Maximum Power Extraction Using Modified Regula Falsi power Tracker Algorithm

Transcription

1 Volume 118 No ISSN: (on-line version) url: Maximum Power Extraction Using Modified Regula Falsi power Tracker Algorithm Dr.S.Muralidharan 1,G.Vaishnavi 2, M.Muhaidheen 3,B.Sakthi Sudhursun 4 1,2,3,4 Department of EEE, Mepco schlenk engg college Sivakasi, Tamilnadu, India Yes murali@yahoo.com, Vaishnavigovind95@yahoo.com, muhaim@gmail.com, sakthisudhursun@gmail.com May 21, 2018 Abstract In todays climate and growing environmental consequences need for renewable energy sources are to be considered as a prime factor for future environment. On which, solar power generation is one of the burgeon technology which never get inactive. Even though they have many calibre on one side they too have other thread since they majorly depend on dynamically changing environment. To gain mastery over this demerit one of the better solutions is Maximum power point tracking at all irradiation level. In this paper, one of the best classical root finding method is adapted to extract maximum power at all dynamic environment. This paper reveals Modified regula falsi optimization method (MRFM) is on the best MPP tracker when compared with other conventional P&O, INC other modified P&O methods. Different MPPT techniques are enrolled to obtain maximum 1

2 power using SEPIC power electronic converter. Three major MPPT techniques are adapted and power output of all the conventional technique is compared with the modified regula falsi method optimization. This type of adaptive modified regula falsi method is independent of environmental condition Keywords:SEPIC converter, PV system, modified regula falsi method(mrfm), P&O, INC 1 INTRODUCTION This paper projects on a concept of maximum power extraction by using modified regula falsi method which is proved to be advantages over other classical root finding methods like newton raphson method, bisecting method, secant method, regula falsi method [1]. Need for alternative energy sources are becoming mandatory for future power generation. Even World is on its truck to get about 30% of its energy from alternative renewable energy source. In order to balance the dilamatic demand in electric energy utilization and generation, sustainable energy sources such as solar, TEG, fuel cells are opted as a secondary sources. Among other sources solar is the major contribution of most renewable energy source in meeting energy demand. However, solar PV system has high installation, capital cost still it has barrier that affects the application in widespread. In order to overcome this short comes and to make solar PV system more effective its mandatory to maximize its utilization on its best at all dynamic environment. In order to obtain the maximum power change in voltage and change in power (dp/dv) is determined when this change is observed as zero then they are at absolute maximum power point. Several techniques are adapted and formulated to obtain the maximum power point (MPP) on which P&O and INC are conventional techniques. Two major approaches are adapted first method is based on voltage feedback and second one is current feedback method [3]. Normally, predetermined value of reference voltage is compared with PV system voltage in feedback looping. Majority of algorithm will try to maintain dp/dv ratio equals to zero. Perturb and observe algorithm which is widely used in many application for tracking maximum power but this method produce more oscillation around the region of MPP [2]. P&O fails to adapt 2

3 to the rapidly changing environment. To overcome this problem modified P&O method is presented but difficulties in choosing the value of threshold were left unsolved [4]. In [5] a P&O algorithm is opted by fixing step size and sample frequency, optimization is done by considering the interfacing of DC-DC converter and environment change. This [6] optimization will reduce oscillation effect around the point of maximum power point and prevents from failure during rapid changing environment. Another conventional method usually employed is incremental conductance method their aim is just similar to P&O but they uses incremental and instantaneous relationship for calculating the resulting power. Modified P&O is implemented they will have better improvement in settling time in SEPIC converter [6]. Classical root finding algorithm mainly are Newton raphson methods, secant method, bisecting method, regula falsi method Among which modified regula falsi method is adapted for maximum power point tracking in rapid changing environment and they have variable step size. They are the fundamental difference between perturb and observe method and Incremental conductance method. In this MRFM method change in dp/dv is compared with zero, when dp/dv is <zero and dp/dv is > zero end condition and proceeding condition of next iteration takes place respectively.mrfm method is one of the best methods for tracking Maximum power point. They are similar to root finding method in mathematical formulation. They have better root convergence and variable step size. Drawbacks like oscillation around maximum point are controlled in these techniques. MRFM method doesnt need any complicate turning process. 3

4 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 I L I D [ Eq(V + IR s) ] (1) mrt Where: I= output current obtained from PV panel(a) current generated by solar panel(a) I D = current flowing through the diode (D) I sh = current flowing through shunt resistance R s = shunt resistance (Ω) Q= electron charge value is C K = Boltzmann constant value is ( J/K) N = diode ideality factor can range of (1-2) Design parameters of simulated solar panel: TABLE: I DESIGN PARAMETERS OF SIMULATED SOLAR PANEL By using MATLAB simulink software solar panel is designed for the above mentioned (Table I) values. Source for the SEPIC converter is solar source. By using MRFM technique maximum utilization of solar power is attained. Solar panel model is designed and its SIMULINK model is shown in fig 2. 4

