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re: system sizing
27 mar 2000
michael wrote:
>>...fig. 5.6 in the 1995 (third) edition of practical photovoltaics by
>>richard j. komp, ph.d. shows ln(#cyc)=8.57-2.31d, approximately,
>>for a motive power battery, where d is the fractional discharge depth,
>>so the energy stored over its lifetime is approximately proportional to
>>dexp(8.57-2.31d), which is maximized at a total of 1296, eg 778 kwh over
>>the lifetime of a 6 v 100 ah battery, when d = 1/2.31 = 0.433, at a
>>43% discharge depth...
>...i got 503kwh using your example.
if total energy stored is proportional to the fractional discharge depth
times the number of discharge cycles (= dn), then a 600 ah 6 v battery
with a single (n=1) 100% discharge (d=1) over its lifetime stores 600 wh
over its lifetime, right? if dn = 1296, it stores 600x1296 = 777,600 wh
or about 778 kwh over its lifetime.
>...typical data on some bp batteries... indicate that the optimum dod
>is around 33%.
looks close to me (in courier font.) with a narrow range (+/- 20% or so.)
>cycles 1200 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500
>dod 90% 70% 52% 45% 38% 34% 30% 26% 23% 20% 18% 16%
>years 3.3 4.1 5.5 6.8 8.2 9.6 11.0 12.3 13.7 15.1 16.4 17.8
dn = cycles x dod ...1125 1140 1190 1200 1170 1150... 1040.
ohoh. taxes.
>no of batteries required (calc)
1.1 1.4 1.9 2.2 2.6 2.9 3.3 3.8 4.3 5.0 5.6 6.3
so the above is the inverse of dod, to make up 100% in each case,
so we can fairly compare these systems.
>total batteries over lifetime (calc)
6.0 6.2 6.3 5.8 5.7 5.5 5.4 5.6 5.7 5.9 6.0 6.3
the number of batteries needed per year is economically interesting:
.34 .35 .35 .32 .32 .31 .30 .31 .32 .33 .34 .35.
a curious lack of variation. the same 20% or so... but then there's
interest on the battery money, and batteries have shelf-lives as well as
discharge lives, ie they wear out (get less efficient) over time, even
if never deliberately discharged. those factors favor fewer batteries.
>but you need to factor in the rate of discharge (and consequent derating
>of capacity) assuming you discharge the batteries over 16 hours
and higher charging loss with about twice that current, over 8 hours?
>discharge rate (cnn) over 16hrs
18 23 31 36 42 47 53 62 70 80 89 100
>battery capacity (of rated)
66% 68% 74% 76% 80% 82% 85% 87% 90% 93% 96% 100%
>dod on revised capacity
93% 80% 64% 58% 50% 46% 41% 36% 31% 26% 21% 16%
i don't quite follow this part.
>now the question is: at what discharge rate are the dod vs cycles
>specified by the manufacturers (c100?)
i guess you mean c/100, if this is a current.
>and are the figures derated for higher discharge rates?
guess we gotta read the fine print.
>anybody know?
bp.
>there are many things i did not factor into this rough analysis including:
>3. the cost of changeover (if you're not doing it yourself)
some people pay themselves more than $0.00 per hour :-)
>5. the cost of housing the batteries
and supporting them, and heating them, sometimes. and moving them...
nick
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