Energy Conversion and Management

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1 Energy Conversion and Management 52 (2011) Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: Thermodynamic analysis and thermoeconomic optimization of a dual pressure combined cycle power plant with a supplementary firing unit Pouria Ahmadi, Ibrahim Dincer Department of Mechanical Engineering, Faculty of Engineering and Applied Science, University of Ontario, Institute of Technology (UOIT), 2000 Simcoe St. North, Oshawa, Canada ON L1H 7K4 article info abstract Article history: Received 13 March 2010 Received in revised form 5 December 2010 Accepted 11 December 2010 Keywords: Combined cycle power plant Energy Exergy Efficiency Optimization Thermoeconomics Genetic algorithm In this paper, a combined cycle power plant (CCPP) with a supplementary firing system is first thermodynamically analyzed through energy and exergy. The optimal design of operating parameters of the plant is then performed by defining an objective function and applying a generic algorithm (GA) type optimization method. In order to optimally find the design parameters, a thermo-economic method is employed. An objective function representing the total cost of the plant in terms of dollar per second is defined as the sum of the operating cost related to the fuel consumption and the capital investment for equipment purchase and maintenance costs. Subsequently, different parts of the objective function are expressed in terms of decision variables. Finally, the optimal values of decision variables are obtained by minimizing the objective function using a GA. Moreover, the influences of changes in the demanded power and fuel cost are studied by considering three different output powers (i.e., 160, 180 and 200 MW). To validate the present model, the results of the present simulation code are compared with the actual data. The results show that the average difference between the model results and the actual data is about 1.41%. Moreover, various cases are investigated to determine how to decrease the objective function (cost, mass flowrate, etc.) for the optimized design and operating parameters (fuel cost, power output, etc.). Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. 1. Introduction Corresponding author. Tel.: address: pouria.ahmadi@uoit.ca (P. Ahmadi). Combined cycle power plants (CCPPs) are attractive in power generation due to their higher thermal efficiency than individual steam or gas turbine cycles. Therefore, the optimal design of such cycles is of great importance due to increasing fuel prices and decreasing fossil fuel resources [1]. The main challenge in designing a combined cycle is proper utilization of a gas turbine exhaust heat in the steam cycle in order to achieve optimum steam turbine output. According to the benefits of CCPP, the number and output power of such cycles have increased recently. Combined cycles have the higher thermal efficiency as well as output power in comparison with gas turbine cycle and steam cycles. Higher efficiencies of combined cycle power plants (CCPPs) compared to Brayton or Ranking cycles have made them quite attractive for power generation. Based on these advantages and less emissions, CCPPs have widely been used all around the world. It is important to note that exergy analysis appears to be a potential tool in analysis, design and performance improvement of power plants. Exergy can be defined as the amount of obtainable work for a system when reaches to a state of thermodynamic equilibrium with the surroundings through reversible processes [2]. The main goal of exergy analysis is to quantitatively detect and evaluate the thermodynamic inefficiencies of the process under consideration [2 4]. During the past decade many researchers have carried out the exergy analysis for power plants. Dincer and Al-Muslim [5] analyzed a Rankine cycle reheat steam power plant to study the energy and exergy efficiencies at different operating conditions with varying boiler temperature, boiler pressure, mass fraction ratio and work output from the cycle. Rosen and Dincer [6] performed a study of industrial steam heating process through exergy analysis. The results suggested that exergy analysis should be used as the central tool in process optimization when the use of large quantities of the steam in energy centers is contemplated. Barzegar et al. [7] performed the exergy, exergoeconomic and exergoenvironmental analysis of a CCPP. The results showed that combustion chamber had the greatest exergy destruction and also had the greatest cost of exergy destruction in comparison with other components of the cycle. Rosen and Dincer [8] performed an exergoeconomic analysis of power plants and applied it on a coal fired electricity generating station. They found that the ratio of thermodynamic loss rate to the capital cost is a significant parameter in evaluating the plant performance, which may lead to a successful trade-off in the design of the plant. Ahmadi et al. [4] carried out energy, exergy and exergoeconomic analyses of a steam power plant in Iran. They also considered the effect of the /$ - see front matter Crown Copyright Ó 2011 Published by Elsevier Ltd. All rights reserved. doi: /j.enconman

