Analyzing, Controlling, And Optimizing.pdf

Original Article

Analyzing, controlling, and optimizing Damavand power plant operating parameters using a synchronous parallel shuffling self-organized Pareto strategy and neural network: a survey

Proc IMechE Part A: J Power and Energy 226(7) 848–866 ! IMechE 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0957650912454822 pia.sagepub.com

Ahmad Mozaffari1, Mofid Gorji-Bandpy1, Pendar Samadian2 and Sina Mohammadrezaei Noudeh1

Abstract In recent decades, analyzing and optimizing thermal systems have become of great interest to researchers. Recently, the engineers concentrated on variant concepts of artificial intelligence such as machine learning, simulation, fuzzy logic, game theory, and evolutionary computing to deal with complicated barriers and obstacles. Artificial intelligence and expert system techniques play an important role for surveying and controlling mechanical systems such as power plants and reservoirs. This is because of their interdisciplinary applications and versatile servicing potential in mathematical modeling of industrial systems. In this article, a new method called synchronous parallel shuffling self-organized Pareto strategy algorithm is presented which synthesizes different artificial techniques, nominally evolutionary computing, swarm intelligence techniques, and time adaptive self-organizing map that apply simultaneously incorporating with a stochastic data sharing behavior. Thereafter, it is applied to verify the optimum operating parameter of Damavand power plant as the biggest constructed power plant in Middle East with the potential of producing about 2300 MW electricity sited in Tehran, capital of Iran, as a multi-objective, multi-modal complex problem. It is also proved that implementing the governing equations of power plant leads to a multi-objective problem where some of these objectives are non-linear, non-convex, and multi-modal with different type of real-life engineering constraints. The results confirm the acceptable performance of proposed technique in optimizing the operating parameters of Damavand power plant. Keywords Damavand power plant, multi-objective optimizing, artificial neural network, exergetic and exergoeconomic analyses Date received: 10 October 2011; accepted: 11 June 2012

Introduction The importance of developing and controlling thermal system such as power plants that effectively use energy resources such as natural gas is apparent. Designing efficient and cost effective systems, which also meet environmental conditions, is one of the foremost challenges that researchers must meet.1 In the world with finite natural resources and large energy demands, it becomes increasingly important to understand the mechanisms which degrade energy and resources and to develop systematic approaches for improving the performance of systems like power plants and also reducing the impact of emission and pollution on environment. One of the common tools in analyzing and optimizing the thermal

systems like power plants derives from combining exergetic and economic properties of the flow stream in such systems. Exergetic and microeconomics forms the basis of thermoeconomics, which is almost known as exergoeconomics.2 Combining the second law of thermodynamic with economics (thermoeconomics) using 1 Department of Mechanical Engineering, Babol University of Technology, Iran 2 Control and Maintenance Section, AAA Linen, UK

Corresponding author: Ahmad Mozaffari, Department of Mechanical Engineering, Babol University of Technology, PO Box 484, Babol, Iran. Email: [email protected]

