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Multi-objective exergy-based optimization of a polygeneration energy system using an evolutionary algorithm
Energy 46 (2012) 21e31
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Multi-objective exergy-based optimization of a polygeneration energy system using an evolutionary algorithm Pouria Ahmadi*, Marc A. Rosen, Ibrahim Dincer Faculty of Engineering and Applied Science, University of Ontario Institute of Technology (UOIT), 2000 Simcoe St. North, Oshawa, ON L1H 7K4, Canada
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 September 2011 Received in revised form 17 November 2011 Accepted 1 February 2012 Available online 13 March 2012
A comprehensive thermodynamic modeling and optimization is reported of a polygeneration energy system for the simultaneous production of heating, cooling, electricity and hot water from a common energy source. This polygeneration system is composed of four major parts: gas turbine (GT) cycle, Rankine cycle, absorption cooling cycle and domestic hot water heater. A multi-objective optimization method based on an evolutionary algorithm is applied to determine the best design parameters for the system. The two objective functions utilized in the analysis are the total cost rate of the system, which is the cost associated with fuel, component purchasing and environmental impact, and the system exergy efficiency. The total cost rate of the system is minimized while the cycle exergy efficiency is maximized by using an evolutionary algorithm. To provide a deeper insight, the Pareto frontier is shown for multiobjective optimization. In addition, a closed form equation for the relationship between exergy efficiency and total cost rate is derived. Finally, a sensitivity analysis is performed to assess the effects of several design parameters on the system total exergy destruction rate, CO2 emission and exergy efficiency. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Efficiency Exergy Polygeneration Energy Multi-objective optimization
1. Introduction The usage of energy is important in many applications, including heating and cooling, power generation, desalination, and air conditioning. Efforts are underway to make energy use more sustainable, economic factors, efficient, clean and secure. Energy utilization is governed by thermodynamic principles and an understanding of exergetic aspects can help identify and understand sustainable energy options [1]. The efficiency of power generation can be improved through the use of combined cycle plants. Also, combined heat and power (CHP) systems permit power generation and heating and are attractive in power markets because of their high efficiency, low emissions, low initial investment, operation and maintenance costs as well as high flexibility [2]. Recently, applications of trigeneration and polygeneration energy systems have increased. Polygeneration systems have higher efficiencies and lower environmental impacts than CHP systems [3]. Trigeneration is the simultaneous production of heating, cooling and electricity from a common energy source. Trigeneration often utilizes the waste heat of a power plant to improve overall thermal performance, essentially utilizing the
* Corresponding author. E-mail addresses: [email protected], [email protected] (P. Ahmadi), [email protected] (M.A. Rosen), [email protected] (I. Dincer). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.02.005
“free” energy available via the waste energy. In trigeneration and polygeneration systems, waste heat from the plant’s prime mover (e.g., gas turbine (GT) or diesel engine or organic Rankine cycle), sometimes with temperature enhancement, drives heating and cooling devices [3]. A common type of polygeneration system involves the simultaneous production of electricity, heating, cooling and hot water from a common energy source. Much research on multi-generation systems has been conducted in recent years. Khaliq et al. [4] carried out an exergy analysis of a combined electrical power and refrigeration cycle, as well as a parametric study on the effects of exhaust gas inlet temperature, pinch-point and gas composition on energy and exergy efficiencies, electricity-to-cold ratio and exergy destruction for the cogeneration system and its components. Minciuc et al. [5] presented a method for analyzing trigeneration systems and established limits for the best performance of gas turbine trigeneration with absorption chilling from a thermodynamic point of view. Recently, combinations of exergy, economic and environmental assessment have received increasing attention around the world, motivated in part by global warming challenges. Ahmadi et al. [3] carried out an exergoenvironmental analysis of a trigeneration system based on a micro gas turbine and an organic Rankine cycle (ORC), and performed a parametric study involving the main design parameters of the trigeneration system. Al-Sulaiman et al. [6] performed an energy analysis of a trigeneration plant based on a solid oxide fuel cell (SOFC), and showed
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P. Ahmadi et al. / Energy 46 (2012) 21e31
that there is at least a 22% gain in efficiency using the trigeneration plant compared to a power cycle (SOFC and ORC). The study also showed that the maximum efficiency of the trigeneration plant is 74%, of heating cogeneration is 71%, of cooling cogeneration is 57% and of net electricity generation is 46%. These results show the importance of exergy and environmental impact analyses of such systems. Although exergy and environmental impact analysis are important for trigeneration and polygeneration energy systems they cannot provide the best system configuration. Rather, applying optimization techniques based on exergy, economics and environmental impact is useful for this task. Some studies have been reported of the exergoeconomic optimization for CHP systems. Sahoo [7] carried out an exergoeconomic analysis and optimization of a cogeneration system using evolutionary programming. He considered a cogeneration system which produces 50 MW of electricity and 15 kg/s of saturated steam at 2.5 bar, and optimized the CHP unit using exergoeconomic principles and evolutionary programming. The results showed that, for the optimum case in the exergoeconomic analysis, the cost of produced electricity is 9.9% lower than for the base case. Therefore, exergy, economic and environmental optimization can provide insights for polygeneration systems. Nonetheless, such analyses have not to date been reported, especially based on multi-objective evolutionary algorithm. The primary objective of this research is to perform thermodynamic modeling, exergy and environmental analyses as well as optimization of a polygeneration energy system for electricity, cooling, heating and hot water, based on a gas turbine prime mover. The specific objectives are as follows: To model a polygeneration energy system based on a micro gas turbine prime mover, a heat recovery steam generator (HRSG), a steam turbine (ST), a single-effect absorption chiller and a domestic water heater for heating, cooling, hot water production and electricity generation. To apply a multi-objective optimization technique based on a code developed in the Matlab software program using an evolutionary algorithm. To propose a new closed-form expression for the exergy efficiency in terms of total cost rate at the optimal design point. To derive an equation for the Pareto optimal points curve to provide an aid for the optimal design of the polygeneration plant. To perform sensitivity analyses of the variation of each objective function with major design parameters of the system. To determine the environmental impacts for three different cycles, ranging from power generation to multi-product generation (including hot water).
2. System description For the polygeneration system considered here (Fig. 1), thermodynamic modeling and analysis is performed. In the energy analysis, the temperature profile in the polygeneration plant and input and output enthalpy values are determined. In the exergy analysis, exergy values of each flow in the plant, exergy destructions and exergy efficiencies are assessed, while environmental impacts are evaluated in the environmental analysis. These results are used subsequently in the optimization study. To perform the thermodynamic modeling of the polygeneration system, several simplifying assumptions are made to render the analysis more tractable, while retaining adequate accuracy to illustrate the principal points of the article: All the processes are considered to be operating at steady state. Air and combustion products are taken to be ideal-gas mixtures.
The fuel injected to the combustion chamber (CC) is assumed to be natural gas. Heat loss from the combustion chamber is taken to be 2% of the fuel lower heating value, and all other components are considered adiabatic. A dual-pressure heat recovery steam generator with high pressure (HP) and low pressure (LP) steam is considered. Both HP and LP pinch temperatures are considered constant at 10 C. The dead state is P0 ¼ 1.01 bar and T0 ¼ 293.15 K.
3. Energy analysis Relevant energy balances and governing equations for the main sections of the polygeneration plant shown in Fig. 1 are described, broken down into the following subsections: topping cycle (Brayton cycle), bottoming cycle (steam turbine and heat recovery steam generator), the single-effect absorption chiller and domestic water heater. 3.1. Toping cycle (Brayton cycle) We model a gas turbine cycle using the first law of thermodynamics. As seen in Fig. 1, air at ambient conditions enters the air compressor at point 1 and, after compression (point 2), is supplied to the combustion chamber (CC). Fuel is injected in the combustion chamber and hot combustion gases exit (point 3) and pass a gas turbine to produce power. The hot gas expands in the gas turbine to point 4. This flue gas is utilized in the dual-pressure heat recovery steam generator (HRSG) to generate lowpressure (LP) and highpressure (HP) steam. Energy balances and governing equations for the gas turbine cycle are given elsewhere [8]. 3.2. Bottoming cycle Energy balances and governing equations for the components of the bottoming cycle (steam turbine cycle and HRSG) are provided here. Dual pressure HRSG A dual-pressure HRSG with two economizers (LP and HP) and two evaporators (LP and HP) is used in the polygeneration cycle to provide both low- and high pressure steam. The LP steam is used to drive the absorption chiller and the HP steam to generate electricity. The temperature profile in the HRSG is shown in Fig. 2, where the pinch-point is defined as the difference between the temperature of the gas at the entrance of the evaporator (economizer side) and the saturation temperature. The dual-pressure HRSG has two pinch points (PPHP and PPLP). The temperature differences between the water leaving the economizers (T20 and T22) and the saturation temperature (T5 and T17) are the approach points (APHP and APLP), which depend on the economizer’s tube layout. Note that the pinch point and approach temperatures are considered constant here. Energy balances for each element of the HRSG are expressed as follows:
_ w;HP ðh17 h23 Þ ¼ m _ g CPg ðT4 Ta Þ m
(1)
_ w ðh23 h22 Þ ¼ m _ g CPg ðTa Tb Þ m
(2)
_ g CPg ðTb Tc Þ _ w;LP ðh5 h21 Þ ¼ m m
(3)
P. Ahmadi et al. / Energy 46 (2012) 21e31
23
Fuel
Combustion Chamber
3
2 Air Compress or
Gas Turbine Net Power
1
4
25
24
HP Steam
Domestic Water heater
17
HP EVP a
23
Steam Turbine
HRSG
HP ECO 26
Power
b
22
18
Heating
LP EVP
Condenser
c
21
LP Steam
LP ECO
5 6
19
20 d
7
Condenser
Generator
14
13
8
Expansion Valve
Heat Exchanger 12
9
15
Pump 11
mCond
Throttling Valve
16
Absorber
10
mEVP
Evaporator
QCooling Fig. 1. Schematic of the polygeneration system for heating, cooling, hot water and electricity generation.