2 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) Nomenclature c Cost per exergy unit [$/MJ] c f Cost of fuel per energy unit [$/MJ] _C Cost flow rate ($/s) c p specific heat at constant pressure [kj/kg.k] _Ex Exergy flow rate [MW] _Ex d Exergy destruction rate [MW] h Enthalpy (kj/kg) LHV Lower heating value [kj/kg] _m Mass flow rate [kg/s] T Temperature (K) _W net Net power output [MW] Z Capital cost of a component [$] _Z Capital cost rate [$/sec] DP Pressure loss (bar) Greek Letters g Efficiency c Specific heat ratio u Maintenance factor n Coefficient of fuel chemical exergy Subscripts and superscripts a Air c CC DB ev ec f F g GT HP HRSG j k LP P p o PP r w x CCPP CRF Compressor Combustion chamber Duct burner Evaporator Economizer Fuel Fuel for a component Combustion gases Gas turbine High pressure Heat recovery steam generator j th stream k th component Lower pressure Product of a component Pump Ambient condition Pinch point Pressure ratio water Molar fraction Combined cycle power plant Capital recovery factor load variations and ambient temperature in order to find the exergy destruction in each component of the cycle. Moreover, some exergy and exergoeconomic analyses have been carried out for CHP plant and other thermal systems [9 13]. Therefore, it shows the importance of exergy and exergoeconomic in thermal systems. Although exergy and exergoeconomic analyses are of great importance and indispensable in thermal systems, they cannot find the optimal design parameters in such systems. Therefore; using an optimization procedure with respect to the thermodynamics laws along with thermoeconomics is essential [14]. Sayyaadi [15] performed an exergoeconomic optimization of a 1000 MW light water reactor power generation system using a genetic algorithm. He considered ten decision variables. Moreover, it was shown that by optimization techniques considered in his research fuel cost of optimized system is increased in comparison to the base case plant, nevertheless this shortcoming of optimized system is compensated by larger monetary saving on other economic sectors. Dincer et al. [16] found the optimum temperatures in a shell and tube condenser with respect to exergy. The optimization problem used in that study was defined subject to condensation of the entire vapor mass flow and it was solved based on the sequential quadratic programming (SQP) method. Ahmadi et al. [17] optimized a combined cycle power plant using (SQP). The objective function of that study was introduced as total cost of the plant in terms of dollar per second, which was defined as the sum of the operating cost, related to the fuel consumption. To the best of our knowledge, optimization of a dual pressure combined cycle power plant with supplementary firing has not been analyzed and optimized with a genetic algorithm. The primary objective of this study is to develop a thermodynamic model, conduct a thermoeconomic optimization and use the actual data obtained from the Neka combined cycle power plant in the north part of Iran near the Caspian Sea for comparison purposes. Therefore, the key objectives are to conduct both exergy and exergoeconomic analyses and optimization of a CCPP through energy and exergy, undertake parametric studies to investigate how system inputs and outputs are affected by the operating conditions, compare the model results with the actual data for validation purposes, and develop an optimization program to determine the best design parameters of the cycle. In this regard, the optimization procedure is considered to be a powerful scheme which is used wide spared recently called evolutionary algorithm (i.e., genetic algorithm). The design parameters of this study are selected as: compressor pressure ratio (r A ), compressor isentropic efficiency (g AC ), gas turbine isentropic efficiency (g GT ), gas turbine inlet temperature (TIT), duct burner mass flow rate (m DB ), High pressure stream (HP), Low pressure stream (LP), HP main steam temperature (T HP ), LP main steam temperature (T LP ) HP pinch point temperature difference (PP HP ), LP pinch point temperature difference (PP HP ), condenser pressure (P Cond ), steam turbine isentropic efficiency (g ST ) and pump isentropic efficiency (g pump ). The objective function representing the total cost of the plant in terms of dollar per second is defined as the sum of the operating cost related to the fuel consumption and the capital investment for equipment purchase and maintenance costs. To have a good insight into this analysis, a sensitivity analysis for fuel cost and net output power is carried out. In summary, the following are the specific contributions of this paper to the subject matter area: A complete modeling of a dual pressure CCPP with supplementary firing (SF) is performed. To have good verification results, the modeling output of the cycle is compared with actual CCPP data taken from a power plant. Both exergy and exergoeconomic analyses of this system are carried out and linked to the optimization. A complete objective function representing the fuel cost, cost of exergy destruction, purchase cost and maintenance cost are considered for optimization study. A modified version of evolutionary algorithm (i.e., genetic algorithm) is used for objective optimization. The code, which is developed based on genetic algorithm, is employed for finding the set of optimal solution with respect to aforementioned objective function. A sensitivity analysis of change in design parameters with change in unit cost of fuel or investment cost is performed. The effects of net output power on the design and operating parameters are studied.

3 2298 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) Energy analysis To find the optimum physical and thermal design parameters of the system, an optimization program is developed in Matlab software. The steam and gas temperature profile in a combined cycle power plant (CCPP), input and output enthalpy and exergy of each line in the plant were estimated to study the optimization of the plant. The energy balance equations for various parts of the CCPP (Fig. 1) are as follows: Air compressor: T B ¼ T A 1 þ 1 c a 1 c r a c 1 g AC _W AC ¼ m a C pa ðt B T A Þ where C pa is considered to be a temperature variable function as follow [1]:! C Pa ðtþ ¼1: :8371T þ 9:4537T !! 5:49031T3 þ 7:9298T4 ð3þ Combustion chamber (CC): ð1þ ð2þ Combustion reaction equations: kc x1 H y1 þðx O2 O 2 þ x N2 N 2 þ x H2 OH 2 O þ x CO2 CO 2 þ x Ar ArÞ! y CO2 CO 2 þ y N2 N 2 þ y O2 O 2 þ y H2 OH 2 O þ y NO NO þ y CO CO þ y Ar Ar y CO2 y N2 ¼ðkx 1 þ x CO2 y CO Þ ¼ x N2 y NO y H2 O ¼ x H2 O þ k y 1 2 y O2 ¼ x O2 k x 1 k y 1 4 y Ar ¼ x Ar k ¼ n fuel n air Gas turbine: 8 2 < T D ¼ T C 1 g GT 41 p C : _W GT ¼ m g C pg ðt C T D Þ p D y CO 2 y NO 2 1 c g c g 39 = 5 ; ð6þ ð7þ ð8þ _m a h B þ _m f LHV ¼ _m g h C þð1 g cc Þ _m f LHV ð4þ _W Net ¼ _ W GT _ W AC ð9þ P C P B ¼ð1 DP cc Þ ð5þ _m g ¼ _m f þ _m a ð10þ Fig. 1. Schematic flow diagram of a dual pressure combined cycle power plant.

