Maximum Power Extraction Using Modi ed Regula Falsi power ... · Modi ed Regula falsi method is a...

Maximum Power Extraction UsingModified Regula Falsi power Tracker

Algorithm

Dr.S.Muralidharan1,G.Vaishnavi2,M.Muhaidheen3,B.Sakthi Sudhursun4

1,2,3,4Department of EEE,Mepco schlenk engg collegeSivakasi, Tamilnadu, India

Yes [email protected],[email protected],

[email protected],[email protected]

May 21, 2018

Abstract

In todays climate and growing environmental consequencesneed for renewable energy sources are to be considered as aprime factor for future environment. On which, solar powergeneration is one of the burgeon technology which never getinactive. Even though they have many calibre on one sidethey too have other thread since they majorly depend ondynamically changing environment. To gain mastery overthis demerit one of the better solutions is Maximum powerpoint tracking at all irradiation level. In this paper, one ofthe best classical root finding method is adapted to extractmaximum power at all dynamic environment. This paperreveals Modified regula falsi optimization method (MRFM)is on the best MPP tracker when compared with other con-ventional P&O, INC other modified P&O methods. Dif-ferent MPPT techniques are enrolled to obtain maximum

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International Journal of Pure and Applied MathematicsVolume 118 No. 24 2018ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

power using SEPIC power electronic converter. Three ma-jor MPPT techniques are adapted and power output of allthe conventional technique is compared with the modifiedregula falsi method optimization. This type of adaptivemodified regula falsi method is independent of environmen-tal condition

Keywords:SEPIC converter, PV system, modified reg-ula falsi method(MRFM), P&O, INC

1 INTRODUCTION

This paper projects on a concept of maximum power extraction byusing modified regula falsi method which is proved to be advan-tages over other classical root finding methods like newton raphsonmethod, bisecting method, secant method, regula falsi method [1].Need for alternative energy sources are becoming mandatory for fu-ture power generation. Even World is on its truck to get about 30%of its energy from alternative renewable energy source. In order tobalance the dilamatic demand in electric energy utilization and gen-eration, sustainable energy sources such as solar, TEG, fuel cells areopted as a secondary sources. Among other sources solar is the ma-jor contribution of most renewable energy source in meeting energydemand. However, solar PV system has high installation, capitalcost still it has barrier that affects the application in widespread.In order to overcome this short comes and to make solar PV systemmore effective its mandatory to maximize its utilization on its bestat all dynamic environment. In order to obtain the maximum powerchange in voltage and change in power (dp/dv) is determined whenthis change is observed as zero then they are at absolute maximumpower point. Several techniques are adapted and formulated to ob-tain the maximum power point (MPP) on which P&O and INCare conventional techniques. Two major approaches are adaptedfirst method is based on voltage feedback and second one is currentfeedback method [3]. Normally, predetermined value of referencevoltage is compared with PV system voltage in feedback looping.Majority of algorithm will try to maintain dP/dV ratio equals tozero. Perturb and observe algorithm which is widely used in manyapplication for tracking maximum power but this method producemore oscillation around the region of MPP [2]. P&O fails to adapt

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International Journal of Pure and Applied Mathematics Special Issue

to the rapidly changing environment. To overcome this problemmodified P&O method is presented but difficulties in choosing thevalue of threshold were left unsolved [4]. In [5] a P&O algorithmis opted by fixing step size and sample frequency, optimization isdone by considering the interfacing of DC-DC converter and envi-ronment change. This [6] optimization will reduce oscillation effectaround the point of maximum power point and prevents from failureduring rapid changing environment. Another conventional methodusually employed is incremental conductance method their aim isjust similar to P&O but they uses incremental and instantaneousrelationship for calculating the resulting power. Modified P&O isimplemented they will have better improvement in settling timein SEPIC converter [6]. Classical root finding algorithm mainlyare Newton raphson methods, secant method, bisecting method,regula falsi method Among which modified regula falsi method isadapted for maximum power point tracking in rapid changing envi-ronment and they have variable step size. They are the fundamen-tal difference between perturb and observe method and Incrementalconductance method. In this MRFM method change in dp/dv iscompared with zero, when dp/dv is <zero and dp/dv is > zero endcondition and proceeding condition of next iteration takes place re-spectively.MRFM method is one of the best methods for trackingMaximum power point. They are similar to root finding method inmathematical formulation. They have better root convergence andvariable step size.

Drawbacks like oscillation around maximum point are controlledin these techniques. MRFM method doesnt need any complicateturning process.

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2 DESIGN PROCESS OF SOLAR PANEL

IN MATLAB SIMULINK MODEL

Fig. 1. Circuit model of solar cell

Characteristics equation of solar cell: From fig.1.

