Author’s Accepted Manuscript Simulation and multi-objective optimization of a combined heat and power (CHP) system integrated with low-energy buildings Jamasb Pirkandi, Mohammad Ali Jokar, Mohammad Sameti, Alibakhsh Kasaeian, Fazel Kasaeian PII: S2352-7102(15)30038-3 DOI: http://dx.doi.org/10.1016/j.jobe.2015.10.004 Reference: JOBE62 To appear in: Journal of Building Engineering Received date: 6 July 2015 Revised date: 1 October 2015 Accepted date: 25 October 2015 Cite this article as: Jamasb Pirkandi, Mohammad Ali Jokar, Mohammad Sameti Alibakhsh Kasaeian and Fazel Kasaeian, Simulation and multi-objective optimization of a combined heat and power (CHP) system integrated with low energy buildings, Journal of Building Engineering http://dx.doi.org/10.1016/j.jobe.2015.10.004 This is a PDF file of an unedited manuscript that has been accepted fo publication. As a service to our customers we are providing this early version o the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain www.elsevier.com/locate/jobe
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Author’s Accepted Manuscript
Simulation and multi-objective optimization of acombined heat and power (CHP) system integratedwith low-energy buildings
Jamasb Pirkandi, Mohammad Ali Jokar,Mohammad Sameti, Alibakhsh Kasaeian, FazelKasaeian
Received date: 6 July 2015Revised date: 1 October 2015Accepted date: 25 October 2015
Cite this article as: Jamasb Pirkandi, Mohammad Ali Jokar, Mohammad Sameti,Alibakhsh Kasaeian and Fazel Kasaeian, Simulation and multi-objectiveoptimization of a combined heat and power (CHP) system integrated with low-energy buildings, Journal of Building Engineering,http://dx.doi.org/10.1016/j.jobe.2015.10.004
This is a PDF file of an unedited manuscript that has been accepted forpublication. As a service to our customers we are providing this early version ofthe manuscript. The manuscript will undergo copyediting, typesetting, andreview of the resulting galley proof before it is published in its final citable form.Please note that during the production process errors may be discovered whichcould affect the content, and all legal disclaimers that apply to the journal pertain.
Cost of fuel per energy unit ($/kJ) C Cost flow rate ($/s) Specific heat at constant pressure (kJ/kg.K)
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CRF Capital recovery factor
Exergy flow rate (kW)
Exergy destruction rate (kW) e Specific exergy (kJ/kmol) h Enthalpy (kJ/kg) k Specific heat ratio (Cp/Cv) LHV Lower heating value (kJ/kg) Mass flow rate (kg/s) N Annual number of the operation hours of the unit P Pressure (KPa) R Gas constant (kJ/kg.K) Compressor pressure ratio
S Entropy (kJ/kg.K) T Temperature (K) U Overall heat transfer coefficient (W/m2.K)
Net power output (kW) Z Capital cost of the component ($)
Capital cost rate of the component ($/s) ΔP Pressure drop (KPa) ΔTLM Log mean temperature difference (K) ƞ efficiency ξ Ratio of chemical exergy to Lower Heating Value Specific heat ratio Maintenance factor of the equipment Molar fraction Subscripts a Air AC Air compressor CC Combustion chamber e Exergetic f Fuel FC Fuel compressor g Combustion gases gen Generator GT Gas turbine HE Heat exchanger Q Heat rate (kW) rec Recuperator W Work (kW) Superscripts ch Chemical ph Physical
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1. Introduction
A Low-energy building is any type of building that from design, technologies, and building
products uses less energy, from any source, than a traditional or average contemporary
house [1]. They are the practice of sustainable design, sustainable architecture, low energy
building, energy-efficient landscaping [2], and energy system optimization [3]. Meanwhile,
distribute generation (DG) is predicted to play an increasing role into the electric power
system for buildings in the near future [4]. Distributed energy resources are small modular
power generation systems that can be located at or near the site where energy is used. In
conventional energy systems, electrical power is conveyed from large-scale plants located
far away from the consuming region, while energy for heating is supplied separately as fuel.
