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re: system sizing
25 mar 2000
george ghio wrote:
>>>>>>the panels put out 100ah per day and we use 100ah per day.
>>>>>>the first day we have no sun but we use 100ah
>>>>>>the next 4 days we get 100ah per day.
>>>on an average day, you used 100 ah, but you only collected
>>>6cycles(4daysx100ah+1dayx0ah)/30days = 80 ah on an average day...
>in the question the panels put out 100amp hours per day.
on sunny days. however, the average output was 80 ah/day, according
to webster. statistical fairies would say the "mode" was 100 ah/day.
>>>how, exactly, is battery lifetime related to the discharge depth
>>>and the number of cycles?
and how, exactly, is "battery lifetime" defined? some say it's mainly
a matter of the inefficiency we choose to tolerate, as the internal
series resistance increases over time (so we get lower terminal voltage
for the same current and charge) and the parallel resistance decreases
(so the self-discharge rate increases, compared to a new battery at
the same temperature.) when we have to put in, say 2 kwh for every
1 kwh we take out, we say its life is over, and go buy new ones.
>>taken from battery energy's data;
>>10% daily depth of discharge - 12-14 years life
>>25% daily depth of discharge - 9-12 years life
>>50% daily depth of discharge - 6-8 years life
>>thanks, george. do they have a lifetime vs temperature curve too?
still waiting.
>>or lifetime vs time spent in various degrees of discharge?
still waiting.
>>how do we combine these factors to predict lifetime?
still waiting.
>>which dod scheme is most cost effective, of these 3? should we use
>>10 batteries with a 10% daily dod, or 2 with a 50% dod? looks like
>>we replace 10 batteries every 13 years in the former case, ie 0.77
>>batteries per year, or 2 every 7 years in the latter, ie 0.29 per
>>year. and 4 every 10.5 years at 25% daily dod, ie 0.38 per year. so
>>fewer batteries with higher dod is best, even if the battery money
>>earns no interest, right?
>well for my hard earned money i would settle for a 20% dod withe the
>batteries kept as close to 25 degrees c as possable
keeping them 25 c when it's 5 c outdoors shortens their lifetime.
>and just have to buy new batteries every 20 - 25 years.
battery energy said
>>10% daily depth of discharge - 13.0 years life
>>25% daily depth of discharge - 10.5 years life
so, interpolating...
>>20% daily depth of discharge - 11.3 years life
why do you believe your batteries would last twice as long
as battery energy specifies for half that discharge depth?
>battery energy give 8 years warranty and claim that there batteries
>will last 13 years.
at a 10% daily depth of discharge, unless they live at george's house.
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. greater or lesser discharge depths result in less
total energy storage over the battery's lifetime. if this battery costs
$60, its lifetime energy storage cost is 8 cents/kwh, ignoring the
interest on the investment.
the time value of money and the fact that batteries wear out over time
(even with no deliberate discharging) seem like good reasons to use
fewer batteries with a greater average discharge depth.
otoh, higher currents reduce efficiency and capacity, which bodes for
more batteries...
can we bring more science to this black art?
nick
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