Maximum Power Point Tracking of Photovoltaic Generation Based on the Type 2 Fuzzy Logic Control Method

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1 Avaabe onne at Energy roceda 2 (2) ICSGCE 2: 27 3 September 2, Chengdu, Chna Maxmum ower ont Trackng of hotovotac Generaton Based on the Type 2 Fuzzy Logc Contro Method Amr Gheb *, S.M.A.Mohammad, M.maghfoor The Eectrca Engneerng Department, Shahd Bahonar Unversty of Kerman, Iran. Abstract Accordng to a nonnear current-votage characterstc hotovotac for expotaton of ths optmzaton we need to track maxmum output nstanty. The am of ths paper s to search maxmum power pont (M) Based on the Type2 Fuzzy ogc controer (T2FLC) whch s a nove method n maxmum power pont trackng (MT). Soar ces M vares wth soar nsoaton and ambent temperature. Wth the mproved effcences of power eectroncs converters, t s now possbe to operate photovotac (V) power systems at ts M n order to mprove the overa system effcency. Ths paper presents a T2FLC method for trackng M n photovotac power systems and the contro system s estabshed smutaneousy. The resuts of smuaton show that the T2FLC sgnfcanty mproves the robustness of controer s V durng the trackng phase as compared to a conventona type fuzzy ogc contro (TFLC) n present of nose n photovotac power systems. Ths nose maybe nsert to system when votage and current are measured. We show that the resuts obtaned wth T2FLC are better than the ones obtaned wth the TFLC method. 2 ubshed by Esever Ltd. Open access under CC BY-NC-ND cense. Seecton and/or peer-revew under responsbty of Unversty of Eectronc Scence and Technoogy of Chna (UESTC) Keywords: Boost converter; MT; hotovotac; Soar ce; Type2 FLC. Introducton Soar energy, as an emerged green energy resource wth characterstcs of copousness, ceanness, envronmenta protecton and no terrtora restrctons and so on, s wdey used. The hotovotac (V) arrays produce eectrc power drecty from sun ght. Due to ther nta hgh costs, soar ces have not yet been an attractve aternatve for eectrcty users who are abe to buy cheaper eectrca energy from the utty grd. V gves the we-known nonnear reatonshp between the current and votage of the V * Correspondng author. Te.: E-ma address: A.gheb@eng.uk.ac.r ubshed by Esever Ltd. Seecton and/or peer-revew under responsbty of Unversty of Eectronc Scence and Technoogy of Chna (UESTC). Open access under CC BY-NC-ND cense. do:.6/j.egypro.2..73

2 Amr Gheb et a. / Energy roceda 2 (2) ces; t can be observed that there s a unque pont, under gven umnaton, at whch the ce produces maxmum power, That s why t s be caed M. Ths pont occurs when the rate of change of the power wth respect to the votage s equa to zero. Because the output characterstc of the soar ces vares wth the envronments, converson effcency of the soar ces s reatvey ow; gettng some benefts from the converted energy by soar ces as much as possbe becomes a key ssue n the soar energy utzaton. The Boost converters are wdey used n V generaton as an nterface between the V pane and the oad, aowng the foow-up of the M. Based on concept, a knd of maxmum power pont trackng (MT) technoogy s suggested. Many MT technques have been proposed, they can be categorzed as: The methods based on a agorthm for exampe perturbaton and observaton (&O)methods [5]-[8] and IC that measured ce characterstcs ( current, votage, power) are empoyed aong wth an onne search agorthm to compute the correspondng M ndependent of nsoaton, temperature. Integent controng methods []-[6]-[3]-[4]. Consst of fuzzy ogc contro (FLC) and Adaptve fuzzy ogc contro (AFLC) and Artfca neura network (ANN). Computatona method [6]-[2].Characterstcs of soar ces s modeed usng mathematca equatons or numerca approxmatons. The mode most be vad under dfferent nsoatons, temperature, and degradaton condtons. The mode whch we consdered n ths paper s based on type2 fuzzy ogc contro (T2FLC). The concept of a type2 fuzzy set was ntroduced by Zadeh []. Ths controer consders uncertanty of the mode whch s characterzed by membershp functons (MFs) that are they fuzzy. FLCs are usuay constructed usng type fuzzy sets. Such FLCs have been apped to many areas, especay for the contro of compex nonnear systems that are dffcut to mode anaytcay. Despte ther popuarty, research has shown that type FLCs may have dffcutes n modeng and mnmzng the effect of uncertantes. The quantfcaton of the degree of uncertanty n a system depends on the type of uncertanty one s tryng to measure and on the partcuar measure seected for that type of uncertanty. 2. The Characterstc of a V The reatonshp between output votage and current of the soar ce at same ght ntensty and temperature as depcted n Fg.. It can be observed that under a certan ght ntensty and temperature there s a unque pont ocated at the knee of the I-V curve, at whch the M can be generated from the V. Boost converter s used to have M of V. Ths controer paced between V and oad. But M vares wth changng temperature and sun ght ntensty. Fg. shows these varatons. 6 6 o w e r (W) T =25 o C W/m 2 8 W/m 2 6 W/m 2 o w e r (W) S = W/m 2 6 o C 4 o C 25 o C Votage (V) Votage (V) (a) (b) Fg.. Varatons of M wth changng: (a) soaton (b) temperature