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availability of energy (exergy) is one of the major objects that an engineer should apply in optimizing the thermodynamic systems. Its goal is to mathematically combine the second law of thermodynamic with the economic factors which predict the unit cost of product such as electricity and quantifies monetary loss due to irreversibility. One of the other important objects in optimizing the thermodynamic systems like power cycles is to apply the exergy analysis which submits the thermodynamic performance of an energy system and the efficiency of the system components by accurately quantifying the entropy-generation of each component in power plant. The third crucial object which an engineer faces in designing the operating parameter of power plant is achieving acceptable properties due to the first law of thermodynamic such as reaching to maximum power, maximum efficiency, and controlling the dependent parameters. Considering all of these objectives will lead to optimum results that yield acceptable providence in the use of energy. During past decades, a variety of methods which are not limited to traditional probabilistic and stochastic methods and involve advanced computational technologies, informative and predictive models have been developed to increase the power plant’s efficiency.3 Cammarata et al.4 formulate the objective function, the sum of capital investment, and the operational and maintenance cost of a district heating network using exergoeconomic concepts. Gorji-Bandpy and Ebrahimian5 analyzed a gas turbine (GT) power plant using exergoeconomic principles and mathematic modeling. Bhargava et al.6 analyzed an intercooled reheat GT for the co-generation applications using exergoeconomic principles and mathematical models. Attala et al.7 used exergoeconomic principles as a design tool for the realization of gas–steam combined power plant principle; whereas Mirsa et al.8,9 optimized a single and double effect H2 O=LiBr vapor absorption refrigeration systems. Esen et al.10 analyzed the exergetic and energetic characteristics of a ground-coupled heat pump system with two horizontal ground heat exchangers using thermodynamical principles. Gorji-Bandpy and Mozaffari11 analyzed the characteristics of Damavand power plant using exergoeconomic principles. There are also many optimization models which utilized algorithmic stochastic searching, prediction methodologies, and advance soft computing techniques. Esen et al.12–16 used several intelligent techniques such as adaptive neuro-fuzzy inference system, artificial neural network (ANN), and support vector machine (SVM) to predict the performance of ground-coupled heat pump. Wang et al.17 developed a parametric optimization design for supercritical CO2 power cycles using genetic algorithm (GA) and ANN. Gorji-Bandpy and Goodarzian18 optimized a GT power plant operating parameters using a multi-objective GA. Valdes et al.19

developed a thermoeconomic optimization of combined cycle GT power plants using GA. Lee and Mohamed20 proposed a real-coded GA with a hybrid crossover operator for power plant control system design. Esen et al.21,22 used ANN and SVM for modeling a solar air heater component. As it was expressed, the feedback of recent research papers obvious that soft computational techniques and machine learning methodologies attract incremental attention of scientists because of their reliability and robustness. Following these principles, in this investigation, the authors have developed a novel multi-objective approach to optimize the operating parameters of Damavand power plant. To elaborate on the performance of the proposed method, authors have also developed a comparative frame work. The results reveal that proposed method is capable to find optimum condition for Damavand power plant. Rest of the article is organized as follows. In ‘Power plant description’, the characteristics of Damavand power are given in detail. In ‘The problem statement’, governing equations required for optimizing the power plant and their corresponding engineering constraints are described. Next, the characteristics of ‘synchronous parallel shuffling self-organized Pareto strategy algorithm’ (SPSSOPSA) optimization methodology is scrutinized. ‘Controlling the power plant using MatlabSimulink software’ and ‘Applying back propagation neural network for predicting the dynamic specific heat ratio during the process’ are devoted to definition of some intelligent tools required for controlling and modeling Damavand power plant. Obtained results are given in ‘Results and discussion’ and ‘Validation of results’. Finally, the last section concludes the article.

Power plant description Figure 1 indicates the schematic diagram of one phase of Damavand power plant and shows the work, exergy flows, and the state points which are accounted for in this case study. Figure 2 shows the temperature profile of power plant components. The power plant consists of 12 symmetric and similar phases that work corporately. As it can be seen, each steam power plant is connected to two GT power plant systems. In other words, each phase consists of two GTs and one stream turbine. This power plant plays an important role by supplying over than 2300 MW electricity for industrial, agricultural and civil, and domestic regions for various provinces. In this model, the net power generated by the system is 2300 MW. This model is treated as the base case with the following nominal properties:23 . amount of compression pressure ratio is: rp ¼ 10:27 . the isentropic efficiency of compressor is: sc ¼ 85%

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22 Feedwater Condensor 21

21’

Generator 20 steam turbine

17

17 Exhaust gases

Exhaust gases economizer

economizer HRSG

17 P

evaporator

19P

HRSG

20’p

20P 17 P

evaporator

18’

18

16

19’p

7

6 15 14

12 Air preheater

2

11

Combustor

Air 10

13

5 Combustor

Air 1

Fuel

8’

3 Air preheater

4 Fuel

9

18

8 Generator

Generator Gas turbine

Compressor

Compressor

Gas turbine

Figure 1. GT system. GT: gas turbine; HRSG: heat recovery steam generator.