In this way, more than 50% of the energy content of the fuel is lost at the power plant alone
because of energy conversion inefficiencies and is discharged in the form of waste. Further
losses occur in the electric power transmission and distribution network in the form of
electric current losses and power transformation losses [5, 6]. DG with a cogeneration
system is one of the options because it can efficiently utilize exhaust heat. Following are the
benefits of such a power generation [7]:
This system can be easily and effectively installed and operated both in high-demand
or rural areas.
Power can be distributed and transmitted with low losses.
Exhaust heat can be used efficiently by this system.
This system can either be used independently or as a supportive system.
Many studies have been conducted many aspects of cogeneration systems. Today the main
potential for CHP dissemination seems to be in the residential sector. Until the present,
several technical, environmental, economic and legislative problems have curbed the spread
of CHP technology in this sector, especially for electric power sizes of a few kW [8-10].
Additionally, authors proposed numerous researches in the operation of CHP systems in
large power plants e.g. [11, 12]. Tehrani et al. [11] presented a method of design a
trigeneration plant. Their idea is to recover the exhaust hot gases of a GT power plant in
order to supply dynamic HVAC (heating, ventilating, and air conditioning) load of the new
town of Parand, and also use the rest heat potential to feed a steam turbine cycle. Karaali et
al. [12] introduced a novel thermoeconomic optimization method for real complex cycles.
The objective of this paper is to apply this method to four cogeneration cycles that are
simple cycle, inlet air cooling cycle, air preheated and air-fuel preheated cycles for analyzing
and optimizing. The four cycles are thermoeconomically optimized for constant power and
steam mass (30 MW and 14 kg/s saturated steamflow rate at 2000 kPa), for constant power
(30 MW) and for variable steam mass, and for variable power and steam mass by using the
cost equation method and the effect of size on equipment method.
Cogeneration systems utilizing internal combustion engines and gas turbines in open cycle
are the most utilized technologies in this field worldwide. The interest of MGTs as
distributed energy systems lies in their low environmental impact in terms of pollutants.
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MGTs present some unique characteristics compared with the larger gas turbine engines
such as the high rotational speeds, the ability to burn various fuels and the radial
turbomachines [13, 14].
MGTs are usually designed for natural gas, but there is the ability to utilize other fuels such
as those based on biomass. Mozafari et al. [15] performed the optimization of MGT by
exergetic-economic-environmental analysis considering various fuels for the system. The
results showed that and the trends of variations of second law efficiency and cost rate of
owning and operating the whole system are independent of the fuels. In this article the fuel
which is used in the combustion chamber is methane (CH4).
Thermodynamic analysis can be a perfect tool for identifying the ways for improving the
efficiency of fuel use, and determining the best configuration and equipment size for a
cogeneration plant [16]. As mentioned above, extending this system to combined heat and
power generation is a way of increasing productivity with recovery of the heat discarded
from the inefficient energy conversion of producing electrical power. These systems are
expected to find applications in the cogeneration market for various heating and power
requirements [17].
A thermodynamic analysis is proposed in this paper to study MGT to minimize fuel
consumption and maximize net exergetic efficiency. Energetic, economic and environmental
performance of the system is investigated. The energy and entropy balance equations of the
entire system will be additionally obtained. To find the optimum design parameters of the
system genetic algorithm is used and a simulation program is developed in MATLAB
software. This simulation investigates the effects of various performance parameters, such
as the compression ratio (rp), mass flow rate of air and turbine inlet temperature (TIT), on
the exergetic efficiency and irreversibility of the plant. Sensitivity studies for two important
parameters including net power generation and exergetic efficiency is done to show the
abilities and authenticity of simulated system. Next, a common economic analysis for the
system is carried out. The quantity of NOx and CO emissions is considered for environmental
purposes. In the present study, the cost of pollution damage is considered to be added
directly to total cost rate of the system production. Therefore, the third objective function is
sum of the thermodynamic and environomic objectives.
In the heat production sector, there is several choices to select the kind of heat production
including hot water, steam water, hot air and even producing cold water after an absorption
chiller cycle. In this article, we really did not discuss this issue and to demystify the exergetic
efficiency of the system and calculate the total cost rate, we assume that a water pump is
driven using electricity produced by micro gas turbine to pump the water in ambient
temperature into the heat exchanger and hot water temperature of 80 °C will be delivered
to the residential consumer.
