Autonomous hybrid photovoltaic power plant using a back-up generator: A case study in a Mediterranean island

Renewa6~ Ener9y, V01. 2 N ~ ~ p~ ~ 1 ,

~

P~9am0n

1~6 C0pyf19M • 1996 E~e~er 5dence Ltd Pf1n~d ~ 6 ~ 8 f 1 ~ . A11f19h~ ~ e d

P11 : 50960-1481(96)00016-X

0960-1~1~6 $15~0+~00

AU70N0M0U5 HY8R1D PH070V0L7A1C P0WER PLAN7 U51N6 A 8ACK-UP 6 E N E R A 7 0 R : A CA5E 5 7 U D Y 1N A M E D 1 7 E R R A N E A N 15LAND 6. N0770N, M. MU5ELL1 and A. L0UCHE cen~e de R ~ h e ~ h ~ ~En~Ne m 5 y ~ + m ~ , uNver51t6 de c0r5e, u.R.A, cNR5 20~, R0me de5 5an9~nNm5, F-20 000 Ajacc10, Fran~ (R~e1ved 16 0a06er 1995; accep~d 4 March 199~

A65tract--U51n9 a ~and-N0ne ph0t0v01ta1c array a5 a un14ue 50urce 0f 5upp~ f0r a 10cN dectr1c demand 9eneraRy ~duce5 a ~9Nf1cant exce55 ~ ener9y pr0duct10n. A 50~t10n t0 the pr0Nem appear5 thr0u9h the u5e 0f a hy6r1d 5y~em, wNch N v ~ a 900d way t01mpr0ve the ener9y 6Mance t09~her w1th m1Nmum ~ve5tment. A ~ n 9 m ~ h 0 d ~art1n9 ~ 0 m memcr~0NcM c0n~t10n51n C0r~ca wa5 extended t0 a tw1n-50urce 5y5mm : 5 0 ~ f u e 1 e1e~r1c 9enerat0r w1th each 50urce c0ntr16ut10n 6~n9 0pt1m12ed. 7he m 5 ~ 06tNned # 0 m 5uch an appr0ach 5h0w that a 75% 50~r r a ~ 15 an 0pt1ma1 v a ~ e t0 06tNn an ener9y 6Mance f1~ed t0 the 10cN demand when c0mpamd t0 0ther 5y~em5 f0r decentraf12ed e ~ r 1 d f f 9enerat10n. 7he m ~ h 0 d ~ 0 9 y wa5 te5ted and v M ~ a t e ~ thr0u9h an e~5t1n9 hy6r1d P v 5y5~m 1n C0r~ca ~ 4 kw). 7N5 paper d0e5 n0t p m ~ n t a 9enerM ~ n 9 m ~ h 0 d f0r the hy6r1d 5y5mm, 6ut 15j u ~ a ca5e 5tudy. C0pyr19ht • 1996 E 1 ~ e r 5dence Ltd

1N7R0DUC710N A pre~0u5

~ u d y [1] 5h0wed that u~n9 an aut0n0m0u5 501ar 5y~em (a ~and-a10ne 501ar 5y~em) ~way5 re5u1~ 1n a ~9n1f1cant exce55 ener9y pr0duct10n. 1n the pre5ent w0rk, we 5tudy m0re prc~5~y th15 e×ce55 0f ener9y pr0duct10n, pan~u1a~y 1n r~at10n t0 the percenta9e 0f the 10ad p r 0 ~ d e d 6y the PV 5y~em. 1t 5h0u1d 6e n0ted that the ener9y 5urp1u5 15 ~ r 0 n ~ y c 0 ~ a t e d w1th th15 ~ parameter. We then 5tudy a ph0t0v01ta1c hy6r1d 5y~em w1th an a u ~ a r y f05511 50urce 50 a5 t0 reduce the ener9y 1055e5 and t0 1mpr0ve the ener9y 5y~em a55e~ment. 7hen, we ex~nd the 0p~m12ed aut0n0m0u5 ph0t0v01ta1c 5y~em ~ n 9 meth0d [1] t0 a hy6r1d aut0n0m0u5 5y~em w1th a pr1n~pM ph0t0v01ta1c 50urce and an aux111ary f05511 0ne. We thu5 dc~rm1ne the 0pt1m12ed 50urce part1~pat10n. A~er that, we va~da~ th15 meth0d 0n a hy6~d PV 501ar 5y~em e~5t1n9 1n C0r~ca =Pa0m~-R0ndu11nu PV p1ant. F1na11y, we c0mpare a hy6r1d 5y5~m, 0n the 0ne hand, w1th a ph0t0v01ta1c 5y~em and, 0n the 0ther, w1th d1e5~ 9enerat0r5. 371

6. N 0 7 7 0 N ~ aL

372

1. REV1EW 0 F P R E V 1 0 U 5 R E 5 U L 7 5 C 0 N C E R N 1 N 6 AN A U 7 0 N 0 M 0 U 5 PH070V0L7A1C 5 Y 5 7 E M

1n a p ~ 0 u 5 paper [1], we appf1ed an 0pt1m12ed ~ n 9 m~h0d 0f an aut0n0m0u5 ph0t0v01ta1c 5y5~m 1n a ca~ ~udy ~ C0r51c~ ta~n91nt0 acc0unt the ~ m p 0 r ~ ~ r 1 6 u t 1 0 n 0f the ener9y 1nput ~ 0 ~ r ra~at10n) and 0utput ~ c t r 1 c ~ ~ad). 7~5 m~h0d ha5 6een 6a5ed 0n a ~mpf1f1ed ener9y 5y5tem1c~ 0 6 ~ appr0ach u51n9 a ~m~at10n 0f the PV 5y~em 6eha~0ur 6y ut1f1~n9 the ener9y eff1~ency 0f each 5u6-5y~em. Ad~n9 phy~c~ and c05t c0n~derat10n5, we have 6een a~e t0 06t~n the 0pt1m~ed aut0n0m0u5 ener9y 5y~em, 1.e. the 5y~em w~ch can 60th 5at15fythe ~ a d and ~ve the ~ w e ~ k w h c0~. Dur1n9 t~5 5tudy, we have p a r t 1 c u ~ y n0~d : -- th e 1mp0~ance 0f the kn0w1ed9e 0f the 10ad and, m0re prec15e1~ ~5 ~mp0ra1 ~ r 1 6ut10n, n0t 0 ~ y ~0m an ener9y p ~ n t 0f ~ew, 6ut ~50 w1th 1t5 p0wer ~ r 1 6 u t 1 0 n dur1n9 the day; - - th e 1nf1uence 0f the f1me~ep 0f the 5y~em 6eha~0ur ~m~at10n ; a re5~t 0f th15 5tudy 15 that the ~ n 9 m~h0d5 u~n9 0 ~ y the d ~ ener9y 10ad data mu5t 6e u5ed w1th 9reat caut10n 6ecau~ they ~ 5 ~ t ~ an u n d e ~ 2 e d 5y~em ; 0n the 0ther hand, u51n9 h0udy d a ~ 15 ~c0mmended ; - - t h e PV 5y~em mu~ 6e 0pt1m12ed ~0m the k w h c0~ p ~ n t 0f ~ew, 6ecau~, acc0rd~9 t0 the 5y5~m c0nf19urat10n ch05en, the c0~ 0f 0ne k w h pr0duced 6y the PV 5y~em vaf1~ 9rea~y (m0re than 3) ; - - th e array 0f an aut0n0m0u5 0pt1m~ PV 5y5~m can pr0duce an de~r1c~ ener9y 6~ween 2 and 2.5 t1me5 m0re than the ener9y needed t0 5upp~ the 10ad c0n~dered a5 c0n5tant thr0u9h0ut the year 1n 0ur ca5e ~udy; 50, an 1mp0~ant part 0f the ener9y capa~f1ff 0fthe 5y5~m 15n0t u5ed 0r ~ . 1n 50me 0ther app11cat10n5, 5uch a5 ~ r c0n~t10n~9, h0f1day h0me5 and recreat10n cen~e~ where the da11y ~ a d dur1n9 the 5ummer m0nth5 15 c0n~dera6~ ~9her 1han ~ w 1 n ~ the 5ur~u51n a w ~ d ~ n e d 5y~em w0~d 6e ~ w ~ . 1n a future w0rk, we w111~udy h0w t0 reduce the5e ener9y 1055e5 and t0 1mpr0ve the PV 5y~em 6~ance. H0wever, the 5y~em ~ n 9 ~ a a t 1 m ~ p ~m~at10n m~h0d ha5 an ~herent u n c e ~ n t ~ 6ecau5e 0f the ~ a d y ment10ned 5~0n9 1nf1uence 0f the t1me pa~ern 0f the data 5et5 0n the c0mputat10n~ ~ 5 ~ . 50, the f0rmer ~udy can 0n~ ~ve 4 u ~ a t N e rather than 4uant1tat1ve ~ 5 ~ 6ecau5e ~ depend5 5~0n~y 0n the 51te 0f the 5tudy. 2. 5 0 L A R C 0 N 7 R 1 8 U 7 1 0 N A N D W A 5 7 E D E N E R 6 Y