4 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) where C pg is taken as a temperature variable function as follow [2]:!! C Pg ðtþ ¼0: þ 6:99703T þ 2:7129T2 1:22442T Duct burner: ð11þ The additional fuel is burnt in the supplementary firing to increase the temperature of the exhaust gas that passes through the HRSG. In a duct burner: _m g h D þ _m f ;DB LHV ¼ð_m g þ _m f ;DB Þh 11 þð1 g DB Þ _m f ;DB LHV ð12þ where LHV is the lower heating value of the natural gas and g DB is the duct burner efficiency and taken as 93% [18,19]. Heat recovery steam generator (HRSG): A dual pressure HRSG is considered here as a common type for the CCPPs. By applying the energy balance for gas and water in each part of the HRSG the gas temperature and water properties will be calculated by solving the following equations: High-pressure superheater: _m w;hp h 10 þ _m w;lp h 6 _m w h 19 ¼ _ W ST High-pressure evaporator: _m g c p ðt 12 T 13 Þ¼ _m s;hp ðh 9 h 8 Þ High-pressure economizer: _m g c p ðt 13 T 14 Þ¼ _m s;hp ðh 8 h 7 Þ Low-pressure superheater: _m g c p ðt 14 T 15 Þ¼ _m s;lp ðh 6 h 5 Þ Low-pressure evaporator: _m g c p ðt 15 T 16 Þ¼ _m s;lp ðh 5 h 4 Þ Deaerator evaporator: _m g c p ðt 16 T 17 Þ¼ _m s;lp ðh 3 h 2 Þ Condensate pre-heater: _m g c p ðt 17 T 18 Þ¼ _m s;lp ðh 2 h 1 Þ ð13þ ð14þ ð15þ ð16þ ð17þ ð18þ ð19þ The combinations of energy and mass balance equations are numerically solved, and the temperature profile in the gas and water/steam side of HRSG are predicted. Steam turbine (ST): By applying the energy balance for a steam turbine, as shown in Fig. 1, the following relation is obtained: _m w;hp h 10 þ _m w;hp h 6 _m w h 19 ¼ _ W ST g ST ¼ W _ STact =W STis ð20þ ð21þ The performances of combined cycle power plant, including the thermal efficiencies for topping cycle, bottoming cycle, and overall efficiency are calculated as given below respectively [1]: Gas turbine cycle efficiency: g GT ¼ W GT W Comp Q in;top ð22þ Steam turbine cycle efficiency: g ST ¼ W ST W pump Q in;bot Combined cycle plant efficiency: g CCPP ¼ W GT W Comp þ W ST W pump Q in;ccpp ð23þ ð24þ The combinations of energy and mass balance equation are numerically solved and the temperature and enthalpy of each line of the plant are predicted. In this analysis, some assumptions are made as follows, e.g., [18,19]: All the processes are steady-state and steady flow. The principle of ideal-gas mixture is applied for the air and combustion products. The fuel injected to the combustion chamber is assumed to be natural gas. Heat loss from the combustion chamber is considered to be 3% of the fuel lower heating value [20]. Moreover, all other components are considered adiabatic. The dead-state conditions are P 0 = 1.01 bar and T 0 = K. 3. Exergy analysis Exergy analysis is a method that uses the conservation of mass and conservation of energy principles together with the second law of thermodynamics for the analysis, design and improvement of energy and other systems. The exergy method is a useful tool for furthering the goal of more efficient energy-resource use, for it enables the locations, types and magnitudes of wastes and losses to be identified and meaningful efficiencies to be determined [14]. Today there is a much stronger emphasis on exergy aspects of systems and processes. The emphasis is now on system analysis and thermodynamic optimization, not only in the mainstream of engineering but also in physics, biology, economics and management. As a result of these recent changes and advances, exergy has gone beyond thermodynamics and become a new distinct discipline because of its interdisciplinary character as the confluence of energy, environment and sustainable development. According to the literature, exergy 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 [21,22]. The physical exergy is defined as the maximum theoretical useful work obtained as a system interacts with an equilibrium state. 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: _Ex Q þ X i _m i ex i ¼ X e _m e ex e þ _ Ex W þ _ Ex D ð25þ where subscripts e and i are the specific exergy of control volume inlet and outlet flow and Ex _ D, is the exergy destruction. Other terms in this equation is as follows [22 24]: _Ex Q ¼ 1 T _Q i ð26þ T i _Ex W ¼ _ W ex ph ¼ðh h Þ T ðs S Þ ð27þ ð28þ