I − IL − ID[Eq(V + IRs)

mRT] (1)

Where:I= output current obtained from PV panel(A)current generated by solar panel(A)ID = current flowing through the diode (D)Ish = current flowing through shunt resistanceRs= shunt resistance (Ω)Q= electron charge value is 1.6 ∗ 10−19 CK = Boltzmann constant value is (1.381 ∗ 10−23J/K)N = diode ideality factor can range of (1-2)Design parameters of simulated solar panel:

TABLE: I DESIGN PARAMETERS OF SIMULATEDSOLAR PANEL

By using MATLAB simulink software solar panel is designedfor the above mentioned (Table I) values. Source for the SEPICconverter is solar source. By using MRFM technique maximumutilization of solar power is attained. Solar panel model is designedand its SIMULINK model is shown in fig 2.

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Fig. 2. MATLAB model of solar panel

3 SOLAR POWERED SEPIC CON-

VERTER

A. Circuit model of conventional SEPIC converter:SEPIC converter is commonly identified as single ended pri-

mary inductor converter (DC-DC Converter).They normally usedto boost the power output of generated power. From(fig 3) Dur-ing pulse high state, MOSFET switch is at ON stage, inductor(L1)is at charging condition which is supplied by input voltage andat the same time inductor(L2) is charged by capacitor(C1).At thisinstant, current in inductor(L1) will get increase and current ininductor(L2) will goes to negative.

Similarly, when the pulse is low (fig 4) Switch will get turn offthis in turn automatically change the flow of current path throughdiode to load. This obvious that capacitor on its path will getcharge at this instant.

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Fig. 3. Circuit diagram of SEPIC converter when pulse is high

Fig. 4. Circuit diagram of SEPIC converter when pulse is low

B. Design parameters of SEPIC converterOutput voltage equation is obtained by:

a (2)

Where: D is defined as duty cycle of SEPIC converterVi = Input voltageDuty cycle is calculated using formula:

DutyCycleD : (3)

Where, Vo = output voltage Inductance value can be obtained by

InductanceL = (4)

Where, ∆Io = current ripple in the inductorF= switching frequencyCapacitance I is calculated by

capacitance (5)

Where, Io = output current obtained∆v = voltage ripple of the capacitor used.Load resistance is calculated using formula:

RLG (6)

By using the formula exact values are calculated and its shown intable II.

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TABLE: II DESIGN PARAMETERS OF SEPICCONVERTER

4 MPPT employed SEPIC Converter

A. Conventional P&O method employed SEPIC Converter:Perturb and observe algorithm is one the traditional algorithm

widely used in tracking maximum power point to utilize the maxi-mum energy from renewable energy sources. It works based on theratio of changes in power to the r changes in voltage. This trackerworks periodically incrementing or decrementing the solar arrayvoltage. In P&O algorithm dp/dv <0, the perturbation moves theoperating point of PV array away from the maximum power pointcondition. Voltage will moves in same direction. On the otherside when dp/dv >0, the perturbation moves away from the maxi-mum power point. This commonly called by the name hill climbingmethod

By using the flow chart of conventional P&O algorithm em-bedded MATLAB program are coded and implemented to obtainmaximum power to act as a input source for SEPIC converter (fig5). By using this conventional MPPT technique SEPIC convertercan yield maximum up to 72W. Major drawback of this method isoscillation at the point near MPP.

B. Conventional INC algorithm employing SEPIC converterIncremental conductance algorithm is another conventional method

used to track maximum power point. They work based on the factdp/dv≥o then lies on left of MPP; dp/dv ≤ 0 then maximum re-gion lies on right of MPP, dp/dv = 0 at MPP. By this methodoscillation around the point of MPP is reduced. When using thisMPPT technique total power at the output side of SEPIC con-verter is about 76.59W.This has better result when compared withthe P&O algorithm.

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Fig. 5 Conventional P&O algorithm employed SEPIC

C. Modified P&O algorithmTo overcome the shortcoming of conventional P&O and INC

new modified version of P&O is introduced. The main advantageof this method is searching time is reduced and they have better set-tling time when compared with conventional P&O. Modified P&Oadopts to the relationship between the load line and I-V curve andthey introduce a fast converging algorithm. When using this modi-fied P&O algorithm SEPIC converter can give out up to 76W withfast converging rate and fast settling time shown in fig.6.

Fig. 6. Modified P&O employing SEPIC converter

D. MRFM employing SEPIC converter:

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Regula falsi method is one of the best methods for linearly con-verging root finding methods for continuous functions with inde-pendent variable. They are the hybrid variant of both bisectionsearch algorithm and secant search algorithm. MPP of the charac-teristics can be found by finding the roots of the following equation:

Ci =xl.

(7)

Where i= 0,1· · · .

i) Continuous function as f(x) initial point is assumed as Xl

andXU ,Where they are assumed random lower and upperpoint at the dp/dv and V curve. According to intermediatetheorem root of f(x) is assumed to located in between theinterval[XL, Xu].

ii) Value for root Ci is determined by formula(7)

iii) —f(Ci)— > where is defined as tolerance . check if f(Ci).f(Xl)¡0 then Xl = Ci else f(Ci).f(Xu)<0 thenXu = Ci.

iv) Iteration will continue until root is acquired.

