ASHRAE Journal - August 2019 - 67

COLUMN IEQ APPLICATIONS

the local and cultural expectations, the ability for people
to make personal adjustments or adaptations, the time
of exposure, expected level of activity and clothing
levels for the occupants, local air movement, local thermal radiation gains (from sun) or losses (through cold
windows), etc. Building overcooling during summer is
a common problem, and typically is the result of poor
latent control, oversized HVAC systems, or a desire to
ensure that indoor humidity problems do not occur.
As an alternative, one could envision that a simple
optimization routine could be established that would
determine an "optimal" zone setpoint by weighing the
predicted thermal comfort preferences of the occupants
in combination with anticipated energy consumption
used to operate the HVAC systems. The optimization
process involves a minimization of an objective function,
which might be written as follows for this situation:
Objective Function = ω × Energy Consumption
+ (1 − ω ) × Thermal Preference

In this equation the Energy Consumption term represents
the predicted amount of energy that would be consumed
to operate the HVAC system at a given setpoint, while the
Thermal Preference represents the absolute value of a predicted mean thermal preference vote of the occupants.
This preference is often expressed on a seven-point
scale, ranging from -3 (prefer this room to be much
colder) to +3 (prefer this room to be much hotter).
The ideal thermal environment would result in most
of the occupants having a thermal preference vote of "0."
The ω term is a weighting factor ranging between 0 and
1 that represents the relative importance assigned to the
two parameters in the optimization function. Since this
equation involves a combination of terms with potentially
a wide difference in numerical values, both parameters
would need to be normalized to a common numerical
range. For example, if the thermal preference values were
to range between -3 and +3 but the energy consumption
were expressed in say thousands of kWh, the objective
function would be biased toward changes in energy use.
The weighting factor ω could be set in a number of
ways. One would be to use a constant value, either set by
the building operations manager or by some other algorithm. It also might be adjusted based on current energy
costs, such as in a building that has a real-time price
electricity tariff, or changed based on other temporary

FIGURE 1 Illustration of how an optimization weighting factor might change based

on the cost of electricity as set by real-time price or rate tariff.
1

B
Weighting Factor ω

A
C

0

Electricity Price (Low to High)

situations such as during a requested demand response
implementation. For the later two situations, the ω
value could be increased as the real-time price increases
or when a demand response request is received.
In practical terms, this function requires having
information about the relationships of the energy and
thermal comfort parameters. It requires insight into
how the HVAC system energy consumption changes with
respect to operational temperature setpoints. It also
requires knowledge about how the building occupant
thermal comfort preferences change based on zone temperature. A simplistic solution would be to use a rule of
thumb estimate for changes in energy consumption and
thermal preference, although the thermal preference
estimates might be biased based on the preconceived
notions of thermal comfort preferences by the person
doing the analysis. Assuming that good relationships
for energy consumption and thermal preferences can
be developed, the optimization function could be built
into the building energy management control system to
determine optimum setpoints based on current conditions (energy costs, occupancy levels, etc.).
The key to developing this optimization process into a
valuable tool is in identifying the ω value. If it were a constant, then this would be a one-time determination and
setup into the building controls. In a demand response
event scenario, the values of ω could be pre-set by the
building owner/operator and might well be a single stepfunction. If the building were on a real-time price tariff,
then the situation becomes more complex. The weighting
factor ω could then be set as a function of the real-time
electricity price, but there are a number of potential
relationships between ω and the real-time price that
could exist, as illustrated in Figure 1. These could include
a step-function that ratchets up the emphasis on energy
A U G U S T 2 0 19

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