INTRODUCTION
In a trigeneration plant, absorption process provides the means to recover
the energy that otherwise would be lost to the environment. The use of Steam
Absorption Chillers (SACs) was resorted to increase the overall thermal efficiency
of a system to as high as 73 to 90% (Hordeski, 2011;
Dincer and Zamfirescu, 2011). SACs are also preferred
to vapor compression chillers since they use less electricity to drive the solution
pumps and use waste heat to create cooling potential. They are also considered
environmentally friendly as they use LiBrH_{2}O solution as working
fluid, which is not a halocarbonbased refrigerant.
The performance of an SAC has to be monitored at all times to ensure that the
system is not deteriorated severely and thus affecting economic operation of
the system. Knowing the current performance is also critical to properly manage
the available resources under actual operating conditions.
Performance characteristics of an absorption process can be demonstrated in
different ways. One way is to use artificial neural network to describe variation
of coefficient of performance, exergetic efficiencies and working fluid properties
(Chow et al., 2002; Sozen
et al., 2003; Manohar et al., 2006;
Sencan et al., 2006; Tamiru
et al., 2009; Cascales et al., 2011;
Congradac and Kulic, 2012; Labus
et al., 2012). Sozen et al. (2004)
studied application of fuzzy systems to absorption system modeling. A comparison
test on alternative multivariable regression models is addressed in the study
of PuigArnavat et al. (2010). It turns out
that though the stated approaches are effective enough to capture characteristics
of the system over the whole operating regions, they are short of revealing
how the system deteriorates with time. The later aspect is specifically important
in multistate reliability modeling (Muhammad et al.,
2010) and optimization of the available resource under realistic conditions.
Data clustering techniques (Jain et al., 1999;
Fung, 2001), on the other hand, has the capacity to systematically
find similarities in a given data set. It has been used successfully for object
recognition, pattern segmentation and information management. In relation to
thermal systems, data clustering methods was applied to optimize combustion
efficiency of a coalfired boiler (Kusiak and Zhe, 2006)
and efficiency of electricutility boiler (Song and Kusiak,
2007). To the authors’ knowledge, there is no previous work on the
use of clustering method in the performance analysis of an absorption process.
The objective of this study is to test the feasibility of data clustering technique
in the performance monitoring of an absorption process. Nondimensional performance
parameters are first calculated and the data clustering method is applied to
the resulting inputoutput data with the intention of identifying a cluster
center that would be considered representative of the operating points.
MATERIALS AND METHODS
Overview: The block diagram representing a generic absorption system
is illustrated in Fig. 1. The SAC is connected to the Heat
Recovery Steam Generator (HRSG) through the Steam Header (SH). Each HRSG uses
exhaust gas from a gas turbine. The HRSG is critical to increase the cogeneration
efficiency. The absorption system was considered operated by the steam produced
by the HRSG. It was further assumed that the steam absorption chillers were
all driven by the saturated steam tapped from the steam header. The SAC was
responsible for the cooling effect needed to cool the water required for cooling
of academic buildings. Since each component involved energy and mass transfer,
the equation for a Steady State Steady Flow (SSSF) system was applied to each
subsystem.
The steps, used to achieve the objectives are as follows:
• 
Step 1: Preparation of a database for the working fluid
properties that could be accessed at ease during model simulation. The whole
system involved exhaust gas, steam, saturated water and LiBrH_{2}O
solution. Hence, it was necessary that a suitable database was arranged
either in terms of lookup tables or regression equations. In the present
study, set of empirical equations were used 
• 
Step 2: Reliable hourly data was selected corresponding to peak
hour operations. Absorption chillers were ideally suitable for base load
applications. However, they were not used to charge a thermal storage system
because of the limitations in the lower temperature they achieved. In most
cases, they were operated starting at around 6:00 a.m. and stopped at about
7:30 p.m. On a daily basis, they experienced transient conditions in the
first 45 min and the last 30 min of the operation duration. For the reason
that the system did not stay longer in transient conditions as compared
to the steady state region, it is not important to consider the transient
data in the evaluation of the system performance over a long period of time 
• 
Step 3: For each hourly operation, energy balance was applied to
calculate for Part Load Ratio (PLR) and Part Load Factor (PLF) 
• 
Step 4: Tabulate the hourly data over a year. Excerpt from one
day operation is demonstrated in Table 1. Similar set
of data were collected for each operating day and arranged in a matrix to
make it suitable for the data clustering process 
• 
Step 5: Data clustering technique was applied to the inputoutput
data in order to determine the cluster centers. The cluster centers would
be considered to characterize the system in a given year 
• 
Step 6: Steps, 1 to 5 were repeated for each year in the considered
time span 