5 2300 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) where Ex _ Q and Ex _ W are the corresponding exergy of heat transfer and work which cross the boundaries of the control volume, T is the absolute temperature (K) and () refers to the ambient conditions respectively. The total exergy rate becomes _Ex ¼ Ex _ ph þ Ex _ ch ð29þ where Ex _ ¼ _mex. The mixture chemical exergy is defined as follows [21]: " # ex ch mix ¼ Xn X n X i ex ch i þ RT 0 X i LnX i þ G E i¼1 i¼1 ð30þ where G E is the excess free Gibbs energy which is negligible at low pressure in a gas mixture. 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 [1,5,20,21]: n ¼ ex f =LHV f ð31þ where ex f is a fuel exergy. 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 [21,24]: n CH4 ¼ 1:06 n H2 ¼ 0:985 ð32þ For gaseous fuel with C x H y, the following experimental equation is used to calculate n [21]: n ¼ 1:033 þ 0:0169 y 0:0698 x x ð33þ 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 [24,25]. However, the exergy destruction in the heat exchanger of the system i.e. HRSG is due to the large temperature difference between the hot and cold fluid. The exergy destruction rate and the exergy efficiency for each component for the whole system in the power plant (Fig. 1) are shown in Table Exergoeconomic analysis 4.1. Economic model Table 1 The exergy destruction rate and exergy efficiency equations for plant components. Components Exergy destruction Exergy Efficiency HRSG ED;HRSG _ ¼ P _ i;hrsg E P _ o;hrsg E g HRSG ¼ E 10þ E _ 6 E 1 E11 E18 Steam turbine ED;T _ ¼ P _ i;t E P _ e;t E W _ g e;s ¼ W _ t=ð E _ i;t E _ e;t Þ Pump ED;P _ ¼ E _ i;p þ W _ P g e;p ¼ð E _ i;p E _ o;pþ= W _ p Compressor E D,AC = E A E B E W,AC g AC ¼ E 2 E 1 W AC Combustion E D,cc = E B + E f,cc E C g cc ¼ EC EBþE f ;cc chamber Gas turbine E D,GT = E C E D W GT g GT ¼ WGT EC ED Duct burner E D,DB = E D E 11 + E f,db g GT ¼ E11 EDþE f ;DB Condenser ED;C _ ¼ P _ i;c E P _ e;c E g Cond ¼ 1 P E D;Cond in;cond Exergoeconomics or thermoeconomic is the branch of engineering that appropriately combines, at the level of system components, thermodynamic evaluations based on an exergy analysis with economic principles, in order to provide the designer or operator of a system with information that is useful to the design and operation of a cost-effective system, but not obtainable by regular energy or exergy analysis and economic analysis [26]. When exergy costing is not applied, authors should use a different term (e.g., thermoeconomics). Thermoeconomics is a more general term and characterizing any combination of a thermodynamic analysis with an economic one [27,28]. In order to define a cost function which depends on optimization parameters of interest, component cost should be expressed as functions of thermodynamic design parameters [28]. The first study in this regard was proposed in the paper called CGAM problem. For each flow line in the system, a parameter called flow cost rate C ($ s 1 ) is defined, and the cost balance equation of each component is written as X _C e;k þ C _ w;k ¼ C _ q;k þ X _C i;k þ Z _ k ð34þ e i Here, the cost balances are generally written so that all terms are positive. one can write the following [22]: X ðce Ee _ Þ k þ c w;k _W k ¼ c q;k Eq;k _ þ X ðc i Ei _ Þ k þ Z _ k ð35þ _C j ¼ c j E j ð36þ In this analysis, it is worth mentioning that the fuel and product exergy should be defined. The exergy product is defined according to the components under consideration. The fuel represents the source that is consumed in generating the product. Both the product and fuel are expressed in terms of exergy. The cost rates associated with the fuel ( C _ F ) and product ( C _ P ) of a components are obtained by replacing the exergy rates ( E). _ For example, in a turbine, fuel is difference between input and output exergy and product is the generated power of the turbine. In the cost balance formulation (Eq. (35)), there is no cost term directly associated with exergy destruction of each component. Accordingly, the cost associated with exergy destruction in a component or process is a hidden cost. Thus, if one combines the exergy balance and cost accounting together, one can obtain the following equation: _E F;K ¼ E _ P;K þ E _ D;K ð37þ Accordingly, the expression for the cost of exergy destruction is defined as: _C D;k ¼ c F;k ED;k _ ð38þ Further details of the exergoeconomic analysis, cost balance equations and exergoeconomic factors are in detail discussed elsewhere [4,7,8,14,20]. In addition, several methods have been suggested to express the purchase cost of equipments in terms of design parameters in Eq. (35). However, we have used the cost functions as suggested by Ahmadi et al. [17] and Rosen et al. [29]. Nevertheless, some modifications have been made to tailor these results to the regional conditions in Iran and considered the inflation rate. To convert the capital investment into cost per time unit, one may write _ Z k ¼ Z k CRF u=ðn 3600Þ ð39þ where Z k is the purchase cost of kth component in dollar. The capital recovery factor (CRF) depends on the interest rate as well as estimated equipment life time. CRF is determined using the following relation [7]: ið1 þ iþn CRF ¼ ð1 þ iþ n 1 ð40þ Here, i, is the interest rate and n is the total operating period of the system in years.