3 54 Amr Gheb et a. / Energy roceda 2 (2) Type Fuzzy Logc Controer Ths controer has been apped to photovotac systems n many papers snce now [4]-[]. Type fuzzy ogc controer s made of fuzzfcaton, knowedge and nference unt, defuzzfcaton and the membershp functon of the nputs and output are ndcated n Fg. 2. The fuzzy contro requres that varabe used n descrbng the contro rues has to be expressed n terms of fuzzy set notatons wth ngustc abes. The rue base that assocates the fuzzy output to the fuzzy nputs s derved by understandng the system behavor. After the rues have been evauated, the ast step to compete the fuzzy contro agorthm s to cacuate the crsp output of the fuzzy contro wth the process of defuzzfcaton. The mpementaton of the fuzzy controer n terms of type and type2 fuzzy sets has two nput varabes; the error et () and the error varaton e(t), gven by: pt () et () =, et () = et () et ( ) () vt () Crsp nputs e(t) Knowedge base Rue base Crsp output Fuzzfcaton Decson makng Defuzzfcaton u(t) e(t) Fg.2. Structure of a type FLC 4. Type2 fuzzy ogc controer A T2FLC composed of four basc eements (Fg.3): the type fuzzyfer, the fuzzy rue-base, the nference engne, and the type defuzzyfer. The fuzzy rue-base s a coecton of rues, whch are combned n the nference engne, to produce a fuzzy output. Tabe shows these rue bases wth Lower Standard Devaton (LSD) and Upper Standard Devaton (USD) whch are one of mportant characterstcs of T2FLC[9]-[2],whch these shows n Fg. 4. The type fuzzyfer maps the crsp nput nto type fuzzy sets, whch are subsequenty used as nputs to the nference engne, whereas the type defuzzyfer maps the type fuzzy sets produced by the nference engne nto crsp numbers. A TFLCs are unabe to hande rue uncertantes drecty, because they use type fuzzy sets that are certan. On the other hand, T2FLCs are very usefu n crcumstances where t s dffcut to determne an exact, and measurement uncertantes [8]. It s known that type2 fuzzy set et us to mode and to mnmze the effects of uncertantes n rue base FLC. Unfortunatey, type2 fuzzy sets are more dffcut to use and understand than type fuzzy sets; hence, ther use s not wdespread yet. A T2FLC A ~, s characterzed by the membershp functon:

4 Amr Gheb et a. / Energy roceda 2 (2) {((, ), µ (, )), [, x ]} = xu xu x X u J ( xu) µ, x Xu Jx (, ) /(, ) [,] = µ xu xu J x et () Crsp nputs Rue Base (2) Fuzzfcato n Inferenc e Type-reducer e(t) Fuzzy nput sets Fuzzy output sets Crsp output u(t) Defuzzfcato n Type-reduced Set (Type) Fg. 3. Structure of a type2 FLC Hence, a type2 membershp grade can be any subset n [, ], the prmary membershp, and correspondng to each prmary membershp, there s a secondary membershp (whch can aso be n [, ]) that defnes the possbtes for the prmary membershp. Ths uncertanty s represented by a regon caed footprnt of uncertanty (FOU) whch can be descrbed n terms of an upper membershp functon (UMF) and a ower membershp functon (LMF) as shown n Fg. 4. M e m b e r s h p f u n c t o n v a u e N e g a t v e Z e r o LMF o s t v e UMF e(t) and de(t) (a)

5 542 Amr Gheb et a. / Energy roceda 2 (2) M e m b e r s h p f u n c t o n v a u e NG N Z G 4.. Fuzzfcaton and the Rues The fuzzfer maps a crsp pont ( p) u(t) (b) Fg.4. membershp functon: (a) nputs (b) output T x = x,..., x X X... X X nto a type2 fuzzy set A % X n 2 X. As a type2 sngeton fuzzfer n a sngeton fuzzfcaton wth the nput fuzzy set havng ony a snge pont on nonzero membershp s used, we have: µ = ' X X ~ = ' A x X X The structure of rues n a TFLC and a T2FLC s the same. However, n the atter the antecedents and the consequents w be represented by T2FLCs. Suppose a T2FLC has p nputs x, x2,..., xp an output y, and a mutpe nput snge output (MISO). It s assumed that there are M rues and the th rue n the type2 FLC can be wrtten as foows: ~ ~ ~ R : IF x s F... IF xp s Fp then ys G =,2,... M (4) 4.2. B. Inference In T2FLC, the nference engne combnes rues and gves a mappng from nput T2FLCs to output T2FLCs. It s necessary to compute the jon (unons), the meet (ntersectons), and the extended F... F = A, Eq. (4) can be re- sup-star composton (sup-star compostons) of type2 reatons. If wrtten as: ~ ~ ~ ~ ~ ~ ~ ~ (3) R : F... F G = A G, =,..., M (5) R Rue s descrbed by the membershp functon µ ( xy, ) µ ( x,..., x, y R ) R p µ = µ = µ µ = where: ( xy, ) ( xy, ) ( x ) ( y) (6) ~ ~ ~ ~ R A G F G