_ w ðh21 h20 Þ ¼ m _ g CPg ðTc Td Þ m
(4)
An energy balance for pump and an isentropic efficiency can be expressed as follows:
Steam turbine An energy balance for the steam turbine in Fig. 1 and an isentropic efficiency are written as follows:
_ _ w h17 ¼ W _ w h18 m ST m _ W
hST ¼ _ ST;act W ST;is
_ _ w h19 þ W _ w h20 m Pomp ¼ m
his hact
(5)
hPump ¼
(6)
3.3. Absorption chiller
Condenser An energy balance for the condenser follows:
_ 18 h18 ¼ Q_ Cond m _ 19 h19 m
Pump
(7)
(8)
(9)
The principle of mass conservation and the first and second laws of thermodynamics are applied to each component of the singleeffect absorption chiller. Each component is considered as a control volume with inlet and outlet streams, and heat transfer and work interactions are considered. Mass balances are applied for the total mass and each material of the working fluid solution. The
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P. Ahmadi et al. / Energy 46 (2012) 21e31
T
PPHP
4 a
17 23
PPLP
b
APHP
c 5
APLP 21
22
d
20
HP EVP
HP ECO
LP EVP
LP ECO
Point number
Specification
4
Hot gases entering HRSG
a
Hot gases exiting high pressure evaporator (HP EVP)
b
Hot gases exiting high pressure economizer (HP ECO)
c
Hot gases exiting low pressure evaporator
d
Hot gases exiting HRSG
20
Cold water entering HRSG
21
Hot water exiting low pressure economizer (LP ECO)
5
Saturated water exiting low pressure evaporator
22
Hot water entering high pressure economizer (HP ECO)
23
Hot water exiting high pressure economizer (HP ECO)
17
Saturated water exiting high pressure evaporator Fig. 2. Temperature profile of HRSG.
X
X
governing and conservation equations for the total mass and each material of the solution for a steady state and steady flow system are expressed as follows [9]:
_ ¼ Q_ W
X
_ 10 h9 Þ Q_ cooling ¼ mðh
_i ¼ m
X
_o m
X X _ i ¼ _ o mx mx
(10)
_ o ho m
_ i hi m
(12)
The cooling load of the absorption chiller is defined as:
(13)
Further information about the thermodynamic modeling and energy balances for each component is given in [10].
(11)
_ is the working fluid mass flow rate and x is mass where m concentration of LieBr in the solution. For each component of the absorption system, a general energy balance is written:
3.4. Domestic water heater The hot gases from the heat recovery heat exchanger enter the water heater to warm domestic hot water to 60 C. Water enters this heater at a pressure and temperature of 3 bar and 15 C,
P. Ahmadi et al. / Energy 46 (2012) 21e31
respectively. The energy balance for this component is given as follows:
_ w;LP ðh6 h26 Þ ¼ m _ w ðh25 h24 Þ m
(14)
4. Exergy analysis Exergy analysis can help develop strategies and guidelines for more effective use of energy, and recently has been applied to various thermal systems, including power generation, CHP and trigeneration systems. Exergy can be divided into four components: physical chemical, kinetic and potential. In this study, the latter two components are assumed to be negligible as elevation changes and speeds are small [8,11e14]. The physical exergy is defined as the maximum theoretical useful work obtained as a system interacts with an equilibrium state [15]. 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 processes [15,16]. Applying the first and the second laws of thermodynamics, the following exergy balance is obtained:
X
_ Ex Q þ
X
_ i exi ¼ m
_ W þ Ex _ D _ e exe þ Ex m
(15)
e
i
where the subscripts e and i denote outlet inlet, respectively and _ D , is the exergy destruction rate. Other terms in this equation are Ex given as follows:
_ Ex Q ¼
1
To _ Qi Ti
_ W ¼ W; _ Ex ex ¼ exph þ exch _ _ Here, Ex Q and ExW are the exergy of heat transfer and work which cross the boundaries of the control volume, T is the absolute temperature and the subscript o refers to the reference environ_ is defined as follows: ment conditions. In Eq. (15), the term Ex
_ ¼ Ex _ _ Ex ph þ Exch
(16)
_ ¼ mex. _ where Ex The mixture specific chemical exergy is defined as follows [15,17]:
" exch mix
¼
n X i¼1
chi
xi ex
þ RT0
n X
# ½xi Lnðxi Þ
(17)
i¼1
The exergy of each flow in the plant is calculated and exergy destructions are determined for each major component. The source of exergy destruction (or irreversibility) in the combustion chamber is mainly chemical reaction and thermal losses. However, the exergy destruction in the heat exchanger of the system, i.e. condenser and HRSG, is due to the large temperature difference between the hot and cold fluid. The exergy destruction for each component of this polygeneration energy system is shown in Table 1. The exergy efficiency, defined as the product exergy output divided by the exergy input, for the overall polygeneration system can be expressed as follows:
jTri ¼
_ _ _ _ _ W net;GT þ W net;ST þ ExHeating þ ExCooling þ ExHotwater _Ex f
(18)
25
Table 1 Expressions for exergy destruction rate for components of the polygeneration energy system. Component
Exergy destruction rate expressions
Compressor Combustion chamber (CC) Gas turbine (GT) HRSG Steam turbine (ST) Steam condenser Absorption generator Absorption heat exchanger Absorber Expansion valve Condenser Pump Domestic water heater
_ _ _ _ þW Ex 1 AC ¼ Ex2 þ ExD _ þ Ex _ _ _ Ex 2 f ¼ Ex3 þ ExD _ _ _ _ Ex 3 ¼ W GT þ Ex4 þ ExD _ þ Ex _ _ _ _ _ Ex 4 20 ¼ Ex5 þ Ex17 þ Exd þ ExD _ _ _ _ Ex 17 ¼ W ST þ Ex18 þ ExD _ _ _ _ Ex 18 ¼ Ex19 þ ExQ þ ExD _ 5 þ Ex _ _ _ _ _ Ex 13 ¼ Ex6 þ Ex14 þ Ex7 þ ExD _ _ _ _ _ Ex 12 þ Ex14 ¼ Ex13 þ Ex15 þ ExD _ _ _ _ Q _ Ex 10 þ Ex16 ¼ Ex11 þ Ex þ ExD _ _ _ Ex 8 ¼ Ex9 þ ExD _ 7 ¼ Ex _ þ Ex _ _ Ex 8 Q þ ExD _ _ _ _ Ex 11 þ W Pomp ¼ Ex12 þ ExD _ þ Ex _ _ _ _ D Ex ¼ Ex þ Ex þ Ex 6
24
25
26
_ _ where Ex f is the fuel exergy flow rate, ExQ is the exergy rate _ _ associated with heating and cooling, and W net;GT and W net;GT are the net output work rates of the gas turbine (GT) and steam turbine (ST) cycles. 5. Environmental impact assessment An important measure for reducing environmental impact, including emissions of carbon dioxide, a primary greenhouse gas, is increasing the efficiency of energy conversion processes and thereby decreasing fuel use. Although numerous exergy and exergoeconomic analyses have been reported for CHP, trigeneration and polygeneration energy systems, many do not address environmental impact. Rectifying this deficiency is one objective of the present work, in which emissions of CO, CO2 and NOx are considered. The amount of CO and NOx produced in the combustion chamber due to the combustion reaction depends on various combustion characteristics including the adiabatic flame temperature [18]. More details about amount of CO, CO2 and NOx emissions for such technologies are given by Gulder [18]. In this analysis, we express the environmental impact as the total cost rate of pollution damage ($/s) due to CO, NOx and CO2 emissions by multiplying their respective flow rates by their corresponding unit damage costs (CCO, CNOx and CCO2 , which are taken to be equal to 0.02086 $/kg, 6.853 $/kg and 0.024 $/kg, respectively) [8,14]. The cost of pollution damage is assumed here to be added directly to other system costs. To improve environmental sustainability, it is necessary not only to use sustainable energy sources, but also to utilize non-renewable sources like natural gas fuel more efficiently, and to limit environmental damage. In this way, society can reduce its use of limited resources and extend their lifetimes. Here, a sustainability index SI is used to relate exergy with environmental impact [19]:
SI ¼
1 DP
(19)
where DP is the depletion number, defined as the ratio of exergy destruction to input exergy. This relation demonstrates how reducing a system’s environmental impact can be achieved by reducing its exergy destruction. 6. Optimization A multi-objective optimization method based on an evolutionary algorithm is applied optimization to the polygeneration system for heating, cooling, electricity and hot water to determine the best design parameters for the system. Objective functions,
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P. Ahmadi et al. / Energy 46 (2012) 21e31
design parameters and constraints, and overall optimization are described in this section. 6.1. Definition of objectives Two objective functions are considered here for multi-objective optimization: exergy efficiency (to be maximized) and total cost rate of product (to be minimized). The cost of pollution damage is assumed to be added directly to the expenditures that must be paid, making the second objective function the sum of thermodynamic and environmental objectives. Consequently, the objective functions in this analysis can be expressed as follows: Exergy efficiency