6 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) In Eq. (39), N is the annual number of the operation hours of the unit, and u (1.06) [17] is the maintenance factor. Finally, in order to determine the cost of exergy destruction for each component, the value of exergy destruction, E D,k, is computed using exergy balance equation as given in the previous section. 5. Optimization (objective function, design parameters and constraints) 5.1. Definition of objective function According to the previous section, a new objective function which is sum of the fuel cost and the cost of exergy destruction as well as purchase cost is considered and minimized using the genetic algorithm. Hence, the objective function is described as follows: _C Tot ¼ _ C F þ X K _Z k þ _ C D ð41þ where _ C F ¼ c f ð _m f ;cc þ _m f ;DB ÞLHV ð42þ Here, _ Zk ; _ C F and _ C D are purchase cost of each component, fuel cost and cost of exergy destruction respectively. Moreover, C f is fuel cost which is considered to be 0.003$/Mj in our analysis [17] Design parameters The design parameters of this study are selected as: compressor pressure ratio (r AC ), compressor isentropic efficiency (g AC ), gas turbine isentropic efficiency (g GT ), gas turbine inlet temperature (TIT), duct burner mass flow rate (m DB ), High pressure stream (HP), Low pressure stream (LP), HP main steam temperature (T HP ), LP main steam temperature (T LP ) HP pinch point temperature difference(pp HP ), LP pinch point temperature difference (PP HP ), condenser pressure (P Cond ), steam turbine isentropic efficiency (g ST ) and pump isentropic efficiency (g pump ). Therefore, these decision parameters should be selected in the way the objective function is minimized Constraints Each optimization problem needs some reasonable number of constrains defined due to the physical limitations. In this particular optimization study, a list of constraints selected is given in Table 2. These constraints are applied to our present code as written in the Matlab program. The search domain is defined between these constraints by a genetic algorithm method for optimization study. As a result, each optimized design parameter lies within this range. Table 2 The list of constraints for optimization [7,20]. Constraints Rationale TIT < 1550 o K Material temperature limit r Comp < 22 Commercial availability g Comp < 0.9 Commercial availability g GT < 0.9 Commercial availability P main < 110 bar Commercial availability g ST Commercial availability g p Commercial availability m DB < 2 kg/s Super heater temperature limitation 5 bar < P Cond < 15 bar Thermal efficiency limitation T main Material temperature limitation T C To avoid formation of sulfuric acid in exhaust gases 5 C < PP < 30 C Second law of thermodynamic limitation 5.4. Evolutionary algorithm Genetic algorithm In recent years, optimization algorithms have received increasing attention by the research community as well as the industry. In the area of evolutionary computation (EC), such optimization algorithms simulate an evolutionary process where the goal is to evolve solutions by means of crossover, mutation, and selection based on their quality (fitness) with respect to the optimization problem at hand [30]. Evolutionary algorithms (EAs) are highly relevant for industrial applications, because they are capable of handling problems with non-linear constraints, multiple objectives, and dynamic components properties that frequently appear in real problems [31]. Genetic algorithms (GAs) are an optimization technique based on natural genetics. GAs were developed by Holland [32] in an attempt to simulate growth and decay of living organisms in a natural environment. Even though originally designed as simulators, GAs have proven to be a robust optimization technique. The term robust denotes the ability of the GAs for finding the global optimum, or a near-optimal point, for any optimization problem. The basic idea behind GAs could be described in brief as follows. A set of points inside the optimization space is created by random selection of points. Then, this set of points is transformed into a new one. Moreover, this new set will contain more points that are closer to the global optimum. The transformation procedure is based only on the information of how optimal each point is in the set, consists of very simple string manipulations, and is repeated several times. This simplicity in application and the fact that the only information necessary is a measure of how optimal each point is in the optimization space, make GAs attractive as optimizers. Nevertheless, the major advantages of these GAs are: Constraints of any type can be easily implemented. GAs usually finds more than one near-optimal point in the optimization space, thus permitting the use of the most applicable solution for the optimization problem at hand. The basic steps for the application of a GA for an optimization problem are summarized in Fig. 2 [30]. A set of strings is created randomly. This set, which is transformed continuously in every step of the GA, is called population. This population, which is created randomly at the start, is called initial population. The size of this population may vary from several tens of strings to several thousands. The criterion applied in determining an upper bound for the size of the population is that further increase does not result in improvement of the near-optimal solution. This upper bound for each problem is determined after some test runs. Nevertheless, for most applications the best population size lies within the limits of strings.the optimality (measure of goodness) of each string in the population is calculated. Then on the basis of this value an objective function value, or fitness, is assigned to each string. This fitness is usually set as the amount of optimality of each string in the population divided by the average population optimality. An effort should be made to see that the fitness value is always a positive number. It is possible that a certain string does not reflect an allowable condition. For such a string there is no optimality. In this case, the fitness of the string is penalized with a very low value, indicating in such a way to the GA that this is not a good string. Similarly, other constraints may be implemented in the GA. A set of operators, a kind of population transformation device, is applied to the population. These operators will be discussed. As a result of these operators, a new population is created, that will hopefully consist of more optimal strings. The old population is replaced by the new one. A predefined stopping criterion, usually a maximum number of generations to be performed by the GA, is checked. If this criterion is not satisfied a new generation