In the open literature, various configurations of integrating micro gas turbine and
regenerator with a process plant have been analyzed through different techniques such as
exergy analysis, thermoeconomics, physical insight based pinch analysis, R-curve analysis
and mathematical optimization (mixed integer linear programming and nonlinear
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programming) [18, 19]. Ameri et al. [20] presented a thermodynamic analysis of a tri-
generation system based on micro gas turbine with a steam ejector refrigeration system and
heat recovery steam generator. Caresana et al. focused on the effect of ambient
temperature on the performance of a microturbine in cogeneration arrangement and by
providing a simulation code, entered in detail into the machines’ behavior. A performance
chart has been drawn showing how the MGT working range changes with temperature in
specific intervals [21]. A conceptual trigeneration system is proposed in ref. [22] based on
the conventional gas turbine cycle for the high temperature heat addition while adopting
the heat recovery steam generator for process heat and vapor absorption refrigeration for
the cold production.
Several researchers carried out the exergoeconomics analysis and optimization for thermal
systems. Barzegar et al. [23] has carried out an excellent review in this issue. The reviewed
results show that although exergoeconomic analyses are so useful in power generation,
they cannot find the optimal design parameters in such systems. So, using the optimization
procedure as thermoeconomics is essential with respect to thermodynamic laws.
Optimization in engineering design has always been of great importance and interest
particularly in solving complex real-world design problems. There are many calculus-based
methods including gradient approaches to search for mostly local optimum solutions and
well documented in ref. [24]. However, some basic difficulties in the gradient methods such
as their strong dependence on the initial guess can cause them to find a local optimum
rather than a global one. This has led to other heuristic optimization methods, particularly
genetic algorithms (GAs) being used extensively during the last decade. The main difference
between GA and traditional calculus based techniques is that GAs work with a population of
candidate solutions, not a single point in search space. This helps significantly to avoid being
trapped in local optima as long as the diversity of the population is well preserved [25].
2. System description
The first generation of micro-turbines has been introduced to the energy market recently.
Their size range from 10 to 250 kW with electrical efficiency of about 30%, and coupled with
thermally activated devices (to produce either heating or cooling by using the exhaust heat),
may achieve high total efficiencies in the range of 65% as shown in recent realistic studies
[26] although the initial analysis envisaged higher efficiencies (in the range of 75%) [27].
Some advantages of microturbines are as follows [28]:
They can be installed on-site especially if there are space limitations. Also they are
compact in size and light in weight with respect to traditional combustion engines.
They are very efficient (more than 80%) and have lower emissions (less than 10 ppm
NOx) with respect to large scale ones.
They have well-known technology and they can start-up easily, have good load
tracking characteristics and require less maintenance due their simple design.
7
They have lower electricity costs and lower capital costs than any other DG
technology costs.
They have a small number of moving parts with small inertia not like a large gas
turbine with large inertia.
Modern power electronic interface between the MT and the load or grid increases
its flexibility to be controlled efficiently.
In this paper a combined cycle micro gas turbine is investigated and for this purpose, a
commercially available C30 engine manufactured from Capstone, which is also sold as part
of the C30 CHP cogeneration unit is considered [29-31]. The unit is usually fired with natural
gas; biofuel (gas or oil) and diesel fuel versions are also available. This micro gas turbine
produces 30 kW of electrical power with 26 ± 2% efficiency at ISO (international standards
organization) conditions. Design parameters are presented in Table 1. In the present paper,
the system is only analyzed at the design point. Thus, all components required for start-up
and partial-load operation are not considered. So, this model consists of following
components: a centrifugal air compressor; a centrifugal fuel compressor; a plate-fin
recuperator, air-gas turbine exhaust heat exchanger; a plate-fin recuperator, fuel-gas
turbine exhaust heat exchanger; a combustion chamber, a radial turbine and a heat
exchanger. Future work will also take into account partial-load operation by using
characteristic maps of the turbine and the compressors. All the rotating components are
mounted on a single shaft. The layout proposed for the plant is shown in Figure 1.
Table 1 Capstone C30 design parameters [29, 30]
Figure 1 Schematic diagram of the cycle power plant
2.1. Thermodynamic modeling
To determine the exergy at different points of the power plant, the thermodynamic
properties of the cycle should be specified. This is done usually through physical modeling.