jTri ¼
f
(20) Total cost rate
X
Z_ k
(21)
k
where the cost rates of environmental impact and fuel are expressed as:
_ Co þ CNOx m _ NOx & C_ f ¼ cf m _ f LHV C_ env ¼ CCo m
(22)
Here, Z_ K is the purchase cost of each component. The amount of CO and NOx produced in the combustion chamber and the combustion reaction are dependent on the adiabatic flame temperature [3,8]. The pollutant emissions (in grams per kilogram of fuel) can be expressed as follows [8]:
mNOx ¼
71100 TPZ 0:5
0:15 1016 s0:5 exp P30:05
DP3
(23)
P3 7800 TPZ 0:5
0:179 109 exp mCO ¼ P32 s
The following decision variables (design parameters) are selected for this study: compressor pressure ratio (RAC), compressor isentropic efficiency (hAC), gas turbine isentropic efficiency (hGT), gas turbine inlet temperature (GTIT), high pressure pinch point temperature (PPHP) difference, low pressure pinch point temperature (PPLP) difference, high pressure (PHP), low pressure (PLP), steam turbine isentropic efficiency (hST), pump isentropic efficiency (hp), and evaporator temperature (TEVP). Although the decision variables may be varied in the optimization procedure, each is normally required to be within a reasonable range. Such constraints, based on earlier reports [17,20], are listed in Table 2. 6.3. Evolutionary algorithm: genetic algorithm
_ _ _ _ _ W net;GT þ W net;ST þ ExHeating þ ExCooling þ ExHot water _Ex
C_ tot ¼ C_ f þ C_ env þ
6.2. Decision variables
DP3
(24)
P3
where s is the residence time in the combustion zone (assumed constant here at 0.002 s [8]), Tpz is the primary zone combustion temperature, P3 is the combustor inlet pressure, and DP3 =P3 is the non-dimensional pressure drop in the combustion chamber. In this analysis, we express the environmental impact as the total cost rate of pollution damage ($/s) due to CO, NOx and CO2 emissions by multiplying their respective flow rates by their corresponding unit damage costs (CCO, CNOx and CCO2 , which are taken to be equal to 0.02086 $/kg and 6.853 $/kg and 0.024 $/kg, respectively) [8]. The cost of pollution damage is assumed here to be added directly to other system costs. To improve environmental sustainability, it is necessary not only to use sustainable or renewable sources of energy, but also to utilize non-renewable sources like natural fuel more efficiently, while minimizing environmental damage. In this way, society can reduce its use of limited resources and extend their lifetimes.
Genetic algorithms apply an iterative, stochastic search strategy to find an optimal solution and imitate in a simplified manner principles of biological evolution [21]. A characteristic of an evolutionary algorithm is a population of individuals, where an individual consists of the values of the decision variables (structural and process variables here) and is a potential solution to the optimization problem [21]. More details about genetic algorithm and its procedure are given elsewhere [8,21,22]. 7. Results and discussion The results of the optimization are given and described. Fig. 2 shows the Pareto frontier solution for this polygeneration system with objective functions indicated in Eqs. (20) and (21) in multiobjective optimization. It can be seen in this figure that the total cost rate of products increases moderately as the total exergy efficiency of the cycle increases to about 56%. Increasing the total exergy efficiency from 56% to 58% increases the cost rate of product significantly. It is shown in Fig. 2 that the maximum exergy efficiency exists at design point A (57.64%), while the total cost rate of products is the greatest at this point (1394 $/h). On the other hand, the minimum value for the total cost rate of product occurs at design point E which is about 1365.7 $/h. Design point A is the optimal situation when efficiency is the sole objective function, while design point E is the optimum point when total cost rate of product is the sole objective function. In multi-objective optimization a process of decision-making for selection of the final optimal solution from the available solutions is required. The process of decision-making is usually performed with the aid of a hypothetical point in Fig. 2 (the equilibrium point), at which both objectives have their optimal values independent of the other objectives. It is clear that it is impossible to have both objectives at their optimum point simultaneously and, as shown in Fig. 2,
Table 2 Optimization constraints and their rationales. Constraint
Reason
GTIT < 1550 K P2/P1 < 22 hAC < 0.9 hGT < 0.9 PHP < 40 bar PLP < 5.5 bar 10 C < PPHP <22 C 12 C < PPLP < 22 C hST < 0.9 hp < 0.9 2 C
Material temperature limit Commercial availability Commercial availability Commercial availability Commercial availability Commercial availability Heat transfer limit Heat transfer limit Commercial availability Commercial availability Cooling load limitation
P. Ahmadi et al. / Energy 46 (2012) 21e31
27
Table 3 Optimized values for design parameters of the system based on multi-objective optimization. Design A parameter
hAC hGT RAC GTIT (K) PLP (bar) PHP (bar) PPHP ( C) PPLP ( C) TEVP ( C)
hFWP hST
B
C
D
E
0.88 0.88 0.88 0.88 0.88 0.9 0.9 0.9 0.9 0.9 19.977 19.999 19.996 19.999 20 1499.6 1499.5 1499.7 1499.7 1499.8 5.6796 5.6405 2.0293 2.043 2.9621 39.949 39.955 39.924 24.719 15.021 8.096 16.233 19.939 19.941 19.897 24.778 24.65 24.981 24.83 24.971 4.1983 4.293 4.3565 5.9145 7.3016 0.77333 0.78133 0.738 0.79267 0.858 0.88945 0.87902 0.76592 0.75 0.75769
the equilibrium point is not a solution located on the Pareto Frontier. The closest point of the Pareto frontier to the equilibrium point might be considered as a desirable final solution. Nevertheless, in this case, the Pareto optimum frontier exhibits weak equilibrium i.e., a small change in exergy efficiency from varying the operating parameters causes a large variation in the total cost rate of product. Therefore, the equilibrium point cannot be utilized for decisionmaking in this problem. In selection of the final optimum point, it is desired to achieve a better magnitude for each objective than its initial value for the base case problem. Because of this the optimized points in the CeE region have the maximum exergy efficiency increment of about 1% and minimum total cost rate increment of about 20 $/h relative to the design point, C. Therefore, design point C can be a good candidate for the multi-objective optimization. Note that in multi-objective optimization and the Pareto solution, each point can be utilized as the optimized point. Therefore, the selection of the optimum solution depends on the preferences and criteria of the decision maker, suggesting that each may select a different point as for the optimum solution depending on his/her needs. Table 3 shows all the design parameters for points AeE. To see the variation of thermodynamic characteristics, three different points (A, C and E) on the Pareto frontier are considered. Table 4 shows the total cost rate of the system, the total exergy destruction, the system efficiency and the sustainability index. From point A to point E in this table both total cost rate of the system and exergy efficiency decrease. As stated above, point A is preferred when exergy efficiency is a single objective function and design point E when total cost rate is a single objective function. Design point C has better results for both objectives. Other thermodynamic properties correctly confirm this trend. For instance, from point A to E, the total exergy destruction increases when the exergy efficiency decreases. To provide further insights, we consider environmental characteristics of the system, namely sustainability index (SI) and CO2 emissions. A decrease in exergy efficiency leads to an increase in CO2 emissions. On the other hand, an increase in the CO2 emissions causes the sustainability index to decrease. This demonstrates the close relationship between exergy efficiency, CO2 emissions and the sustainability index. To better understand the variations of all design parameters, the scattered distribution of the design parameters are shown in
Fig. 3. Pareto Frontier: Best trade off values for the objective functions.
