(CHP) system integrated with low-energy buildings

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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 www.elsevier.com/locate/jobe

PII: DOI: Reference:

S2352-7102(15)30038-3 http://dx.doi.org/10.1016/j.jobe.2015.10.004 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 lowenergy 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 for publication. As a service to our customers we are providing this early version of 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.

Simulation and multi-objective optimization of a combined heat and power (CHP) system integrated with low-energy buildings

Jamasb Pirkandi1, Mohammad Ali Jokar2, Mohammad Sameti2* Alibakhsh Kasaeian2, Fazel Kasaeian3

1

Department of Aerospace Engineering, Malek Ashtar University of Technology, Tehran, Iran 2

3

Department of Renewable Energies, University of Tehran, Tehran, Iran

Department of Materials Science and Engineering, Sharif University of Technology, Tehran, Iran *

Corresponding Author: Mohammad Sameti Department of Renewable Energies, Faculty of New Sciences and Technologies University of Tehran, North Karegar St., Tehran, Iran E-mails: [email protected] Tel: +98 9132124120 Fax: +98 21 88617087

1

Abstract One of the novel applications of gas turbine technology is the integration of combined heat and power (CHP) system with micro gas turbine which is spreading widely in the field of distributed generation and low-energy buildings. It has a promising great potential to meet the electrical and heating demands of residential buildings. In this study, A MATLAB code was developed to simulate and optimize the thermoeconomic performance of a gas turbine based CHP cycle. Three design parameters of this cycle considered in this research are compressor pressure ratio, turbine inlet temperature, and air mass flow rate. Firstly, two objective functions including exergetic efficiency and net power output were chosen to achieve their maximum level. Genetic algorithm (GA) was used as the optimization technique to determine the optimum behavior of the system. Variation of exergy destruction rate and exergetic efficiency with turbine inlet temperature (TIT) and air mass flow rate were also studied for each component. Based on the exergetic analysis, suggestions were given for reducing the overall irreversibility of the thermodynamic cycle. To have a good insight into this study, a sensitivity analysis for important parameters was also carried out. Finally, based on the exergy analysis and utilization of economic and environmental functions, a multi-objective approach was performed to optimize the system performance.

Keywords low-energy buildings, cogeneration, micro gas turbine (MGT), optimization, genetic algorithm (GA), economic analysis, environmental consideration

Nomenclature C

Cost of fuel per energy unit ($/kJ) Cost flow rate ($/s) Specific heat at constant pressure (kJ/kg.K) 2

CRF ̇ ̇ e h k LHV ̇ N P R S T U ̇ Z ̇ ΔP ΔTLM ƞ ξ

Capital recovery factor Exergy flow rate (kW) Exergy destruction rate (kW) Specific exergy (kJ/kmol) Enthalpy (kJ/kg) Specific heat ratio (Cp/Cv) Lower heating value (kJ/kg) Mass flow rate (kg/s) Annual number of the operation hours of the unit Pressure (KPa) Gas constant (kJ/kg.K) Compressor pressure ratio Entropy (kJ/kg.K) Temperature (K) Overall heat transfer coefficient (W/m2.K) Net power output (kW) Capital cost of the component ($) Capital cost rate of the component ($/s) Pressure drop (KPa) Log mean temperature difference (K) efficiency Ratio of chemical exergy to Lower Heating Value Specific heat ratio Maintenance factor of the equipment Molar fraction

Subscripts a AC CC e f FC g gen GT HE Q rec W

Air Air compressor Combustion chamber Exergetic Fuel Fuel compressor Combustion gases Generator Gas turbine Heat exchanger Heat rate (kW) Recuperator Work (kW)

Superscripts ch ph

Chemical 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. 4

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 5

programming) [18, 19]. Ameri et al. [20] presented a thermodynamic analysis of a trigeneration 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. 6



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).