Fig. 1: 
Flow sheet for steam and absorption process 
Table 1: 
Excerpt of actual data collected from SAC monitoring system 

RT: Ton of refrigeration, m_{st}: Mass flow rate of
steam, P_{st}: Steam pressure, m_{ch}: Mass flow rate of
chilled water, T_{ch,in}: Chilled water inlet temperature, T_{ch,out}:
Chilled water outlet temperature, T_{co,in}: Cooling water inlet
temperature, T_{co,out}: Cooling water outlet temperature 
Properties of working fluids: In applying the energy conservation equation
to the components of the absorption process, specific enthalpy at the inlet
and outlet, respectively, of each component was calculated. The enthalpy is
a function of stagnation temperature T and pressure P and Air and combustion
product are mixtures of such gases as N_{2}, O_{2}, Ar, CO_{2}
and Ne. Hence, for the ith specie in air mixture or combustion product, the
specific enthalpy was calculated by:
where, T_{0} and h_{0}^{(i)} represent temperature
and specific enthalpy, respectively, at the reference point or dead state, C_{p}^{(i)}(T)
is the specific heat at constant pressure. In Eq. (1), the
empirical equations for C_{p}^{(i)}(T) that correspond to air
and combustion products were taken from the literature (Walsh
and Fletcher, 2004). For the combustion product, C_{p}^{(i)}(T)
is a function of FueltoAir Ratio (FAR). The empirical equation for the combustion
gases were also adopted from the same literature. Using Eq. 1,
specific enthalpy of the working fluid were approximated by Eq.
2:
where, n_{i} is the mass fraction for ith specie. Empirical equations
applicable for estimation of steam properties for a given temperature and pressure
are adapted from standard gas tables (Irvine and Liley, 1984).
Heat recovery steam generator (HRSG): The exhaust gas from a Gas Turbine
Generator (GTG) is used as energy source to run the HRSG. The purpose of the
HRSG is to produce saturated steam at 0.85 MPa by taking feed water at a temperature
of about 90°C. A diverter damper at the inlet controls the amount of exhaust
gas admitted to the HRSG. For loads higher than 30% of nominal capacity, a threeelement
controller is used to ensure constant water level in the steam drum. The pressure
in the steam drum is made stable by controlling the position of the diverter
damper in response to the pressure feedback. Assuming multiple HRSG in the absorption
process, for i th HRSG, the energy transferred to the feed water was calculated
by:
where, m_{s}^{(i)} is the steam flow rate, h_{g} is
enthalpy of saturated vapor at 0.85 MPa, h_{f} is enthalpy of saturated
liquid at 90°C, n_{h} is the number of HRSG in the system. Heat
energy of the exhaust gas, which otherwise would have been lost to the environment,
is recovered at the evaporator and economizer. Since, the part of the energy
in the blowdownsteam is exchanged to the feed water, the energy balance in
Eq. 3 is the combination of all that. Disregarding the effect
of the diverter damper, the energy available to the system that includes the
gas turbine generator is:
where, m_{f,gas} is flow rate of gas fuel, LHV is lower heating value
in kJ kg ^{1} K.
One of the parameters commonly used to evaluate the performance of HRSG is
efficiency of steam generation η_{H,st}. This parameter is related
to Q_{H,st}^{(i)} and Q_{total}^{(i)} as:
η_{H,st}^{(i)} is being used by the Supervisory Control
And Data Acquisition (SCADA) system. Equation 5 is suitable
to quantify the amount of input energy recovered by the gas turbine and HRSG.
However, it hides the exact amount of energy made available to HRSG. The actual
mass and energy experienced by the HRSG are:
and:
where, m_{g}^{(i)} is mass flow rate of the exhaust gas passing
through the HRSG,
and m_{air} are mass flow rate of exhaust gas and air, respectively,
is enthalpy of the exhaust gas, T_{g} is temperature of exhaust gas
in K; C_{g, g} is specific heat of the exhaust gas in kJ kg ^{1
}K and at constant pressure.
To calculate the performance parameters, the following relation was used:
where, η_{GTG} is efficiency of the GTG connected to the HRSG;
α is a constant assumed to account for the energy lost in the GTG. Note
that Eq. 8 assumed all the lost energy in the GTG was available
to run the HRSG. η_{GTG} varies in the range of 0.15 to 0.29 depending
up on the electric load.
Steam absorption chiller (SAC): The steam produced by the HRSG was used