Fig. 4. Scatter distribution of compressor isentropic efficiency with population in Pareto frontier.
Table 4 Thermodynamic characteristics of three different points on the Pareto frontier. $ h
Point
_ tot ðMWÞ Ex
C_ tot
A C E
35.4 37.3 38.4
1393.4 1375.5 1365.8
J
Zk ð$Þ
SI
CO2 (kg/MWh)
57.58 56.28 52.8
8:7 106 7:92 106 7:47 106
2.19 2.09 2.01
130.14 134.97 143.75
Fig. 5. Scatter distribution of gas turbine isentropic efficiency with population in Pareto frontier.
28
P. Ahmadi et al. / Energy 46 (2012) 21e31
Fig. 6. Scatter distribution of GTIT with population in Pareto frontier.
Fig. 9. Scatter distribution high pressure with population in Pareto frontier.
Fig. 7. Scatter distribution of compressor pressure ratio with population in Pareto frontier.
Fig. 8. Scatter distribution of low pressure with population in Pareto frontier.
Fig. 10. Scatter distribution of low pressure pinch point with population in Pareto frontier.
Fig. 11. Scatter distribution of high pressure pinch point with population in Pareto frontier.
P. Ahmadi et al. / Energy 46 (2012) 21e31
29
Fig. 12. Scatter distribution of steam turbine isentropic efficiency with population in Pareto frontier.
Figs. 3e13. The results show that gas turbine inlet temperature, compressor pressure ratio and gas turbine isentropic efficiency tend to become as high as possible. This observation means that an increase in these parameters leads to the better optimization results. Due to physical limitations, however, it is not allowed to extend this region. The reason for the compressor pressure ratio is that an increase in this parameter increases the outlet temperature and decreases the mass flow rate injected to the combustion chamber. As the first term in the total cost rate (Eq.(24)) is directly associated with the mass flow rate of the fuel, any decrease in this term results in a decrease in the objective function. This is why in the scattered distribution for the compressor pressure ratio achieves a maximum value in its range. Similar results are seen for the gas turbine isentropic efficiency. In addition, the maximum value for the gas turbine inlet temperature (GTIT) is selected based on the evolutionary algorithm. The higher the GTIT, the higher the achieved exergy efficiency will be, since one of the objective functions is supposed to be maximized. It can be concluded that compressor pressure ratio and gas turbine inlet temperature have positive effects on both objective functions since they attain high values. To see this trend, the effect of change in compressor pressure ratio for point AeE on the Prato frontier on both objective functions is shown in Fig. 14. Fig. 15 shows that an increase in compressor pressure ratio leads to increase in system exergy efficiency and consequently results in a decrease in the total cost of the system. The main reason for the reduction of the total cost of the plant is the reduction of the mass flow rate injected to the combustion chamber. An increase in pressure ratio leads to an increase in compressor outlet temperature. The higher is the outlet temperature, the lower is the mass
Fig. 13. Scatter distribution of feed water pump isentropic efficiency with population in Pareto frontier.
Fig. 14. Scatter distribution of evaporator temperature with population in Pareto frontier.
Fig. 15. Effect of compressor pressure ratio on both objective functions.
Fig. 16. Effect of gas turbine inlet temperature on both objective functions.
30
P. Ahmadi et al. / Energy 46 (2012) 21e31
ex _ Ex _ D Ex h _ m P Q_ R s T _ W
Fig. 17. Fitted curve on the optimal values in the Pareto frontier.
flow rate required. A reduction in mass flow rate results in a decrease in the first and second terms of Eq. (21). Fig. 16 shows the variation of GTIT on both objective functions. As it is shown in this figure, an increase in GTIT has positive effect on both objective functions. This is why in Fig. 5; points tend to be as much as possible. Other design parameters exhibit reasonable distributions in Figs. 4e14. Thus, it can also be determined that these parameters are selected effectively, since they do not all reach maximum or minimum values. As shown in Fig. 1, the optimized values for exergy efficiency on the Pareto frontier range between 53% and 58%. To provide a good relation between exergy efficiency and total cost rate, a curve is fitted on the optimized points obtained from the evolutionary algorithm. This fitted curve is shown in Fig. 17. The expression for this fitted curve is given as follows:
17:42j5 23:75j4 19:24j3 þ5:2j2 þ37:6j 15:94 C_ total ¼ j5 3:5j4 þ4:65j3 3:01j2 þ0:97j 0:12 (25) 8. Conclusions The comprehensive thermodynamic modeling and multiobjective optimization of a polygeneration energy system provide useful information. A calculus-based optimization approach using evolutionary algorithms (i.e. genetic algorithms) allows multiobjective optimization of the polygeneration plant. Environmental impacts are quantified conveniently as pollution-related costs in the economic objective function, transforming the environmental objective to a cost function. Merging the new environmental cost function with the thermoeconomic objective yields a useful thermoenvironomic function. Fitting a curve on the optimized points provides a closed form equation. The results suggest that gas turbine inlet temperature, compressor pressure ratio and gas turbine isentropic efficiency tend to maximum values, and that an increase in these parameters results in better system performance. Acknowledgment The authors acknowledge the support provided by the Natural Sciences and Engineering Research Council of Canada. Nomenclature Cp C
Specific heat at constant pressure (kJ/kg K) Cost ($)
Specific exergy (kJ/kg) Exergy flow rate (kW) Exergy destruction rate (kW) Specific enthalpy (kJ/kg) Mass flow rate (kg/s) Pressure (bar) Heat rate (kW) Gas constant (kJ/kg K) Specific entropy (kJ/kg K) Temperature (K) Work rate (kW)
Greek letters Specific heat ratio Air compressor isentropic efficiency Gas turbine isentropic efficiency Steam turbine isentropic efficiency Pump isentropic efficiency Exergy efficiency
g hAC hGT hST hPump J
Subscripts a Air AC Air compressor act Actual CC Combustion chamber Cooling Cooling load D Destruction Depletion number DP e Exit condition EVP Evaporator ex Exergy f Fuel FWP Feed water pump g Combustion gases h Hour GT Gas turbine GTIT Gas turbine inlet temperature Heating Heating load HP High pressure HRSG Heat recovery steam generator i Inlet condition is Isentropic LP Lower pressure mix Mixture net Net output power PP Pinch point R Compressor pressure ratio ST Steam turbine tot Total Superscripts . rate Ch Chemical References [1] Rosen MA, Dincer I. A study of industrial steam process heating through exergy analysis, International Journal of Energy Research 2004;28(10): 917e30. [2] Tom K. Combined heating and power and emissions trading: options for policy makers. International Energy Agency; 2008. [3] Ahmadi P, Dincer I, Rosen MA. Exergoenvironmental analysis of a trigeneration system based on micro gas turbine and organic Rankine cycles. In: Proceedings of the global conference on global warming 2011, Lisbon, Portugal; 11e14 July 2011.
P. Ahmadi et al. / Energy 46 (2012) 21e31 [4] Khaliq A, Kumar R, Dincer I. Performance analysis of an industrial waste heatbased trigeneration system. International Journal of Energy Research 2009;33: 737e44. [5] Minciuc E, Corre O, Athanasovici V, Tazerout M, Biti I. Thermodynamic analysis of trigeneration with absorption chilling machine. Applied Thermal Engineering 2003;23:1391e405. [6] Al-Sulaiman F, Dincer I, Hamdullahpur F. Exergy analysis of an integrated solid oxide fuel cell and organic Rankine cycle for cooling, heating and power production. Journal of Power Sources 2010;195(8):2346e54. [7] Sahoo PK. Exergoeconomic analysis and optimization of a cogeneration system using evolutionary programming. Applied Thermal Engineering 2008; 28(13):1580e8. [8] Ahmadi P, Dincer I. Exergo-environmental analysis and optimization of a cogeneration plant system using Multimodal Genetic Algorithm (MGA). Energy 2010;35:5161e72. [9] Dincer I, Dost S. Exergy analysis of ammoniaewater absorption refrigeration system. Energy Sources 1996;18(6):727e33. [10] Florides GA, Kalogirou SA, Tassou SA, Wrobel LC. Design and construction of a LiBrewater absorption machine. Energy Conversion and Management 2003; 44:2483e508. [11] Dincer I, Rosen MA. Exergy: Energy, Environment and Sustainable Development. Elsevier; 2007. [12] Ahmadi P, Rosen MA, Dincer I. Greenhouse gas emission and exergoenvironmental analyses of a trigeneration energy system. International Journal of Green House Gas Control 2011;5:1540e9.