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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 T 0 =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)

(

T

(3)

̇

) ⁄

T {

(4) First recuperator, (5) (6) (7) Fuel compressor, (8)

̇ ̇

̇

(T

[ P

P

T) P P( P P(

8

(T ̇ ΔP ΔP

̇ ̇

]} T)

̇

) )

̇

(9)

(T ̇

T ) (

T

(10)

) ⁄

T

{ [ ]} Second recuperator, P P (11) (T ) (T ̇ T ̇ T) (12) P P ( ΔP ) (13) P P( ΔP ) (14) Combustion chamber, ( ) ̇ L ̇ ̇ L ̇ (15) (T T) (16) (T T) (17) (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)

̇ ̇

̇ (

T

(26) (27) Heat exchanger, (28) (29) (30) (31)

P P

T ̇

{

(T ̇ ̇ ̇

̇

) ⁄

[ ̇

T) ̇

(T

T)

]}

(T T) (T T) ̇ ( T ) ̇ P ⁄ ̇

9

P P( ΔP ) (32) 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 ̇

(36)

̇

ξ

̇ 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) (39) (40) (41)

̇

∑ ̇

̇ ̇

̇

̇ ̇ ̇ )

̇

( ̇ 10

T ) T ̇ T(

)

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]: ⁄L (43) ξ 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: ξ ξ (44) 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 wellknown 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, P r, 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

11

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. 12

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 )

(ΔP ⁄P ) ( ⁄T ) ̇ (54) 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:

̇

P

̇

̇ ⁄

(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 13

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 14

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 15

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 16

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 T 3 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).

17

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

21

Specific heat at constant pressure (kJ/kg.K)

78

68

58

48

38

28 300

400

500

600

700

800

900

1000

1100

1200

Temperature (˚K) H2 Cengel

H2 Bejan

CH4 Cengel

CH4 Bejan

CO2 Cengel

CO2 Bejan

H2O Cengel

H2O Bejan

N2 Cengel

N2 Bejan

O2 Cengel

O2 Bejan

Figure 2 Comparison between thermodynamic properties of material used in this article based on references [31, 32]

22

Begin

Coding of parameter space

Random creation of initial population

Population evaluation Finesses

Application of operators

New population (Replacement of the old)

No

Is any of stop criteria satisfied?

Yes End

Figure 3 GA flow chart

23

10

8.9147

Esergy destruction rate (kw/s)

9 7.6412

8 7 6

5.8406

6.3677

6.7405

8.0886

9.4367

8.1768

7.0087

5 4 3 2 1 0 0.25

0.3

0.35

Air mass flow rate (kg/s) TIT = 1000 ˚K, rp=4

TIT = 1100 ˚K, rp=4.75

TIT = 1200 ˚K, rp=5.4

Figure 4 Exergy destruction rate with TIT and air mass flow rate for air compressor

16

14.6436

Exergy destruction rate (kW)

14 12 10

12.8871

12.5516 10.4597 9.2051

11.0461

11.6697

10.0026

8.3355

8 6 4 2 0 0.25

0.3

0.35

Air mass flow rate (kg/s) TIT = 1000 ˚K, rp=4

TIT = 1100 ˚K, rp=4.75

TIT = 1200 ˚K, rp=5.4

Figure 5 Exergy destruction rate with TIT and air mass flow rate for first recuperator

24

0.2

0.1879

Exergy destruction rate (kW)

0.18

0.161

0.1525

0.16 0.1342

0.14

0.1

0.1146

0.109

0.12

0.1308 0.0983

0.0819

0.08 0.06 0.04 0.02 0 0.25

0.3

0.35

Air mass flow rate (kg/s) TIT = 1000 ˚K, rp=4

TIT = 1100 ˚K, rp=4.75

TIT = 1200 ˚K, rp=5.4

Figure 6 Exergy destruction rate with TIT and air mass flow rate for fuel compressor

2.5

Exergy destruction rate (kW)

2.1681 1.8584

2 1.5567

1.5486 1.5

1.2972

1.816 1.4969

1.2831

1.0693 1

0.5

0 0.25

0.3

0.35

Air mass flow rate (kg/s) TIT = 1000 ˚K, rp=4

TIT = 1100 ˚K, rp=4.75

TIT = 1200 ˚K, rp=5.4

Figure 7 Exergy destruction rate with TIT and air mass flow rate for second recuperator

25

80

74.3763

Exergy destruction rate (kW)

70

63.7511 57.9324

60 50

53.126 48.2726

67.5659 59.9389

51.3988

42.8323

40 30 20 10 0 0.25

0.3

0.35

Air mass flow rate (kg/s) TIT = 1000 ˚K, rp=4

TIT = 1100 ˚K, rp=4.75

TIT = 1200 ˚K, rp=5.4

Figure 8 Exergy destruction rate with TIT and air mass flow rate for combustion chamber

