[BLDG-SIM] Statistical Estimate of Number of Units ON (peak demand)

BKoran at aol.com BKoran at aol.com
Wed Jun 2 15:51:14 PDT 1999

This is a statistics problem.  I'm extremely competent with thermodynamics 
and most energy analysis, but I've only recently tried to estimate peak 
demand by month.  I can estimate the kW of an individual unit, but what is 
the expected peak kW during the month for a given number of similar units?

I'm very curious, how do hourly analysis program do this?  It's easy to see 
that they might not handle peak demand very well.

As I'm certain you're all aware, large businesses are
generally charged each month according to the highest electrical demand
recorded over a 15-minute period.

Consider a site with number of packaged units for cooling.  The problem is to 
find out the maximum number of units that would be on at
simultaneously (for at least 15 minutes), so that the peak electrical demand 
and associated demand charges can be estimated.

N_units	=number of units
A_pct	=fraction of time each unit is on
	 during each time period considered
N_pers	=number of time periods to be considered
A_Prob	=minimum acceptable probability of occurrence

For example, if I have 3 units, and each unit operates only 5 minutes each
hour, the probability that all units are operating at once is low if I only
look at 1 hour.  

However, if I consider 100 hours, the probability that all units are
operating at once is much higher.

If I have a large number of units, the number of units likely to be
operating simultaneously will approach the product of the total number of
units times the fraction of time each unit is on.

I suppose I need to use a threshold probability to constrain the problem. 
So, with a probability greater than 70%, what is the maximum number of
units operating simultaneously?  Even better, what is the maximum average
number of units operating simultaneously over a 15-minute period?

How do DOE-2, Trace, HAP, BLAST, etc. calculate a 15-minute peak demand?

Bill Koran

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