2.1. Def1n~n5 F1r5t1y, we mu~ def1ne, 0r ~ e w , tw0 expr~f10n5: the def1~t ener9y and the wa~ed ener9y; then, we deduce ~0m the5e expre5f10n5 tw0 0ther p a r a m e ~ : the 5Car c0ntr16ut10n and ener9y exce55. 7he ener9y def1~t DE(7) 15 def1ned a5 the ener9y c0n5umed 6y the ~ a d and w~ch the 5y~em 15 n0t a6~ t0 5up~y. 7~ 5 0ccur5 when the e ~ c f f ~ p0wer pr0duced 6y the PV array (Pp) 15 10wer than the p0wer ~ 4 ~ r e d 6y the 10ad (P~ and when the 6attery 5t0ra9e ha5 reached 1~ maf1m~ auth0r12ed depth 0f ~ h a r 9 e (D0D)C~: 7

DE(7)=

~ ~<~ C<~

[P~(t)-P~(t)]dt.

(1)

Am0n0m0~ hy6r1d ~ ~ c

Nam

373

7he wa~ed ener9y ~ ( ~ 15 def1ned a5 the ener9y pr0duced 6y the PV array and unu5ed 6y the ~ e m . 1t 15 the ener9y pr0duced 6y the PV m0dM~, 6 N wNch 15 n0t u5ed t0 5upNy the 10ad, when the a ~ u m ~ 0 ~ have reached thNr m a ~ m u m c a p a d f f ~ : 7

~(~=

~

~ - - ~ d t .

~)

~>~ C>~

7h15 ener9y 1510~ 0r n0t pr0duced depend1n9 0n the 6attery char9e~115char9e pr0~ct10n pr0ce55.7h15 ener9y ha5 0~en 6een ut11~ed 1n prev10u5 re5earch 5uch a5 that 6y Nava et aL [2] and 51drach de Card0na and M0ra L0pe2 [3]. Fr0m the5e tw0 def1n1t10n~ we can def1ne tw0 0ther d1menf10n1e55 parame~r5, re5pect1ve1y ca11ed 501ar c0ntr16ut10n and ener9y exce55. 7he 501ar c0ntr16ut10n 5C 15 the rat10 0f the 10ad 5uppf1ed 6y the PV 5y~em dur1n9 a 91ven t1me per10d 7 t0 the t 0 t ~ 10ad dur1n9 the 5ame per10d. 50, a 501ar c0ntr16ut10n e4ua1 t0 1 c0rre5p0nd5 t0 a 10ad ~way5 5upp1~d and a 501ar c0ntr16ut10n e4uM t0 0 t0 the 10ad never 6~n9 5at15f1ed 6y the PV 5y~em :

(3) 8arra et aL [4] and Am6r050ne et aL [~ have u5ed th15 5ame parameter cM~d the fract10n 0f c0vered 10ad 1n the w0rk1n9 per10d. We current~ u5e the n0t10n 0f LLP 0055 0f 10ad pr06a61f1ty) wh1ch 15 a mathemaf1c~ characmr15f1c 0f the 5y~em rd1a61f1ty ~ v d , and wh1ch 15 def1ned a5 the pr06a6111ty 0f the 10ad n0t 6e1n9 5at15f1ed 6y the ener9y 5y~em. 7h15 parameter c0rre5p0nd5 t0 D E ( 7 ) / L ( 7 ) w1th 5C = 1 - L L P . D1fferent meth0d5 have 6een devd0ped [6-11] t0 determ1ne PV 5y~em character15t1c5 5et (5, C) f0r 5pedf1ed LLP and a rev1ew 0f a11 the5e meth0d5 ha5 6een ~ven 6y E ~ d 0 and L0ren20 [1~. 7h15 parameter can a150 6e u5ed 1n part1cu1ar f0r c0mpar1n9 PV 5y~em5 w1th 0ther e~ctr1ca1 pr0duct10n 5y~em5 uf1n9 a c0nvenf10n~ 50urce. We can 5ay that th15 n0t10n 15 p a ~ u 1 a f 1 y u5ed 1n f1f1n9 meth0d5 6a5ed 0n pr06a61f15f1c ~ud1e5. 7he ener9y exce55 p a ~ 15 the wa~ed ener9y d1v1ded 6y the t0ta1 ener9y pr0duced 6y the PV array :

~c(~-

~

~

,

~

where: Pp and PL are, re5pect1vdy, the array 0utput p0wer and 10ad p0wer; C, Cm~ and Cm~ the ener9y 5tate 0f the 6atter~ m1n1mum ener9y 5tate and max1mum ener9y 5tate ; L 15 the ener9y 10ad dur1n9 the f1mu1af10n per10d; 5 the PV m0du1e 5urface; H the 501ar 1rrad1at10n 1nddent 0n m0du1e 5urface dur1n9 the f1mu1af10n per10d ; 7 the t1me per10d 0f f1mu1at10n and 4 15 the PV array eff1dency. 2.2. Mathemat1ca1f0rmu1at10n 1t 15 nece55ary t0 r ~ N n the f0ur 10ad pr0f1~5 ~ 0 d u c e d 1n a p ~ 0 u 5 paper [1] and p~n~d 1n F19. 1.1f we 5tudy the ener9y 6Mance m ~ n 9 Nace ~ the 6at~ry, we n 0 ~ 1hat the 6attery 1nput ener9y can 6e ~ p r e ~ n ~ d 6y :

374

6. N 0 7 7 0 N et aL W

80

40

4

8

12

16

0

t 24

20

~ 0

4

1

~

12

16

20

24

t

12

16

20

24

W 2~ W

40 0 0

4

8

12

16

20

24

0

4

8

F19. 1. L0ad pr0f11e type5 f0r a dN1y ener9y e4uN t0 1 kwh.

7 P

•

#~

~(0-~(0]

dt

0

~>PL ~ < C < ~

and the 6 ~ r y

0utput ener9y can 6e wf1~en : 7 P

(1~ch)

1 d 0

~(0-~]

d~

~
Pch and Pa~h [~ are, r e ~ e ~ v d ~ the 6 a t ~ r y char9e and ~ 5 c h a ~ e eff1~ency. We pre5ent 1n ~ 9 . 2, the 5um 0f the5e tw0 ener#e5 ~ r ~ r e ~ 5t0ra9e capa~de5 ~e5~v~y, 2, 4, 10, 30, 50, 100, 200 and 300 k W ~ and ~ r the ~ a d p r 0 ~ e 1V ( ~ r the 0ther pr0~e5, the curve5 6~n9 ~ 0 We n0te, ~ r 5 m ~ m 0 d d e area5, a n ~ w 0 r k 0f curve5 y = ~ c0n5tant and ~ r ~ e area5, we 065erve the va~e5 are near t0 2er0. F0r 5 m ~ area5, the ~ 0 ~ v ~ c array 15 n0t aNe t0 5 ~ 5 ~ the 10ad, the 6a~ery 5et 15 w 0 r ~ n 9 ~ke a p0wer 9enerat0r f1m~ed 6y the 5t0ra9e capa~ty, 50 at the end 0f the ~ m ~ a d 0 n ped0d, ~ e ener9y 6 ~ a n c e ~ e 4 u ~ t0 - ~ . F0r ~ r 9 e area5, the 6 ~ r y w0rk5 ~ke a 6 u ~ r 1.e. 1t ~ 0 w 5 a d m e 4 a 9 ~ r e n c e 6~ween ~ u ~ 0 n and 10ad; ~ e n , at the Where

Am0n0m0~ hy6r1d ~ 0 m v ~ ~~

1~ 0

~ ~

~

~2

1

~

#am ~6

3

~

375 ~4

~

~

-1~

-2~

F19. 2.8attery ener9y 6a1ance (7ype 1V).

end 0f the ~mu1af10n per10d, the 1nput ener9y 1n the 6a~ery and the 0utput ener9y w1H 6e e4u1v~enL 50 the ~ 0 6 ~ ener9y 6a~nce w1H 6e e 4 u ~ t0 2er0. 7he ener9y 5tate var1at10n 0f the 6a~ery 15 f1nked t0 PL and 6y the rdaf10n :

