Study on tracking control of maximum power point for chemical photovoltaic power system

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1 Avalable ole Joural of Checal a Pharaceutcal Research, 04, 6(6: Research Artcle N : CODEN(UA : JCPRC5 tuy o tracg cotrol of axu ower ot for checal hotovoltac ower syste N Qaqa a Xue Hegyu tate Gr Jbe Electrc Power Co., LTD, Lagfag Power uly Coay, Lagfag, Hebe Togj Uversty, hagha ABTRACT orer to acheve the tracg cotrol of axu ower ot for checal hotovoltac syste, a rove the trasferrg effcecy of solar eergy, the fuzzy PD cotroller s ale t. Frstly, the worg theory of hotovoltac cell s aalyze. ecoly, the fuzzy PD cotroller of axu ower ot of checal hotovoltac syste s esge. Fally, the cotrollg sulato of tracg cotrol of axu ower ot s carre out, a the results show that the fuzzy PD cotroller ca get goo cotrollg effect. Key wors: Checal Photovoltac Power yste; Maxu Power Pot; Cotrol Wth eco growth a sal rogress, seeg ew sources of eergy s a urget tas that a faces. The solar eergy s a exhaustble a eless source. olar ower wth hgh effcecy a o-olluto has bee cere, whch s urestrcte rego. Photovoltac ower s a a for of usg solar ower, whch has vast rosect for eveloet. The hotovoltac ower has bee ale checal ustral ar wely. The rch checal raw aterals checal ustral ar ca offer suffcet resource suort for hotovoltac ustry, a reuce the roucto costs of checal eterrse. There have always bee soe robles hotovoltac ower syste. The outut characterstcs of hotovoltac cell are greatly affecte by the exteral evroet, such as evroetal teerature a outer lght testy. ato, the coverso effcecy of hotovoltac cell s low, a the rce s hgh, the the tal ut s bg. The t s ecessary to f out a effectve etho to rove the coverso effcecy of hotovoltac cell. The axu ower ot tracg crcut s collecte betwee hotovoltac cell a loa []. recet years, a lot of algorths of axu ower ot tracg have bee ut forwar, such as erturbato a observato etho, creetal couctace etho a costat voltage tracg etho. The curret algorths are sle a easy to leet, however there are ay savatages, for exale, the covergece see s low, a the steay state stablty s oor. orer to avo the efects, the tratoal algorth has bee rove, the aatve ste s trouce, a the relablty a covergece see ca be obtae. But the worg ot ca ot be trasferre to the axu ower ot whe the lght stregth chages suely. orer to reuce the stable error of syste, the fuzzy PD cotroller s ale t, the quc resose ablty of the hotovoltac ower o outer evroet ca be rove, a stablty ear the axu ower ot ca be reuce, at the sae te the PD cotroller ca elate ths ollato []. Worg theory of hotovoltac cell T-V feature of the hotovoltac cell has soethg wth lght stregth a evroet teerature. recet years, a lot of hotovoltac cell uses crystalle slco as ateral. The equvalet crcut of the hotovoltac cell s show fgure. 047

2 N Qaqa a Xue Hegyu J. Che. Phar. Res., 04, 6(6: Fgure Equvalet crcut agra of the hotovoltac cell The outut curret a outut voltage of the hotovoltac cell satsfes the followg exresso [3]: = h [ e q( V + Rs V + KT ] Rs R 0 ( sh where, eotes the outut curret of hotovoltac cell, A ; reverse saturato curret A ; q eotes quatty of electrc charge, Boltza costat, T eotes the surface teerature of hotovoltac cell late, K ; h eotes the hoturret, A ; 0 eotes 9 q =.6 0 C ; K eotes the 3 K =.38 0 J / K ; eotes the eal factor of hotovoltac cell late, = 5 The saturato curret wthout lght ca be calculate accorg to the followg exresso: q( V + Rs 0 KT = [ e ] ( ; where eotes the saturato curret wthout lght, A. The egeerg oel of hotovoltac cell uses the short-crcut curret curret at axu ower ot, outut voltage, the short-crcut voltage V, outut V at axu ower ot offere by aufacturer, other electrcal araeters of hotovoltac cell uer fferet lght stregth a cell teerature ca be obtae accorg to the followg exressos [4]: = ( + A T (3 V V where V ( C T l( e + B = (4 = ( + A T (5 = V ( C T l( e + B (6 T T + ar = K, T ar eotes the evroetal teerature,, T = T T 3 A =.5 0 /, 3 = 0 W /, B = 6 0 /, 3 C = 3 0 /,, =, eotes the erece lght stregth, Uer a certa lght stregth a teerature, the hotovoltac ower syste ca acheve the steay status of 048