This section includes the rules that form the physical model. The major portion of this
modeling consists of the application of the mass and energy balance equations. The
principle of operation can be summarized as follows:
Air is compressed by the air compressor up near to the combustion chamber
operating pressure. The air is then preheated in the plate-fin heat exchanger and
brought to the combustion chamber (state point 3).
Similarly, the fuel (natural gas) is compressed by the fuel compressor, preheated in
the fuel-exhaust gas, plate-fin heat exchanger and then brought to the combustion
chamber (state point 3f).
8
The chemical reactions, occurring in the combustion chamber, produce thermal
energy. The high energy stream at state point 4 is first enter to the turbine and then
used to preheat air and fuel in the counter-flow heat exchangers.
The expansion in the gas turbine supplies mechanical energy and then electric
power. As mentioned, the gas turbine outlet stream (state point 5) can be used to
preheat both fuel and air flows. Any residual thermal energy left over is available for
cogeneration purposes: to this scope, a water–gas, plate-fin heat exchanger is
included.
For the purpose of analysis the following assumptions are made:
The whole system operates at a steady state condition.
Ideal-gas mixture principles apply for the air, fuel and the combustion products.
All components operate without heat loss.
The exit temperature is above the dew point temperature of the combustion
product.
The reference environmental state for the system is T0 =250C and P0= 101.3 KPa.
The turbine and the compressors have been assumed as adiabatic.
The energy variation and the kinetic and potential exergies have been assumed as
negligible.
The result of friction and other irreversibilities for flow through the compressor is
explained with an isentropic efficiency.
Pressure drop in combustion chamber, two recuperators and heat exchanger are as
follow: P P P P .
Developing equation for each component leads to the following systems of equations:
Air compressor, (1) (2) (T T )
(3) T T
{
[
( ) ⁄
]
}
(4) P P
First recuperator,
(5) (T T ) (T T )
(6) P P ( ΔP )
(7) P P ( ΔP )
Fuel compressor, (8)
9
(9) (T T )
(10) T T
{
[
( ) ⁄
]
}
Second recuperator,
(11) P P
(12) (T T ) (T T )
(13) P P ( ΔP )
(14) P P ( ΔP )
Combustion chamber,
(15) L ( ) L
(16) (T T )
(17) (T T )
(18) P P ( ΔP ) (19)
Since we should have the molar values of output gases in order to obtain the chemical
exergy at the exit point of the combustion chamber, we need to solve the combustion
equation of the combustion chamber. In this case, the molar values of air are considered as
fixed and by using the equation below, the molar values of gases leaving the combustion
chamber are obtained from:
(20) ( ) ( )
In the equation (20), the value of λ and α obtained from the energy law in the combustion
chamber, and knowing this value, the molar values of gases exiting the combustion chamber
are calculated and subsequently used in the step associated with the calculation of chemical
exergy:
(21)
(22)
(23)
(24)
Gas turbine,
(25)
(26) T T
{
[
P P
( ) ⁄
]
}
(27) (T T )
Heat exchanger,
(28) (T T ) (T T )
(29) (T T )
(30) ( T )
(31) P
⁄
10
(32) P P ( ΔP )
The net electrical power output of the gas turbine, , can be expressed as:
(33) ( )
(34) ( )
The other important criterion is exergetic efficiency of the system, and it can be given as the
ratio of total exergy output to exergy rate of fuel:
(35) L ξ
(36)
L ξ
Here, LHV is lower heating value (for methane it is equal to 50000 KJ/Kg). Equation 35 is
considered for the power generation system regardless of the heat exchanger and equation
36 for the CHP system.
It should be noted that the calculation of the specific heat of the materials is often done
using relationships depicted in [32, 33]. In this article we use the relationships in [32].
Comparison between these references is carried out in Figure 2.