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[13] Ameri M, Ahmadi P, Hamidi A. Energy, exergy and exergoeconomic analysis of a steam power plant: a case study. International Journal of Energy Research 2009;33:499e512. [14] Barzegar H, Ahmadi P, Ghaffarizadeh AR, Saidi MH. Thermo-economicenvironmental multi-objective optimization of a gas turbine power plant with preheater using evolutionary algorithm. International Journal of Energy Research 2011;35(5):389e403. [15] Kotas TJ. The exergy method of thermal plant analysis. London: Butterworths; 1985. [16] Rosen MA, Dincer I, Kanoglu M. Role of exergy in increasing efficiency and sustainability and reducing environmental impact. Energy Policy 2008;36(1): 128e37. [17] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New York: Wiley; 1996. [18] Gulder OL. Flame temperature estimation of conventional and future jet fuels. ASME Journal of Engineering for Gas Turbine and Power 1986;108(2):376e80. [19] Dincer I, Naterer GF. Assessment of exergy efficiency and sustainability index of an air water heat pump. International Journal of Exergy 2010;7(1):37e50. [20] Roosen P, Uhlenbruck S, Lucas K. Pareto optimization of a combined cycle power system as a decision support tool for trading off investment vs. operating costs. International Journal of Thermal Sciences 2003;42:553e60. [21] Srinivas V, Deb K. Multiobjective optimization using no dominated sorting in genetic algorithms. Journal of Evolutionary Computation 1994;2(3):221e48. [22] Ghaffarizadeh A. Investigation on evolutionary algorithms emphasizing mass extinction. B.Sc thesis, Shiraz University of Technology, Shiraz, Iran; 2006.
Contents lists available at SciVerse ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Multi-objective exergy-based optimization of a polygeneration energy system using an evolutionary algorithm Pouria Ahmadi*, Marc A. Rosen, Ibrahim Dincer Faculty of Engineering and Applied Science, University of Ontario Institute of Technology (UOIT), 2000 Simcoe St. North, Oshawa, ON L1H 7K4, Canada
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 September 2011 Received in revised form 17 November 2011 Accepted 1 February 2012 Available online 13 March 2012
A comprehensive thermodynamic modeling and optimization is reported of a polygeneration energy system for the simultaneous production of heating, cooling, electricity and hot water from a common energy source. This polygeneration system is composed of four major parts: gas turbine (GT) cycle, Rankine cycle, absorption cooling cycle and domestic hot water heater. A multi-objective optimization method based on an evolutionary algorithm is applied to determine the best design parameters for the system. The two objective functions utilized in the analysis are the total cost rate of the system, which is the cost associated with fuel, component purchasing and environmental impact, and the system exergy efficiency. The total cost rate of the system is minimized while the cycle exergy efficiency is maximized by using an evolutionary algorithm. To provide a deeper insight, the Pareto frontier is shown for multiobjective optimization. In addition, a closed form equation for the relationship between exergy efficiency and total cost rate is derived. Finally, a sensitivity analysis is performed to assess the effects of several design parameters on the system total exergy destruction rate, CO2 emission and exergy efficiency. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Efficiency Exergy Polygeneration Energy Multi-objective optimization
1. Introduction The usage of energy is important in many applications, including heating and cooling, power generation, desalination, and air conditioning. Efforts are underway to make energy use more sustainable, economic factors, efficient, clean and secure. Energy utilization is governed by thermodynamic principles and an understanding of exergetic aspects can help identify and understand sustainable energy options [1]. The efficiency of power generation can be improved through the use of combined cycle plants. Also, combined heat and power (CHP) systems permit power generation and heating and are attractive in power markets because of their high efficiency, low emissions, low initial investment, operation and maintenance costs as well as high flexibility [2]. Recently, applications of trigeneration and polygeneration energy systems have increased. Polygeneration systems have higher efficiencies and lower environmental impacts than CHP systems [3]. Trigeneration is the simultaneous production of heating, cooling and electricity from a common energy source. Trigeneration often utilizes the waste heat of a power plant to improve overall thermal performance, essentially utilizing the
* Corresponding author. E-mail addresses: [email protected], [email protected] (P. Ahmadi), [email protected] (M.A. Rosen), [email protected] (I. Dincer). 0360-5442/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2012.02.005
“free” energy available via the waste energy. In trigeneration and polygeneration systems, waste heat from the plant’s prime mover (e.g., gas turbine (GT) or diesel engine or organic Rankine cycle), sometimes with temperature enhancement, drives heating and cooling devices [3]. A common type of polygeneration system involves the simultaneous production of electricity, heating, cooling and hot water from a common energy source. Much research on multi-generation systems has been conducted in recent years. Khaliq et al. [4] carried out an exergy analysis of a combined electrical power and refrigeration cycle, as well as a parametric study on the effects of exhaust gas inlet temperature, pinch-point and gas composition on energy and exergy efficiencies, electricity-to-cold ratio and exergy destruction for the cogeneration system and its components. Minciuc et al. [5] presented a method for analyzing trigeneration systems and established limits for the best performance of gas turbine trigeneration with absorption chilling from a thermodynamic point of view. Recently, combinations of exergy, economic and environmental assessment have received increasing attention around the world, motivated in part by global warming challenges. Ahmadi et al. [3] carried out an exergoenvironmental analysis of a trigeneration system based on a micro gas turbine and an organic Rankine cycle (ORC), and performed a parametric study involving the main design parameters of the trigeneration system. Al-Sulaiman et al. [6] performed an energy analysis of a trigeneration plant based on a solid oxide fuel cell (SOFC), and showed
22
P. Ahmadi et al. / Energy 46 (2012) 21e31
that there is at least a 22% gain in efficiency using the trigeneration plant compared to a power cycle (SOFC and ORC). The study also showed that the maximum efficiency of the trigeneration plant is 74%, of heating cogeneration is 71%, of cooling cogeneration is 57% and of net electricity generation is 46%. These results show the importance of exergy and environmental impact analyses of such systems. Although exergy and environmental impact analysis are important for trigeneration and polygeneration energy systems they cannot provide the best system configuration. Rather, applying optimization techniques based on exergy, economics and environmental impact is useful for this task. Some studies have been reported of the exergoeconomic optimization for CHP systems. Sahoo [7] carried out an exergoeconomic analysis and optimization of a cogeneration system using evolutionary programming. He considered a cogeneration system which produces 50 MW of electricity and 15 kg/s of saturated steam at 2.5 bar, and optimized the CHP unit using exergoeconomic principles and evolutionary programming. The results showed that, for the optimum case in the exergoeconomic analysis, the cost of produced electricity is 9.9% lower than for the base case. Therefore, exergy, economic and environmental optimization can provide insights for polygeneration systems. Nonetheless, such analyses have not to date been reported, especially based on multi-objective evolutionary algorithm. The primary objective of this research is to perform thermodynamic modeling, exergy and environmental analyses as well as optimization of a polygeneration energy system for electricity, cooling, heating and hot water, based on a gas turbine prime mover. The specific objectives are as follows: To model a polygeneration energy system based on a micro gas turbine prime mover, a heat recovery steam generator (HRSG), a steam turbine (ST), a single-effect absorption chiller and a domestic water heater for heating, cooling, hot water production and electricity generation. To apply a multi-objective optimization technique based on a code developed in the Matlab software program using an evolutionary algorithm. To propose a new closed-form expression for the exergy efficiency in terms of total cost rate at the optimal design point. To derive an equation for the Pareto optimal points curve to provide an aid for the optimal design of the polygeneration plant. To perform sensitivity analyses of the variation of each objective function with major design parameters of the system. To determine the environmental impacts for three different cycles, ranging from power generation to multi-product generation (including hot water).
2. System description For the polygeneration system considered here (Fig. 1), thermodynamic modeling and analysis is performed. In the energy analysis, the temperature profile in the polygeneration plant and input and output enthalpy values are determined. In the exergy analysis, exergy values of each flow in the plant, exergy destructions and exergy efficiencies are assessed, while environmental impacts are evaluated in the environmental analysis. These results are used subsequently in the optimization study. To perform the thermodynamic modeling of the polygeneration system, several simplifying assumptions are made to render the analysis more tractable, while retaining adequate accuracy to illustrate the principal points of the article: All the processes are considered to be operating at steady state. Air and combustion products are taken to be ideal-gas mixtures.
The fuel injected to the combustion chamber (CC) is assumed to be natural gas. Heat loss from the combustion chamber is taken to be 2% of the fuel lower heating value, and all other components are considered adiabatic. A dual-pressure heat recovery steam generator with high pressure (HP) and low pressure (LP) steam is considered. Both HP and LP pinch temperatures are considered constant at 10 C. The dead state is P0 ¼ 1.01 bar and T0 ¼ 293.15 K.