5 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 primary inductor converter (DC-DC Converter).They normally used to boost the power output of generated power. From(fig 3) During pulse high state, MOSFET switch is at ON stage, inductor(l1) is at charging condition which is supplied by input voltage and at the same time inductor(l2) is charged by capacitor(c1).at this instant, current in inductor(l1) will get increase and current in inductor(l2) will goes to negative. Similarly, when the pulse is low (fig 4) Switch will get turn off this in turn automatically change the flow of current path through diode to load. This obvious that capacitor on its path will get charge at this instant. 5

6 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 converter Output voltage equation is obtained by: a (2) Where: D is defined as duty cycle of SEPIC converter V i = Input voltage Duty cycle is calculated using formula: DutyCycleD : (3) Where, Vo = output voltage Inductance value can be obtained by Where, I o = current ripple in the inductor F= switching frequency Capacitance I is calculated by InductanceL = (4) capacitance (5) Where, I o = output current obtained v = voltage ripple of the capacitor used. Load resistance is calculated using formula: R LG (6) By using the formula exact values are calculated and its shown in table II. 6

7 TABLE: II DESIGN PARAMETERS OF SEPIC CONVERTER 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 maximum energy from renewable energy sources. It works based on the ratio of changes in power to the r changes in voltage. This tracker works periodically incrementing or decrementing the solar array voltage. In P&O algorithm dp/dv <0, the perturbation moves the operating point of PV array away from the maximum power point condition. Voltage will moves in same direction. On the other side when dp/dv >0, the perturbation moves away from the maximum power point. This commonly called by the name hill climbing method By using the flow chart of conventional P&O algorithm embedded MATLAB program are coded and implemented to obtain maximum power to act as a input source for SEPIC converter (fig 5). By using this conventional MPPT technique SEPIC converter can yield maximum up to 72W. Major drawback of this method is oscillation at the point near MPP. B. Conventional INC algorithm employing SEPIC converter Incremental conductance algorithm is another conventional method used to track maximum power point. They work based on the fact dp/dv o then lies on left of MPP; dp/dv 0 then maximum region lies on right of MPP, dp/dv = 0 at MPP. By this method oscillation around the point of MPP is reduced. When using this MPPT technique total power at the output side of SEPIC converter is about 76.59W.This has better result when compared with the P&O algorithm. 7

8 Fig. 5 Conventional P&O algorithm employed SEPIC C. Modified P&O algorithm To overcome the shortcoming of conventional P&O and INC new modified version of P&O is introduced. The main advantage of this method is searching time is reduced and they have better settling time when compared with conventional P&O. Modified P&O adopts to the relationship between the load line and I-V curve and they introduce a fast converging algorithm. When using this modified P&O algorithm SEPIC converter can give out up to 76W with fast converging rate and fast settling time shown in fig.6. Fig. 6. Modified P&O employing SEPIC converter D. MRFM employing SEPIC converter: 8

9 Regula falsi method is one of the best methods for linearly converging root finding methods for continuous functions with independent variable. They are the hybrid variant of both bisection search algorithm and secant search algorithm. MPP of the characteristics can be found by finding the roots of the following equation : Where i= 0,1. C i = xl. (7) i) Continuous function as f(x) initial point is assumed as X l andx U,Where they are assumed random lower and upper point at the dp/dv and V curve. According to intermediate theorem root of f(x) is assumed to located in between the interval[x L, X u ]. 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 thenx u = C i. iv) Iteration will continue until root is acquired. Modified Regula falsi method is a improved version of regula falsi method (RFM). Drawback of RFM is root get converge very slowly as because one end of the RFM is fixed. Other disadvantage 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 replaced by the fp (Xu) = f (Xu)/2 and fp (Xl)= f(xl) where i=0,1.. C i = x 1.f p (x u ) x U.f P (x l ) f p (x u ) f p (x l ) = x l.f(x u ) x u f(x u ) f(+0.5) (8) ii) Check wheather f(xl).f(xu) <0 and f(xl) is changed by fp(xl) = f(xl)/2 and fp(xu)=f(xu) 9

10 C i = x 1.f p (x u ) x U.f P (x l ) = x l.f(x u ) f p (x u ) f p (x l ) f(x u ) where i= 0,1. (9) Fig. 7. Characteristics curve of (dp/dv) Vs Voltage i) Let Y axis on the curve be the change in power to change in voltage 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 assume two limit point by using polynomial equation of the characteristics curve of dp/dv. iv) Interval value be [Xl,Xu] which is probably Xl lower limit point and Xu upper point on the axis v) Co is the coefficient value. Root lies between the point Xl and Xu.. In this MRFM both the ends are movable. Root can lies on any of these interval. But in RFM Xu is fixed at one 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 root value is reached. 10