3 N Qaqa a Xue Hegyu J. Che. Phar. Res., 04, 6(6: axu ower ot. Near the axu ower ot, the outut ower of hotovoltac ower syste ca be exresse as follows: P( t u R PV ( t = (7 MPP where P (t eotes outut ower, R MPP eotes the resstace of the axu ower ot. Whe outut loa of hotovoltac ower syste s equal to R MPP, a the syste ca exort axu ower. The hotovoltac cell grou s ae u of ay hotovoltac cells wth a sall ut seres or arallel. The hotovoltac cell seres cobato ca rove the axu outut rect curret of checal solar eergy ower syste, a the hotovoltac cell arallellg cobato ca also rove t. Theore the seres or arallelg cobato of hotovoltac cells ca obta the execte rect curret or voltage, the outut characterstcs of the hotovoltac cells grou s exresse as follows: q( V + Rs s AT = L [ e ] (8 where LG os eotes the uber of hotovoltac cells seres, eotes the lght curret, L os eotes the ar saturato curret. s eotes hotovoltac cells arallelg. Desg of Fuzzy PD cotroller of axu ower ot The tratoal PD cotroller has soe savatages, for exale, the structure s sle, a the erforace s steay. However, t has soe savatages, t ca be affecte by the sturbace, a the relablty s oor. The fuzzy cotrol belogs to a tellget cotrollg techology, has a goo self aatve characterstcs, but the statc error ca ot be elate urg the resso of cotrollg the axu ower ot of checal hotovoltac ower syste. Theore the fuzzy cotrollg techology a PD cotroller ca be cobe coserg the above factors, the relatg araeters of PD cotroller ca be regulate accorg to the fuzzy cotrollg rcle, the real te cotrol of axu ower ot of the of checal hotovoltac ower syste ca be acheve [5]. orer to cotrol the axu ower ot of hotovoltac ower syste, the fuzzy PD cotroller s ale t. The covetoal fuzzy PD has sall exceeg regulato a slow resose see coarg wth the tratoal PD cotroller, however the fuzzy PD cotroller exsts a lot of savatages, for exale, a the fuzzy cotroller ca be aee whe t s esge, a the self-aatvty of t s oor. f the ut a outut of fuzzy cotroller have bg chages, oly a art of rcles ca be ale. Whe the rage of the ourse oa s sall, the ut a outut of the fuzzy cotroller s out of rage of the ourse oa, the fuzzy cotroller ca ot wor effectvely. Whe the rage of ourse oa s bg, the uber of rcles of the fuzzy cotroller s sall, the the cotrollg recso ca reuce, the fucto of fuzzy PD cotroller ca ot be eveloe. orer to avo the savatages, varable ourse oa s ale t. The ba eas of t are to reuce or rove the rage a ut value of ourse oa of fuzzy set sultaeously. The ecrease a exaso of ourse oa ca rove the fuzzy cotrollg uber that affects t sgfcatly, a the the cotrollg recso ca be rove. The a roble of the varable ourse oa s to cofr the otal exteso a cotracto echas, the the otal cotrollg effect ca obtae. The ut varable of the ourse oa X s efe as x, the outut varable of the ourse oa Y s efe as y, the varable ourse oa ers that a Y ca regulate wth chages of x a y. The chage ourse oa ca be exresse as follows [6]: X Y = [ α ( x E, α ( x E ] (9 [ β ( y U, βu( y] = (0 LG X 049

4 N Qaqa a Xue Hegyu J. Che. Phar. Res., 04, 6(6: where, α ( x a β ( y eote cotracto-exaso factor of the ourse oas outut of the varable ourse oa cotroller s exresse as follows: u VFC ( x x 0 β = β A y ( = = α( x The cotracto-exaso factors of the ourse oas are exresse as follows: X a Y, the ε x α( x =, 0 < ε < ( X ε y β ( x =, Y 0 < ε < (3 where ε a ε are the value factor of the u ourse oas, whch has bg effect o the cotrollg recso of the syste, the value of ε a ε ca be regulate accorg to the sulato aalyss, ε, ε 35. a the fal results are lste as follows: = = 0. The fuzzy theory a tratoal PD cotrollg techology ca be cobe to costruct the aatve PD cotroller, the evace e a chagg rate of evace, tegrate coeffcet a fferetal coeffcet ec are the fucto of roorto coeffcet, the followg the exresso ca be obtae [7]: = h ( e, ec (4 = h ( e, ec (5 = h ( e, ec (6 The aatve PD cotrollg syste of axu ower ot of the hotovoltac ower syste s show fgure. Cotracto-exaso factor Fuzzy cotrol ut Devato e t PD cotroller Maxu ower ot of hotovoltac ower syste Outut Fgure Aatve PD cotrollg syste of axu ower ot The fuzzy self aatve PD cotroller ca be ale cotrollg the axu ower ot of the hotovoltac ower syste. Accorg to the evaces, chagg rate of the esstace a fuzzy theory, the fuzzy cotrollg 050