. the temperature of combustion products entering the turbine is: T5 ¼ 1320 K . the isentropic efficiency of turbine is: sc ¼ 88% . environmental conditions of the air at the inlet are: P0 ¼ 1:013 bar and T0 ¼ 298:1 K . the power plant operates at steady state . fuel is assumed to be pure natural gas . air and combustion gases are considered as ideal gas with variable specific heats . the exit temperature is above the dew point temperature of the combustion products . the pressure drop in the air preheater (AP) and combustion chamber (CC) is 4% . the effectiveness of the AP is 75% . optimizing the heat recovery steam generator (HRSG) is also take into considered

It must be notioned that standard air is an ideal gas consists of 78.1% nitrogen, 20.95% oxygen, 0.92% argon, and 0.03% carbon dioxide. The properties of natural gas are explicitly explained in Gorji-Bandpy and Ebrahimian.24

The problem statement In general, a thermal system faces three conflicted objectives: (a) maximizing the power output and first law efficiency, (b) increasing the exergetic efficiency, and (c) decreasing the product cost. All of these objectives should be satisfied simultaneously. The first two objectives are governed by thermodynamic requirements and the last one derived from economic constraints. Therefore, total objective function should be defined in

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T 5 ,T 14 T6 ,T 15

T3 ,T 12

gases T6 ,T 15

gases T 7 ,T 16 air

T2 ,T 11

air

T2 ,T 11 T1 ,T 10 Air preheater

Compressor and Turbine T 5 ,T 14

T 7 ,T 16

T17P ,T 17’P Pinch point T 17 ,T 17’

T 3 ,T 12

T20

ignition

approach point

T20P T4 ,T 13

T 21 Heat Recovery steam Generator

Combustion chamber

Figure 2. Temperature profiles of Damavand power plant components.

a manner that the optimizing procedure satisfied all of requirements. For that, the optimization problem should be formulated as a minimization or maximization problem. The exergoeconomic analysis gives a clear picture about the costs related to the exergy destruction, exergy losses, maximum power output, optimum exergy efficiency, etc. Damavand power plant as a thermodynamic system follows the above rules, so the objective function for this system is defined as minimizing a total cost function Cp, tot and maximizing the power output (efficiency of first law) and exergetic efficiency which can be derived a model that will be explained more closely. It is important to mention that Damavand power plant contains six independent phases and following equations are valid for each of independent phases.

Ebrahimian24 and Gorji-Bandpy et al.25 considered following policies for analyzing the energy efficiency of steam power plan. . The heat leakage during the process is taken into consideration to gain more accurate solution. . The variable specific heat changes during the procedure. . Kinetic and potential energies are neglected because they are not important. . In order to simplify the calculation, for each component, the average temperature is utilized for determination of variable specific heat. This simplification can be mathematically expressed as Tav ¼

Modeling the objective functions The proposed optimization model possesses three different objective functions for each independent phase. These objectives are scrutinized in following sections. Maximizing the power output and energy efficiency. Obtaining optimum performance of power plant is strongly related to maximizing the power output and energy efficiency. Gorji-Bandpy and

Ti  Tj   ln TTij

ð1Þ

where i and j are, respectively, the final and prior temperatures of each component. . Following approximation is used for determining the gas enthalpy hstate ¼ CP Tstate

ð2Þ

. Due to trivial amount of fuel in mixture gas (1:61 3%), the effect of fuel (natural gas) is neglected.