7 2302 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) Coding of parameter space Random creation of initial population Generati Evaluation of population Finesses New population (Replacement of old one) Is Number of Generation exceeded? Fig. 2. Genetic algorithm flowchart. is started, otherwise the GA terminates. It is now evident that when the GA terminates, a set of points (final population) has been defined, and in this population more than one equivalently good (optimal) point may exist. As it was discussed, this advantage of the GAs permits the selection of the most appropriate solution for the optimization problem. 6. Results and discussion 6.1. Modeling verification Table 3 Input parameters of HRSG thermal modeling for the HRSG at Neka CCPP (with duct burner). Input Inlet gas temperature: K Inlet gas flow rate: m g = 500 kg/s Inlet water temperature = 320 K Total water flow rate: _m w = kg/s Inlet water enthalpy h w = 185 kj/kg Ambient temperature: T o = 293 K Temperature (C) Stack LP Economizer Deaerator Evaporator To verify the modeling results, one of the most significant parts at CCPP (so-called:hrgs) is considered and the results of HRSG are compared with the corresponding measured values obtained from an actual running HRSG (Neka combined cycle power plant) in North of Iran. The list of input values for thermal modeling of HRSG at Neka CCPP is shown in Table 3. The gas temperature variation of Neka dual pressure HRSG with duct burner obtained by the simulation program and the corresponding measured values are shown and compared in Fig. 3. The results show that the average of difference between the numerical and the measured values of parameters at various sections of HRSG was about (1.14%) with the maximum of 1.36% in LP superheater. This verifies the correct performance of the developed simulation code to model the thermal performance of HRSG as well as the whole plant Number of generation Simulation LP Evaporator Typical power Plant LP Superheater HP Economizer HP Evaporator HP Superheater Fig. 3. Variation of hot gas temperature for various heat transfer elements of HRSG at Neka CCPP (comparison of modeling results with measured values). The genetic algorithm optimization is applied to obtain the CCPP optimum design parameters. Fig. 4 shows the convergence of the objective function with number of generation (40 in our case study at which there was no noticeable change in the value of the objective function). From this figure, it can be concluded that the

8 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) Total Cost Rate ($/s) developed genetic algorithm has a good and powerful convergence rate. It has two important benefits: (i) lower running time of the computer and (ii) better optimization results Optimization results Number of Generations Fig. 4. Variation of objective function of the system with number of generation (C f =.003$/MJ). By applying the developed genetic algorithm code for this problem and considering both objective function and constraints the optimal design parameters of the combined cycle are found. The optimal decision variables of the plant are shown in Table 4. It can be concluded that by selecting these design parameters the objective function defined in Eq. (41) has the lowest value. It is worth mentioning that in the objective function (i.e., Eq. (41), fuel cost has the significant effect. Therefore, the design parameters Table 4 Optimal design parameters of the dual pressure combined cycle power plant. Decision variable Value r C g C g GT TIT (K) m DB (kg/s) 0.80 PP HP (C) PP LP (C) HP (bar) LP (bar) HP Temp (C) LP Temp (C) P Cond (kpa) g Pump g ST should be selected in the way that both combustion chamber and duct burner mass flow rate have the minimum value. On the other hand, by decreasing the mass flow rate the amount of impact by emissions is reduced, and also the total efficiency of the cycle is decreased Sensitivity analysis To have a good insight into this real optimization problem, the sensitivity analysis has been performed. In this part, two important factors are considered. These two significant factors are unit cost of fuel and net output power of the combined cycle power plant. Thus, by change in these two cases and applying the genetic algorithm the sensitivity analysis is performed. It should be noted that to find the optimal design parameters for each unit cost of fuel and output power the new optimization procedure is applied. Hence, each optimal value is the best one for each cost and output power. The benefit of this method is to predict the trend of design parameters when any changes in the unit cost of fuel and output power are occurred. Unit cost of fuel: as it was discussed before, the unit cost of fuel has an essential rule in the objective function. Therefore, any changes in this parameter can affect the value of objective function as well as the design parameters. It means that when the unit cost of fuel increases, the optimal design of the cycle should be selected in the way that other terms in the objective function, i.e., Eq. (41) decrease. In order to investigate the effects of fuel price of optimum design parameters, the simulation and optimization procedures are repeated with different input values. For instance, by increase in the C f the mass flow rate of the combustion chamber and duct burner should be decreased by an increase in the compressor isentropic efficiency. Figs show the effect of changes in the unit cost of fuel. Figs. 5 and 6 show that at a constant output power both gas turbine isentropic efficiency and compressor isentropic efficiency increase by any increment in unit cost of fuel. The reason is that when the unit cost of fuel is increased, first term in the objective function increases, and other terms decreases respectively. When the output power increases at a constant unit cost of fuel, some parameters should be changed in order to achieve the required power. As we know, the changes in Gas Turbine Inlet temperature (TIT) is not drastic due to the material limitation. Therefore, it can be assumed that TIT is fixed. By increasing the output power, the mass flow rate must be increased. Increase in the mass flow rate is caused by two ways, first by an increase of the air mass flow rate and second the fuel mass flow rate. Since an increase of the fuel mass flow rate leads to an increase in the first term in the objective function (C f m f LHV); it should be selected as low as Fig. 5. The effects of unit cost of fuel and net power demand on the optimal value of compressor isentropic efficiency g Comp.