Pp

dC

~[Pp(0--PL(0],

--

1.e. d C = a [ P p ( 0 - - P L ( 0 ]

d~

(5)

~th

C < ~ , {111/pd~0P~1~;~--P~=>001fp~pL<°r0andandC>CC~-~C~, °r

c0n5e4uent1y : 7

c(7) = c(~ +pc~

f

7

[Pp(0 -- PL(01 d t +

(1/Pdch) f

0

6>~

6<~

~
1 m r 0 d u ~ n 9 5 C ( 7 ) and

~

: {~ ~ ~

[Pp(0-- PL(0]dL

0

c ~ < c < c~.~

EXC(~, after 5ever~ Wan5~rmaf10n5 t~5 e4uat10n 6ec0me5 :

~"~c~.~-~

(Ac 1
376

6. N 0 7 7 0 N et aL

+[1+(p~a~ ~

1)/~

~)

f0 r 1d~. t< ~5

5 ~

=

Pdch[~t = ~ -- C ( ~ ] L 1< PL~5

p~hpd~h~HEXC(~ L

(8) 1
where 115 the 501ar 1rrad1ance rec~ved dur1n9 t1me dt. 2.3. Re5uh5 and d15cu5510n We pre5ent 1n F19. 3, f0r the f0ur 10ad pr0f11e5 prev10u~y def1ned, the var1at10n 0f the 501ar c0ntr16ut10n and the ener9y exce55 part a5 a funct10n 0f the m0du1e 5urface area5 f0r d1fferent 5t0ra9e capa~f1e5. 51drach de Card0na and M0ra L0pe2 [3] dem0n5trated that the percenta9e wh1ch 15 c0vered 6y the PV 5y~em ~ a1m05t 1ndependent 0f the 5t0ra9e capac1ty. 7h15 065ervat10n ha5 6een made f0r 5t0ra9e capadt1e5 vary1n9 6etween 2 and 7 day5 0f aut0n0my. 1n th15 capac1ty ran9e we can 065erve, 1n F19. 3, th15 0ccur5 0n1y 1n 5evera1 ran9e5 0f the m0du1e 5urface area ( fr0m 0 t0 1.8 m 2 and f0r very 1ar9e area~ 6ut n0t 1n the wh01e m0du~ 5urface area var1at10n d0ma1n. 06ta1n1n9 a va1ue 0f the ener9y exce55 part near 2er0 5h0w5 that, f0r 50me va1ue5 0f a

1 0,9

0,8 ~7 ~6 0~ 0~

0,3 0,2 ~ 0 1

2

3

4

5

6

7

8

9

m=

10

~9.3. 501ar c0ntr16ut10n and ener9y exce55 part a5 a ~nct10n 0f m0d~e 5ur~ce area5 ~ype 1~.

Aut0n0m0u5 hy6r1d ph0t0vNta1c p1ant

377

m 0 d u ~ 5urface, 1t 15 1mp05516~, a5 5een 1n the preced1n9 para9raph, t0 fu11y char9e a9Nn the 6attery. We n0te that t0 06tNn a t0ta1 501ar c0ntr16ut10n (5C = 1), m0re than 50% 0f the PV ener9y pr0duct10n 15 unu5ed un~55 the 6 a t ~ r y capac1ty 15 very 1ar9e, 6ut w1th a 501ar c0ntr16ut10n 0f 90% th15 ener9y 1055 15 reduced t0 20-25%. 7h15 065ervat10n 1nduce5 the need t0 5tudy fu~her the 1nf1uence 0fthe 501ar c0ntr16ut10n 0n the PV 5y5tem c0nf19urat10n5. We 065erve, 0n the 0ne hand, that f0r an ener9y exce55 p a ~ near 2er0, the 501ar c0ntr16ut10n 5eem510 6e a f1near funct10n 0 f t h e m0du1e area whate~er the ~0ra9e capac1ty 15, wh1~ 0n the 0ther hand, f0r Nr9e area5, aH the curve5 meet. 7he5e tw0 065ervat10n5 can 6e pr0ved 6y the 5tudy 0f the pre~0u5 f0rmu1a. 1t 15 1mp0~ant t0 exp1Nn 60th 0f the5e 065ervat10n5. F1r5t 065e~at~n. W1th EXC(7) = 0, e4. (8) 6 e c 0 m ~ :

5c(7) = 0~[c(t =L~-

c(7)1 + (1

-p,.~p~)(1- ~

P~(00t)1 1< PL~5

1 ,d1

1< P~5

1t 15 a ~ra19ht 11ne w1th a d1rect0r c0eff1dent 1ndependent 0f the 5t0ra9e c a p a d t y and w1th an 0rd1nate at the 0f1Nn e4uM t0 p~,,~[C(t= 0)/L]. 1n fact, 1f 5 = 0, the 5y~em 15 ju5t made up 0f a 6attery w1th an 0f191nM ener9y C(t = 0) ~ 0 m wh1ch 1t w1116e a 6 ~ t0 re5t0re an ener9y pa,.~C(t = 0) and c0n5e4uent1y, 1ead5 t0 a 501ar p a ~ e4ua1 t0 p~[C(t = 0)/L]. F0r the part1cu1ar ca5e 0f the 10ad pr0f11e 1V, we have : 7 ~ 1dt= 0 1
7 H

and

~ PL(0dt= 0 1
L.

e4uat10n can 6e wf1~en :

(1~ W1th the meth0d 0f f1near re9re5~0n, we have determ1ned the va1ue5 0f the f1near c0eff1~en~ f0r d1fferent 5t0ra9e capaNf1e5 [13]. 7he re5uR5 0f th15 re9re5~0n are 1n 900d acc0rdance w1th the a60ve e4uat10n. 7he ~0pe 0f the 11ne depend5 0n the pr0f11e type, 6ut 15 1ndependent 0f the 5t0ra9e capaNty. 1n fact, the c0nd1t10n (1 < P~45) f0r the tw0 1n~9rM5 d0e5 n0t m0d1fy the va1ue5 0f the5e 1nte9rM5 1n funct10n 0f the m0du1e area, 6ut 15 dependent 0n the 10ad pr0f11e. A5 5een a60ut the 6 a t ~ r y ener9y 6aNnce, f0r the5e va1ue5 0f m 0 d u ~ area5, the 6a1ance 15 e4ua1 t0 C(t = 0), 50 the 6aUery ener9y 5tate at the end 0f the Nmu1at10n per10d 15 near 2er0.1n a f1~t appr0~mat10n and f0r a Nven 10ad pr0f11e, the 501ar p a n can 6e c0n~dered a5 a f1near funct10n 0f the m0du1e 5urface when the ener9y exce55 part 15 c105e t0 2er0.

378

6. N 0 7 7 0 N et aL

5ec0nd 065ervat~n. When the 501ar part reache5 1, the exce55 part curve5 are 1dent1c~. F0r a ~ v e n m0du1e area, 1f the m1n1mum 5t0ra9e c a p a d t y 0f a 6attery 5et A a110w1n9 a 501ar p a ~ e 4 u ~ t0 1 15 C 0 ~ , the ener9y 5tate 0f the 6 a t ~ r y 5et 8 0f wh1ch 5t0ra9e c a p a d t y 15 C > C 0 ~ w111 vary 6etween C and ( C - C0~,~), 50 the c a p a d t y ( C - C 0 ~ ) w111 never 6e u5ed. 8attery 8 w1~ have an 1dent1ca1 6eha•0ur t0 6attery A, 50 1t w1~ 6e c0mp1e~1y char9ed at the 5ame t1me a5 A. 0 n c e the 6attery ha5 reached that 5ta9e, then the p0wer pr0duced 6y the PV array w1H 6ec0me a 5urp1u5. F0r a ~ v e n area and f0r a 5t0ra9e c a p a d t y 9reater than the m1n1mum c a p a d t y wh1ch can 5at15fy 100% 0f the 10ad, ff0m an ener9y exce55 p01nt 0f ~ew, a 6attery w1116ehave 11ke the 6attery 0f m1n1m~ capadty. 2.4. Ener9y exce55 a5 a funct10n 0 f 501ar c0n~16ut10n A reduct10n 1n the 501ar c0ntr16ut10n decrea5e5 the exce55 ener9y unu5ed. 50 a5 t0 m1n1m12e th15 exce5~ we w1H 5tudy the 1nf1uence 0f a 501ar c0ntr16ut10n decrea5e 0n the PV 5y5tem character15t1c5 and 0n the k w h c05t. 1n F19. 4, we p10~ed f0r the 10ad pr0f1~ 1V, the exce55 a5 a funct10n 0f the 501ar c0ntr16ut10n. We 065erve that f0r a 501ar c0ntr16ut10n up t0 75%, th15 exce55 6ec0me5 e4ua1 t0 2er0. F r 0 m a 501ar c0ntr16ut10n e4ua1 t0 1, a decrea5e 0f 501ar c0ntr16ut10n 0f 2.5% ~ad5 t0 a decrea5e 0 f t h e exce55 0f a60ut 50% and a decrea5e 0f 10% 1ead5 t0 a fa11 0f 75% 1n th15 5ame exce55. C0n5e4uent1y, redudn9 the 501ar c0ntr16ut10n w1H reduce the ener9y exce55, 6ut, we have t0 keep 1n m1nd that the 10ad m u ~ 6e t0ta11y 5upphed, 50 1t 15 nece55ary t0 f111 th15 9ap 0f ph0t0v0~a1c ener9y up 6y an aux1f1ary 50urce: the en91ne 9enerat0r. 3. P H 0 7 0 V 0 L 7 A 1 C