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General conservation equation and energy balance can be written as follows _ þ Q_ þ W

n X

m_ i hi ¼

i¼1

m X

m_ e he

ð3Þ

e¼1

The conservation equation and energy balance is applied for the operating components: . air compressor _ AC1 þ ma h1 ¼ ma h2 ,  W _ AC2 W þ ma h10 ¼ ma h11

ð4Þ

mg ¼ ma þ mf

ð5Þ

capital recovery factor CRF (i, n) and present worth factor PWF (i, n), the levelized annual cost may be written as C_ ½$ per year ¼ ½PEC  ðSVÞ PWF ði, nÞ CRF ði, nÞ ð13Þ where SV ¼ 0:1PEC, CRFði, nÞ ¼ i=ð1  ð1 þ iÞn Þ, PWFði, nÞ ¼ ð1 þ iÞn , and PEC is purchased equipment cost. Equations for calculating the purchased equipment costs for the components of the power plant are:

Q_ CC1 þ ma h3 þ mf h4 ¼ mg h5 , Q_ CC2 þ ma h12 þ mf h13 ¼ mg h14

ð6Þ

. air compressor      71:1 m_ a P2 P2 PECAC1 ¼ ln 0:9  c P1 P1      71:1 m_ a P11 P11 PECAC2 ¼ ln 0:9  c P10 P10

Q_ CCi ¼ m_ f  LHV, i ¼ 1, 2

ð7Þ

. combustion chambers

. combustion chamber

. gas turbine

PECCC1

_ GT1 þ mg h5 ¼ mg h6 ,  W _ GT2 W þ mg h14 ¼ mg h15

!

PECCC2 ¼

Q_ AP1 þ ma h2 þ mg h6 ¼ ma h3 þ mg h7 ,  Q_ AP2 þ ma h11 þ mg h15 ¼ ma h12 þ mg h16 ð9Þ where Q_ AP implies on the probable heat leakage occurs in AP. The total power output can be formulated as follows       _ net ¼ W _ GT2   W _ AC1  _ GT1  þ W W     _ AC2  þ W _ ST   W

! 46:08m_ a ¼ ½1 þ expð0:018T5  26:4Þ 0:995  PP53

ð8Þ

. air preheaters

ð14Þ

ð15Þ

46:08 m_ a ½1 þ expð0:018T14  26:4Þ 0:995  PP1412 ð16Þ

. gas turbines PECGT1

    479:34 m_ g P5 ¼ ln 0:92  T P6

½1 þ expð0:036T5  54:4Þ     479:34 m_ g P14 ln PECGT2 ¼ 0:92  T P15 ½1 þ expð0:036T14  54:4Þ

ð17Þ

ð18Þ

ð10Þ . air preheaters

By pursuing the abovementioned equations, the energy efficiency can be defined as _ net W , i ¼ 1, 2 I ¼ P i mfi  LHV

ð11Þ

The first objective function is



PECAP1 PECAP2

 m_ g ðh6  h7 Þ 0:6 ¼ 4122 _ AP1 0:018 mT   m_ g ðh15  h16 Þ 0:6 ¼ 4122 _ AP2 0:018 mT

ð19Þ

where TAP mathematically expressed as ð12Þ

TAP1 ¼

ð20Þ

Minimizing total cost. All costs due to owning and operating a plant depend on the type of financing, required capita, expected life of a component, etc. The levelized cost method of Moran26 is used here. By hiring the

ðT7  T2 Þ  ðT6  T3 Þ   2Þ log ððTT76 T T3 Þ

TAP2 ¼

ðT16  T11 Þ  ðT15  T12 Þ   11 Þ log ððTT1615 T T12 Þ

ð21Þ

F1 ¼ max ðI Þ

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853 C_ F, tot ¼ cF, tot m_ f LHV

