INTRODUCTION
In a cogeneration plant, the waste heat from the turbine can be used to generate
steam for driving either steam turbines or absorption chillers. Recovering the
energy from the gas turbine waste heat increases overall thermal efficiency
of the cogeneration plant to as high as 73 to 90% (Hordeski,
2011; Dincer and Zamfirescu, 2011). For the case
of a district cooling plant, the steam is used to energize Steam Absorption
Chillers (SAC) to generate chilled water. Among the advantages of using SAC
compared to vapor compression chillers are:
• 
SAC need less electricity to drive the solution and refrigerant
pumps 
• 
SAC involve few moving parts hence reduced noise and vibration 
• 
SAC use water and LiBr as working fluids and this assist in protecting
the environment 
The performances of the SAC are monitored from time to time for reasons of
safety, greenhouse gas emissions, reliability and economic concerns. In cases
where the performances deteriorate significantly, the SAC are retrofitted or
overhauled. Studies on performances of SAC covering various aspects on technical
and economics have been undertaken by various authors. Some of the studies are
highlighted below.
Kato et al. (2001), have developed the environmental
load and part load performance assessment that involved optimization. In modeling
the cooling load demand, they considered the trend for a typical summer day.
Linear relationships between input and output variable was assumed. This assumption
fails to recognize the nonlinear trend in offdesign operation.
Chow et al. (2002) adopted neural network models
to capture the relationship between fuel consumption and cooling load. Separate
models were produced for the coefficient of performance as well. The neural
network models were trained by LevenbergMarquardt (LM) algorithm. The training
data was a collection of experimental data and data collected from manufacturer’s
catalogue.
Braun (2006) discussed the different models common in
control optimization for absorption chillers. Models are also developed in terms
of part load ratio and part load factor. While assuming multivariable linear
regression, the models considered cooling water inlet temperature and cooling
load as independent variables.
Most reported studies on cooling loads used data for a new system. This assumption
is valid in the optimization of operating strategies for a new system. However
it is not applicable for old systems whose performance dropped by some percent
due to fouling and malfunctions. Hence if cooling load demand models for an
old system are to be formulated, recent operation data should be used.
The objective of the study is to develop a model for an absorption process
using waste heat from a cogeneration plant. The model uses actual plant operation
data collected over eight years. However, for the generalized model, it uses
data from literatures.
MATERIALS AND METHODS
The system adopted for modeling is an absorption system for a district cooling
plant. The system configuration is as shown in Fig. 1. The
system consists of two Heat Recovery Steam Generators (HRSG), one unit Auxiliary
Gas Boiler (AGB) and two units SAC. AGB will be used for the case maximum cooling
load is required and when one of the HRSG is down for maintenance.
The approach adopted is to treat each subsystem separately. Conservation of
mass and energy equations are used to derive a governing equation for each subsystem.
It is assumed that all data for working fluid properties are available. The
final models are formulated in terms of normalized quantities. To normalize
each variable, the design point data for a new system is considered.
Heat recovery steam generator: The HRSG use the energy in the exhaust
gas from two gas turbines rated 5.2 MW at ISO condition. The function of the
HRSG is to produce saturated steam at 0.85 MPa by taking feed water at a temperature
of about 90°C. For ith HRSG, assuming a steam flow rate ,
the energy transferred to the feed water is calculated as (Treado
et al., 2011):
where, h_{g} is enthalpy of saturated vapor at 0.85 MPa; h_{f}
is enthalpy of saturated liquid at 90°C. Disregarding the effect of the
diverter damper, the energy available to the system that includes the gas turbine
is:
where,
and
are flow rate of gas fuel and oil fuel, respectively; LHV is lower heating value
in kJ kg^{1} K^{1}.
Performance of the HRSG can be analyzed based on the ratio between Eq.
1 and 2. The approach is suitable to quantify the amount
of input energy recovered by the gas turbine and HRSG. However, it hides the
exact amount of energy going to the HRSG. The energy truly available for the
HRSG is:
where,
is mass flow rate of the waste heat used in the HRSG;
and
are mass flow rate of waste heat and air, respectively. h_{g} is enthalpy
of the waste heat:
T is temperature in K; C_{p,g} is specific heat of the waste heat in
kJ kg^{1} K^{1}. For the calculation of properties of steam
and waste heat, empirical equations adopted from Hinrichen
and Pritchard (2011) and Widiyanto et al. (2003),
respectively, are applied.
In cases where mass flow rate of the waste heat at part load is not known,
the energy available to the HRSG can be estimated by the following relation:
where, η_{GTG} is efficiency of the Gas Turbine Generator (GTG)
connected to the HRSG; α is a constant assumed to account for the energy
lost in the GTG. Note that, Eq. 4 assumes all the lost energy
in the GTG is available to run the HRSG. η_{GTG} varies in the
range of 0.15 to 0.29.