5 Y 5 7 E M W ~ H AN AUX1L1ARY E N 6 1 N E 6 E N E R A 7 0 R

3.1. 6 e n ~ p 0 ~ a60ut en9~e 9 e n e r a ~ 1n 0ur 5tud~ we ch05e an aux1hary 50urce, eaf1~ u5aNe ~ 1501~ed M ~ the character15t1c5 0f w ~ c h are : 0~

0,7 ~6 0,5 W

0,4 0,3 0,2 ~1 0 ~7

~75

~8

~

~9

5~ar C0ntd6U~0n

F19.4. Ener9y exce55 part a5 a funct10n 0f 501ar pa~ (7ype 1V).

Aut0n0m0u5 hy6r1d phm0vNta1c ~ant

379

the 9enerat0r type: 9a50f1ne 0r d1e5d (1500 rpm 0r 3000 rpm) ; the rated capadty ; - - t h e fue1 c0n5umpt10n. 7he ch0~e 0f the 9enerat0r type depend5 0n the 5~e and the nature 0f the 10ad. A 9a50hne 9enerat0r can 6e u5ed f0r 10w p0wer demand. 0 n the French market, the ma~mM n0m1nM p0wer avNN61e f0r a 9a50hne enNne 15 7 kVA and 1t5 runn1n9 t1me can 6e c0nt1nu0u5.7he d1e5d 9enerat0r runn1n9 5peed ch05en depend5 0n the expected run t1me, 1f 1t 15 u5ed 0 n ~ 0cca~0nM~, t0 char9e a 6attery f0r examp~ (hy6r1d 5y5~m ca5~, a 3000 rpm un1t may 6e 5uff1~ent ; 6ut, f0r m0re ~e4uent u5e, a 1500 rpm 15 rec0mmended. 7 0 determ1ne the rated capadty 0f the enNne 9enerat0r t0 6e 1 n 5 t a 1 ~ tw0 ca5e5 m u ~ 6e c0n~dered : - - t h e 9enerat0r ~ d1rect1y c0nnec~d t0 the 10ad, then the rated capa~ty 0f the 9enerat0r m u ~ 6e at ~ a ~ e 4 u ~ t0 the m a ~ m u m p0wer demand dur1n9 the c0nNdered per10d ; - - t h e 9enerat0r 15 u5ed a5 a 6attery char9e~ then acc0rd1n9 w1th 5and1a Nat10nM La60rat0r1e5 [1~, the current pr0duced 6y the 9enerat0r m u ~ n0t 6e 9reater than CA~5 A where CAh 15 the a m p e r e - h 0 u ~ capadty 0f the 6at~ry. 7 0 e5t1mate the hy6r1d 5y~em c0~ 0r the enNne 9enerat0r c05t, 1t 15 nece55ary t0 kn0w the runn1n9 c05t 0f the 9enerat0r 1.e. the fue1 c0n5umpt10n c05t and the f1~ t1me 0f the 9enerat0r. 5ch0~ [15] and 7 h a 6 0 r [1~ 5h0wed that:

et aL

--Q (4~p~--~1,,.Q~)~+(1 ~,~rpC1,..Q~), P° Q~.

(11)

where and Q~ are, r e 5 p e c t 1 v ~ the fue1 c0n5umpt10n per h0ur at a p0wer P and at the rated p0wer 0f the 9enerat0r P° ; 4~ 15 the mechan1ca1-e~r1ca1 p0wer c0nver~0n and 15 the heat1n9 v~ue 0 f f u ~ (kWh/1). Fr0m data 06t~ned ~ 0 m 9enerat0r manufacture~, we determ1ne (7a61e 1) f0r each 9enerat0r type, the v~ue 0f 4~r f0r en~ne 9enerat0r w1th a rated p0wer 1n~r10r t0 5 kVA. 7he v~ue 0f th15 p a r a m e ~ r can vary f0r h19her p0wer. 7he app11cat10n 0f e4. (11) w1th the5e c0eff1den~ and w1th c0n5truct0f5 data 1ead5 t0 F19. 5. 1t 15 d1ff1cu1t t0 c0rre1ate Q~ w1th P° 6ecau5e 1t depend5 0n 5ever~ paramem~ charac~f1~n9 the 4uaf1ty 0f the m0t0r. 1n fact, we p10tmd 1n F19. 6 the 5pedf1c fue1 c0n5umpt10n (1/kWh) a5 a funct10n 0f the r a ~ d p0wer (ff0m m a n u f a ~ u r e f 5 data). We n0te that th15 parameter var1e5 9reat~ f0r 10w rated p0wer ( < 5 kVA) 6ut 15 re1at1ve1y c0n5tant f0r h19h p0wer [16-18]. 50, 1n 0ur 5tudy, we u5e a data 6ank 9r0up1n9 the character15t1c5 0f the en~ne 9enerat0r and u5e the paramem~ re1evant t0 the 9enerat0r 6~n9 ~mu1ated.

PC1~.

7aNe 1. EnNne 9en~amr character15t1c5

Fu~ 1500 rpm Fu~ 3000 rpm 6a50f1ne

.~

PC1(kWh/1)

32% 39% 25%

10.08 10.08 9.43

380

6. N 0 7 7 0 N ~ aL Q ~

~J

1 ~9 ~8 ~7 ~6 ~8

~ + ~

~2 ~

~e5e1 1 ~ 0 r ~ D1~e1 3 ~ 0 rpm 6~11ne

~4 ~3 0

~1

~2

~3

~4

~5

~6

~7

~8

~9

p~"

1

F19. 5. Fue1 c0n5umpt10n a5 a funct10n 0f p0wer 5upp11ed 6y the en91ne 9enerat0~ ~kWh 1,4

• 1,2 ~

0

E

1

~• •

90

~1~

0,8

• ~"

,

0~

,

•

0,6

--,

0,4

0,2

,

,

0 0

5

10

15 P e a k P0Wer

N9.6.5pedf1c ~

~

25

(kVA)

c0n5umpt10m

7he 1n1t1a1 cap1tM expen5e ha5 6een 06tNned fr0m the 9enerat0r data 6ank 6ecau5e the c05t 0f an en91ne 9enerat0r 0f a 91ven p0wer can vary 9reat1y. C0ncern1n9 the mNntenance c05t M, m a n y auth0r5 [17-19] 9ave d1fferent re5u1~. F0r Ca110way [1~, ~ 15 9% 0f the f u n c05t; Mu59r0ve [1 2 e5t1mated that the annum mNntenance 15 a60ut 20% 0f the 1n1t1a1 expen5e, 6ut can reach 30% 1f the en91ne 0perate5 ju5t at 25% 0f 1t5 rated c a p a ~ t y and f0r 5tarr [1~, the annum mNntenance c05t 15 7.5% 0f the 1n1f1M c05t. F r 0 m the mNntenance 1nterva15 (011 chan9e, f11ter rep1acement . . . . ), 1t 15 ea5y