5 N Qaqa a Xue Hegyu J. Che. Phar. Res., 04, 6(6: rcles of the roorto coeffcet chage coeffcet chage, tegrate coeffcet chage, a fferetal ca be establshe, the fuzzy ourse oa s set as [-3,3], whch s ve to seve graes a s eote as {PL,PM,P,ZE,N,NM,NL},where PL eotes ostve large, PM eotes ostve eu, P eotes the ostve sall, ZE eotes the zero, N eotes egatve sall, NM eotes the egatve eu, NL eotes egatve large. The corresog cotrollg rcles are show table, table a table 3 resectvely. Table Cotrollg rcle of ec e NL NM N ZE P PM PL NL N ZE ZE N NM NL NL NM P P ZE N N NM NM N PL PL PM ZE ZE N N ZE PL PM P P ZE ZE N P PM PM PM PM P ZE ZE PM PL PM PM ZE N ZE ZE PL PL PL PL PM PM P ZE ec Table Cotrollg rcle of e NL NM N ZE P PM PL NL ZE N N NM NM NL NL NM PM PM P P ZE ZE N N P ZE ZE N N NM NM ZE P P ZE ZE ZE N N P PM PM P P ZE ZE N PM PL PM PM P P ZE ZE PL PL PL PL PM PM ZE ZE Table 3 Cotrollg rcle of ec e NL NM N ZE P PM PL NL P ZE N N NM NM NL NM PM P ZE ZE N NM NM N PL P P ZE ZE N N ZE P P ZE ZE NL N N P PL PL ZE N N N NM PM PL PL PM PM ZE N N PL PL PM PM P P ZE N Accorg to the actual requreet of cotrollg axu ower ot of checal hotovoltac ower syste, the corresog cotrollg rcles are set as follows: F F e = N AND ec = PL THEN u = NL e = PM AND ec = NM THEN u = N Accorg to the fuzzy above cotrollg rcle, the fuzzy logcal oerato table of fuzzy cotrol ca be obtae. The outut value of fuzzy araeter self regulato PD cotroller ca be calculate accorg to the weghte average etho, the corresog reure s lste as follows: te : Calculate the core eleets of all eleets fuzzy reasog cluso. te : Obta the corresog recso value after the core eleets are fuzze, the corresog calculatg exresso s lste as follows: 05

6 N Qaqa a Xue Hegyu J. Che. Phar. Res., 04, 6(6: u * = u = φ( = φ( (7 * Where, u eotes the exact soluto, φ ( eotes the ebersh egree fucto of, a, eotes the uber of outut eleets. The tegrate value of, a ca be calculate through regulatg the recso value. A the ut araeter of fuzzy araeter self regulato PD cotroller ca be obtae by the followg exresso: = = = (8 where, 0, 0 a 0 eote orgal value of, a. REULT AND DCUON Accorg to the ba theory of fuzzy PD cotroller, the cotrollg sulato rograer s cole by MATLAB software, at the sae te the tratoal PD cotroller s ale cotrollg the sae syste. A checal hotovoltac ower syste s use as researchg object, the corresog araeters are lste as follows: short-crcut curret s equal to 4.88A, the oe crcut voltage V s equal to 0.6V, the curret of axu ower ot s equal to 4.8A, the voltage of axu ower ot V s equal to 6.8V. The evroetal teerature T =30, a the lght stregth chages fro 750W/ to 50W/ s. The corresog sulato curve s show fgure. Fgure Cotrollg sulato curves of axu ower ot of checal hotovoltac ower syste As see fro fgure, the cotrollg sulato curves base o tratoal PD cotroller has a sall ollato, whle the cotrollg sulato curves base o fuzzy PD cotroller ca get the outut ower curves wth sooth chages. Theore cotrollg effect of the fuzzy PD cotroller s better tha that of tratoal PD cotroller. 05

7 N Qaqa a Xue Hegyu J. Che. Phar. Res., 04, 6(6: The the trasferrg effcecy of solar eergy of checal hotovoltac ower syste ca be rove effectvely. CONCLUON The fuzzy PD cotroller s ale cotrollg the axu ower ot of the checal hotovoltac ower syste a the aee factor s trouce regulatg the araeters of fuzzy PD cotroller, a the correctess a stablty of the checal hotovoltac ower syste ca be rove, cotrollg sulato results show that the fuzzy PD cotroller ca acheve the tracg a cotrollg of the axu ower ot, the feasblty of fuzzy PD cotroller o the checal hotovoltac ower syste s verfe. REFERENCE [] NA Ahe, AK Al-Otha, MR AlRash. Electrc Power ystes Research, 0, 8(5, [] B Para, ya, R G. Reewable a ustaable Eergy Revews, 0, 5(3, [3] L Zhu, RF Boeh, YP Wag. olar Eergy Materals a olar Cells, 0, 95(, [4] GK gh. Eergy, 03, 53(, -3. [5] JD Par, ZY Re. Joural of Power ources, 0, 05(5, [6] K Yg. Joural of Checal a Pharaceutcal Research, 04, 6(3, [7] T Kuag, Zhu. Joural of Checal a Pharaceutcal Research, 04, 6(,

ELEMENTS OF NUMBER THEORY. In the following we will use mainly integers and positive integers. - the set of integers - the set of positive integers

ELEMENTS OF NUMBER THEORY. In the following we will use mainly integers and positive integers. - the set of integers - the set of positive integers ELEMENTS OF NUMBER THEORY I the followg we wll use aly tegers a ostve tegers Ζ = { ± ± ± K} - the set of tegers Ν = { K} - the set of ostve tegers Oeratos o tegers: Ato Each two tegers (ostve tegers) ay