Fig. 1: 
Flow sheet for steam and absorption process for the district
cooling plant 
Auxiliary gas boiler: The AGB is a direct fired one through boiler.
It is comprised of evaporator, economizer and blowdown heat exchanger. Since
it is a dual fuel boiler and produces saturated steam, Eq. 1
and 2 can be used to calculate the energy transferred to the
feed water
and the input energy _{},
respectively.
Steam absorption chiller: The SAC produce chilled water using steam
generated by HRSG. The SAC being studied is a twostage absorption chiller of
LiBr and H_{2}O type. Part load operation of an SAC can be evaluated
applying Eq. 5 and 6:
where,
is the steam energy available to drive the SAC;
the cooling effect actually available from the system;
and
are the mass flow rate of steam and chilled water, respectively. h_{g}
and h_{f} and h_{in} and h_{out} are enthalpies of steam
and chilled water, respectively.
The model adopted for instant energy usage for each subsystem in the absorption
process has been simplified for analysis. For ith (i = 1, 2, …,
n_{s}) subsystem the energy usage are defined as:
where,
is the rated capacity of the subsystem;
is hourly, weekly or yearly energy consumption; PLF^{(i)} is the part
load factor; γ^{(i)}(k)ε{0,1} is the control variable;
is performance at the rated condition. For the case of HRSG and ABG, it is equal
to thermal efficiency. While for SAC it is equal to Coefficient of Performance
(COP).
The Part Load Factor (PLF) for a given system is often correlated with the
Part Load Ratio (PLR) (Treado et al., 2011)
and it is defined as the ratio between assumed load and rated capacity. The
relationship is normally determined from experimental data. For a new system,
the manufacturers may provide the graph for PLF versus PLR. For the system in
service, the graph has to be redefined as the system may deteriorate with time.
Parameter estimation: The model relating the PLF with PLR is considered
as the following form:
Where, i = {1, 2, …, n_{s}}
is the index for a subsystem in the absorption process. In the present work,
since two HRSG and two SAC are available, i is limited to a maximum of 2. y^{(i)}
is the output vector; X^{(i)} is the regression matrix constructed from
input vectors; θ^{(i)}εR^{m+1} is vector of model
parameters:
The solution for Eq. 8 is obtained applying ordinary least
squares. It can be shown that (Hinrichen and Pritchard, 2011),
the optimum estimate for the model parameters is given by:
where, IεR^{(m+1)x(m+1)} is an identity matrix and α is the
regularization parameter assumed to avoid singular condition.
Model performance parameters: There are several statistical methods
applied to evaluate the performance of a model. In the present work, three of
the most commonly used methods are selected. These include correlation coefficient
(R^{2}), the reduced chisquare (χ^{2}) and Root Mean Squared
Error (RMSE).
RESULTS AND DISCUSSION
Universiti Technologi PETRONAS gas district cooling plant has been considered
as a case study for testing the proposed approaches. The setup has two HRSGs,
each with separate supply of exhaust gas. The steam from the two HRSGs is collected
in the steam header. The steam from the steam header is supplied to SAC. Nominal
capacity of one HRSG is 12 ton h^{1}. Design point data for all subsystems
are given in Table 1. Schematic diagram for the HRSG is shown
in Fig. 2. As can be seen from Fig. 2, the
HRSG is a natural circulation drum boiler with economizer and blowdown heat
exchanger. Flow rate of the exhaust gas going to the HRSG is controlled by varying
the position of the diverter damper.

Fig. 2: 
Schematic diagram for the heat recovery steam generator 
Table 1: 
Design point data for the main components in the steamchilled
water system 

RT: Ton of refrigeration 
Models for cooling loads: The models for cooling load demands are constructed
applying statistical analysis on actual data collected over eight years. The
calculated trends on hourly, daily and monthly basis are shown in Fig.
3ac, respectively. The peak hours were between 8:00 a.m.
and 6:00 p.m. In the monthly case, the peak in a particular month of the year
is included for the estimation of average value over eight years. The mean μ
and standard deviation σ of the cooling load demand corresponding to each
month in a year is depicted in Table 2. The maximum cooling
load experienced by the system is about 2392 RT, Fig. 3c.
The trend over the year is useful in addressing optimization of operating strategies
as chance constrained problem, which is an assumption closer to the reality
on the ground. In (Kato et al., 2001; Widiyanto
et al., 2003), the hourly heat and cooling demands are set to a typical
model without mentioning how it is calculated.
Table 2: 
Monthly average (μ) and standard deviation (σ) for
the year 2004 to 2011 

It can be said that, given the eight years data, the proposed models are better
representations of the variations in the cooling load demands. Since environmental
load and part load performance assessment involves these kinds of models, the
result is seen as a good contribution.
Models for the SAC, HRSG and AGB: Kato et al.
(2001), assumed that any output variable is linearly correlated to the corresponding
input. The linear assumption, though easy to apply, is not always true as verified
by data from actual plants. Manufacturer supplied performance map for a 1250
RT steam absorption chiller and other similar designs (Braun,
2006; Yamaguchi and Shimoda, 2010; Petchers,
2003; Matsushita et al., 2002) is shown
in Fig. 4. The actual steam needed for a certain refrigeration
effect is a function of cooling water temperature. As can be seen from Fig.
4, the trend at some operating points could be better approximated by higher
order polynomials. For the 1250 RT chillers, model parameters estimated according
to Eq. 9 is given in Table 3.