Figure 2 Comparison between thermodynamic properties of material used in this article
based on references [31, 32]
2.2. Exergy analysis
In summary, exergy is a measure of the maximum capacity of a system to perform useful
work as it proceeds to a specified final state in equilibrium with its surrounding. And it can
be divided into four distinct components. The two important ones are the physical exergy
and chemical exergy. In this study, the two other components which are kinetic exergy and
potential exergy are assumed to be negligible as the elevation and speed have negligible
changes. The physical exergy is defined as the maximum theoretical useful work obtained as
a system interacts with an equilibrium state [34, 35]. The chemical exergy is associated with
the departure of the chemical composition of a system from its chemical equilibrium. The
chemical exergy is an important part of exergy in combustion process. Applying the first and
the second law of thermodynamics, the following exergy balance is obtained:
(37) ∑
∑
In this equation is the exergy destruction. Other terms in this equation is as follow:
(38) ( T T)
(39) (40)
(41) ( ) T ( )
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Where and are the corresponding exergy of heat transfer and work which cross
the boundaries of the control volume, T is the absolute temperature and (K) and (0) refers
to the ambient conditions respectively. The mixture chemical exergy is defined as follows
[35]:
(42) [∑
T ∑ L
]
For the evaluation of the fuel exergy, the above equation cannot be used. Thus, the
corresponding ratio of simplified exergy is defined as the following [35]:
(43) ξ L ⁄ Due to the fact that for the most of usual gaseous fuels, the ratio of chemical exergy to the
LHV is usually close to unity, one may write:
(44) ξ ξ
For gaseous fuel with CxHy, the following experimental equation is used to calculate ξ:
(45) ξ
Recently exergy analyses have been employed for analysis, design, performance
improvement and optimization of thermal systems, including microCHP plants. It is well-
known that exergy can be used as a potential to determine the location, type and true
magnitude of exergy loss (or destruction) too [36]. Therefore, it can play an important issue
in developing strategies and in providing guidelines for more effective use of energy in the
existing power plants [37]. In the present work, for the exergy analysis of the plant, the
exergy of each line is calculated at all states and the changes in the exergy are determined
for each major component. The source of exergy destruction (or irreversibility) in
combustion chamber is mainly combustion (chemical reaction) and thermal losses in the
flow path. However, the exergy destruction in the heat exchangers of the system is due to
the large temperature difference between the hot and cold fluids. The exergy destruction
rate and the exergetic efficiency for each component for the whole system in the power
plant are shown in Table 2.
Table 2 The exergy destruction rate and exergy efficiency equations for plant components
The code developed for thermodynamic optimization purposes is written in MATLAB
software and is based on a number of built-in functions, tools and externally developed
subroutines. The model includes 6 important fixed parameters (see Table 3) and the
variables selected for the optimization are: The compressor pressure ratio, Pr, the turbine
inlet temperature (TIT) and the air mass flow rate ( ). Fixed parameters remain constant
during the optimization. The decision variables can vary in a given range and represent the
independent variables in design optimization of the system (Table 4). Obviously, only some
of the possible sets of values for the decision variables correspond to actual feasible
designs. The others are automatically rejected by the code. For any acceptable design, the
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model calculates all energy, entropy, and exergy flow rates entering and leaving each
component.
Table 3 Important fixed parameters and their values
Table 4 Decision variables and their values
2.3. Thermoeconomical Analysis
Thermoeconomics combines the exergy analysis with the economic aspects and consider
the related costs of the thermodynamic inefficiencies in the total product cost of the
system. The total cost rate of operation for the installation is obtained from:
(46) ∑
Where is the total cost rate of fuel ($/s) and is the capital cost rate ($/s) of the kth
equipment item. is introduced in the next section.
(47) ⁄
Where Zk, CRF, N (8000 hours) and (1.06) are the purchase cost of kth component in
dollar, the capital recovery factor, the annual number of the operation hours of the unit and
the maintenance factor. The expression for each component of the MGT plant and
economic model is presented in Table 5. Constants used in the equation of Table 5 are
showed in Table 6. The CRF depends on the interest rate as well as estimated equipment life
time. (Value of CRF this paper is: 0.182) [33, 38, 39].
Cost of fuel rate is defined as follows:
(48) L
Where Cf = 0.004 $/MJ is the regional cost of fuel per unit of energy (on LHV basis) [33, 38],
is the fuel mass flow rate.
Table 5 Equation for calculation the purchase costs for the system components
Table 6 Constants used in the equation of Table 5 for the purchase cost of the components
2.4. Environmental Analysis
In order to minimize the environmental impacts, the objective is to increase the efficiency of
energy conversion processes and, thus, decrease the amount of fuel and the related overall
environmental impacts, especially the release of carbon dioxide as a major greenhouse gas.