3. Energy analysis Relevant energy balances and governing equations for the main sections of the polygeneration plant shown in Fig. 1 are described, broken down into the following subsections: topping cycle (Brayton cycle), bottoming cycle (steam turbine and heat recovery steam generator), the single-effect absorption chiller and domestic water heater. 3.1. Toping cycle (Brayton cycle) We model a gas turbine cycle using the first law of thermodynamics. As seen in Fig. 1, air at ambient conditions enters the air compressor at point 1 and, after compression (point 2), is supplied to the combustion chamber (CC). Fuel is injected in the combustion chamber and hot combustion gases exit (point 3) and pass a gas turbine to produce power. The hot gas expands in the gas turbine to point 4. This flue gas is utilized in the dual-pressure heat recovery steam generator (HRSG) to generate lowpressure (LP) and highpressure (HP) steam. Energy balances and governing equations for the gas turbine cycle are given elsewhere [8]. 3.2. Bottoming cycle Energy balances and governing equations for the components of the bottoming cycle (steam turbine cycle and HRSG) are provided here. Dual pressure HRSG A dual-pressure HRSG with two economizers (LP and HP) and two evaporators (LP and HP) is used in the polygeneration cycle to provide both low- and high pressure steam. The LP steam is used to drive the absorption chiller and the HP steam to generate electricity. The temperature profile in the HRSG is shown in Fig. 2, where the pinch-point is defined as the difference between the temperature of the gas at the entrance of the evaporator (economizer side) and the saturation temperature. The dual-pressure HRSG has two pinch points (PPHP and PPLP). The temperature differences between the water leaving the economizers (T20 and T22) and the saturation temperature (T5 and T17) are the approach points (APHP and APLP), which depend on the economizer’s tube layout. Note that the pinch point and approach temperatures are considered constant here. Energy balances for each element of the HRSG are expressed as follows:
_ w;HP ðh17 h23 Þ ¼ m _ g CPg ðT4 Ta Þ m
(1)
_ w ðh23 h22 Þ ¼ m _ g CPg ðTa Tb Þ m
(2)
_ g CPg ðTb Tc Þ _ w;LP ðh5 h21 Þ ¼ m m
(3)
P. Ahmadi et al. / Energy 46 (2012) 21e31
23
Fuel
Combustion Chamber
3
2 Air Compress or
Gas Turbine Net Power
1
4
25
24
HP Steam
Domestic Water heater
17
HP EVP a
23
Steam Turbine
HRSG
HP ECO 26
Power
b
22
18
Heating
LP EVP
Condenser
c
21
LP Steam
LP ECO
5 6
19
20 d
7
Condenser
Generator
14
13
8
Expansion Valve
Heat Exchanger 12
9
15
Pump 11
mCond
Throttling Valve
16
Absorber
10
mEVP
Evaporator
QCooling Fig. 1. Schematic of the polygeneration system for heating, cooling, hot water and electricity generation.
_ w ðh21 h20 Þ ¼ m _ g CPg ðTc Td Þ m
(4)
An energy balance for pump and an isentropic efficiency can be expressed as follows:
Steam turbine An energy balance for the steam turbine in Fig. 1 and an isentropic efficiency are written as follows:
_ _ w h17 ¼ W _ w h18 m ST m _ W
hST ¼ _ ST;act W ST;is
_ _ w h19 þ W _ w h20 m Pomp ¼ m
his hact
(5)
hPump ¼
(6)
3.3. Absorption chiller
Condenser An energy balance for the condenser follows:
_ 18 h18 ¼ Q_ Cond m _ 19 h19 m
Pump
(7)
(8)
(9)
The principle of mass conservation and the first and second laws of thermodynamics are applied to each component of the singleeffect absorption chiller. Each component is considered as a control volume with inlet and outlet streams, and heat transfer and work interactions are considered. Mass balances are applied for the total mass and each material of the working fluid solution. The
24
P. Ahmadi et al. / Energy 46 (2012) 21e31
T
PPHP
4 a
17 23
PPLP
b
APHP
c 5
APLP 21
22
d
20
HP EVP
HP ECO
LP EVP
LP ECO
Point number
Specification
4
Hot gases entering HRSG
a
Hot gases exiting high pressure evaporator (HP EVP)
b
Hot gases exiting high pressure economizer (HP ECO)
c
Hot gases exiting low pressure evaporator
d
Hot gases exiting HRSG
20
Cold water entering HRSG
21
Hot water exiting low pressure economizer (LP ECO)
5
Saturated water exiting low pressure evaporator
22
Hot water entering high pressure economizer (HP ECO)
23
Hot water exiting high pressure economizer (HP ECO)
17
Saturated water exiting high pressure evaporator Fig. 2. Temperature profile of HRSG.
X
X
governing and conservation equations for the total mass and each material of the solution for a steady state and steady flow system are expressed as follows [9]:
_ ¼ Q_ W
X
_ 10 h9 Þ Q_ cooling ¼ mðh
_i ¼ m
X
_o m
X X _ i ¼ _ o mx mx
(10)
_ o ho m
_ i hi m
(12)
The cooling load of the absorption chiller is defined as:
(13)
Further information about the thermodynamic modeling and energy balances for each component is given in [10].
(11)
_ is the working fluid mass flow rate and x is mass where m concentration of LieBr in the solution. For each component of the absorption system, a general energy balance is written:
3.4. Domestic water heater The hot gases from the heat recovery heat exchanger enter the water heater to warm domestic hot water to 60 C. Water enters this heater at a pressure and temperature of 3 bar and 15 C,
P. Ahmadi et al. / Energy 46 (2012) 21e31
respectively. The energy balance for this component is given as follows:
_ w;LP ðh6 h26 Þ ¼ m _ w ðh25 h24 Þ m
(14)
4. Exergy analysis Exergy analysis can help develop strategies and guidelines for more effective use of energy, and recently has been applied to various thermal systems, including power generation, CHP and trigeneration systems. Exergy can be divided into four components: physical chemical, kinetic and potential. In this study, the latter two components are assumed to be negligible as elevation changes and speeds are small [8,11e14]. The physical exergy is defined as the maximum theoretical useful work obtained as a system interacts with an equilibrium state [15]. 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 processes [15,16]. Applying the first and the second laws of thermodynamics, the following exergy balance is obtained:
X
_ Ex Q þ
X
_ i exi ¼ m
_ W þ Ex _ D _ e exe þ Ex m
(15)
e
i
where the subscripts e and i denote outlet inlet, respectively and _ D , is the exergy destruction rate. Other terms in this equation are Ex given as follows:
_ Ex Q ¼
1
To _ Qi Ti
_ W ¼ W; _ Ex ex ¼ exph þ exch _ _ Here, Ex Q and ExW are the exergy of heat transfer and work which cross the boundaries of the control volume, T is the absolute temperature and the subscript o refers to the reference environ_ is defined as follows: ment conditions. In Eq. (15), the term Ex
_ ¼ Ex _ _ Ex ph þ Exch
(16)
_ ¼ mex. _ where Ex The mixture specific chemical exergy is defined as follows [15,17]:
" exch mix
¼
n X i¼1
chi
xi ex
þ RT0
n X
# ½xi Lnðxi Þ
(17)
i¼1
The exergy of each flow in the plant is calculated and exergy destructions are determined for each major component. The source of exergy destruction (or irreversibility) in the combustion chamber is mainly chemical reaction and thermal losses. However, the exergy destruction in the heat exchanger of the system, i.e. condenser and HRSG, is due to the large temperature difference between the hot and cold fluid. The exergy destruction for each component of this polygeneration energy system is shown in Table 1. The exergy efficiency, defined as the product exergy output divided by the exergy input, for the overall polygeneration system can be expressed as follows:
jTri ¼
_ _ _ _ _ W net;GT þ W net;ST þ ExHeating þ ExCooling þ ExHotwater _Ex f
(18)
25
Table 1 Expressions for exergy destruction rate for components of the polygeneration energy system. Component
Exergy destruction rate expressions
Compressor Combustion chamber (CC) Gas turbine (GT) HRSG Steam turbine (ST) Steam condenser Absorption generator Absorption heat exchanger Absorber Expansion valve Condenser Pump Domestic water heater
_ _ _ _ þW Ex 1 AC ¼ Ex2 þ ExD _ þ Ex _ _ _ Ex 2 f ¼ Ex3 þ ExD _ _ _ _ Ex 3 ¼ W GT þ Ex4 þ ExD _ þ Ex _ _ _ _ _ Ex 4 20 ¼ Ex5 þ Ex17 þ Exd þ ExD _ _ _ _ Ex 17 ¼ W ST þ Ex18 þ ExD _ _ _ _ Ex 18 ¼ Ex19 þ ExQ þ ExD _ 5 þ Ex _ _ _ _ _ Ex 13 ¼ Ex6 þ Ex14 þ Ex7 þ ExD _ _ _ _ _ Ex 12 þ Ex14 ¼ Ex13 þ Ex15 þ ExD _ _ _ _ Q _ Ex 10 þ Ex16 ¼ Ex11 þ Ex þ ExD _ _ _ Ex 8 ¼ Ex9 þ ExD _ 7 ¼ Ex _ þ Ex _ _ Ex 8 Q þ ExD _ _ _ _ Ex 11 þ W Pomp ¼ Ex12 þ ExD _ þ Ex _ _ _ _ D Ex ¼ Ex þ Ex þ Ex 6
24
25
26
_ _ where Ex f is the fuel exergy flow rate, ExQ is the exergy rate _ _ associated with heating and cooling, and W net;GT and W net;GT are the net output work rates of the gas turbine (GT) and steam turbine (ST) cycles. 5. Environmental impact assessment An important measure for reducing environmental impact, including emissions of carbon dioxide, a primary greenhouse gas, is increasing the efficiency of energy conversion processes and thereby decreasing fuel use. Although numerous exergy and exergoeconomic analyses have been reported for CHP, trigeneration and polygeneration energy systems, many do not address environmental impact. Rectifying this deficiency is one objective of the present work, in which emissions of CO, CO2 and NOx are considered. The amount of CO and NOx produced in the combustion chamber due to the combustion reaction depends on various combustion characteristics including the adiabatic flame temperature [18]. More details about amount of CO, CO2 and NOx emissions for such technologies are given by Gulder [18]. In this analysis, we express the environmental impact as the total cost rate of pollution damage ($/s) due to CO, NOx and CO2 emissions by multiplying their respective flow rates by their corresponding unit damage costs (CCO, CNOx and CCO2 , which are taken to be equal to 0.02086 $/kg, 6.853 $/kg and 0.024 $/kg, respectively) [8,14]. The cost of pollution damage is assumed here to be added directly to other system costs. To improve environmental sustainability, it is necessary not only to use sustainable energy sources, but also to utilize non-renewable sources like natural gas fuel more efficiently, and to limit environmental damage. In this way, society can reduce its use of limited resources and extend their lifetimes. Here, a sustainability index SI is used to relate exergy with environmental impact [19]:
SI ¼
1 DP
(19)
where DP is the depletion number, defined as the ratio of exergy destruction to input exergy. This relation demonstrates how reducing a system’s environmental impact can be achieved by reducing its exergy destruction. 6. Optimization A multi-objective optimization method based on an evolutionary algorithm is applied optimization to the polygeneration system for heating, cooling, electricity and hot water to determine the best design parameters for the system. Objective functions,
26
P. Ahmadi et al. / Energy 46 (2012) 21e31
design parameters and constraints, and overall optimization are described in this section. 6.1. Definition of objectives Two objective functions are considered here for multi-objective optimization: exergy efficiency (to be maximized) and total cost rate of product (to be minimized). The cost of pollution damage is assumed to be added directly to the expenditures that must be paid, making the second objective function the sum of thermodynamic and environmental objectives. Consequently, the objective functions in this analysis can be expressed as follows: Exergy efficiency
jTri ¼
f
(20) Total cost rate
X
Z_ k
(21)
k
where the cost rates of environmental impact and fuel are expressed as:
_ Co þ CNOx m _ NOx & C_ f ¼ cf m _ f LHV C_ env ¼ CCo m
(22)
Here, Z_ K is the purchase cost of each component. The amount of CO and NOx produced in the combustion chamber and the combustion reaction are dependent on the adiabatic flame temperature [3,8]. The pollutant emissions (in grams per kilogram of fuel) can be expressed as follows [8]:
mNOx ¼
71100 TPZ 0:5
0:15 1016 s0:5 exp P30:05
DP3
(23)
P3 7800 TPZ 0:5
0:179 109 exp mCO ¼ P32 s
The following decision variables (design parameters) are selected for this study: compressor pressure ratio (RAC), compressor isentropic efficiency (hAC), gas turbine isentropic efficiency (hGT), gas turbine inlet temperature (GTIT), high pressure pinch point temperature (PPHP) difference, low pressure pinch point temperature (PPLP) difference, high pressure (PHP), low pressure (PLP), steam turbine isentropic efficiency (hST), pump isentropic efficiency (hp), and evaporator temperature (TEVP). Although the decision variables may be varied in the optimization procedure, each is normally required to be within a reasonable range. Such constraints, based on earlier reports [17,20], are listed in Table 2. 6.3. Evolutionary algorithm: genetic algorithm
_ _ _ _ _ W net;GT þ W net;ST þ ExHeating þ ExCooling þ ExHot water _Ex
C_ tot ¼ C_ f þ C_ env þ
6.2. Decision variables
DP3
(24)
P3
where s is the residence time in the combustion zone (assumed constant here at 0.002 s [8]), Tpz is the primary zone combustion temperature, P3 is the combustor inlet pressure, and DP3 =P3 is the non-dimensional pressure drop in the combustion chamber. In this analysis, we express the environmental impact as the total cost rate of pollution damage ($/s) due to CO, NOx and CO2 emissions by multiplying their respective flow rates by their corresponding unit damage costs (CCO, CNOx and CCO2 , which are taken to be equal to 0.02086 $/kg and 6.853 $/kg and 0.024 $/kg, respectively) [8]. The cost of pollution damage is assumed here to be added directly to other system costs. To improve environmental sustainability, it is necessary not only to use sustainable or renewable sources of energy, but also to utilize non-renewable sources like natural fuel more efficiently, while minimizing environmental damage. In this way, society can reduce its use of limited resources and extend their lifetimes.
Genetic algorithms apply an iterative, stochastic search strategy to find an optimal solution and imitate in a simplified manner principles of biological evolution [21]. A characteristic of an evolutionary algorithm is a population of individuals, where an individual consists of the values of the decision variables (structural and process variables here) and is a potential solution to the optimization problem [21]. More details about genetic algorithm and its procedure are given elsewhere [8,21,22]. 7. Results and discussion The results of the optimization are given and described. Fig. 2 shows the Pareto frontier solution for this polygeneration system with objective functions indicated in Eqs. (20) and (21) in multiobjective optimization. It can be seen in this figure that the total cost rate of products increases moderately as the total exergy efficiency of the cycle increases to about 56%. Increasing the total exergy efficiency from 56% to 58% increases the cost rate of product significantly. It is shown in Fig. 2 that the maximum exergy efficiency exists at design point A (57.64%), while the total cost rate of products is the greatest at this point (1394 $/h). On the other hand, the minimum value for the total cost rate of product occurs at design point E which is about 1365.7 $/h. Design point A is the optimal situation when efficiency is the sole objective function, while design point E is the optimum point when total cost rate of product is the sole objective function. In multi-objective optimization a process of decision-making for selection of the final optimal solution from the available solutions is required. The process of decision-making is usually performed with the aid of a hypothetical point in Fig. 2 (the equilibrium point), at which both objectives have their optimal values independent of the other objectives. It is clear that it is impossible to have both objectives at their optimum point simultaneously and, as shown in Fig. 2,
Table 2 Optimization constraints and their rationales. Constraint
Reason
GTIT < 1550 K P2/P1 < 22 hAC < 0.9 hGT < 0.9 PHP < 40 bar PLP < 5.5 bar 10 C < PPHP <22 C 12 C < PPLP < 22 C hST < 0.9 hp < 0.9 2 C
Material temperature limit Commercial availability Commercial availability Commercial availability Commercial availability Commercial availability Heat transfer limit Heat transfer limit Commercial availability Commercial availability Cooling load limitation
P. Ahmadi et al. / Energy 46 (2012) 21e31
27
Table 3 Optimized values for design parameters of the system based on multi-objective optimization. Design A parameter
hAC hGT RAC GTIT (K) PLP (bar) PHP (bar) PPHP ( C) PPLP ( C) TEVP ( C)
hFWP hST
B
C
D
E
0.88 0.88 0.88 0.88 0.88 0.9 0.9 0.9 0.9 0.9 19.977 19.999 19.996 19.999 20 1499.6 1499.5 1499.7 1499.7 1499.8 5.6796 5.6405 2.0293 2.043 2.9621 39.949 39.955 39.924 24.719 15.021 8.096 16.233 19.939 19.941 19.897 24.778 24.65 24.981 24.83 24.971 4.1983 4.293 4.3565 5.9145 7.3016 0.77333 0.78133 0.738 0.79267 0.858 0.88945 0.87902 0.76592 0.75 0.75769
the equilibrium point is not a solution located on the Pareto Frontier. The closest point of the Pareto frontier to the equilibrium point might be considered as a desirable final solution. Nevertheless, in this case, the Pareto optimum frontier exhibits weak equilibrium i.e., a small change in exergy efficiency from varying the operating parameters causes a large variation in the total cost rate of product. Therefore, the equilibrium point cannot be utilized for decisionmaking in this problem. In selection of the final optimum point, it is desired to achieve a better magnitude for each objective than its initial value for the base case problem. Because of this the optimized points in the CeE region have the maximum exergy efficiency increment of about 1% and minimum total cost rate increment of about 20 $/h relative to the design point, C. Therefore, design point C can be a good candidate for the multi-objective optimization. Note that in multi-objective optimization and the Pareto solution, each point can be utilized as the optimized point. Therefore, the selection of the optimum solution depends on the preferences and criteria of the decision maker, suggesting that each may select a different point as for the optimum solution depending on his/her needs. Table 3 shows all the design parameters for points AeE. To see the variation of thermodynamic characteristics, three different points (A, C and E) on the Pareto frontier are considered. Table 4 shows the total cost rate of the system, the total exergy destruction, the system efficiency and the sustainability index. From point A to point E in this table both total cost rate of the system and exergy efficiency decrease. As stated above, point A is preferred when exergy efficiency is a single objective function and design point E when total cost rate is a single objective function. Design point C has better results for both objectives. Other thermodynamic properties correctly confirm this trend. For instance, from point A to E, the total exergy destruction increases when the exergy efficiency decreases. To provide further insights, we consider environmental characteristics of the system, namely sustainability index (SI) and CO2 emissions. A decrease in exergy efficiency leads to an increase in CO2 emissions. On the other hand, an increase in the CO2 emissions causes the sustainability index to decrease. This demonstrates the close relationship between exergy efficiency, CO2 emissions and the sustainability index. To better understand the variations of all design parameters, the scattered distribution of the design parameters are shown in
Fig. 3. Pareto Frontier: Best trade off values for the objective functions.
