Abstract²This paper presents a power control system for DC DC boost converter integrated with Photovoltaic (PV) arrays using optimized back propagation ...
WK,QWHUQDWLRQDO&RQIHUHQFHRQ.QRZOHGJHDQG6PDUW7HFKQRORJ\ .67
$3RZHU&RQWURO6\VWHPLQ'&'&%RRVW&RQYHUWHU ,QWHJUDWHGZLWK3KRWRYROWDLF$UUD\VXVLQJ2SWLPL]HG %DFN3URSDJDWLRQ$UWLILFLDO1HXUDO1HWZRUN 1-LWHXUWUDJRRO&:DQQDERRQDQG:6DQ8P
,QWHOOLJHQW(OHFWURQLF6\VWHPV5HVHDUFK/DERUDWRU\ )DFXOW\RI(QJLQHHULQJ7KDL1LFKL,QVWLWXWHRI7HFKQRORJ\ 71, 3DWWDQDNDUQ6XDQOXDQJ%DQJNRN7KDLODQG7HO ([W )D[ &RUUHVSRQGLQJ$XWKRU(PDLO$GGUHVV ZLPRO#WQLDFWK
$EVWUDFW²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
,
,1752'8&7,21
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
,(((
107
,Q SDUWLFXODU IRU VWDQGDORQH 39 V\VWHPV WKDW JHQHUDWH FRQVWDQW DQG VSHFLILF RXWSXW SRZHU WKH HOHFWURQLFV LQWHUIDFH V\VWHPLV QHFHVVDU\EHWZHHQWKHRXWSXWRIWKH39V\VWHPDQG WKH ORDG 7\SLFDOO\ 39 V\VWHPV HPSOR\ D '&±'& ERRVW FRQYHUWHU ZKLFK LV D FODVV RI VZLWFKLQJ SRZHU UHJXODWRU WKDW SURYLGHV DQ RXWSXW YROWDJH JUHDWHU WKDQ D UHFHLYHG LQSXW YROWDJH6XFKDERRVWFRQYHUWHUDOVRIL[HVWKHRXWSXWSRZHUHYHQ WKRXJK WKH VRODU FHOOV GHOLYHU XQVWDEOH LQSXW SRZHU GXH WR YDULDWLRQV RI UDGLDWLRQ LQWHQVLW\ DQG DPELHQW WHPSHUDWXUHV ,Q JHQHUDO WKH ERRVW FRQYHUWHU RSHUDWHV DW D FHUWDLQ GXW\ F\FOH UHVXOWLQJ LQ D VSHFLILF RXWSXW YROWDJH YDOXH ,Q WKH FDVH ZKHQ WKH LQSXWYROWDJHLVFKDQJHGZKLOHWKHGXW\F\FOHLVVWLOONHSWFRQVWDQW WKH RXWSXW YROWDJH ZLOO YDU\ 0RVW ERRVW FRQYHUWHUV DUH FRQWUROOHG E\ D SXOVH ZLGWK PRGXODWLRQ 3:0 WHFKQLTXH WKDW UHJXODWHV WKH FRQVWDQW RXWSXW YROWDJH WKURXJK WKH FKDQJH LQ WKH GXW\F\FOHLQWKHFRQWUROVLJQDO 7UDGLWLRQDO GHVLJQ WHFKQLTXHV DUH EDVHG RQ 3URSRUWLRQDO ,QWHJUDO'HULYDWLYH 3,' FRQWUROOHUV LQ ZKLFK SDUDPHWHUV FDQ EH DGMXVWHG IRU DSSURSULDWH VHWWOLQJWLPH RYHUVKRRW DQG VSHFLILF RXWSXW YDOXHV >@ +RZHYHU WKH 3,' FRQWUROOHUV RSHUDWH LQ 6LQJOH,QSXW 6LQJOH2XWSXW 6,62 