6 Amr Gheb et a. / Energy roceda 2 (2) In genera, the p-dmensona nput to functon s: ( X) ( x ) ~ ~ AX X R s gven by the type2 fuzzy set A % X whose membershp µ = µ (7) where X ~ (;... ; p) are the abes of the fuzzy sets descrbng the nputs. Each rue type2 fuzzy set ~ ~ B = A R such that: ~ B ( y) ~ ( y) µ = µ = C x X Ax or X ~ ( ) µ X µ ( X, y), y Y =,..., M R Ax R determnes a Ths equaton s the nput / output reatonshp between the T2FSLC that actvates one rue n the nference engne and the T2FLC at the output of that engne as descrbed n Fg. 3. In the FLC we used nterva T2FLCs and meet under product t-norm, so the resut of the nput and antecedent operatons, whch are contaned n the frng set, frngset µ ( x ) F ( x' ) = f ( x', ) f ( x' ) f, f where: ( ) ~ ' ~ ' f x' = µ ( x )*...* µ ( x ) F F ~ ' ~ ' f ( x' ) = µ F ( x )*...* µ F ( x ) Note * s the product operaton Type-reducer and defuzzfcaton =, s an nterva TFLC set : ' ~ F The type-reducer generates a TFLC output whch s then converted nto a crsp output through the defuzzfer. Ths TFLC s aso an nterva set. For the case of our FLC we used center of sets (cos) type reducton, Ycos whch s gven by: Ycos = [ y, yr ] = M () f y / M M M M M M M f y [ y, yr ] y [ y, y ] f [ f, f ] f [ f, f ] r Ths nterva set s determned by ts two end ponts, the type2 nterva consequent set G ~ expressed as: G N yθ... / [, r] θ J y θn J θ y N y and (8) (9) () y r, whch correspond to the centrod of C % = = y y (2) Before the computaton of Y ( X ), we must evauate (2), and ts two end ponts, cos y and y r. Let the vaues of f and y that are assocated wth y are denoted by f and y, respectvey, and the vaues of f and y that are assocated wth yr are denoted by fr and y r, respectvey, then from (), we have:

7 544 Amr Gheb et a. / Energy roceda 2 (2) y y M f y = M = f M fr yr r = M = fr From the type-reducer we obtan an nterva set Y ( X ), to defuzzfy t we use the average of y and y, so the defuzzfed output of an nterva sngeton T2FLS s: r y + yr yx ( ) = (5) 2 Tabe. shows the characterstcs of the nputs and output of the T2FLC system wth three parameters for tunng (the mean of the nputs' and outputs' membershp functon (MF)). cos Tabe : Characterstcs of the Inputs and Output of the T2 Fc Varabe Term Center Lower Standard Devaton Upper Standard Devaton (3) (4) Input e Negatve Zero ostve -Me Me Input deta-e Output Negatve Zero ostve NG N Z G -Mde Mde -Mo -Mo/2 Mo/2 Mo In ths experment, the ower and upper standard devatons are fxed. 5. Smuaton By recevng controng sgna from controer, Boost converter kept votage at a vaue whch has maxmum power (Fg. 5). Assume an expected nose s mported to system. Equaton (5) shows ths nose: s SNR = = 2 η 2 sgna nose Because most sgnas have a very wde dynamc range, SNR s usuay expressed n terms of the ogarthmc decbe scae, SNR (db): sgna SNR( db) = og nose (6) (7)

8 Amr Gheb et a. / Energy roceda 2 (2) Usuay ths nose s mported to system when votage and current are measured. Nose s apped to system s shown n Fg. 5. We have been exerted nose n TFLC [7] and have been compared performance of TFLC and T2FLC whch was smuated n MATLAB wth dfferent SNR s shown on tabe 2. Fg. 5. Structure of photovotac array wth apped nose Tabe (2) ndcates for a constant vaue of SNR T2FLC has ess error than TFLC because t coverts more uncertanty. The above appcatons have demonstrated that T2FLC s better at modeng uncertantes than TFLC. Fg. 6 shows MT wth nose n V pane. Tabe 2: Compare Between Rates of Error Typeand Type2 e(t) SNR(db) Type Type o w e r (W) o w e r (W) Tme (s) Tme (s) (a) (b) Fg. 6. Comparng MT wth nose n (a)tflc (b)t2flc 6. Concuson In ths paper we apped T2FLC on photovotac pane. We observed t s proper for performance n nosy envronments just ke these envronments. Nose mportaton s unavodabe.so usng controer whch s coud decrease nose effect s very mportant. By consderng the resuts of smuaton whch were acheved n ths paper t s notceabe; T2FLC has better operaton than FLCT whenever nose was present. On the other hand because of ts compcatng and tme consumng cacuaton T2FLC s sower than TFLC.

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