Aut0n0m0u5 hy6r1d ph0t0v0k~c phnt

381

t0 5h0w that the ma1ntenance c05t5 are pr0p0rt10n~ t0 the 9enerat0r runn1n9 t1me R 7 (h0ur~. 7ak1n9 1nt0 acc0unt the 1ntervent10n c05t and 0n the 6a~5 0f the mean c05t 0f mater1a15, we have 5h0wn that: f0r d~5~ 1500 rpm and 9a50~ne 9enerat0r: M ($U5) = 0.18 × R 7 (h0ur~ and f0r d1e5e1 3000 rpm 9enerat0r : M ($U5) = 0.36 × R 7 (h0ur~. 7he runn1n9 c05t R ($U5) 15 a funct10n 0f the runn1n9 t1me R 7 (h0ur5), 0f the fu~ c05t F ($U5/1) and 0f the 9enerat0r c0n5umpt10n Q~ (1/h0u~ 6y: R = Q~ × F x R7. 7he rep1acement c05t depend5 0n the 9enerat0r f1~ cyde and 0n the annua11ntere5t rate ~aken t0 6e e 4 u ~ t0 6% a5 5u99e5ted 6y Cha60t ~ ) acc0rd1n9 t0 the meth0d pre5en~d 6y Kre65 and 5tarr ~1]. 7he ~fe t1me 0f an en~ne 9enerat0r 15, re5pect1ve1y, 5000 h0ur5 f0r 9a50f1ne type, 8000 h 0 u ~ f0r d1e5~ 1500 rpm and 3000 h0ur5 f0r a d1e5d 3000 rpm. 1f the 9enerat0r 15 d~ect1y c0nnected t0 the 10ad, R715 e4ua1 t0 the 10ad t1me and 1f the 9enerat0r ~ u5ed a5 a 6attery Char9er and tak1n9 1nt0 acc0unt the current ~m1tat10n, then R 7 = 5" (365" DL/C) where DL 15 the da1~ 10ad ener9y. A5 5ta1ed p r e ~ 0 u ~ y ~ , the m 0 ~ 1mp0~ant c0~ parameter 0f an ec0n0m1c a n a ~ 5 15 the fue1 pr1ce. Due t0 d1fferent nat10n~ ener9y p0~de~ d1e5~ fue1 p~ce d1ffe~ H1 0ver the w0r1d 6y a w1de ran9e : 1n 1991, fue1 pr1ce5 were 1n the ran9e 0f $U5 0.2/1 t0 $U5 0.84/11n dev~0p1n9 c0untr1e5 ~ . 7ran5p0~ c0~5 1ncrea5e the fu~ pr1ce 6y $U5 0.134).26/1 f0r 1000 km 6y r0ad and up t0 40 t1me5 m0re f0r ~an5p0~ 6y Mr ~ . 1n th15 ~udy, we t00k a fue1 pr1ce e4ua1 t0 $U5 0.44f1 and a 9a50~ne pr1ce 0f $U5 0.94/1. C0n5e4uent1~ a11 the re5u18 pre5ented 1n th15 ~udy m u ~ 6e c0n~dered a5 a ca5e ~udy 6ut n0t a5 9ener~ re5uR5. 3.2. 5 ~ 9 m e ~ 0 d 7he m ~ h 0 d u5ed here 15 an exmn~0n 0f the aut0n0m0u5 ph0t0v01ta1c 0pt1m12ed 5121n9 meth0d [1]. Fr0m the 5y~em 6eha~0ur ~mu1at10n, 1n chan~n9 the aut0n0my c 0 n ~ r ~ n t 1nt0 a c 0 n ~ r ~ n t re1at1ve t0 the p a ~ 0f the 10ad 5upp~ed 6y the PV 5y~em (5#%) and keep1n9 the ~ c h n 1 c ~ - p h y 5 ~ c 0 n 5 ~ n t ~ we determ1ned the 5et 0f PV 5y5~m charac~r15f1c5 (55cj, C5~) wh1ch ~ad5 t0 the 501ar p a ~ 5c~%. F0r each c0up~, we a ~ 0 d a m d an en~ne 9enerat0r 1n 5uch a way that the ener9y 5y~em 15 aut0n0m0u5 1n 1t5 wh0~ and we added a new c 0 n ~ r ~ n t c0ncern1n9 the f1m1tat10n 0f the 6attery char9e cu~ent. 50, the 5et 0f c0up~5 6ecame a 5et 0f tr1p1~5 (55c~, C5c~, P5c~) 1ead1n9 t0 an aut0n0m0u5 hy6r1d 5y~em where 5Cj% 0f the 10ad 15 5upp1~d 6y the 501ar 5y~em, and P5~ 15 the rated capa~ty 0f the en~ne 9enerat0r 1 n ~ d 1n the pr0duct10n 5y~em. 7he k w h c05t pr1ce 15 c 0 m p u ~ d f0r each tr1p1et; f0r the 501ar part, the c~cu1at10n 15 de5cr16ed 1n a pre~0u5 paper [1] and f0r the en~ne 9enerat0r pa~, the hyp0the5e5 are ~ven 1n 5ect10n 3.1. F0r each 5Cj, we 06t~ned the tr1p1et re5u1t1n91n the ~ w e ~ k w h c05t. 7hen, 5tud~n9 the var1at10n 0f 5Cj, we determ1ned the 0pt1m~ 501ar pa~ 1n the hy6r1d 5y5~m. Re5u1~ 0f th15 5ta9e are ~ven 1n 7 a 6 ~ 2. A 501ar c0ntr16ut10n decrea5e ff0m 100 t0 90% ~ad5 t0 a m0du1e 5urface area decrea5e 0f 30~40% acc0rd1n9 t0 the 10ad d~tr16ut10n type and t0 a 5t0ra9e capa~ty decrea5e 6etween 70 and 90%. F0r a 501ar c0ntr16ut10n e4ua1 t0 70%, th15 reduct10n ~ m0re than a fact0r 0f 2 f0r the m0du1e 5urface area and a fact0r 0f 8 f0r the 5t0ra9e capadty. 1n F195 7.1 t0 7.3, we p10t~d the k w h c05t f0r a 10ad pr0f11e 1V, f0r d1fferent 501ar part1c1pat10n5, d1fferent da11y 10ad ener~e5 and d1fferent en~ne ~enerat0r type5.7he d 0 m ~ n

6. N 0 7 7 0 N ~ aL

382

7a6~ 2. Charac~f15t1c5 5et a5 a func~0n 0f the 50hr c0ntr16ut10n 5C f0r Mad ~r16uf10n 1, 11 and 1V 5C

55c (m2) C5c (kWh) 7ype 11 55c (m2) C5c (kWh) 7ype 1V 55c (m 2) C5c (kWh) 7ype 1

100%

95%

90%

85%

80%

75%

70%

4.5 10.3 5 11.6 5.5 11.8

3.5 2.7 4 3.8 4.5 3.8

3 1.2 3.5 2 3.5 3.3

2.5 0.9 3 1.5 3 2.5

2 0.9 2.5 1.2 2.5 3.3

2 0.7 2.5 0.9 2.5 1.7

2 0.7 2 1.4 2.5 1.5

0 m ~

mm ~

~ ~

~ d

~ ~

~ ~

+0 ~

5 0 ~ r c0~d6ut10n

F19.7.1. kwh C05t f0r many 5~ar pa~5 w1th 9a50f1ne enDne 9ener~0r (7ype 1V). 0f var1at10n 0f 5Cj 15 reduced 1n acc0rdance w1th re5u1~ 9Nen 1n 5ect10n 2.4. 7he c05t 0f the k w h pr0duced 6y a PV 5y5~m ~ c0n5tant 6ecau5e the character15t1c5 0f the 5y5~m are pr0p0rt10na1 t0 the 10ad ener9y. 7he curve pre5ent5 a m1n1mum f0r a 501ar part 0f 75% ; then, the hy6r1d 5y~em ~ad1n9 t0 the 10we5t c 0 ~ 15 the 5y~em f0r wh1ch 75% 0f the 10ad 15 5upp1~d 6y the PV and 25% 6y the enNne 9enerat0r. 1n the5e c0nd1t10n5, the k w h c05t pr1ce pr0duced 6y the 0pt1m12ed hy6r1d 5y~em 15 3 t1me5 ~ w e r than the k w h c 0 ~ pr0duced 6y a ~and-M0ne PV 5y~em. Ndrach de Card0na and M 0 r a L0pe2 [3] ~ud1ed the 0pt1m12ed 5121n9 0f an hy6r1d PV 5y~em. 7hey u5ed a 10~-0~10ad pr06a61f1ty m ~ h 0 d and c11mat1c data 0f d N ~ ~06a1 rad1at10n. 7he1r 0pt1m~at10n cr1ter10n wa5: the 6e5t 5y~em 15 0ne wh1ch take5 the m05t advanta9e 0f 501ar rad1at10n. F0r the c0nf1dered reN0n (Anda1udm 5pNn) the 0pf1mM f12e 0f the m0du1e 5urface 1n the hy6r1d 5y~em 15 ach1eved when the 1n~N~d p0wer 15 6etween 70 and 90% 0f the peak p0wer that 1t w0u1d 6e nece55ary t0 1n5ta~ 1f the PV 5y~em wa5 aut0n0m0u5 (w1th0ut enNne 9 e n e r a t 0 0 . 1 n th15 ca5e, the percenta9e 0f the 10ad wh1ch 15 c0vered 6y the PV 5y~em var1e5 6 ~ w e e n 90 and 95%. C0ncern1n9 the f12e 0f the PV array c0~e5p0nd1n9 t0 a 50~r c0ntr16ut10n e4uN t0 90%, we f0und a reduct10n 0f 70% re1at1ve