PRGH ZKLFK LV QRW VXIILFLHQW IRU QRQOLQHDU V\VWHPV &RQVHTXHQWO\ WKH WUHQG RI FRQWURO WHFKQLTXHV KDV DOWHUQDWLYHO\ IRFXVHG RQ DUWLILFLDO LQWHOOLJHQW DQG IX]]\ ORJLF WHFKQLTXHV 1RQHWKHOHVV WKH IX]]\ ORJLF FRQWURO PD\ QRW VWDEOH LQ VRPH FLUFXPVWDQFHV DQG GLIILFXOW IRU KDUGZDUH LPSOHPHQWDWLRQV >@ 7KHUHIRUH DQ $UWLILFLDO 1HXUDO 1HWZRUN $11 KDV EHFRPH D SURPLVLQJ VROXWLRQ IRU QRQOLQHDU V\VWHP FRQWUROV ZLWK FDSDELOLW\ RI OHDUQLQJ WKH SUREOHPV SUHGLFWLQJ WKH QH[W VROXWLRQ DQG SURYLGLQJORZUHVSRQVHWLPHZLWKKLJKSUHFLVLRQ 5HFHQWO\ $11 FRQWUROOHUV KDYH EHHQ HPSOR\HG LQ 0D[LPXP3RZHU3RLQW7UDFNLQJ 0337 DQGYROWDJHWUDFNLQJ V\VWHPV RI PDQ\ '&'& ERRVW FRQYHUWHUV >@ +RZHYHU YDULDWLRQV LQ LQSXW YROWDJHV XQGHU WKH FKDQJHV LQ WHPSHUDWXUH DQGLUUDGLDWLRQKDYHQRWPXFKVWXGLHGHVSHFLDOO\WKHUHVSRQVH FKDUDFWHULVWLFVRI$11XQGHUVXFKHQYLURQPHQWYDULDWLRQV
,3+
,39
Q ,' ,6
,3 '
,'
Q
/
56 53
,/
Q
939
&LQ
/DVW WKH FXUUHQW IORZLQJ WKURXJK WKH UHVLVWRU 53 FDQ EH REWDLQHGXVLQJ2KP¶V/DZDVIROORZV
Q
' 6:
&2
92
,3
5/
93:0
D 3KRWRYROWDLF6\VWHP0RGHO
)LJXUH 7KHFLUFXLWGLDJUDPRIWKHLQYHVWLJDWLQJVRODUSRZHUJHQHUDWLRQ IURQWHQG D DSKRWRYROWDLFPRGHODQG E '&'&ERRVWFRQYHUWHU
, 39 , 3+ , ' , 3
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
&RQVLGHULQJ DQ RSHQORDG FRQGLWLRQ DQG DSSO\LQJ .LUFKKRII¶V FXUUHQW ODZ DW WKH LQSXW QRGH Q WKH FXUUHQW HTXDWLRQFDQEHFRQFOXGHGDV,6& ,',3,39,QRWKHUZRUGV
E '&'&%RRVW&RQYHUWHU
,,
, 39 56 939 53
ZKHUH,6&LVDVKRUWFLUFXLWFXUUHQWDW R&DQGN:PNLLVD VKRUWFLUFXLW FXUUHQW WHPSHUDWXUH FRHIILFLHQW 7& LV DQ DFWXDO WHPSHUDWXUH LQ .HOYLQ 75 LV WKH UHIHUHQFH WHPSHUDWXUH LQ .HOYLQ DQG + LV WKH VRODU LVRODWLRQ LQ N:P 6HFRQG WKH GLRGHFXUUHQW,'FDQEHH[SUHVVHGDV
§ T( 7 75 ·§ § T 939 , 39 56 · · §7 · ¸¸¨ H[S ¨¨ ¸¸ ¸ , ' , 56 ¨¨ & ¸¸ H[S ¨¨ * & ¨ ¸ E E.7& 7 7 7 . 5 & © 5¹ © ¹© © ¹ ¹
ZKHUH ,56 LV D UHYHUVH VDWXUDWLRQ FXUUHQW DW D UHIHUHQFH WHPSHUDWXUH DQG VWDQGDUG VRODU UDGLDWLRQ T LV DQ HOHFWURQ FKDUJH(*LVDEDQJJDSHQHUJ\RIWKHVHPLFRQGXFWRUXVHGLQ WKH FHOO . LV D %ROW]PDQQ¶V FRQVWDQW ȕ LV DQ LGHDOLW\ IDFWRU
