Fault Detection and Diagnostics for Rooftop Air Conditioners

independent of the moisture content in the air. Thus, if the operation between these
two regimes can be separated, the problem of developing a model for the rooftop unit
can be expressed as a function of two independent variables instead of three. To
separate wet coil operation from dry coil operation, Rossi (1995) suggested using the
following form for the models
f( T , T , T ) = f ( T − T )* g ( T , T )
amb ra wb wet dpt evap wet amb wb
+ ( 1− f ( T −T ))* g ( T , T
wet dpt evap dry amb ra
)
where
f( Tamb, Tra , Twb
)
is any state in the vapor compression cycle dependent on all
three inputs, T
dpt
is the dew point temperature of the evaporator inlet air,
f
wet
( T − T )
dpt
evap
is a function which returns a value of 0 when the coil is dry and 1
when the coil is wet, and g ( T , T ) and g ( T , T ) are models for individual
wet amb wb
properties for the wet and dry operating regimes. Using data generated by the
simulation model, Rossi found that the function f
dry amb ra
as a step function with a threshold value of 2.7º C. Thus, when T
T evap
wet
( T − T evap
) can be approximated
dpt
is greater than
by more than 2.7º C, the coil is considered to be wet, and when this difference is
less than 2.7º C the coil is considered to be dry.
Using this form, Rossi (1995) developed models for the total capacity of the rooftop
unit as a function of the driving conditions. In the dry coil region, he found that the
capacity could be approximated by a linear function of the two independent variables.
In the wet region, a much more complex non-linear function was developed to fit the
shape of the data which appeared to saturate at high wet bulb temperatures. Although
Rossi did suggest that these model forms could be used to model the temperatures
required by his FDD method, he did not attempt to fit any of the temperatures.
Breuker and Braun (1998) did extensive research on polynomial modeling for a
rooftop unit with a fixed orifice expansion device. They examined the form of the
experimental data over a range of driving conditions and compared different order
polynomial models. The polynomial orders necessary to produce a satisfactory fit to
both simulation and experimental data are given in table 2.1 shows. Three-inputs and
two-inputs model were compared also. It was concluded that a polynomial model with
three independent variables (three-inputs) provides the most accurate predictions of
the test data, given a large set of training data.
dpt
10