in the SAC to produce cooling potential. The cooling was used for airconditioning.
SAC worked by exchanging heat between the steam, cooling water and refrigerant.
In part of the whole cycle, an absorbent, LiBr, was used to drive the refrigerant
vapor. The performance of an SAC was evaluated by applying:
and:
where,
is the steam energy available to drive the SAC;
is the cooling effect actually available from the system;
and
are the mass flow rate of steam and chilled water, respectively and n_{s}
is the number of SAC in the system.
Models in terms of nondimensional parameters: The performance of the
subsystems in the absorption process was evaluated by using the nondimensional
parameters called Part Load Factor (PLF) and Part Load Ratio (PLR) (Treado
et al., 2011). The PLR is defined as the ratio between assumed load
and rated capacity. The PLF is given by the ratio between the current input
energy and the energy needed at the design point, also known as rated demand.
In terms of PLF, for i th (I = 1,2,...,n_{s}) subsystem, the energy
usage was calculated by:
where,
is rated capacity of the subsystem;
is hourly, weekly or yearly energy consumption; PLF^{(i)} is the part
load factor; γ^{(i)}_{(k)} is the control variable and
takes a value in the range of zero to one; K^{(i)}_{rated} is
performance at the rated condition. For HRSG and SACs, K^{(i)}_{rated}
is equivalent to the thermal efficiency and coefficient of performance (COP),
respectively.
Data clustering methods: There are alternative approaches for data clustering.
Among them are Principal Component Analysis (PCA), KMeans Clustering, Fuzzy
CMeans, Mountain Clustering, Subtractive Clustering, possibilistic clustering
and rough set theory. The present study is based on Kmeans clustering (Wu,
2012) as it is the simplest to apply. The algorithm works first by calculating
cluster centers for a given number of clusters. Once the cluster centers are
known, the classification of a data point to a cluster is decided based on shortest
distance formula. The Euclidian distance form (Babbar et
al., 2009) is given by:
where, x is the data vector; μ_{i} is the cluster center; Σ
is the covariance matrix.
RESULTS
Application of the proposed method is demonstrated by considering an absorption
system having two HRSG and two SAC. The design specifications of the subsystems
are shown in Table 2. The two HRSG were identical in design.
Each of them was intended to generate saturated steam at 0.85 MPa by using the
exhaust gas from a singleshaft GTG rated 5.2 MW at ISO condition. Details about
the GTG are not included for the scope is limited to the absorption system only.
The feed water flowing into the evaporator section of the HRSG was preheated
by the blowdown steam and exhaust gas at the blowdown heat exchanger and economizer,
respectively. The steam, after passing through a steam header, was used to operate
the SAC.
Operating points: As stated in the methodology, PLR and PLF were calculated
for each HRSG. The clusters were then estimated by using Kmeans clustering.
The program used for Kmeans was from MATLAB R2008a.
Plots of the operating points and cluster centers calculated for HRSG1 and
HRSG2 are shown in Fig. 2 and 3, respectively.
As can be seen, two clusters seem reasonable to characterize all the operating
points. For each HRSG, one cluster seems containing more than 70% of the operating
points in a year (Table 3). It can be implied that, based
on the percentage of operating points (τ) residing to each cluster, the
operating point trajectory can be constructed by choosing the cluster with the
highest density.
For both HRSGs, the available energy slightly changes about part load factor
of 0.6238. For HRSG1, 70% of the operating points are featured by a part load
ratio of 0.4345 while the rest 30% indicates operating points with a part load
ratio of 0.8012. Based on the locations of the clusters, in 70% of the total
operating points, about 0.3667 of the PLR that is potentially convertible to
steam is lost to the environment. In Fig. 2 and 3,
a shift in the operating point from left to right is due to the admission of
more exhaust gas into the HRSG.
Considering a twomonth data of year 2006, 95% of the operating points indicate
that HRSG1 wasted 47.54% of the input energy to the environment. For HRSG2,
89% of the operating points are featured by 49.24% of the supplied energy released
to the environment.