Am0n0m0u5 hy6r1d phm0vNta1c Nam

~ ~ 5 d

1500~m

=~,~2 ~43 1

383

V 897 6 5 4 3Da1~2~Wh~ 1 ~ad

0~

=~

=0

#

0~

~

10

~

~ ~ ~ ~ ~ ~ ~ 50~ ~ n ~9. 7.2. k w h C05t ~ r many 50hr part5 ~ t h ~ e 5 d 1500 rpm en~ne ~ n e r ~ 0 r ~ e

4 ~ ~11H 1

1~ 8 ~

1 =~ ~

~

~

0 =0 ~

/

1V).

1

9 ~ ~

5~ar~ n

~ ~

~ ~

~9. 7.3. k w h C05t ~ r many 50~r ~ r t 5 ~

~0 ~ ~e~

3000 en~ne ~ n e r a ~ r ~ e

1~.

t0 an aut0n0m0u5 PV 5y5mm (5ee 7a61e 2), 1.e. the 5ame reduct10n f12e a5 0ne f0und 6y 51drach de Card0na ~]. H0wever, the 0pt1m12at10n cr1ter10n 15 d1fferent. 0 u r cr1ter10n c0nduce5 t0 an 0pt1m12ed 501ar p a n 0f 75%, 1ndu~n9 a PV array reduct10n e4ua1 t0 a60ut 50% (5ee 7 a 6 ~ 2). •

VAL1DA710N

0F 7HE ME7H0D

7 0 v M ~ e t~5 m ~ h 0 d , we appf1ed 1t t0 a ca5e 5mdy 1n an e~5t1n9 hy6r1d PV ~ a n t ~ M ~ d 1n C0rf1ca : Pa0mh-R0nduf1nu ~ 5 ~ m .

384

6. N 0 7 7 0 N

et aL

7he Pa0m1a p r ~ e ~ ha5 6een de~9ned a5 a ~and-a10ne fac111ff 5up~f1n9 a h a m ~ t 1n C0r~ca, a Med~erranean 1~and 1n the 50uth 0f France 02°09 ~ N 0 ~ h ) ; t~5 ham~t 15 10cated 0n the 5par5 0f the m0unt~n5 at a h e ~ h t 0f a60ut 400 m. 7 ~ 5 p110t ~ a n t wa5 1m~emented 1n 1983, w1t~n 1he 50~r PV R•D Eur0pean Ec0n0m~ C 0 m m u ~ f f Pr09ram (CEC-D6XVH). 7he charac~r15t1c5 0f the P a 0 m ~ PV ~ a n t are : 508 m ~ m 0 d ~ e (44 kW) and 560 k w h 0f ener9y ~0ra9e acc0r~n9 t0 the d15char9e rate ~500 Ah/C10--168 V). 7he 9enerat1n9 5et c 0 n ~ 5 0f a 9a5 en~ne w1th a n 0 m ~ p0wer 0utput 0f 25 kVA. 7he the0~t1c~ ~ a d c0n5umpt10n pr0f11e u5ed f0r the PV ~ n 9 ~ ~ven ~ F19.8 acc0rd~9 t0 the 5ea50n. Fr0m the ~ 0 6 ~ ener9y m ~ h 0 d d15cu55ed p ~ 0 u 5 ~ , we have c0mputed the ~ n 9 0f the PV 5y5~m 50 a5 t0 5at15fy the a60ve ham1et 10ad f0r ~fferent part5 0f the 10ad 5uppf1ed 6y the PV 5y5~m, the 0ther p a ~ 6~n9 5at15f1ed 6y an en~ne 9enerat0r (5ee F19.9). 7 0 r e ~ e th15 5tudy, we u ~ d 501ar ~ra~af10n data c0~ected ~ Ajacc10-V19n01a and the 10ad pr0ff1e def1ned ~ F19. 8. F0r ~1 5u6-5y~em m0d~5 ~5 PV array, 6a~ery, char9e/ ~ h a r 9 e ~9~af10n), we t00k the 5ame c0n~deraf10n5 and hyp0the5e5 a5 th05e deve10ped 1n [1]. We added t0 the pre~0u5 h a m ~ t 10ad c0n5umpt10n the 1nver~r ~1f-c0n5umpt10n and 1t5 eff1dency acc0r~n9 t0 1he DC e ~ f 1 c ~ p0wer 0utput 0f the c0nve~er. 7 a ~ n 9 1nt0 acc0unt the charac~r15t1c5 0f the P a 0 m ~ PV p1ant, t~5 5y~em 15 n0t aut0n0m0u5 and can 5up~y 98% 0f the dectr1ca1 need5, c0n5e4uent~ the 9a5 9 e n ~ 0 r 5upp11e5 1he 01her 2%. Fr0m the rea1 c0~5 ~3] 0f the PV p ~ n t 0n $U5 1983) and ~ n 9 a f1~t1me 0f 20 yea~ f0r the m 0 d ~ and 5 year5 f0r the 6attery 5et and an actua112ed rate 0f 6% a5 5u99e5~d 6y Cha60t [2~, we c~cu1~ed the a ~ u ~ e d k w h c0~. F0r t~5 c~c~af10n, we t00k an en~ne 9enerat0r w1th a peak p0wer e 4 u ~ t0 that 0f the 9enerat0r 1 n ~ d 0n the ~te ~ 5 kVA). 7he re5u1t5 0f t~5 c05t Mudy are pre5ented ~ F19. 10 where we f1nd, f0r ~ f f e ~ n t percenm9~ 0f 10ad pr0~ded 6y PV, the k w h c05t acc0r~n9 t0 the m 0 d u k area. 7he c0~ 5tudy M10w5 u5 t0 0pt1m12e the p1ant ~ n 9 f0r each 501ar p a ~ 6ut~ a5 ~ e n 6ef0~, the 6e~ 501ar c0ntr16ut10n 15 75%. We n0te that the k w h c05t var1e5 t0 a 9reat de9ree. 1n the pre5ent c0nf19urat10n, t~5 c05t 15 a60ut $U5 3.6 6ut, ~ the 0pf1mM c0nf19urat10n had 6een ch05en (m1n1mum at 75%), 1t w0u1d have 6een e4u~ t0 $U5 1.9~ 1.e. a60ut 0ne ha1~ 7he ke5t c0nf19urat10n5 f0r each 501ar c0ntr16ut10n, 1.e. the c0nf19urat10n k a ~ n 9 t0 the Mwe~ k w h c05t, are pr~ented 1n 7 a 6 ~ 3. F0r the p r e ~ n t c0nf19urat10n c0~e5p0n~n9, a5 5ta~d p m ~ 0 u 5 ~ t0 a 501ar c0ntr16ut10n 0f 98%, 0ur cak~at10n ha5 ~ d t0 an en~ne 9enerat0r peak p0wer e4uM t0 24 kW~ that 15 1n 900d acc0rdance w1th the ex15t1n9 9enerat1n9 5et ~ 5 kVA). We have c0mpared 0ur re5uk5 t0 0ther ~5~t5 06ta1ned p ~ 0 u 5 ~ ~ (7a61e ~ u51n9 a very c 0 m ~ e x m ~ h 0 d t0 ~ m ~ e each 5u6-5y5~m 0f the PV ~ant. We 065erve, c0mpar1n9 t h ~ e ~ 5 ~ w1th 0ur ~ n 9 ( 7 a 6 k 3), a d e c m a ~ 1n m 0 d ~ e area and an 1ncrea5e 0f 5t0ra9e capac1ty. H 0 w e v ~ we have ~ m ~ m e d the PV ~ a n t 6eha~0ur u~n9 chara~er15~c5 ~ven 6y 8uchet and we have d ~ e r m ~ e d the c 0 ~ p 0 n ~ n 9 501ar p a n : F0r 8uche~5 c0nf19urat10n m 95%, we f0und 95.2% ~ - - F 0 r 8uchef5 c0nf19urat10n at 90%~ we f0und 89.8% ; - - F 0 r 8uchef5 c0nf19urat10n at 80%, we f0und 75%. 7he acc0rdance 6~ween ~ 5 ~