. heat recovery steam generators PECHRSG1 ¼ 3650



m_ steam ðh20P  h21 Þ 0:8 T1

where LHV is the fuel low heating value,24 k the number of components, C_ F, tot the total fuel cost, and cF, tot is considered to be 0.000004 $=Kj . The second objective function is



 m_ steam ðh20  h20P Þ 0:8  T2 þ 11820 m_ steam þ 658 m_ 1:2 g PECHRSG2

ð22Þ



m_ steam ðh200 P  h210 Þ 0:8 ¼ 3650 T3 "    h20  h200 P Þ 0:8  m_ steam T4 þ 11820 m_ steam þ 658 m_ 1:2 g

T2 ¼

ðT17P  T20 Þ  ðT16  T20 Þ   T20 Þ log ððTT17P 16 T20 Þ 

T3 ¼

T170  T210  ðT170 P  T200 P Þ   ðT170 T210 Þ log T 0 T 0 ð 17 P 20 P Þ

T170 P  T20  ðT7  T20 Þ T4 ¼  T 0 T  ð P 20 Þ log ðT177 T 20 Þ

F2 ¼ minðC_ p, tot Þ

ð31Þ

Additional standard engineering equations, known as exergoeconomic variables, that are vital for evaluating the performance of thermal systems are listed in below: ð23Þ

where T1 , T2 , T3 , and T4 are formulated as

ðT17  T21 Þ  ðT17P  T20P Þ   T1 ¼ 17 T21 Þ log ðTðT17P T20P Þ

ð30Þ

ð24Þ

. average unit cost of the fuel C_ f, K cf, K ¼ E_ f, K . average unit cost of product C_ P, K cP, K ¼ E_ P, K

ð32Þ

ð33Þ

. exergy destruction ð25Þ C_ D, K ¼ c_f, K E_ D, K ð26Þ

. exergy economic factor Z_ K fk ¼ _ ZK þ C_ D, K

ð34Þ

ð35Þ



ð27Þ

Dividing the levelized cost by 8000 annual operating hours yields the capital cost rate for the Kth component of power plant ;k C_ K Z_ K ½$ per hours ¼ 8000

ð28Þ

The maintenance cost is taken into consideration through the factor ;k ¼ 1:1 for each plant components whose expected life is assumed to be 20 years and the interest rate is 17%. Number of hours of power plant operating per year and maintenance factor are the typical numbers employed in standard exergoeconomic analysis.26 The objective function for minimizing the costs can be written as C_ p, tot ¼ C_ F, tot þ

X k

Z_ k

ð29Þ

Maximizing the exergetic efficiency. Exergy balance equation, applicable to any component of a thermal system may be formulated by utilizing the first and the second law of thermodynamics. The thermodynamical exergy stream may be decomposed into its thermal and mechanical components. Ebadi and Gorji-Bandpy23 applied these rules and derived to following exergy balances equation for analyzing any power plant  T  MEC _m _ _T _ E_ m  E_ mMEC i  Eo ¼ Ei  Eo þ Ei o

ð36Þ

where the subscripts i and o, respectively, denote exergy flow streams entering or leaving the plant component. The thermal and mechanical components of the exergy stream for an ideal gas with constant specific heat may be written as follows  

T T _ _ P ðT  Tref Þ  Tref ln E ¼ mC ð37Þ Tref   P _ E_ MEC ¼ mRT ln ð38Þ ref Pref

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With the decomposition defined by equation (36), the general exergy balance can be written as follows _ CHE

E

þ

X

E_ Ti



inlet

þ

X

E_ MEC  i

X

2

S_i 

inlet

X

! E_ MEC o !