8

7.4176 6.821

Exergy destruction rate (kW)

7

6.358 5.8466

6 5

4.8722

5.2983

5.9872

5.1319

4.2766

4 3 2 1 0 0.25

0.3

0.35

Air mass flow rate (kg/s) TIT = 1000 ˚K, rp=4

TIT = 1100 ˚K, rp=4.75

TIT = 1200 ˚K, rp=5.4

Figure 9 Exergy destruction rate with TIT and air mass flow rate for gas turbine

26

99.16

100

Exergetic efficiency (%)

99.14

92.38

95.39

95.01

94.59

95 90

99.16

92.84 91.86

92.79 91.53

91.2

89.01

88.54

87.86

85 80

79.45

78.37

77.2

75 70 1000

1100

1200

TIT (˚K) Air Compressor

First Recuperator

Fuel Compressor

Second Recuperator

Combustion Chamebr

Gas Turbine

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))

Net power (kW)

30 28 26 24 22 20 3.75

3.85

3.95

4.05

4.15

4.25

Compressor pressure ratio

Air mass flow rate = 0.25 (Kg/s)

Air mass flow rate = 0.3 (Kg/s)

Air mass flow rate = 0.35 (Kg/s)

Figure 11 Variation of compressor pressure ratio and mass flow rate of air on net power generation (TIT = 1000 ˚K)

27

23.55

Exergetic efficiency I (%)

23.5 23.45 23.4 23.35 23.3 23.25 23.2 23.15 4.5

4.55

4.6

4.65

4.7

4.75

4.8

4.85

4.9

4.95

5

Compressor pressure ratio

Figure 12 Variation of compressor pressure ratio on exergetic efficiency I (without heat generation) (TIT = 1100 ˚K)

Exergetic efficiency II (%)

71.8 71.7 71.6 71.5 71.4

71.3 71.2 71.1 71 5.15

5.2

5.25

5.3

5.35

5.4

5.45

5.5

5.55

5.6

5.65

Compressor pressure ratio

Figure 13 Variation of compressor pressure ratio on exergetic efficiency II (with heat generation) (TIT = 1200 ˚K)

28

Total cost rate ($/hour)

4

3.5

3

2.5

2 67.2

67.7

68.2

68.7

69.2

69.7

70.2

70.7

71.2

71.7

Exergetic efficiency (%) TIT = 1000 ˚K

TIT = 1100 ˚K

TIT = 1200 ˚K

Figure 14 Distribution of Pareto optimal points solutions for exergetic efficiency and total cost rate of the CHP system Table 1 Capstone C30 design parameters [29, 30] Electrical power (kW) Air mass flow rate (kg/s) Net Heat Rate (MJ/kWh) Exhaust Gas Flow (Kg/s) Exhaust gas temperature (0C) System efficiency (%) Compressor isentropic efficiency (%) Turbine isentropic efficiency (%) Generator efficiency (%)

28-30 0.31 13.8 0.31-0.32 275 26 ± 2 79.6 84.6 95

Table 2 The exergy destruction rate and exergy efficiency equations for plant components Components

Exergy destruction rate ̇

Air Compressor ̇

Recuperator (I)

( ̇ ̇

Fuel Compressor Recuperator (II)

̇

̇

̇

( ̇

̇

̇ ) ̇

Exergetic efficiency ̇ ̇

( ̇

̇ ̇ )

29

̇ ̇

∑ ̇

̇ ( ̇

̇

̇ )

̇

̇

̇ )

̇ ∑

̇

̇

Combustion Chamber ̇

Gas Turbine

̇

̇

̇

̇ ̇

̇

̇

̇ ̇

̇ ̇

̇

Table 3 Important fixed parameters and their values Description Compressor isentropic efficiency Turbine isentropic efficiency Recuperator efficiency Recuperator effectiveness Invertor efficiency Generator efficiency

Value 79.6% 84% 90% 80% 95% 90%

Table 4 Decision variables and their values Description compressor pressure ratio turbine inlet temperature air mass flow rate

