Fault Detection and Diagnostics for Rooftop Air Conditioners

2. Background work
There are a lot of literature on modeling of vapor compression systems. The following
sections contain a review some models that were developed for FDD.
2.1 Physical modeling and gray-box modeling
Rossi and Braun (1995) developed a steady-state physical model, known as ACMODEL,
which simulates the operation of vapor compression cycles. The model solves the mass,
momentum, and energy balances for each component and performs a charge inventory for
the entire system. This model was used to aid in the original development and evaluation
of an FDD method. ACMODEL is a modular toolkit. Individual components are
modeled as subroutines (e.g., compressor, condenser, evaporator, expansion device) with
specified inputs and outputs. A robust numerical equation solver capable of converging to
the operating state with a tight tolerance is included. A tuning program adjusts less well
known model parameters based on simple measurements at an operating point to provide
for more accurate perfomance predictions at different operating conditions.
The compressor of the ACMODEL is semi-empirical and uses empirical curve fits to
manufacturer’s performance data for compressor volumetric efficiency (to calculate mass
flow rate) and power. The outlet enthalpy is calculated assuming a polytropic compression
process with a constant polytropic efficiency.
The condenser and evaporator models use physically based tube-by-tube analyses where
each tube is broken into small segments. Mass, momentum, and energy balance are applied
to each tube segment, and the heat transfer, pressure drop, and refrigerant mass are
calculated for the segment. However, there are some differences between the condenser
and evaporator models. The condenser model considers only heat transfer whereas the
evaporator model considers both heat transfer and mass transfer. The condenser and
evaporator coil models are built from functions which are provided for a finned tube,
return bend and manifold. Geometric information about the tubes and fins are entered in
an input file.
The throttling valve is modeled as a fixed orifice expansion device which is assumed to
have two-phase Fanno flow (one-dimensional, adiabatic, compressible, with friction).
The equations for each of these components as well as a charge inventory must be solved
simultaneously to find the steady-state operating point for the air conditioning unit. The
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