# [BLDG-SIM] Statistical Estimate of Number of Units ON

James F Pegues James.F.Pegues at carrier.utc.com
Thu Jun 3 09:44:55 PDT 1999

```Mr. Koran,

simulation software including Carrier's HAP program handle this issue.  An
explanation for HAP follows:

In HAP heat flow and equipment performance are calculated for a series of 8760
1-hour time steps.  Variations in heat flow or equipment performance over
intervals shorter than 60 minutes cannot be determined because of the lack of
sufficient data - weather data, schedules, loads, etc... for shorter periods of
time aren't available.  Therefore, hourly simulation results represent the
integrated performance over a 1-hour period.  Another way of viewing the results
is as representing the average state of operation over the 1-hour period.  With
this data the best estimate of demand that can be made is to assume steady
consumption (e.g., 40 kWh consumed by a compressor during a 1-hour period
equates to a steady 40 kW power level for the compressor for that hour). Similar
kW data is derived for all components in a building - fans, lights, office eqpt,
compressors, pumps, etc.. - to assemble the total building kW profile.  These
profiles are then evaluated to identify the peak kW during each billing period.
This can be interpreted as either assuming that the demand window is 60 minutes,
or that it is 15 minutes, but performance is steady for all 15 minute windows
during each 1-hour time-step.

In real life, of course, thermal and equipment behavior changes in significant
ways over periods of time shorter than one hour.  You've pointed out one example
- cycling of the DX unit and the effect it can have on demand determination.

Probably the only way to account for all the factors that affect demands set in
a sliding 15-minute window is to use a short-time step simulation which looks at
time intervals much less than one hour.  I think one version of BLAST provides
short time step simulations, but I don't know if it carries the analysis through
to determine peak demand.

If you use your statistical approach with hourly simulation data as raw
material, there may be several factors beyond the ON/OFF status of the packaged
DX units that are worth considering.  Over your 100 hour sample period the
variations in the following may affect probabilities:

a. Varying outdoor air temperature which affects the capacity of the DX
equipment and influences the cycling rate of the equipment.  This in turn
affects the probability of units being on.

b. Varying outdoor air temperature also affects the efficiency of the unit and
thus influences kW use.

c. Varying building loads which affect the cycling rate of the equipment.

Best Regards,
Jim Pegues
Carrier Corporation

Subject: [BLDG-SIM] Statistical Estimate of Number of Units ON (peak
Author:  BKoran at aol.com at Internet
Date:    6/2/99 6:51 PM

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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