Fig. 2: 
Performance map for HRSG1 (Year 2004) 

Fig. 3: 
Performance map for HRSG2 (Year 2004) 
Table 2: 
Design point data for the main subsystems in the absorption
process 

RT: Ton of refrigeration; HRSG: Heat recovery steam generator;
SAC: Steam absorption chiller 
Table 3: 
Operating points and percent classification (year 2004) 

μ_{11}, μ_{12}, μ_{21},
μ_{22}: Coordinates of cluster centers, τ_{1}
and τ_{2}: Percentage of points to each cluster 
If the comparison is based on data of year 2009, HRSG1 operated almost all
the time with 42.86% of the input heat lost to the surrounding. Regarding HRSG2
the energy loss amounts to 43.97% of the input energy. Similar behaviors were
observed in the data of other years too.

Fig. 4: 
Performance map for SAC1 (Year 2004) 

Fig. 5: 
Performance map for SAC2 (Year 2004) 
Table 4: 
Cluster location for each year and percent of total data
in the cluster 

τ_{1} and τ_{2}: Percentage of points
to each cluster 
The SAC considered in the case study were both of doubleeffect, LiBrH_{2}O,
absorption chillers. For SAC1, 88% of the operating points indicated 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. The scatter plots for the two
cases are shown in Fig. 4 and 5, respectively.
The figures also illustrate a trend supplied by the manufacturer. The cluster
centers were close to the manufacturer supplied trend since the SACs were still
new.
Cluster centers corresponding to nine years data and for SAC1 and SAC2 are
shown in Fig. 6 and 7, respectively. The
calculated values for each cluster centers shown in Fig. 6
and 7 are listed in Table 4.

Fig. 6: 
Performance based on nine years data for SAC1 

Fig. 7: 
Performance based on nine years data for SAC2 
As can be observed from Fig. 6 and 7, both
chillers were operated at reduced capacity due to malfunctions. In 2012, the
steam consumed by SAC2 was as high as that needed to run a new chiller at full
capacity. Utilizing high quantity of steam, it was able to provide about 0.55
PLR only. SAC2 needed more than one PLF to operate at 0.75 PLR. This was true
for years 2008 to 2012. It can be said that, as compared to SAC1, SAC2 deteriorated
the most.
DISCUSSION
In general, the use of a heat recovery steam generator increases the overall
efficiency to about 80% (Hordeski, 2011). In the present
study, the efficiencies were lesser than expected for most of the energy in
the exhaust gas was lost to the environment. The average efficiency of steam
generation for each system was about 45%, which made the overall efficiency
reduced to 65%. Both SACs demonstrated higher steam consumption for a reduced
cooling potential. The deteriorated performance could be attributed to fouling
in the cooling water loop, crystallization due high temperature in the generators
and air leak into the system. It can be concluded that, direct use of a performance
map supplied by a manufacturer to study the SAC that had served for more than
three to nine years may lead to erroneous result. To overcome the problem, models
need to be developed based on recent actual operation data. In the multiple
input multiple output cases, neural network and fuzzy approach could be an ideal
solution.
CONCLUSION
The feasibility of data clustering method for the estimation of operating trajectory
of an absorption process was tested in this study. By adopting Kmeans clustering,
the objective was successfully achieved. Through analysis of the results, the
following conclusions can be made:
In a situation where plenty of measured data are available, Kmeans is an effective
method to clearly demonstrate the most repeated operating points. By using Kmeans,
the operating trajectories of the SACs over the course of nine years clearly
demonstrated feasibility of the method.
The HRSG and SAC are all seen deteriorated in performance. Hence, a multivariable
regression or artificial neural network model developed on the bases of data
from a new engine could not be used directly to optimize operating strategies
of the same system served more than three years.
The method presented in the present study can be extended to other parts of
the trigeneration plant. Future study will focus on extending the proposed
method to thermoeconomic and environmental load assessment.
ACKNOWLEDGMENT
The project is funded under Ministry of Science, Technology and Innovation
(MOSTI). Authors acknowledge the support of MOSTI and Universiti Teknologi PETRONAS
for the project.