108
6XEVWLWXWLQJ LQWR DQGDUUDQJLQJIRUWKH939\LHOGV 939 , 3+ , ' , 39 53 , 39 56
(TXDWLRQ LQGLFDWHV WKDW WKH SKRWRYROWDLF YROWDJH 939 PDLQO\GHSHQGVXSRQWKHWKUHHFXUUHQWV ,3+,'DQG,3ZKRVH QXPHULFDOYDOXHVFDQEHREWDLQHGIURPVSHFLILFSDUDPHWHUVHWV RIDFRPPHUFLDOO\DYDLODEOHVRODUFHOOOHDYLQJVROHO\ 7&DQGȜ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ª ,/ º « » ¬92 ¼
ª « X & 2 ¬
X /º ª , / º ª /º ª939 º 5/ &2 »¼ «¬92 »¼ «¬ »¼ «¬ »¼
ZKHUHXLVDGXW\F\FOHRIWKH3:0FRQWUROVLJQDODQGIDOOVLQ WKHUHJLRQ ,WFDQEHFRQVLGHUHGIURP(T WKDWWKHYDOXH RI RXWSXW YROWDJH 92 JUHDWO\ GHSHQGV RQ X DQG LV HYROYHG LQ WLPHGHULYDWLYHGXHWRWKHFDSDFLWRU&2UHVXOWLQJLQVRPHVPDOO ULSSOHV 8SRQ FRQVLGHUDWLRQ RI YROWDJHFXUUHQW FKDUDFWHULVWLFV RI(TQV WKH PDWKHPDWLFDO IXQFWLRQVRIWKH V\VWHPV LQ )LJV D DQG E PD\EHGHVFULEHGDV 92
I 939 X
I I 7& O X
,W FDQ EH FRQVLGHUHG IURP WKDW WKH SDUDPHWHUV 7& DQG Ȝ DUHLQGHSHQGHQWSDUDPHWHUVZKLOVWXLVFRQWUROODEOHDQGKHQFH WKHFKDQJHLQVXFK7&DQGȜYDOXHVZRXOGUHVXOWLQWKHFKDQJH LQ92ZKLFKFDQEHUHJXODWHGWKURXJKWKHGXW\F\FOHX ,,, 352326('28738792/7$*(&21752/2)%2267 &219(57(5,17(*5$7(':,7+3+27292/7$,&02'(/6 )LJ D VKRZV WKH SURSRVHG RXWSXW YROWDJH FRQWURO LQ ERRVWFRQYHUWHULQWHJUDWHGZLWKSKRWRYROWDLFPRGHO7KHFLUFXLW FRQVLVWV RI WKH W\SLFDO ERRVW FRQYHUWHU FRQWDLQLQJ / &2 5/ GLRGHDQG026)(7ZLWKDJDWHGULYHU,QDGGLWLRQWKHLQSXW
7& Ȝ
+\SHUEROLF 7DQJHQW 6LJPRLG WDQVLJ QRQOLQHDU DFWLYDWLRQ IXQFWLRQLQWKHKLGGHQOD\HUGHVFULEHGDV
6WDQGDUG'&'&%RRVW&RQYHUWHU
/
,39 39
1
\Q
,5)=Q
&LQ
&2
*DWH 'ULYHU
939
5/ 92
93:0 Ȉ
%DFN 3URSDJDWLRQ 1HXUDO1HWZRUN &RQWUROOHU
'$
$'
92
7KH)HHGEDFN&RQWURO6HFWLRQXVLQJ%DFN3URSDJDWLRQ1HXUDO1HWZRUN
D
2SWLPL]HG1HXURQ1XPEHUV
E Ȉ
Z D
ZQ
E
I6
,9 %2267&219(57(5'(6,*16$1'$11237,0,=$7,216
\ Z2
I6 Ȉ
\
E2 Ȉ
I3