Modified Regula falsi method is a improved version of regulafalsi method (RFM). Drawback of RFM is root get converge veryslowly as because one end of the RFM is fixed. Other disadvan-tage is they have constant magnitude at f(x) at a particular point.MRFM is similar to RFM except the following changes: From fig.7

i) Check if f(XL).f(Xu)<0 and f(Xl)>0 then f(Xu) is replacedby the fP (Xu) = f (Xu)/2 and fp (Xl)= f(Xl)

Ci =x1.fp(xu) − xU .fP (xl)

fp(xu) − fp(xl)=

xl.f(xu) − xu

f(xu) − f(+0.5)(8)

where i=0,1..

ii) Check wheather f(Xl).f(Xu) <0 and f(Xl) is changed by fp(Xl)= f(Xl)/2 and fp(Xu)=f(Xu)

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Ci =x1.fp(xu) − xU .fP (xl)

fp(xu) − fp(xl)=

xl.f(xu) + 0.5

f(xu) + 0.5(9)

where i= 0,1· · · .

Fig. 7. Characteristics curve of (dp/dv) Vs Voltage

i) Let Y axis on the curve be the change in power to change involtage value and consider X axis be voltage of PV panel.

ii) Consider an imaginary axis similar and parallel to x axis.

iii) Extend the curve line to touch the imaginary axis and assumetwo limit point by using polynomial equation of the charac-teristics curve of dp/dv .

iv) Interval value be [Xl,Xu] which is probably Xl lower limitpoint and Xu upper point on the axis

v) Co is the coefficient value. Root lies between the point Xland Xu.. In this MRFM both the ends are movable. Rootcan lies on any of these interval. But in RFM Xu is fixed atone end only Xl is varied to get the optimum root.

vi) Iteration will get repeated by comparing the obtained F(x)value with the f(ci).This process get stop until optimum rootvalue is reached.

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The main concept behind this MRFM method is to reduce themagnitude of F(x) by 1/2 and by this convergence speed can beincreased both for concave and convex function. In MPPT method,we consider dp/dv Vs V so its mandatory to differentiate all thefunctions of the term f(Xl) and f(Xu) respectively in equation (8)&(9). To extract maximum power during all dynamic environmen-tal condition MRFM is the best optimization algorithm. In thiscase, MRFM algorithm is used to obtain maximum power outputat SEPIC converter (fig 8). To evident, MRFM algorithm is bet-ter than all conventional P&O, INC and Modified P&O algorithmpower output of SEPIC converter is compared and proved.

Fig. 8. MRFM employing SEPIC converter

5 MATLAB SIMULATED RESULTS AND

DISCUSSION

A. Output of SEPIC converter with Conventional MPP tracker:From the fig.9, it could be clearly observed by using conventional

P&O MPP tracker maximum power up to 72W can be obtained. Toimprove the output still higher modified P&O algorithm is adapted.When using this modified P&O algorithm output can be increasedfrom 72W to 76W.Output result is shown in the fig.10

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Fig. 9. Output waveform of conventional P&O employed SEPICconverter

When comparing the output result of SEPIC converter employedwith conventional P&O and modified P&O method power outputat SEPIC converter is increased and there is reduction in oscillationat the output side near the point of MPP.

Fig. 10. Output waveform of SEPIC converter using modifiedP&O algorithm

B. output results of SEPIC converter using MRFM methodBy using MRFM method, maximum power can be attained at

the converter output side. PV and IV Characteristics of solar panelafter using MRFM MPP tracker is shown in the fig. 11,12 respec-tively. This method is suitable for all rapid changing environmentsand irrespective of irradiation level. MRFM method can yield up to0.5 duty cycles during extreme adverse condition. Overall outputlevel of SEPIC converter using MRFM tracker is about 80W.Whichis obvious, that MRFM can yield about 10% more power than otherconventional methods. Output waveform of SEPIC converter usingMRFM is shown in fig.13.

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Fig. 11. PV characteristics of solar panel using MRFM tracker

Fig. 12. IV characteristics of solar panel using MRFM tracker

Fig. 13. Output waveform of SEPIC converter employing MRFMalgorithm

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6 CONCLUSION

Table: III POWER OUTPUT OF SEPIC CONVERTER USINGDIFFERENT MPP TRACKERS

Results of all the conventional methodology has be presented intable III by this it could be concluded that Modified regula falsimethod is one of the best classical root finding method used intracking maximum power point at all dynamic changing environ-ment. In this a dc to dc converter is supplied with solar powereddc supply which always target to extract maximum utilization withproper tracker Different Conventional techniques are employed forSEPIC converter also their results are compared and graphicallyrepresented in fig.14

Fig. 14. Power output of different conventional techniques

References

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[11] T.Esram and P.Chapman, Comparison of Photovoltaic ArrayMaximum power point Tracking Techniques, IEEE Transac-tion on Energy Conversion, vol.22,no.2,pp. 439-449,june 2009.

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[15] Dr.S.Muralidharan,,M.Muhaidheenperformance investigationof power quality in distributed generation system fed smartgrid using different control strategies ,Journal of Electrical en-gineering ,vol 17. no2,pp.363-374, July 2017.

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