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re: wind and solar power aren't just for tree-huggers anymore
4 oct 2002
daestrom  wrote:

>> ...even conventional sources have downtimes and failures. they need
>> some overcapacity to account for that, ie to provide some definite
>> high system availability, eg 0.99999, meaning power for all but 5
>> minutes per year, on average.

>...conventional sources have such 'overcapacity'.  but the key is when
>it is available.  plants schedule their maintenance outages around each
>other and the expected demands of the system.  in large part, man decides
>when to turn a plant off for maintenance, taking into consideration other
>power availability and demand.  with wind/solar, nature would determine

planning is nice, but randomness is fine, statistically-speaking.

>...if you build 150% capacity of a wind system and the wind isn't blowing
>today, you still have to 'turn off lights'.

the same can be said of a conventional grid on an unlucky day.

>for every mwh that is not generated by wind today because the wind isn't
>blowing, there would need to be an alternative source to provide that mwh.

this could be a smaller windmill somewhere else :-)

>if not in 'conventional' sources, then storage mechnisms and/or larger
>transmission systems to bring in power from where mother nature *is*
>supplying today.

i'm not sure we need larger transmission systems,
with lots of small distributed sources. 

>*some* form of backup (conventional/storage/transmission), is needed
>with these 'unsteady' technologies.  and they require more backup than
>conventional sources because although the probability of a conventional
>source not being available isn't zero, it is much lower than wind/solar.

with equal numbers of sources, the backup cost is higher, but alternative
sources tend to be smaller and more widespread and numerous.

>> a large enough number of sufficiently diverse alternative sources could
>> provide any specified availability, even with no conventional backup...

>true, but they have to be diverse and not vary at the same time.

no. they can vary, and diversity is a matter of numbers. we might
encourage diversity by paying more for more independent sources.

>...if wind makes up 20% of that mix, then you need 20% from another source
>(biomass perhaps) for days when the wind doesn't blow.

nonono. you need less than 20%. in the example below, we blithely replace
a 1 gw nuke (booo) with an unavailability of 5 minutes per year with lots of
windmills sprinkled over a large area, eg 1076 4 mw units with an average
output of 1 mw (2 mw 50% of the time, otherwise none, like a coin flip),
or 10,236 400 kw units, or 100,740 at 40 kw, or 1,002,334 at 4 kw, or
10,007,380 400 watt windmills...

notice that the total overcapacity needed decreases as the number of sources
increases, because of the magic of large numbers.

10 q=5/(8765*60)'grid unavailability (5 minutes per year)
20 p=.2316419'estimate error function using the technique of
30 t=1/(1+px)'m. abramowitz and i. stegun as described in the
40 a1=.127414796#'handbook of mathematical functions, 
50 a2=-.142248368#'national bureau of standards,
60 a3=.710706871#'applied mathematics series no. 55,
70 a4=-.726576013#'washington, d.c.; u.s. government printing office,
80 a5=.530702714#'1964, page 932.
90 t=1/(1+px)
100 f=((((a5*t+a4)*t+a3)*t+a2)*t+a1)*t
110 xl=x
120 x=sqr(2*log(f/q))'erfc(x) = q
130 if abs((x-xl)/x)>.01 goto 90'iterate to 1%
140 print "grid unavailability:",,q
150 print "number of standard deviations from mean:",x
160 p=1e+09
170 print"desired total power (w):",,p
180 for lpw=2 to 6'log of average source power
190 pw=10^lpw
200 print "peak source power (w):",,4*pw
210 print "average source power (w):",,pw
220 m=(x/2+sqr((x/2)^2+4*p/pw))/2
230 n=m^2
240 print "number of sources:",,n
250 next lpw


grid unavailability:                     9.507511e-06
number of standard deviations from mean: 4.662678

desired total power (w):                 1e+09

peak source power (w):                   400
average source power (w):                100
number of sources:                       10007380

peak source power (w):                   4000
average source power (w):                1000
number of sources:                       1002334

peak source power (w):                   40000
average source power (w):                10000
number of sources:                       100740

peak source power (w):                   400000
average source power (w):                100000
number of sources:                       10236

peak source power (w):                   4000000
average source power (w):                1000000
number of sources:                       1076

>or, we learn to live a little more in harmony with our energy sources and
>accept that somedays the wind doesn't blow so we reduce production/usage.

dynamic demand reduction has a place too. these days, it can be done
automatically and economically, eg for lots of 1 kw loads. 


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