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ȝ)ZDVLQFOXGHGLQ RUGHU WR VWDELOL]H WKH LQSXW YROWDJH GXH WR WKH SHDN FXUUHQW UHTXLUHPHQWRIDVZLWFKLQJSRZHUVXSSO\6HFRQGWKHVHOHFWLRQ RILQGXFWRUYDOXHZDVFDOFXODWHGE\
\2
Z D
,QSXW/D\HU
ZQ
EQ Ȉ
I6Q
\Q
ZQ2
2XWSXW/D\HU
+LGGHQ/D\HU
Q
WK ZKHUH \Q UHSUHVHQWV WKH RXWSXW IURP WKH KLGGHQ OD\HU DW Q QRGH ZQ2 LV D ZHLJKW IRU HDFK KLGGHQ OD\HU RXWSXW IURP QWK QRGHE2LVDELDVRIWKHRXWSXWOD\HU,WFDQEHFRQVLGHUHGWKDW WKHSHUIRUPDQFHRIWKH$11GHSHQGVXSRQWKHQXPEHUQRGHV LQ WKH KLGGHQ OD\HU 7KLV ZRUN DOVR RSWLPL]HV VXFK QXPEHU QRGHVLQRUGHUWRILQGWKHDSSURSULDWHQRGHQXPEHUVLQWHUPVRI RSHUDWLQJVSHHGDQGFRPSOH[LW\
5
6DZWRRWK6LJQDO
SXUHOQ ¦L \Q ZQ2 E2
\2
ELWV
Q
ZKHUHDEUHSUHVHQWVWKHLQSXWELQDU\ELWVDDEDQGE ZEQ LVDZHLJKWIRUHDFKLQSXWELWDWQWKQRGHEQLVDELDVIRUQWK QRGH /DVW WKH RXWSXW OD\HU SURFHVVHV WKH RXWSXWV IURP WKH KLGGHQ OD\HU XVLQJ SXUH OLQH SXUHOQ DFWLYDWLRQ IXQFWLRQ DV IROORZV
5
39 :0;6
WDQVLJ ¦L DE ZEQ EQ
E )LJXUH D 'LDJUDPRIWKHSURSRVHGRXWSXWYROWDJHUHJXODWLRQV\VWHPLQ ERRVWFRQYHUWHULQWHJUDWHGZLWKSKRWRYROWDLFPRGHOV E WKHGHVLJQHGDQG RSWLPL]HGEDFNSURSDJDWLRQQHXUDOQHWZRUN
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
109
/
92 939 9' X L/ )6
ZKHUH 9' LV D YROWDJH GURSSHG DFURVV WKH GLRGH ,W VKRXOG EH QRWHG WKDW VHOHFWLQJ D KLJK LQGXFWRU YDOXH PD\ KHOS GHFUHDVH WKH VHWWOLQJWLPH EXW KLJK RYHUVKRRW ZLOO EH DSSHDUHG >@ 7KHUHIRUH WKH KLJKHIILFLHQF\ P+ LQGXFWRU ZDV VHOHFWHG /DVWWKHRXWSXWFDSDFLWDQFH&2ZDVFDOFXODWHGE\ &
92 X 5/9ULSSOH)V
ZKHUH 9ULSSOH LV D ULSSOH YROWDJH 7KH RXWSXW FDSDFLWRU LV FKRVHQWRPHHWDQRXWSXWYROWDJHULSSOHDQG(TXLYDOHQW6HULHV 5HVLVWDQFH (65 DIIHFWV HIILFLHQF\ /RZ(65 FDSDFLWRUV ZLOO EHXVHGIRUEHVWSHUIRUPDQFH7KHYDOXHRIWKHRXWSXWFDSDFLWRU &2 ZDV VHOHFWHG DW ȝ) 8QGHU QRUPDO RSHUDWLRQ WKH GXW\ F\FOH ZDV VHW WR IRU WKH H[DFW RXWSXW YROWDJH RI 9 ,QFUHDVLQJ WKH GXW\ F\FOH WR DSSUR[LPDWHO\ UHVXOWV LQ KLJKHU RXWSXW YROWDJH YDOXH XS WR 9 ZKLOH GHFUHDVLQJ WKH GXW\ F\FOH WR OHDGV WR ORZHU RXWSXW YROWDJH YDOXH RI DSSUR[LPDWHO\9