Fig. 4. Scatter distribution of compressor isentropic efficiency with population in Pareto frontier.
Table 4 Thermodynamic characteristics of three different points on the Pareto frontier. $ h
Point
_ tot ðMWÞ Ex
C_ tot
A C E
35.4 37.3 38.4
1393.4 1375.5 1365.8
J
Zk ð$Þ
SI
CO2 (kg/MWh)
57.58 56.28 52.8
8:7 106 7:92 106 7:47 106
2.19 2.09 2.01
130.14 134.97 143.75
Fig. 5. Scatter distribution of gas turbine isentropic efficiency with population in Pareto frontier.
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P. Ahmadi et al. / Energy 46 (2012) 21e31
Fig. 6. Scatter distribution of GTIT with population in Pareto frontier.
Fig. 9. Scatter distribution high pressure with population in Pareto frontier.
Fig. 7. Scatter distribution of compressor pressure ratio with population in Pareto frontier.
Fig. 8. Scatter distribution of low pressure with population in Pareto frontier.
Fig. 10. Scatter distribution of low pressure pinch point with population in Pareto frontier.
Fig. 11. Scatter distribution of high pressure pinch point with population in Pareto frontier.
P. Ahmadi et al. / Energy 46 (2012) 21e31
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Fig. 12. Scatter distribution of steam turbine isentropic efficiency with population in Pareto frontier.
Figs. 3e13. The results show that gas turbine inlet temperature, compressor pressure ratio and gas turbine isentropic efficiency tend to become as high as possible. This observation means that an increase in these parameters leads to the better optimization results. Due to physical limitations, however, it is not allowed to extend this region. The reason for the compressor pressure ratio is that an increase in this parameter increases the outlet temperature and decreases the mass flow rate injected to the combustion chamber. As the first term in the total cost rate (Eq.(24)) is directly associated with the mass flow rate of the fuel, any decrease in this term results in a decrease in the objective function. This is why in the scattered distribution for the compressor pressure ratio achieves a maximum value in its range. Similar results are seen for the gas turbine isentropic efficiency. In addition, the maximum value for the gas turbine inlet temperature (GTIT) is selected based on the evolutionary algorithm. The higher the GTIT, the higher the achieved exergy efficiency will be, since one of the objective functions is supposed to be maximized. It can be concluded that compressor pressure ratio and gas turbine inlet temperature have positive effects on both objective functions since they attain high values. To see this trend, the effect of change in compressor pressure ratio for point AeE on the Prato frontier on both objective functions is shown in Fig. 14. Fig. 15 shows that an increase in compressor pressure ratio leads to increase in system exergy efficiency and consequently results in a decrease in the total cost of the system. The main reason for the reduction of the total cost of the plant is the reduction of the mass flow rate injected to the combustion chamber. An increase in pressure ratio leads to an increase in compressor outlet temperature. The higher is the outlet temperature, the lower is the mass
Fig. 13. Scatter distribution of feed water pump isentropic efficiency with population in Pareto frontier.
Fig. 14. Scatter distribution of evaporator temperature with population in Pareto frontier.
Fig. 15. Effect of compressor pressure ratio on both objective functions.
Fig. 16. Effect of gas turbine inlet temperature on both objective functions.
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P. Ahmadi et al. / Energy 46 (2012) 21e31
ex _ Ex _ D Ex h _ m P Q_ R s T _ W
Fig. 17. Fitted curve on the optimal values in the Pareto frontier.
flow rate required. A reduction in mass flow rate results in a decrease in the first and second terms of Eq. (21). Fig. 16 shows the variation of GTIT on both objective functions. As it is shown in this figure, an increase in GTIT has positive effect on both objective functions. This is why in Fig. 5; points tend to be as much as possible. Other design parameters exhibit reasonable distributions in Figs. 4e14. Thus, it can also be determined that these parameters are selected effectively, since they do not all reach maximum or minimum values. As shown in Fig. 1, the optimized values for exergy efficiency on the Pareto frontier range between 53% and 58%. To provide a good relation between exergy efficiency and total cost rate, a curve is fitted on the optimized points obtained from the evolutionary algorithm. This fitted curve is shown in Fig. 17. The expression for this fitted curve is given as follows:
17:42j5 23:75j4 19:24j3 þ5:2j2 þ37:6j 15:94 C_ total ¼ j5 3:5j4 þ4:65j3 3:01j2 þ0:97j 0:12 (25) 8. Conclusions The comprehensive thermodynamic modeling and multiobjective optimization of a polygeneration energy system provide useful information. A calculus-based optimization approach using evolutionary algorithms (i.e. genetic algorithms) allows multiobjective optimization of the polygeneration plant. Environmental impacts are quantified conveniently as pollution-related costs in the economic objective function, transforming the environmental objective to a cost function. Merging the new environmental cost function with the thermoeconomic objective yields a useful thermoenvironomic function. Fitting a curve on the optimized points provides a closed form equation. The results suggest that gas turbine inlet temperature, compressor pressure ratio and gas turbine isentropic efficiency tend to maximum values, and that an increase in these parameters results in better system performance. Acknowledgment The authors acknowledge the support provided by the Natural Sciences and Engineering Research Council of Canada. Nomenclature Cp C
Specific heat at constant pressure (kJ/kg K) Cost ($)
Specific exergy (kJ/kg) Exergy flow rate (kW) Exergy destruction rate (kW) Specific enthalpy (kJ/kg) Mass flow rate (kg/s) Pressure (bar) Heat rate (kW) Gas constant (kJ/kg K) Specific entropy (kJ/kg K) Temperature (K) Work rate (kW)
Greek letters Specific heat ratio Air compressor isentropic efficiency Gas turbine isentropic efficiency Steam turbine isentropic efficiency Pump isentropic efficiency Exergy efficiency
g hAC hGT hST hPump J
Subscripts a Air AC Air compressor act Actual CC Combustion chamber Cooling Cooling load D Destruction Depletion number DP e Exit condition EVP Evaporator ex Exergy f Fuel FWP Feed water pump g Combustion gases h Hour GT Gas turbine GTIT Gas turbine inlet temperature Heating Heating load HP High pressure HRSG Heat recovery steam generator i Inlet condition is Isentropic LP Lower pressure mix Mixture net Net output power PP Pinch point R Compressor pressure ratio ST Steam turbine tot Total Superscripts . rate Ch Chemical References [1] Rosen MA, Dincer I. A study of industrial steam process heating through exergy analysis, International Journal of Energy Research 2004;28(10): 917e30. [2] Tom K. Combined heating and power and emissions trading: options for policy makers. International Energy Agency; 2008. [3] Ahmadi P, Dincer I, Rosen MA. Exergoenvironmental analysis of a trigeneration system based on micro gas turbine and organic Rankine cycles. In: Proceedings of the global conference on global warming 2011, Lisbon, Portugal; 11e14 July 2011.
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