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Therefore, optimization of thermal systems based on this fact has been an important
subject in recent years. Although there are many papers in the literature, dealing with
optimization of CHP plants, they consider no environmental impacts. For this reason, one of
the major goals of the present work is to consider the environmental impacts as producing
the CO and NOx. As discussed in ref. [40], the amount of CO and NOx produced in the
combustion chamber and combustion reaction also change mainly by the adiabatic flame
temperature. The adiabatic flame temperature in the primary zone of the CC is derived as
follows:
(49) T ( ( ) )
Where π is a dimensionless pressure p/pref (p being the combustion pressure p3, and pref =
101.3 KPa); θ is a dimensionless temperature T/Tref (T being the inlet temperature T3, and
Tref = 300 K); ψ is the H/C atomic ratio (ψ = 4, the fuel being pure methane); σ = φ for being
the fuel to air equivalence ratio (φ is assumed constant); It is considered 0.64 for the
combustion equation with the fuel of methane. x, y and z are quadratic functions of σ; A, α,
β and λ are constants (different sets of constants are used for different ranges of θ). The
constants for equations (49 – 52) are obtained from references [33, 38].
(50)
(51)
(52)
The adiabatic flame temperature is used in the semi analytical correlations proposed by Rizk
et al. [41] to determine the pollutant emissions in grams per kilogram of fuel:
(53) ( T ⁄ )
P (ΔP P ⁄ )
(54) ( T ⁄ )
P (ΔP P ⁄ )
Where τ is the residence time in the combustion zone (τ is assumed constant and is equal to
0.002 s); Tpz is the primary zone combustion temperature; p3 is the combustor inlet
pressure; Δp3/p3 is the non-dimensional pressure drop in the combustor. The cost of
environmental impacts is derived as follow:
(55)
Where:
(56) ⁄ (57) ⁄
3. The Genetic Algorithm
The genetic algorithm (GA) is a stochastic global search method that mimics the metaphor
of natural biological evolution. GAs operates on a population of potential solutions applying
the principle of survival of the fittest to produce (hopefully) better and better
approximations to a solution. At each generation, a new set of approximations is created by
the process of selecting individuals according to their level of fitness in the problem domain
14
and breeding them together using operators borrowed from natural genetics. This process
leads to the evolution of populations of individuals that are better suited to their
environment than the individuals that they were created from, just as in natural adaptation
[25]. Individuals, or current approximations, are encoded as strings, chromosomes,
composed over some alphabet(s), so that the genotypes (chromosome values) are uniquely
mapped onto the decision variable (phenotypic) domain. Having decoded the chromosome
representation into the decision variable domain, it is possible to assess the performance, or
fitness, of individual members of a population. This is done through an objective function
that characterizes an individual’s performance in the problem domain. Thus, the objective
function establishes the basis for selection of pairs of individuals that will be mated together
during reproduction. During the reproduction phase, each individual is assigned a fitness
value derived from its raw performance measure given by the objective function. This value
is used in the selection to bias towards more fit individuals. Highly fit individuals, relative to
the whole population, have a high probability of being selected for mating whereas less fit
individuals have a correspondingly low probability of being selected [35].
A GA usually some operators that act on the chromosomes of each generation include
recombination and mutation. The recombination operator is used to exchange genetic
information between pairs, or larger groups of individuals. A further genetic operator, called
mutation, causes the individual genetic representation to be changed according to some
probabilistic rule. Mutation is generally considered to be a background operator that
ensures that the probability of searching a particular subspace of the problem space is never
zero. After recombination and mutation, the individual strings are then, if necessary,
decoded, the objective function evaluated, a fitness value assigned to each individual and
individuals selected for mating according to their fitness, and so the process continues
through subsequent generations. In this way, the average performance of individuals in a
population is expected to increase, as good individuals are preserved and multiplied with
one another and the less fit individuals die out. The GA is terminated when some criteria are
satisfied, e.g. a certain number of generations, a mean deviation in the population, or when
a particular point in the search space is encountered [42]. The basic steps for the application
of a GA for an optimization problem are summarized in Figure 3.