S_o þ Q_ CV =Tref ¼ E_ W

ð39Þ

outlet

The term E_ CHE denotes the rate of exergy flow of fuel in the plant and Q_ CV in the fourth term denotes the heat transfer between the component and the environment. The exergy balance equations for each component in the GT power plant can be derived from general exergy balance equation. The exergy balances for the components of GT are: . air compressors

6

7

ð47Þ According to above equation there is a relation between network power output and exergy flow stream. The objective function for maximizing exergetic efficiency can be written as "¼P

 T  E_ 1  E_ T2 þ E_ 1MEC  E_ 2MEC  _ AC1 þ T0 S_1  S_2 ¼ W

3

þ ðE_ MEC  E_ MEC þ E_ MEC  E_ MEC Þ 2 3 6 7 ! Q_ AP1 ¼0 ð46Þ þ Tref S_2  S_3 þ S_6  S_7 þ Tref  T E_ 11  E_ T12 þ E_ T15  E_ T16 MEC MEC MEC MEC þ ðE_ 11  E_ 12 þ E_ 15  E_ 16 Þ ! Q_ AP2 _ _ _ _ ¼0 þ Tref S11  S12 þ S15  S16 þ Tref

E_ To

outlet

X

 T E_  E_ T þ E_ T  E_ T

!

outlet

inlet

þ Tref

X

. air preheaters

_ CHE i Efi

_ net W , i ¼ 1, 2 þ E_ Tfi þ E_ MEC fi

max F3 ¼ "

ð48Þ ð49Þ

ð40Þ

Controller rules and constraints  T  MEC MEC  E_ 11 E_ 10  E_ T11 þ E_ 10  _ AC2 þ T0 S_10  S_11 ¼ W

Economical constraints ð41Þ

. combustion chambers   E_ CHE þ E_ T3 þ E_ Tf  E_ T5 þ E_ 3MEC þ E_ fMEC  E_ 5MEC ! _ CC Q 1 þ Tref S_3 þ S_f þ S_5  ¼ 0: ð42Þ Tref

Equality constraints. For a component receiving a heat transfer and generating power, cost balance equation may be written as11 X X ð50Þ C_ e,K þ C_ W, K ¼ C_ Q, K þ C_ i,K þ Z_ K e

i

where C_ denotes a cost rate associated with an exergy stream and the variable Z_ the non-exergetic costs. The formulation of cost balance for plant components leads to following constraints:

  MEC MEC . air compressor E_ CHE þ E_ T12 þ E_ Tf  E_ T14 þ E_ 12 þ E_ fMEC  E_ 14 ! _ QCC2 þ Tref S_12 þ S_f þ S_14  ¼ 0: ð43Þ C_ 2 ¼ C_ 1 þ C_ 9 þ Z_ AC1 Tref C_ 11 ¼ C_ 10 þ C_ 18 þ Z_ AC2

. gas turbines

ð51Þ ð52Þ

. combustion chamber ðE_ T5  E_ T6 Þ þ ðE_ 5MEC  E_ 6MEC Þ _ GT1 þ Tref ðS_5  S_6 Þ ¼ W MEC MEC ðE_ T14  E_ T15 Þ þ ðE_ 14  E_ 15 Þ _ _ _ GT2 þ Tref ðS14  S15 Þ ¼ W

ð44Þ

C_ 5 ¼ C_ 4 þ C_ 3 þ Z_ CC1

ð53Þ

C_ 14 ¼ C_ 13 þ C_ 12 þ Z_ CC2

ð54Þ

. gas turbine ð45Þ

C_ 6 þ C_ 9 þ C_ 8 ¼ C_ 5 þ Z_ GT1

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ð55Þ

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C_ 15 þ C_ 18 þ C_ 80 ¼ C_ 14 þ Z_ GT2

ð56Þ

C_ 6 C_ 5 C_ 15 C_ 14 ¼ , ¼ E_ 6 E_ 5 E_ 15 E_ 14

ð57Þ

. air preheater

13004T5 , T14 41450

ð69Þ

6004T3 , T12 41500

ð70Þ

4504T2 , T11 4700

ð71Þ

3004T1 , T10 4480

ð72Þ

C_ 3 þ C_ 7 ¼ C_ 2 þ C_ 6 þ Z_ AP1

ð58Þ

4004mai 4530, i ¼ 1, 2

ð73Þ

C_ 12 þ C_ 16 ¼ C_ 11 þ C_ 15 þ Z_ AP2

ð59Þ

84mfi 49:5, i ¼ 1, 2

ð74Þ

C_ 6 C_ 7 C_ 15 C_ 16 ¼ , ¼ E_ 6 E_ 7 E_ 15 E_ 16

ð60Þ

Auxiliary equations (54) and (56) are written assuming the same unit cost of incoming and outgoing fuel exergy streams. Additional auxiliary equation (57) is formulated based on the concept that both the net power exported from the system and the power entered to the compressor, consume same energy cost C_ 8 C_ 9 ¼ , E_ 8 E_ 9