7$%/(,
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
6,08/$7,215(68/76
6LPXODWLRQ UHVXOWV KDYH EHHQ SHUIRUPHG XVLQJ 0$7/$% 6LPXOLQN 7DEOH VXPPDUL]HV 39 SDUDPHWHUV LQ D FRPPHUFLDOO\DYDLODEOH.\RFHUD.'*;/3,WLVVHHQIURP
110
)LJXUH )XQFWLRQDOEORFNGLDJUDPVLQ0$7/$%6LPXOLQN D 39DUUD\ HTXLSYDOHQWFLUFXLWPRGHO E %DFNSURSDJDWLRQQHXUDOQHWZRUNPRGHO
7DEOH WKDW WKHUH DUH FHOOV FRQQHFWHG LQ VHULHV 7KH VHULHV DQG SDUDOOHO UHVLVWDQFH LQ WKH 39 V\VWHP DUH JLYHQ E\ ȍ DQG ȍ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
,UUDGLDWLRQ :P
)LJXUH 3ORWVRILQSXWYROWDJHYHUVXVFXUUHQWDQGSRZHURIWKH39PRGHO
9287 9
9
5LSSOHV 9
,/2$' $
$
2XWSXW3RZHU :
2XWSXW9ROWDJH 9
D
9
2XWSXW&XUUHQW $
2XWSXW9ROWDJH 9
7LPH PV
939
2XWSXW9ROWDJH 9
6HWWOLQJ7LPH PV
,QSXW9ROWDJH 9
Ȝ
7LPH XV
E
)LJXUH 2XWSXWYROWDJHZDYHIRUPVRIWKHERRVWFRQYHUWHULQWLPHGRPDLQ LQGLFDWLQJ D VHWWOLQJWLPHDQG E YROWDJHULSSOHV
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
111
3287 :
: 7LPH V
)LJXUH 9DULDWLRQVRILUUDGLDWLRQXQGHUDFRQVWDQWWHPSHUDWXUHDWR&DQG WKHUHVXOWLQJLQSXWYROWDJH 939 2XWSXWYROWDJH 92 2XWSXWFXUUHQW ,2 DQG RXWSXWSRZHU 32
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
7HPSHUDWXUH 2&
7
,QSXW9ROWDJH 9 2XWSXW9ROWDJH 9 2XWSXW&XUUHQW $ 2XWSXW3RZHU :
:P WR :P 8QGHU D SDUWLFXODU FRQGLWLRQ RI 9 RXWSXW YROWDJH DQG UHVLVWLYH ORDG WKH RXWSXW SRZHU YDULDWLRQV RI LUUDGLDWLRQ LV : ZKLOH WKH RXWSXW SRZHU RI YDULDWLRQV LQ WHPSHUDWXUH LV : 7KH V\VWHP SRVVHVVHV UHODWLYHO\IDVWVHWWOLQJWLPHRIPVZLWKORZULSSOHYROWDJHRI DSSUR[LPDWHO\ :LWKD FRPSOHWHGHVLJQ IURP FKDQJHV LQ HQYLURQPHQW FRQGLWLRQ WR RXWSXW SRZHU RI HOHFWURQLF LQWHUIDFLQJV\VWHPWKLVSDSHUKDVRIIHUHGDSRWHQWLDODOWHUQDWLYH WRUREXVWRXWSXWYROWDJHFRQWUROLQPRGHUQ39V\VWHPV
939 9
$&.12:/('*(0(176 7KH DXWKRUV DUH JUDWHIXO WR 7KDL1LFKL ,QVWLWXWH RI 7HFKQRORJ\ 71, IRUUHVHDUFKIXQGVXSSRUWV 5())(5(1&(6
9287 9 9
,/2$' $ 5/2$' ȍ $
3287 : :
7LPH V