Figure 3 GA flow chart
4. Results and discussion
4.1. Model verification
After applying the thermodynamic relations listed in section 2, and using the developed
simulation code, the results of thermodynamic optimization are obtained. The assumptions
of the design variables are presented in Table 7. In order to validate the modeling output
results, the operating parameters were compared with the corresponding data from the
15
available literature [29] for the same input parameters. The paper deals with the
examination of a hybrid system consisting of a pre-commercially available high temperature
solid oxide fuel cell and an existing recuperated microturbine. The irreversibilities and
thermodynamic inefficiencies of the system are evaluated after examining the full and
partial load exergetic performance and estimating the amount of exergy destruction and the
efficiency of each hybrid system component. Table 8 compare two groups of data and their
corresponding differences in percentage. Results show that the model was capable of
predicting the thermal performance of the system quite precisely.
Table 7 Comparison between Capstone C30 parameters and proposed design variables in
this study
Table 8 Comparison between ref. [29] and optimized data in this study
There are always things to be improved, but as seen from Table 7 and Table 8, the model
shows a great similarity with the measured values from the real microturbine and the
proposed reference.
4.2. Optimization results
For optimization using genetic algorithm package written in MATLAB software, the
parameters of Table 9 was used and stopping criteria are shown in Table 10 were
considered. The optimal values obtained are presented in Table 11, Table 12. The results
presented in Table 11 are to maximize exergetic efficiency and the results presented in
Table 12 are to maximize net power output. As seen, due to the desired accuracy for
optimization, a range of optimum pressure ratio is presented in both tables.
Table 9 GA parameters
Table 10 Stopping criteria for optimization with GA
Table 11 Optimized values for pressure ratio of the system based on exergetic efficiency
optimization in different TITs
Table 12 Optimized values for design parameters of the system based on maximum net
power generation
As one can see from results:
To optimize the exergetic efficiency, air mass flow differences don’t create large
differences. In other words, after calculating the optimum pressure ratio to achieve
16
maximum exergetic efficiency, due to the required output power the rate of air mass
flow should be calculated.
By increasing the maximum temperature of the cycle, which means turbine inlet
temperature, exergetic efficiency and power output increase. It should be noted that
the maximum temperature of the cycle has its own limitations determined according
to user needs and the investment rationale for the design of the gas turbine.
By increasing the turbine inlet temperature, the optimal amount of pressure ratio for
maximum exergetic efficiency and power output increases.
Since in this model assumed that fuel before entering the combustion chamber,
enters a heat recovery heat exchanger with hot exhaust gases from the turbine,
lower fuel consumption than similar systems are obtained. The reason for the higher
system efficiency of this system than similar systems is this assumption too.
As mentioned above in section 2, energy analysis which is based on the first law of
thermodynamics, does not provide a clear picture of thermodynamic efficiency and losses.
Exergy analysis overcomes these deficiencies and can help identify pathways to sustainable
development. Exergy is a useful tool for determining the location, type and true magnitude
of exergy losses, which appear in the form of either exergy destructions or waste exergy
emissions. Therefore, exergy can assist in developing strategies and guidelines for more
effective use of energy resources and technologies. Figures 4 to 9 shows the variation of
exergy destruction rate with TIT and air mass flow rate of each components of the system
respectively. It is seen that the highest exergy loss takes place at the combustion chamber.
The sources of exergy destruction (or irreversibility) in combustion chamber are mainly the
combustion or chemical reaction and thermal losses in the flow path. Another important
source of exergy loss is the heat exchanger of the system i.e. two recuperators and heat
exchanger, which is related to the big temperature difference between the hot and cold
fluids.
Figure 4 Exergy destruction rate with TIT and air mass flow rate for air compressor
Figure 5 Exergy destruction rate with TIT and air mass flow rate for first recuperator
Figure 6 Exergy destruction rate with TIT and air mass flow rate for fuel compressor
Figure 7 Exergy destruction rate with TIT and air mass flow rate for second recuperator
Figure 8 Exergy destruction rate with TIT and air mass flow rate for combustion chamber
Figure 9 Exergy destruction rate with TIT and air mass flow rate for gas turbine
Figure 10 shows the variation of exergetic efficiency with TIT of each components of the
system respectively. As seen from it, the value of exergetic efficiency of combustion
chamber is lower than that of other components, and can be increased by increasing the
17
combustion inlet temperature (T3) and turbine inlet temperature (T4). However, it should be
noted that due to physical constraints, the turbine material resistance to creep and capital
cost limitations, these temperatures can be changed only within allowable extents. This
means that the improvement of the exergetic efficiency by increasing T3 and T4 may move
the design point from the optimum situation to a new situation at which, the objective
function is not minimum.