Unit --C Kg/s

Min. value 3 1000 0.25

Max. value 5 1200 0.35

Table 5 Equation for calculation the purchase costs for the system components Components Air compressor First recuperator Fuel compressor Second recuperator Combustion chamber

Capital or investment cost functions ̇ P P P P ) ̇ ( ( ) (ΔTLM) P P ̇ P P ) ̇ ( ( ) (ΔTLM) ̇ ( T ( P ⁄P ̇

Gas turbine

(

Heat exchanger

P P ̇ (ΔTLM)

( )

̇

(

T

))

)) ̇

Table 6 Constants used in the equation of Table 5 for the purchase cost of the components

30

Components Air compressor & fuel compressor Recuperators

Capital or investment cost functions ⁄( ⁄ ) ⁄ ⁄( ⁄( ⁄ )

Combustion chamber

⁄(

Gas turbine

⁄ ) ⁄(

Heat exchanger

⁄(

)

⁄ )

⁄ ) ⁄(

⁄ )

Table 7 Comparison between Capstone C30 parameters and proposed design variables in this study Capstone C30 0.31 3.6 26 ± 2 30

Air mass flow (Kg/s) Compressor pressure ratio System efficiency Net power (kW)

Proposed values in this study 0.31 3.6 24.87 33.57

Table 8 Comparison between ref. [29] and optimized data in this study

Air mass flow (Kg/s) Compressor pressure ratio System efficiency Net power (kW) Compressor inlet temperature (K) Compressor outlet temperature (K) Turbine inlet temperature (K) Turbine outlet temperature (K) Turbine exergy destruction (kW) Turbine exergy efficiency Compressor exergy destruction (kW) Compressor exergy efficiency

Optimized data in ref. [29] 0.307 3.6 25.1 31.1 298 462 1113 885 5.2 94 7.1 86

Optimized data in this study 0.31 3.6 26.4 33.57 298.15 459.68 1117 886 4.541 95.55 6.815 87.73

Table 9 GA parameters Population type Population size Creation function

Double vector 20 Constraint dependent 31

Difference between values (%) --------0.05 0.50 0.35 0.11 12.67 1.65 4.01 2.01

Scaling function Selection function Elite count Crossover fraction Mutation function Crossover function Migration Direction Migration Fraction Migration Interval Constraint parameters Population type

Rank Stochastic uniform 2 0.8 Constraint dependent Scattered Forward 0.2 20 Double vector 20

Table 10 Stopping criteria for optimization with GA Generation Time limit Fitness limit Stall generations Stall time limit

100 106 10-6 50 20

Table 11 Optimized values for pressure ratio of the system based on exergetic efficiency optimization in different TITs Tmax = 1000 K Pressure Exergetic ratio efficiency 3.95 – 4.05 20.1

Tmax = 1100 K Pressure Exergetic ratio efficiency 4.6 – 4.9 23.7

Tmax = 1200 K Pressure Exergetic ratio efficiency 5.2 – 5.6 26.7

Table 12 Optimized values for design parameters of the system based on maximum net power generation Tmax = 1000 K

Tmax = 1100 K

Air mass flow (Kg/s)

Pressure ratio

Net power (kW)

0.1 0.2 0.3 0.4 0.5

4.6 – 5.2 4.6 – 5.2 4.7 – 5.1 4.7 – 5.1 4.7 – 5.1

8.6 17.7 26.7 34.8 42.9

Air mass flow (Kg/s) 0.1 0.2 0.3 0.4 0.5

Tmax = 1200 K

Pressure ratio

Net power (kW)

5.7 – 6.1 5.7 – 6 5.9 - 6 5.9 - 6 5.9 - 6

12.3 25.3 37.9 49.5 61.7

32

Air mass flow (Kg/s) 0.1 0.2 0.3 0.4 0.5

Pressure ratio

Net power (kW)

7 – 7.5 7.75 7.1 – 7.4 7 – 7.4 7 – 7.4

16.2 32.3 48.2 61.5 80.3

Graphical abstract

Highlights

    

A methodology was proposed for design of MGT based CHP systems to be used by decision makers. A computer code was developed to simulate the performance of the building integrated CHP system. Multiobjective genetic optimization is used for Pareto approach for system performance. Suggestions were offered to reduce the overall system irreversibilities. The thermoenviroeconomic objective and the exergetic efficiency reached their optimum levels.

33