# [BLDG-SIM] Stat Est. response to Larry Degelman

BKoran at aol.com BKoran at aol.com
Thu Jun 3 16:21:38 PDT 1999

```In a message dated 6/3/99 12:27:27 AM Pacific Daylight Time,
Larry at taz.tamu.edu writes:

>  If you look at this purely as a statistics problem, it's interesting to
note
> that the larger the number of units operating with independent
probabilities of
> being on at any one time, the lower will be the probability of all of them
being
> on at any one time.

Yes, that is partly why I brought this issue up.

>  What I'm skeptical of is applying statistics to
>  building cooling loads.   I don't agree that this is a statistics problem.

> It has a bit of probability in it, but the air conditioner's operation is a
> reaction to a fairly predictable pattern of thermal loads.

Absolutely, for an individual A/C unit.  But I am concerned with the case for
which the impact of the load and ambient T on equipment cycling, efficiency,
and capacity have already been accounted.

> To back this up
> (admittedly not by a scientific method), just look at the electric codes
again and you
> will see that even though diversity is allowed in plug loads, you are
required to
> sum 100% of all air conditioner loads when sizing the service panel.

That makes sense, because there is (nearly) always the possibility that all
units could be on at once.  (Conversely the probability that the all of the
units will NEVER be on at the same time is < 1.)

However, for estimating peak demand by month, (on average, over a several
year period) one might look at, for Pr =0.5, how many units would be on
simultaneously for at least 15 minutes, or perhaps more units on for less
than 15 minutes if that results in a greater 15-minute integrated demand.

So, I think I agree with you, except I think it is at least partly a
statistics problem.  The biggest uncertainty I have is whether zonal load
diversity has such a big impact on the peak kW (few of the units ever see
peak demand at the same time, most months) that this type of statistical
diversity becomes insignificant.  The zone load diversity impact is certainly
dependent upon lots of factors, but my guess is that it does not always
dominate the statistical diversity.  For example, many schools have little
diversity between zones, especially if there are not east- or west-oriented
windows.

Thanks for your response!  This is an interesting subject for me.

Bill

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