Fig. 3(ac): 
Cooling load demand at (a) Hourly, (b) Daily and (c) Monthly
bases 

Fig. 4: 
Performance map for various designs 
The R^{2} value is close to 1 and χ^{2} and RMSE are both
small indicating high correlation between the actual and predicted result. A
generalized model is also produced fitting all the data in Fig.
4 by a single second order model. The estimated model parameters are θ_{0}
= 0.0532, θ_{1} = 0.7313 and θ_{2} = 0.1942. The corresponding
performance parameters are correlation coefficient (R^{2}) 0.9938, chisquare
(χ^{2}) 4.6098e4 December 15, 2012 and Root Mean Squared Error
(RMSE) 0.0210.
Table 3: 
Partload model parameters for HRSGs and SACs 

θ_{i} (i = 1, 2, 3) are constants in the regression
Eq. 8 
However, the developed models could not be used for a deteriorated SAC.
Based on year 2006 data, for SAC1, 88% of the operating points indicate that
the system was run at part load ratio of 0.8835. In case of SAC2, 80% of the
operating points were located at part load ratio of 0.93. Both chillers were
running with steam consumptions higher than normally required when they were
new. The deteriorated performance could be attributed to fouling in the cooling
water loop, crystallization due high temperature in the generators and air leak
in to the system. Based on the observations, it can be said that direct use
of a performance map supplied by a manufacturer to study SAC that served for
more than three to eight years may lead to erroneous result. To overcome the
problem, models were developed based on recent actual operation data. The new
models are presented as follows:
• 
For SAC1: θ_{0} = 0.1100, θ_{1}
= 2.2183 and θ_{2} = 0.6625. The corresponding performance
parameters are R^{2} = 0.9084, χ^{2} = 0.0063 and RMSE
= 0.0795 
• 
For SAC2: θ_{0} = 0.2171, θ_{1} = 3.5709 and
θ_{2} = 2.3406, with corresponding performance parameters
of R^{2} = 0.8958, χ^{2} = 0.0061 and RMSE = 0.0783 
Table 4: 
Models performance parameter 

For the new models, the lower value of R^{2} and higher values of χ^{2}
and RMSE, respectively, are due to measurement noise. Besides, it was assumed
that the cooling water inlet temperature is in the range of 29 to 32°C,
which may be true all the time.
For the HRSG, the heat input is a function of the fuel flow rate and variable
inlet guide vane position in the GTG supplying the waste heat to the heat recovery
steam generator. Since the waste heat temperature and flow rate were also involved,
the final model for the heat going to the heat recovery system must be a function
of these variables. It is possible to develop the performance map for the HRSG
relying on data obtained by simulating thermodynamic models for the GTG and
HRSG. However, in the present work, the steam flow rate from the HRSG was modeled
as a function of the diverter damper position (θ_{DD}) using actual
plant operation data. The parameters estimated using Eq. 9
are given in Table 3 while the corresponding performance parameters
are listed in Table 4. For the two chillers, the developed
models are featured by a correlation coefficient close to one indicating higher
accuracy. The models identified in this section are applicable for thermoeconomic
and environmental load assessment.
The AGB uses gas fuel directly. Since there is no reliable data available,
model for AGB could not be formulated.
CONCLUSION
The objective of this study is to develop models for an absorption process
that is easy to use in thermoeconomic and environmental load assessment and
optimization of operating strategies. From the analysis results, the following
conclusions are made:
• 
For cooling water temperatures in the range of 29 to 32°C,
part load performance of SAC can be accurately described by a single generalized
curve 
• 
The HRSG and SAC are all seen deteriorated in performance. Hence, the
models provided by the manufacturers and the generalized model could not
be used directly. Here, it is recommended to work on a fault detection and
diagnostic system which can be applied to early identify the cause for performance
drop 
• 
The maximum cooling load experienced by the absorption system is 2392RT,
which is 4.32% lower than the design capacity. Since the system is underutilized,
it is necessary to implement better operating strategies 
The method discussed in the present work can be extended to electric chillers
and gas turbines. Future work will focus on the use of the developed models
in thermoeconomic, environmental load and performance optimization studies.
ACKNOWLEDGMENTS
The project is funded under FRGS. Authors acknowledge the support of Jabatan
Pengajian Tinggi Malaysia and UTP for the project.