C_ 8, C_ 18 ¼ E_ 8, E_ 18

ð61Þ

Note that the cost of fuel stream (C_ 4 ) is taken as 0:1 $ per kg and a zero unit cost is allocated to air entering to the air compressor (AC). These are mathematically expressed as C_ 4 & C_ 13 ¼ 3067:2 $ per hour and C_ 1 & C_ 10 ¼ 0 $ per hour

ð62Þ

The governing mechanical constraints can be modeled as well as economic ones. Inequality constraints. T2 4 T1 , T11 4 T10

ð75Þ

T3 4 T2 , T12 4 T11

ð76Þ

T5 4 T3 , T14 4 T12

ð77Þ

T7 4 T20 , T16 4 T20

ð78Þ

TP ¼ T17P  T20 4 0, T170 P  T20 4 0

ð79Þ

T17 4 T21 þ TP , T170 4 T210 þ TP

ð80Þ

 HRSG 41

ð81Þ

where HRSG is the efficiency of heat recovery steam generation system. Non-ideality in APs structure, leads to following engineering constraints

Inequality constraints. Z_ K 4 0, k ¼ 1, 2, . . . , 10

ð63Þ

C_ p, tot 4 0

ð64Þ

0 5 fk 5 1, k ¼ 1, 2, . . . , 10

ð65Þ

T6 4 T3 & T7 4 T2

ð82Þ

T15 4 T12 & T16 4 T11

ð83Þ

In addition, due to the interaction in AP T6 4 T7 , T15 4 T16

ð84Þ

Following constraints are set due to the information that was reported in Damavand power plant data base and Gorji-Bandpy and Mozaffari11

Physical constraints Decision variable spans. The admissible ranges of mechanical operating parameters are considered as follows 84rp 416

ð66Þ

0:754T 40:92

ð67Þ

0:754c 40:92

ð68Þ

T2  T1 530, T11  T10 530

ð85Þ

T3  T2 550, T12  T11 550

ð86Þ

T5  T3 5100, T14  T12 5100

ð87Þ

T6  T7 540, T15  T16 540

ð88Þ

T170 , T17 5378:15

ð89Þ

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Equality constraints. " g#  1 T6 P5 g ¼ 1  GT 1  T5 P6

ð90Þ

" g#  1 T15 P14 g ¼ 1  GT 1  T14 P15

ð91Þ

T16  T17 T7  T170 ¼ T16  T21 T7  T210

ð92Þ

h20  h210 h20  h21 m_ gas ¼ ¼ h7  h170 h16  h17 m_ steam

ð93Þ

m_ air h6  h7 h15  h16 ¼ ¼ m_ gas h3  h2 h12  h11

ð94Þ

HRSG ¼

"AP ¼

in asynchronous parallel model, which improves the data processing speed and increases the local search ability (intensity). The population is sorted and enters in each phase based on a random shuffling procedure. The results indicate that an adjustable random data sharing between these two algorithms, called shuffling process, enhances the robustness of proposed method explicitly. In following sections, the authors interpret the structure of SPSSOPSA more closely.