06tMned 6y the ~ n 9

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M0du1e 5urface (m 2)

5t0ra9e capac1ty (kWh)

5t0ra9e capac1ty (Ah)

k w h c0N ($U5)

550 530 460 400 360 340 310

1082 433 311 172 148 120 72

5306 2123 1525 843 824 588 353

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5t0ra9e capa~ff (Ah)

397 352 263

4130 4130 3700

95 90 80

5. C 0 M P A R 1 5 0 N 0 F D1FFEREN7 ELEC7R1C17Y P R 0 D U C 7 1 0 N 5 Y 5 7 E M 5 F 0 R RURAL AREA5

7he m05t c0mm0n ~ectr1~ty pr0duct10n 5y~em u5ed when the ~ e c t r c ~ y 9r1d 15 n0t av~1a61e 15 the en~nc 9enerat0r wh1ch 15 a 900d parame~r 0f c0mpar150n w1th 501ar and hy6r1d 5y~em5. We pre5ent 1n F19. 11, f0r d1fferent ener9y 10ad5 and f0r a 10ad pr0f11e 1V, the k w h c05t f0r the 13 decentrah2ed pr0duct10n 5y5~m5 wh1ch are : three en~ne 9enerat0r5 d1rect1y c0nne~ed t0 the 10ad repre5en~d 6y a ~ r d e ~a50hne (9rey), D1e5e1 1500 rpm (wh1te) and 3000 rpm (6~ck)] ; --three en~ne 9enerat0r5 u~n9 a 6uffer 6ef0re 5upp1~n9 the 10ad w1th tw0 6attery capa~f1e5 : 1 day ~ 4 u a r ~ 0r 2 day5 (tr1an9~) 0f 5t0ra9e capa~ty ; --three hy6r1d 50~Uen~ne 9enerat0r 5y~em5 (d~m0nd) (9a5011ne, D1e5~ 1~00 rpm and 3000 rpm) and --0ne 50~r 5y5~m. U~n9 a 6a~ery a5 a 6uffer a110w5 the en~ne 9enerat0r t0 w0rk at 1t5 rated capac1ty (w1th a 900d eff1dency) and f0r a 5h0~er t1me each day. An 1denf1c~ 5y~em type ha5 6een ~ud1ed 6y Van D~k et aL ~ . 7he 1rre9u1ar1ty 0f the curve5 pre5en~d 15 due t0 the d1fferent 9enerat0r rated capadty chan9e5 cau5ed 6y the en~ne 9enerat0r chan9e. A1th0u9h 1t 15 n0t a1way5 p05~6~ t0 f1nd 0n the French market a 9enerat0r w1th exact1y the re4u1red rated capadty. 7he c05t d1fference5 6etween the tw0 D1e5e1 en~ne 9enerat0r5 are n0t ~9n1f1cant, 50 we ~p5~w~

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ju5t made c0mment5 0n the ~ f f e ~ n c e 6~ween 9a50f1ne and ~e5e1 9enerat0r5. 1n dffect c0nnect10n, the 9a5011ne 9enerat0r 15 6etter a d a p ~ d t0 the 10w da11y 10ad and 15 m0re pr0f1ta~e f0r dM~ 10ad5 1e55 than 8 kWh/day ~ c0mpar150n w1th ~ e ~ 1 0~e5. F0r m 0 ~ than 8 k W h / d a ~ the ~e5e1 9 e n ~ 0 r 15 m0re pr0f1ta~e 6ecau5e 0f the ~ f f e ~ n c e 0f fu~ c05t. 7he5e ~5M~ can M50 6e app1~d t0 the 5y~em 9enerat0r/6attery, 6ut the reduct10n 0f the fud c0~ ~ad5 t0 a reduct10n 0f k w h c0~ ~ c0mpar150n w1th ~ r e ~ 5 u p ~ n 9 . 7he 501ar ~ e m 15 never f1nanda11y ~ a 6 ~ c0mpared t0 the hy6r1d 5y~em, wh115t 1n c0mpar150n w1th the en~ne 9enerat0~ 1t 5tay5 pr0f1ta~e up t0 2 kWhMay. 7he hy6r1d 5y~em5 are the "6e5~ 5y5~m5 f0r t~5 10ad ran9e. 7he k w h c0~ ha5 6een e5f1m~ed j u ~ 0n the 6a~5 0ff1nand~ ~a~11t% w1th0ut ~ n 9 1 n t 0 acc0unt the 5 0 d 0 ~ c M and ec~0DcM 1mpact5 ; t~5 15 a p r 0 ~ e m w ~ c h m u ~ n0t 6e n e ~ e ~ e d 6ut ~ 15 ~ff1c~t m evMu~e. 7 a ~ n 9 ~ t 0 acc0unt t h e ~ ~ d d e ~ c0~5 5h0Md ~ d u c e the ~ f f e ~ n c e 6~ween ~deaW~ and ••50ft•• e n e r D ~ and f05511 0ne5 ~ . A6enav0f1 ~ , affer a c0mparat1ve ~udy 0f ~verM ener9y 5y~em5 f0r rura1 area5 (PV, fue1 9enerat0~ 9r1d e~en~0n), 5h0wed t h ~ the PV 5y~em 15 j u ~ ~ a 6 ~ , ~ c0mpar150n w1th a fue1 9enerat0~ 6 d 0 w a da11y 10ad 0f 4 kWh/day ; ~ 0ur 5tudy 0ur ~5M~ f1m~ t~5 c0mpet1t1ven~5 t0 3 kWh/day. Fr0m ~ud~5 devd0ped 6y 17 P0wer Ltd ~8], f0r the 5ame fu~ c0~, the PV k w h 15 pr0f1ta~e f0r dM~ Mad5 ~ r 1 ~ r t0 6 kWh/day. Van D~k et aL ~5] c 0 m p a r e ~ f0r a 2.7 kWh/day Mad, three ener9y 5y5~m5 f0r rura1 ~ 5 : an aut0n0m0u5 PV 5y5~m, a fu~ 9 e n ~ 0 r w1th 5t0~a9e and a P V / ~ 0 r a 9 ~ 9 e n e r ~ 0 r hy6r1d 5y~em. W1th ec0n0m1c p a r a m ~ e ~ and c0~5 d 0 ~ t0 0ur hyp0the~5, and f0r a 5~e (Madr1d) w1th an annum mean dM~ 501ar 1rra~at10n e 4 ~ v a ~ n t ~ t h ~ 0 f 0 u r 51te (Madr1d : 4.37 kWh/m 2 per day ; Ajacd0 : 4.4 kWh/m ~ p ~ d a ~ , the ~5M~ are 5h0wn ~ 7 a ~ e 5 : 7 h e ~ ~5u~5 5h0w the w1de ran9e ~atter1n9 due t0 var10u5 c0~5 and ec0n0m~ c0n~t10n5 enc0unte~ed a11 0~er t~e w0r1d a5 ment10ned 6y H111eand D1enha~ ~ . C0NCLU~0N A11 the re5u1~ pre5ented 1n th15 paper have 6een 06tNned tak1n9 a dN1y c0n5tant 10ad thr0u9h0ut the year and cann0t 6e 9enera112ed t0 10ad5 vary1n9 acc0rd1n9 t0 the 5ea50n. 1n th15 pape~ we have pre5ented the c h a r a c t e r 1 ~ 9106M e4uat10n 0f the aut0n0m0u5 PV 5y~em 6ehav10uC wh1ch f1nk5 the 50~r c0ntr16ut10n and the ener9y exce55 0f the 5y5~m. 7h15 5tudy ha5 5h0wn that f0r an ener9y 5y~em f0r wh1ch the 0n1y ener9y 50urce 15 the ph0t0v0Ra1c array, the t0tM 10ad 5uppf1ed 6y the PV 5y~em re4u1re5 a pr0duct10n capaNty tw0 t1me5 1ar9er. 7he ~ u d y 0fth15 unu5ed ener9y 6r0u9ht t0 the f0re that th15 exce55 decrea5e5 very 4u1ck1y a5 a funct10n 0f the 501ar c0ntr16ut10n. A 10ad 5upp1~d at 95% reduce5 the exce55 6y 0ne

7a~e 5. C0mpar150n 0f ~ 5 ~

~ven 6y Van D~k and t~5 w0rk

Van D~k et aL ~ Fud 9 e n ~ 0 r w1th ~0ra9e Am0n0m0u5 PV ~ e m P V / ~ 0 r a 9 e ~ e n ~ 0 r ~5~m