Figure 10 Variation of exergetic efficiency with TIT for each component of system
(Compressor pressure ratio is optimized in each TIT (4, 4.75 and 5.4))
4.3. Sensitivity analysis
In this section, to have an understanding of variation of each design parameters on the
objective function a sensitivity analysis has been performed. This analysis is carried out
based on the change in a related parameter as well as some other modeling parameters and
helps us to predict the results while some modifications are necessary in modeling and
optimization. Figure 11 shows the effect of compressor pressure ration and mass flow rate
on system net output power in fixed turbine inlet temperatures. As seen from it variation of
net power output is low sensitive to the compressor pressure ratio. Figures 12 and 13 show
the variation of compressor pressure ratio on the cycle exergetic efficiency. These figures
are proving the ability of desired model to identify the optimum point of the cycle to
achieve maximum exergetic efficiency. For simplicity, in each figure one of abovementioned
TITs is considered.
Figure 11 Variation of compressor pressure ratio and mass flow rate of air on net power
generation (TIT = 1000 ˚K)
Figure 12 Variation of compressor pressure ratio on exergetic efficiency I (without heat
generation) (TIT = 1100 ˚K)
Figure 13 Variation of compressor pressure ratio on exergetic efficiency II (with heat
generation) (TIT = 1200 ˚K)
4.4. Economical results
Figure 14 shows the Pareto frontier solution for CHP system with the objective functions
described in previous sections including exergetic efficiency and total cost rate regarding
environmental aspects. In this figure three TITs are assumed 1000, 1100 and 1200 K. it is
worth to mention that compressor pressure ratio varies around its suggested range resulted
from physical constraints (Table 4).
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Figure 14 Distribution of Pareto optimal points solutions for exergetic efficiency and total
cost rate of the CHP system
As seen from this figure (for TIT = 1000 K as an example) while the total exergetic efficiency
increases from 67.69% to about 71.52%, the total cost rate increases only slightly from 2.20
to 2.57 ($/hour). In addition, increase in the exergetic efficiency from 71.52% to a little
higher value (71.53%) leads to a drastic increase of the total cost rate from 2.57 to 3.32. This
is corresponding to the moderate increase in the fuel cost rate as a result of increasing air
mass flow rate.
Another conclusion from Figure 14 is that increase in TIT leads to increase in the exergetic
efficiency, however, it results in decrease of the total cost rate first and then this increase
causes a drastic increment in total cost rate of the system. It should be mentioned that in
multiobjective optimization, a process of decision-making for the selection of optimal
solution is necessary. In the Pareto solution, each point can be considered as an optimized
set. Therefore, choosing of the optimum solution depends on preferences and criteria of
each decision-maker. Therefore, they may select a different point as the final optimum
solution which better suits with they requirements.
5. Conclusions
Micro gas turbine engine offers solution to reduce largely the cost and reliability of micro
CHP. A MGT system for combined heat and power generation has been evaluated by means
of system modeling and simulation and optimized for various power outputs (sizes) using
genetic algorithm optimization. The objective functions were selected as the total exergetic
efficiency and the system net power. Some energetic results of the developed model have
been compared with those of literature to indicate its capability at steady-state conditions.
The important parameters of MGT such as fuel consumption, exergetic efficiency and net
power have been analyzed in the wide range of pressure ratio and rate of air mass flow to
have an insight into their influences on exergetic performances of the CHP system. The
results from sensitivity analysis proved the validity of proposed model and also showed that
increasing gas turbine inlet temperature decreases the exergy destruction rate in
combustion chamber (and recuperator) and saves fuel consumption as well. For TIT 1000 K,
the total exergetic efficiency increases from 67.69% to about 71.52% while the total cost
rate increases only slightly from 2.20 to 2.57 ($/hour).
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Figure 1 Schematic diagram of the cycle power plant
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Figure 2 Comparison between thermodynamic properties of material used in this article
based on references [31, 32]
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48
58
68
78
300 400 500 600 700 800 900 1000 1100 1200
Spec
ific
hea
t at
co
nst
ant
pre
ssu
re (
kJ/k
g.K
)
Temperature (˚K)
H2 Cengel H2 Bejan CH4 Cengel CH4 Bejan CO2 Cengel CO2 Bejan
