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re: rolling blackouts hit houston again, today...
25 jul 1999
gigg a watt  wrote:

>i always preach, that reliability can be applied to almost everything...
>even a wife.... what good does it do, if she is not around when
>you need her...

that's "availability," which can be dramatically enhanced by redundancy :-)

>the same with electricity... you are depending on others, to provide
>you with this important commodity... and it these providers become
>unreliable... then alternative sources of electricity has to be found...

grid electricity is becoming more unreliable under deregulation. our local
utility peco now deliberately undersizes pole transformers (fused at 10x the
power rating), figuring that they have little to lose, economically, on the
average, when a transformer catches on fire in the statistically unlikely
event that a half-dozen neighbors all turn on their hair dryers, electric
dryers, ranges, air conditioners and toasters at the same time. 

>...the by-product of home,  pv produced electrical energy...   is
>energy  independence....

one might argue that the world needs more interdependence, vs teenagers,
rogue armies and rugged individualists.  

>you can now live  in places  that you might like better, without
>considering the local power monopoly's,  electrical lines...

but pv electricity is often less reliable than the grid, by itself.

otoh, having pv and the grid (or 2 complete pv systems, or a generator
and pv, candles, drums full of water, etc.) makes for a much more available
system than either alone, if you can tell that one subsystem is broken
and send it out to get fixed before the others fail.

if an inverter fails once a year ("mtbf=8760 hours") and takes a week
to get fixed, this sort of (markov) model might predict its availability:

                        where l = is the failure rate, 1/(52 weeks),
	   l                  r = is the repair rate, 1/(1 week),  
 ----  --------> ----         p1 is the probability that the inverter works
| p1 |          | p0 |    and p0 is the probability that it doesn't.
 ---- <--------  ----
	   r 

since it works or it doesn't, but not both, p1 + p0 = 1, and p0 = l/r p1, so
r/l p0 + p0 = 1, or p0 = 1/(1+r/l) = 1/(1+1/1/(1/52)) = 1/53, so we might
expect the inverter to be out of service an average of 1/53 of the time,
ie 165 hours, or a bit less than one week per year.

add another inverter and this becomes
                        
	  2l              l             p2 <--> both work
 ----  --------> ----  -------> ----    p1 <--> one works
| p2 |          | p1 |         | p0 |   p0 <--> none work
 ---- <--------  ---- <-------  ----
	  2r              r

again, p2 + p1 + p0 = 1, p1 = 2l/2r p2 and p0 = l/r p1, so
2r/2l p1 + p1 + p0 = 1, or r^2/l^2 p0 + r/l p0 + p0 = 1, or 
p0 = 1/(1+r/l + r^2/l^2) = 1/(1+ 52 + 52x52) = 0.00036, so we
might expect both inverters to be out of service an average of
0.00036x8760 = 3 hours per year. (reducing the repair time to 4 hours
decreases the average unavailability to 1/2 hour per year.)

add another inverter and this becomes
                        
	 3l            2l             l           p3 <--> 3 work
 ----  ------> ----  ------>  ---- ------> ----   p2 <--> 2 work
| p3 |        | p2 |         | p1 |       | p0 |  p1 <--> 1 works
 ---- <------  ---- <-------  ---- <-----  ----   p0 <--> 0 work
	 3r            2r             r

again, p3 + p2 + p1 + p0 = 1, p2 = 3l/3r p3, p1 = 2l/2r p2 and p0 = l/r p1,
so p0 = 1/(1+r/l+ r^2/l^2+r^3/l^3) = 1/143,365, so might expect all three
inverters to be out of service an average of 8760/143,365 = 0.061 hours or
3.7 minutes per year.

nick




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