

A)



0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Volta

ge (V

) and

curr

ent (

A)



7 Conclusions






0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30Gain = 55

Gain = 75

Gain = 95

(a)

0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30

Gain = 55

Gain = 75

(b)




References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 5 10 15 20 250

5

10

15

20

25

30

35

40

45

50

55

Voltage (V)

Pow

er (W

)

G = 1100Wm2

G = 1000Wm2G = 900Wm2


0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT




0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

Time (s)

Volta

ge (V

) and

curr

ent (

A)



0 2 4 6 8 100

5

10

15

20

25

30

35

40

45

50

Time (s)

Pow

er (W

)

ESC MPPTBICO MPPT





0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Volta

ge (V

) and

curr

ent (

A)



7 Conclusions






0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30Gain = 55

Gain = 75

Gain = 95

(a)

0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30

Gain = 55

Gain = 75

(b)




References














































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 2 4 6 8 100

2

4

6

8

10

12

14

16

18

20

Time (s)

Volta

ge (V

) and

curr

ent (

A)



7 Conclusions






0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30Gain = 55

Gain = 75

Gain = 95

(a)

0 2 4 6 8 10

0

10

20

30

40

50

Time (s)

Pow

er (W

)

minus10

Gain = 30

Gain = 55

Gain = 75

(b)




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










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

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Research Article BICO MPPT: A Faster Maximum Power Point ...downloads.hindawi.com/journals/ijp/2014/586503.pdf · power point Array current, Irradiance I Terminal voltage, V F : -