9 2304 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) Fig. 6. The effects of unit cost of fuel and net power demand on the optimal value of gas turbine isentropic efficiency g GT. Air Comp Pressure Ratio (rc) MW 180 MW 160 MW Unit Cost of Fuel ($/MJ) Fig. 7. The effects of unit cost of fuel and net power demand on the optimal value of compressor ratio r Comp. possible. On the other hand, at constant unit cost of fuel, by increase in the output power, if the compressor pressure increases, the compressor outlet temperature increases which leads to increase of the compressor work as well as increase in the exergy destruction. Hence, genetic algorithms are utilized to optimize the objective function. Therefore, the optimal values for compressor pressure ratio decreases by an increase in the output power at a constant unit cost of fuel. According to the literature information [7,20], increasing the isentropic efficiency leads to a decrease in the cost of exergy Fig. 9. The effects of unit cost of fuel and net power demand on the optimal value of duct burner mass flow rate. destruction. Therefore, the last term in Eq. (41) is decreased. It can be concluded that study of the variation of the optimal decision variables versus fuel unit cost reveals that by increasing the fuel cost, the optimal decision variables generally result in a more thermodynamically efficient design. As it is shown, the values of decision variables r Comp, g Comp, g GT and TIT increase with increasing the fuel unit cost. Increasing the inlet gas turbine temperature plays a crucial rule in decreasing the exergy destruction of the combustion chamber. On the other hand, according to the cost of exergy destruction which is proportional to the exergy destruction, the last term of the objective function decreases. Moreover, an increase in the turbine inlet temperature, TIT, reduces the exergy destruction in the combustion chamber and turbine. Since increasing TIT results in higher exhaust temperature of exhaust gases, the constraint T 18 > 120 C does not cause any limitation for rising TIT. However, due the fact that any increase in TIT affects the turbine investment cost, TIT only increase within a certain limit. Thus, these changes result in decrease in the objective function. Fig. 9, shows the effect of change in the duct burner mass flow rate versus unit cost of fuel. As it is shown, by increase in the unit cost the mass flow rate of the duct burner is decreased due to the fact that the objective function should be decreased respectively. Since the mass flow rate has a positive effect on increasing the first term of the objective function, the genetic algorithm tends to optimally find the design parameters which result in a decrease in the duct burner mass flow rate. Also, this reduction in the mass flow rate can decrease the environmental impacts as discussed earlier [7,20]. One of the most important parameters in designing the heat recovery steam generators is the pinch temperature difference. The pinch temperature is defined as a temperature difference 200 MW 180 MW 160 MW Gas Turbine Inlet Temperature (K) Unit Cost of Fuel ($/MJ) Fig. 8. The effects of unit cost of fuel and net power demand on the optimal value of gas turbine temperature TIT.

10 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) Fig. 10. The effects of unit cost of fuel and net power demand on the optimal value of high pressure pinch temperature (PP HP ). Fig. 11. The effects of unit cost of fuel and net power demand on the optimal value of low pressure pinch temperature (PP LP ). Fig. 12. The effects of unit cost of fuel and net power demand on the optimal value of HP steam turbine temperature. between the outlet gas from the evaporator and the saturation temperature. A smaller pinch temperature corresponds to a larger heat transfer surface area and more costly system as well as higher exergy efficiency and lower operating cost. A good HRSG is a system in which its pinch temperature has the minimum value. However, based on the second law of thermodynamic this temperature cannot be zero. Therefore, decrease in the pinch temperature results in decreasing the HRSG cost of exergy destruction [1,7]. The HRSG has both high- and low-pressure pinch temperatures. Figs. 10 and 11 show the effect of pinch temperatures on unit cost of fuel. It is shown that at constant output power, increasing the unit cost of fuel results in a decrease in the pinch temperature due to increasing the HRSG exergy efficiency as well as decreasing the HRSG cost of exergy destruction. Figs. 12 and 13 show the variation of super heater temperatures versus unit cost of fuel. As shown in these figures, the increase in the unit cost of fuel causes increasing both HP and LP superheater temperatures. As it was discussed earlier, increasing the unit cost

11 2306 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) MW 180 MW 160 MW 250 LP SH Temperature (C) Unit Cost of Fuel ($/MJ) Fig. 13. The effects of unit cost of fuel and net power demand on the optimal value of LP steam turbine temperature. HP drum pressure (bar) 200 MW 180 MW 160 MW Unit Cost of Fuel ($/MJ) Fig. 14. The effects of unit cost of fuel and net power demand on the optimal value of HP drum pressure. Fig. 15. The effects of unit cost of fuel and net power demand on the optimal value of LP drum pressure. of fuel leads to an increase in the first term in the objective function. Thus, a developed genetic algorithm code should select the design parameters in the way to decrease the objective function. Therefore, any increments in the superheater steam temperature result in a decrease in the last term of the objective function. Because higher steam turbine inlet temparture causes more output power in the Ranking cycle. Moreover, increasing the main steam temperature from HRSG results in a increase in the HRSG efficiency as well as reducing its exergy destruction. Moreover, the effect of changes in the unit cost of fuel on HP drum pressure and LP drum pressures are shown in Figs. 14 and 15. It is obvious that at constant output power by increase in the unit cost of fuel both HP and LP drum pressures are increased in order to decrease the last term in the objective function. Increaseing