)LJXUH 9DULDWLRQVRIWHPSHUDWXUHXQGHUDFRQVWDQWLUUDGLDWLRQDW :PDQGWKHUHVXOWLQJLQSXWYROWDJH 939 2XWSXWYROWDJH 92 2XWSXW FXUUHQW ,2 DQGRXWSXWSRZHU 32
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
112
>@ 0 (OVKDHU $0RKDPHGDQG 20RKDPPHG ³6PDUW 2SWLPDO &RQWURO RI '&'& %RRVW &RQYHUWHU LQ 39 6\VWHPV´ 7UDQVPLVVLRQ DQG 'LVWULEXWLRQ &RQIHUHQFH DQG ([SRVLWLRQ /DWLQ $PHULFD 7 '/$ SS >@ )HQJELQ 3HQJ 4LDQJ /LXDQG =KLTLDQJ /L ³$ 1RYHO 3VHXGR 3,' $OJRULWKP RI '&'& &RQYHUWHU´ ,QWHUQDWLRQDO &RQIHUHQFH RQ $GYDQFHG&RPSXWHU7KHRU\DQG(QJLQHHULQJYROSS >@ 1) 1LN ,VPDLO , 0XVLULQ 5 %DKDURP DQG '-RKDUL³)X]]\ /RJLF &RQWUROOHURQ'&'&%RRVW&RQYHUWHU´,(((,QWHUQDWLRQDO&RQIHUHQFH RQ3RZHUDQG(QHUJ\ >@ 57KDLOD³$QDO\VLVDQG&RQWURORI'&'&&RQWUROOHUIRU6RODU(QHUJ\ 6\VWHP´ ,QWHUQDWLRQDO &RQIHUHQFH RQ &RPSXWLQJ DQG &RQWURO (QJLQHHULQJ >@ :08WRPR =$ +DURQ $ $ %DNDU 0= $KPDGDQG 7DXILN ³9ROWDJH 7UDFNLQJ RI D '&'& %XFN%RRVW &RQYHUWHU 8VLQJ 1HXUDO 1HWZRUN &RQWURO´ ,QWHUQDWLRQDO -RXUQDO RI &RPSXWHU 7HFKQRORJ\ DQG (OHFWURQLFV(QJLQHHULQJYROSS >@ 55DPDSUDEKDDQG%/0DWKXU³,QWHOOLJHQW&RQWUROOHUEDVHG0D[LPXP 3RZHU 3RLQW 7UDFNLQJ IRU 6RODU 39 6\VWHP´ ,QWHUQDWLRQDO -RXUQDO RI &RPSXWHU$SSOLFDWLRQVYROQRSS >@ )D U]DG 6HGDJKDWL $OL 1 DKDYDQGL 0RKDPPDG $OL %DGDPFKL]DGHK 6HKUDQHK *KDHPL DQG 0HKGL $EHGLQSRXU )D OODK ³39 0D[LPXP 3RZHU3RLQW 7UDFNLQJ E\ 8VLQJ$UWLILFLDO 1HXUDO 1HWZRUN´ 0DWKHPDWLFDO3UREOHPVLQ(QJLQHHULQJ >@ +XQJ&KLQJ /XDQG 7H/XQJ 6KLK³'HVLJQ RI '&'& %RRVW &RQYHUWHU ZLWK)116RODU&HOO0D[LPXP3RZHU3RLQW7UDFNLQJ&RQWUROOHU´,((( &RQIHUHQFH RQ ,QGXVWULDO (OHFWURQLFV DQG $SSOLFDWLRQVLVSS > @ -RVHSK-DZKDU6 'U160DULPXWKX DQG $OEHUW 6LQJK1 ³$Q 1HXUR )X]]\&RQWUROOHUIRUD 1RQ/LQHDU3RZHU(OHFWURQLF%RRVW&RQYHUWHU´ ,QIRUPDWLRQDQG$XWRPDWLRQSS >@ 5RQJ-RQJ :DL DQG /L&KXQJ 6KLK³$GDSWLYH )X]]\1HXUDO1HWZRUN 'HVLJQ IRU 9ROWDJH 7UDFNLQJ &RQWURO RI D '& '& %RRVW &RQYHUWHU´ ,(((7UDQV3RZHU(OHFWURQLFVYROQRSS >@ *DXUDQJ 3DQFKDO $PLW *DQDWUD