$U5 1.6~Wh $U5 L9~kWh $U5 1.7~Wh

Cu~em 5mdy $U5 1.~kWh $U5 2.02•Wh m $U5 2.2~kWh $U5 1.57~Wh m $U5 1.63~Wh

Aut0n0m0u5 hy6r1d ph0~v~ta1c ~ant

389

h ~ f and th15 h5t 0ne, f0r any 10ad pr0f11e 6ec0me5 n11 when the ph0t0v0R~c 5y~em 5upp11e5 75% 0f the 10ad. 7 0 5upp1y th15 un5at15f1ed 10ad, we added an a u ~ h a r y f05511 50urce t0 the 50hr 5y~em. 7he meth0d deve10ped f0r an aut0n0m0u5 ph0t0v0R~c 5y5~m ha5 6een ex~nded t0 an ener9y 5y5~m w1th tw0 ener9y 50urce5 and 1t f01~w5 that a 50hr c0ntr16ut10n 0f 75% ~10w5 0pt1mum pr0duct10n. A c0mpar150n 0f d1fferent pr0duct10n 5y~em5 5h0wed that, except f0r a very 5m~1 c0n5umpt10n, the 50hr 5y5~m 15 n0t f 1 n a n ~ ~a61e c0mpared w1th the f05f11 5y5~m5. 7he c0m61nat10n 0f a 75% 501ar w1th a 25% f05f11 5y~em 15 the m0re ~a61e 501Ut10n f0r d ~ 10ad ener9y 1n~f10r t0 10 k w h . We c0u1d ver1fy, ~ 0 m expef1ment~ data c0Hec~d 1n the Pa0m1a-R0ndu11nu PV 5y5~m, that the f1mpf1f1ed f1mu1at10n we have u5ed t0 determ1ne, 0n the 0ne hand, the hy6r1d PV 5y~em c0nf19urat10n5 and 0n the 0ther hand, ener9y exce55 and def1d~ ~ve5 re5u1~ 1n 900d acc0rdance w1th exper1ment~ 0ne5. We have 5h0wn the 1ntere5t 0f th15 5tudy 6ecau5e 1t5 app1~at10n t0 th15 ex~t1n9 5y~em 5h0u1d a110w t0 reduce the k w h c 0 ~ 6y a f a ~ 0 r 0f 2. 7he5e c0mpar150n5 were made uf1n9 f u d and e n ~ n e c0~5 av~h61e 1n France. 1t 5h0u1d 6e n0ted that f u d c05t5 1n r e m 0 ~ area5, part1cu1a~y 1n devd0p1n9 c0untr1e5, may 6e much h19her than th05e a55umed 1n th15 5tudy. H0wever, the meth0d0109y pre5en~d 1n th15 paper can 6e u5ed 6a5ed 0n 0ther c05t5 t0 w0rk 0ut the m05t effect1ve c05t 501ut10n f0r every ~rcum~ance. Ackn0w1ed9ement5--7he auth0r5 w 0 ~ d f1ke t0 thank Pr0~550r R 0 6 e ~ H111, Newca5f1e

Ph0t0v01ta1c5 App11cat10n5 CenW~ U~ver51ff 0f N0rff1um6f1~ E n ~ a n d f0r ~5 c0mment5 and 5u99e5t10n5 w ~ c h have 6een 9reat1y a p p ~ d a ~ d . N0MENCLA7URE

C

DE DL D0D

F H

~

L M P

P~

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5t0ra9e capad~ 0f the 6a~ery ~ W ~ 1~t1a1 6attery en~9y 5ta~ ~ W ~ m1~mum 6 a t ~ ene19y 5 ~ ~ W ~ ma~mum 6attery ener9y 5tate ~ W ~ ener9y def1c~ ~Wh) da11y 10ad ~ W ~ 6 ~ de~h 0f ~ h ~ 9 e ener9y pr0duced 6y the PV array dur1n9 0ne h0ur ~ W ~ en~9y c0n5umed 6y ~ e ~ad dur1n9 0ne h0ur ~ W ~ ener9y exce55 pa~ ~d c~t ~U5~ 50hr ffradhf10n ~ W h - m - ~ t0t~ 50hr ffra~ance 0n a phne t11ted t0 f1° (W• m ~ ener9y 10ad dur1n9 the f1m~at10n per10d ~ W ~ m ~ e n a n c e c0~ ~ U ~ p0w~ (W) r~ed p0w~ 0f the 9enerat0r (W) PV a~ay 0u~ut p0w~ (W) 10ad p0wer t0 5upp~ (W) heat1n9 va1ue 0f fue1 ~Wh~1 -~) ~e1 c0n5umpt10n per h0ur 0" h - ) ~ d c0n5umpt10n p ~ h0ur ~ ~ e r~ed p0wer

390 R

R7 5 5c 7 wE dt t

6. N0770N ~ aL ~ n ~ 0 r run~n9 c0~ ~ u ~ ~ n e r ~ run~n9 t1me (h) m0d~e 5 u r ~ a~a (m2) 501ar c0ntr16ut10n hp5e 0f t1me (5) wa~ed ener9y ~ w ~ hp5e 0f t1me (~ t1me ~)

6reek character5 4 ~9r Pch P~

Ac A7

c0eff1dent c01~ct0r t1R (de9ree) PV array eff1c1ency mechan1ca1-e1ectr1ca1p0wer c0nverN0n eff1dency c0eff1c1ent 6attery char9e eff1c1ency 6attery d15char9e eff1c~ncy 6attery 5tate 0f char9e var1at10n (kWh) 1ap5e 0f t1me (5).

REFERENCE5

1. 6. N0tt0~ A. L0uche, M. Mu5e111 and P. P09~, Aut0n0m0u5 ph0t0v0R~c 5y~em: 1nf1uence5 0f 50me parameter5 0n the ~ n 9 : ~mu1af10n f1m~5~p, 1nput and 0utput p0wer pr0f11e. Renewa6~ Ener9y 7, 353-369 (1996). 2. H. P. Nava, R. Ar1n9h0ff and H. He55, A c0mputer a1ded t001600k f0r PV-Hy6r1d 5y~em de~9n. Pr0c. 8 ~ E.C. Ph0t0v0~a~ 5 0 ~ r Ener9y C0nference, pp. 358-362. F10rence, 1ta1y (1988). 3. M. ~drach de Card0na and L. 1. M0ra L0pe~ 0pt1m12at10n 0f hy6r1d ph0t0v01ta1c/au~11ary 9enerat0r 5y5~m5 f0r 1n~1at10n5 0 f r u r ~ ~ectrf1caf10n. Pr0c. 11 ~ Ph0Wv0#a~ E.C. 5 0 ~ r Ener9y C0nference, pp. 1287-1290. M0ntreu~ 5w1~e~and (1992). 4. L. 8arra, 5. CatMan0tt1, F. F0ntana and F. Lav0rante, An anMyt1cM mNh0d t0 determ1ne the 0pf1mN f12e 0f a ph0t0v0RNc p~nt. 5 0 ~ r Ener9y 33, 509-514 (1984). 5. 6. Am6r050n~ 5. Cata1an0tt1, U. C05d~ 6. 7r015e and 6. C0curuH0, C0mpar150n 6etween p0wer and ener9y m~h0d5 0f anMy5e5 0f ph0t0v01ta1c p1ant5. 5 0 ~ r Ener9y 34, 1-8 (1985). 6. L. L. 8ucdardf1, E5t1mat1n9 10~-0~p0wer pr06a61f1f1e5 0f 5tand-a10ne p h 0 t 0 v 0 ~ c 501ar ener9y 5y~em5. 501ar Ener9y 32, 205-209 (1984). 7. L. L. 8uc~ardf1, 7he effect 0f day-t0-day c0~daf10n 1n 501ar rad1a~0n 0n the pr06a61f1ty 0f 10~-09p0wer 1n a 5tand-~0ne ph0t0v01t~c ener9y 5y~em. 501ar Ener9y 36, 11-14 (1986). 8. J. M. 60rd0n, 0pf1mM NNn9 0f ~and-M0ne ph0t0v01ta1c 50~r p0wer 5y5~m5.50~r Ce115 20, 295-313 (1987). 9. 5. A. K1e1nand W. A. 8eckman, L0~-0910ad pr06a61f1t1e5 f0r ~and-N0ne ph0t0v0RNc 5y~em5.50~r Ener9y 39, 49%512 (1987).

Am0n0m0u5 hy6r1d phm0v01ta1c ~ant

391

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