11 The main concept behind this MRFM method is to reduce the magnitude of F(x) by 1/2 and by this convergence speed can be increased both for concave and convex function. In MPPT method,we consider dp/dv Vs V so its mandatory to differentiate all the functions of the term f(xl) and f(xu) respectively in equation (8) &(9). To extract maximum power during all dynamic environmental condition MRFM is the best optimization algorithm. In this case, MRFM algorithm is used to obtain maximum power output at SEPIC converter (fig 8). To evident, MRFM algorithm is better than all conventional P&O, INC and Modified P&O algorithm power 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. To improve the output still higher modified P&O algorithm is adapted. When using this modified P&O algorithm output can be increased from 72W to 76W.Output result is shown in the fig.10 11

12 Fig. 9. Output waveform of conventional P&O employed SEPIC converter When comparing the output result of SEPIC converter employed with conventional P&O and modified P&O method power output at SEPIC converter is increased and there is reduction in oscillation at the output side near the point of MPP. Fig. 10. Output waveform of SEPIC converter using modified P&O algorithm B. output results of SEPIC converter using MRFM method By using MRFM method, maximum power can be attained at the converter output side. PV and IV Characteristics of solar panel after using MRFM MPP tracker is shown in the fig. 11,12 respectively. This method is suitable for all rapid changing environments and irrespective of irradiation level. MRFM method can yield up to 0.5 duty cycles during extreme adverse condition. Overall output level of SEPIC converter using MRFM tracker is about 80W.Which is obvious, that MRFM can yield about 10% more power than other conventional methods. Output waveform of SEPIC converter using MRFM is shown in fig

13 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 MRFM algorithm 13

14 6 CONCLUSION Table: III POWER OUTPUT OF SEPIC CONVERTER USING DIFFERENT MPP TRACKERS Results of all the conventional methodology has be presented in table III by this it could be concluded that Modified regula falsi method is one of the best classical root finding method used in tracking maximum power point at all dynamic changing environment. In this a dc to dc converter is supplied with solar powered dc supply which always target to extract maximum utilization with proper tracker Different Conventional techniques are employed for SEPIC converter also their results are compared and graphically represented in fig.14 Fig. 14. Power output of different conventional techniques References [1] Seunghyum chum, Alexis Kwasinski Modified Regula Falsi Optimization Method Approach to Digital Maximum Power Point Tracking For Photovoltaic application, Applied Power Electronics conference and Exposition(APEC),2011 (IEEE) 14

15 [2] Seunghyum chum, Alexis Kwasinski Analysis of classical Root finding methods applied to digital Maximum power tracking for Sustainable Photovoltaic Energy Generation, IEEE transaction on power electronics,vol-6,issue12 Dec-2011,page no(s) [3] M.Dowell and D.jarratt, A modified regula falsi method for computing the root of an equation, BIT vol 11,no 2,pp ,1991. [4] Manish Srivastava, Sunil Agarwal, Ekta Sharma, Design and simulation of Perturb and Observe MPPT algorithm for 72 cell solar PV system International Journal Of Soft computing and engineering(ijsce),vol-4,no,6. [5] Tekeshwar Prasad Sahu,T.V.Dixit and Ramesh kumar, Simulation and analysis of Perturb and Observe MPPT Algotihm for PV array using CUK converter,advance in Electronic and Electric Engineering,vol.4,No.2,pp ,2014 [6] S.Muralidharan,Deepak Hari, Simulation of Perturb & Observe MPPT Technique Using SEPIC Converter, International Journal of Innovative Works in Engineering and Technology,Vol.3, No.2,pp [7] X.weidong and W.G Dunford, A Modified adaptive hill climbing MPPT method for Photovoltaic power system, In proceeding of.ieee 35th Annual power Electron.Spec.conf.,vol.3, pp ,2004. [8] Roberto F.Coelho,Filipe Concer,Denizar C.Martins, A study of the basic DC-DC converter applied in Maximum Power point tracking,ieee-2009 [9] Fang Luo,Pengwei Xu,Yongkang,Shangsu Duan, A variable step maximum power point tracking method using Differential Equation solution, Second IEEE conference on Industrial electronics and Application, pp , May [10] Wang peng.et al, A Novel Approach of Maximizing energy harvesting in photovoltaic systems based on Bisection search Theorem, The Applied Power Electronics conference and Exposition (APEC2010)USA. 15

16 [11] T.Esram and P.Chapman, Comparison of Photovoltaic Array Maximum power point Tracking Techniques, IEEE Transaction on Energy Conversion, vol.22,no.2,pp ,june [12] American Enegy: The Renewable path to Energy security,worldwatchinstitute.september2006.[online]. Availableathttp:// [13] NREL, Best Research cell Efficiency, [online] Available at: film/docs/koz best research cells.ppt [14] Dr.S.Muralidharan, Deepak Hari, presented paper on Simulation of variable step size incremental conductance MPPT technique using SEPIC converter, on IEEE international conference on Innovations in Information, Embedded and Communication systems, during March ,vol-2,pp.214- march [15] Dr.S.Muralidharan,,M.Muhaidheenperformance investigation of power quality in distributed generation system fed smart grid using different control strategies,journal of Electrical engineering,vol 17. no2,pp , July