12 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) MW 180 MW 160 MW 0.16 Condenser Pressure (bar) Unit Cost of Fuel ($/MJ) Fig. 16. The effects of unit cost of fuel and net power demand on the optimal value of condenser pressure P Cond. drum pressures, results in decreasing the HRSG cost of exergy destruction and hence the objective function. The main purpose of increasing the drum pressure is to produce steam with a higher enthalpy as well as exergy. In addition, higher drum pressure causes the steam temperature and mass flow rate to increase which provides higher steam turbine power output. That is why a high pressure pump is used in such HRSGs. Fig. 16 shows the effect of changes in the condenser pressure on the unit cost of fuel. While the unit cost of fuel increases, the condenser pressure decreases in order to decrease the objective function. Also, decrease in the Fig. 17. The effects of unit cost of fuel and net power demand on the optimal value of steam turbine isentropic efficiency g ST. condenser pressure results in an increase in the total exergy efficiency of the cycle. Therefore, it has a positive effect on both objective function and the combined cycle efficiency. Finally, the effects of steam turbine isentropic efficiency and pumps efficiency on the unit cost of fuel are shown in Figs. 17 and 18. Increasing the unit cost of fuel results in an increase in both turbine and pump isentropic efficiencies. In this case, more efficient devices result in increasing the exergy efficiency as well as reducing the cost of exergy destruction. Therefore, the main aim of increasing the efficiency is to decrease the last term in the objective function. It reveals that while the unit cost of fuel increases, the more efficient devises are needed to reduce the irreversibilities. Another important parameter in CCPPs is the net power output. Therefore, in order to have a good insight into this study, three different power outputs are considered. Hence, for each power output a new run of the genetic algorithm is done to find the best optimal design parameters. Figs show the effect of changes in the design parameters on the net power output. Figs. 5 9, show that optimal decision variables (except for r c ) generally increase as the net electrical power rises. When the net output power increases, the devices should be selected thermodynamically to produce the necessary output power. For instance, Fig. 8 shows that at constant unit cost of fuel, increasing the net output power results in increasing the gas turbine inlet temperature. It is worthwhile to mention that increasing the net output power results in increasing both combustion chamber mass flow rate and duct burner mass 200 MW 180 MW 160 MW 0.85 Pump Isentropic Efficiency Unit Cost of fuel ($/MJ) Fig. 18. The effects of unit cost of fuel and net power demand on the optimal value of pump isentropic efficiency g pump.

13 2308 P. Ahmadi, I. Dincer / Energy Conversion and Management 52 (2011) flow rate. Hence, the first term in the objective function tend to be increased. Therefore, genetic algorithm is used to find the optimal design parameter which can compensate this rise in the objective function. Furthermore, as discussed in the previous section, increasing the TIT results in decreasing the cost of exergy destruction as the last term in the objective function. The same result is obvious for the pinch temperature difference. Figs. 10 and 11 show that at constant unit cost fuel, increasing the output power leads to decrease the pinch temperature. It is due to the fact that the power output can be increased by increasing the HRSG efficiency and decreasing the pinch point temperature difference. In this case, more energy is obtained from the GT exhaust gases across the HRSG. The same result is obtained for superheater steam temperature as shown in Figs. 11 and 12. These figures show that increasing the net power output has the direct effect on the objective function due to an increase in the injected mass flow rate to the combustion chamber and duct burner. As a result, the optimal design parameters are selected in which the other terms in the objective function decrease. This is achieved by applying a developed genetic algorithm under the above mentioned constraints. 7. Conclusions In the present study, a comprehensive modeling of a dual pressure combined cycle power plant has been conducted. In order to validate the model results, we compare with the actual data obtained from a combined cycle power plant. Therefore, the comparisons show that the model results are in good agreement with the actual data. Moreover, exergy and exergoeconomic analyses for the CCPP are performed. The optimization method used is genetic algorithm, as developed in the Matlab program. Moreover, a new objective function representing the sum of the fuel cost and the cost of exergy destruction as well as purchase cost is considered and minimized using a genetic algorithm. The optimum design parameters obtained for the plant show a trade-off between thermodynamic and economic optimal designs. For example, from the thermodynamical point of view, the decision variable g T should be selected as high as possible while this leads to an increase in capital cost. It should be noted that any change in the numerical values of a decision variable not only affects the performance of the related equipment but also changes the performance of other equipment as well. It is concluded that by increasing the fuel price the numerical values of decision variables in the thermoeconomically optimal design tend to those of the thermodynamically optimal design. References [1] Ameri M, Ahmadi P, Khanmohammadi S. Exergy analysis of a 420 MW combined cycle power plant. 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