Time adaptive self-organizing map

T3  T2 T12  T11 ¼ T6  T2 T15  T11

ð95Þ

m_ air h3 þ CC m_ f LHV ¼ m_ gas h5

ð96Þ

m_ air h12 þ CC m_ f LHV ¼ m_ gas h14

ð97Þ

where HRSG is heat recovery steam generation efficiency, g the gas specific heat ratio, and "AP the AP effectiveness that is equal to 0.75 in this case study. Considering all of the abovementioned constraints turns the problem to a highly complex multi-modal problem that makes the decision making too intricate. Hence, many researchers have omitted some of these constraints to provide a convenient framework. However, neglecting these constraints lead to an imprecise decision. In the next part, we introduce a novel method that is able to make a suitable engineering decision by considering all of the modeled objective functions and their constraints.

Synchronous parallel shuffling self-organized Pareto strategy Application of hybrid evolutionary-learning algorithms began by Michalski’s27 researches who hired machine learning technique and evolutionary algorithm to generate new population. These types of algorithms are simply called learnable evolutionary models (LEMs). After the proposition of LEM, many researchers have focused on this concept and developed new optimization models. In this study, a time adaptive self-organizing map (TASOM) method that utilizes a conscience mechanism fuses to elitism non-dominated sorting GA (NSGA-II) and artificial bee colony (ABC) in order to conserve the diversity of populations. Besides, ABC operator applies

TASOM proposed by Shah-Hosseini and Safabakhsh28 is a modification of SOM that automatically adapts the learning rate and neighborhood function of neuron weights independently. One of its explicit dominance comparing to classic SOM is its ability to normalize all distance calculation between any input vector and the neuron’s weight vector since the basic SOM often fails to provide a suitable topological ordering for input distribution. Figure 3 exposes a schematic of weight adaption during the process. TASOM with conscience mechanism uses following learning rule   Wnþ1 ðtÞ ¼ Wnj ðtÞ þ yj ðtÞ  hj ðnÞ  Rni ðtÞ  Wnj ðtÞ , j t ¼ 1, 2, . . . , T

ð98Þ

where t is sub-generation in SOM network and n the SPSSOPSA generation number. yj ðtÞ is a controlling parameter that leads weight vectors to a non-dominated solution which is transferred from external archive to network as an input. In other words, if the input’s, which is a non-dominate solution, fitness value fR is lower than fWj ðnÞ then yj ðtÞ ¼ 1 and neuron center moves toward the non-dominated solution (networks input), otherwise yj ðtÞ ¼ 0 and neuron center does not approach to the solution. This is mathematically expressed as  yj ðtÞ ¼

1 if R ðtÞ dominate Wj ðtÞ 0 other wise

ð99Þ

Wnþ1 ðtÞ refers to updated weight vector and Wnj ðtÞ the j old weight vector. kRni  Wnj k represents the distance between input vectors where Rni is the ith non-dominated solution in nth generation. The learning rate which is a descending function is defined as    1 n n kR ðtÞ  Wj ðtÞk hj ðt þ 1Þ ¼ hj ðtÞ þ  f sf :slðtÞ j ð100Þ

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Low Quality

Good Quality

Winner

Figure 3. Weight adaption during the process.

The learning rate parameter hj ð0Þ should be initialized with value close to unity.  obtains any arbitrary value between 0 and 1. sf is a descending constant and should be set due to the problem condition. In this article, we set sf ¼ 1000.29 Function f ð:Þ should be designed in a manner that following criteria derived appropriately df ðzÞ 50 fð0Þ ¼ 0, 04fðzÞ41 and dz for positive values of z:

8 < 0:8bi ðtÞ or bi ðt þ 1Þ ¼ : bi ðtÞ  0:3

ð104Þ

Synchronous parallel shuffling self-organized Pareto strategy

In this article, fðzÞ set as fðzÞ ¼ 1 

mechanism. In this article, a simple well-known mechanism is utilized which tunes the bias of each node (neuron) by following formula

1 1þz

ð101Þ

Shah-Hosseini and Safabakhsh29 produced a scaling value for a two-dimensional (2D) input. In this article, scaling value is extended to a 9D input due to the number of our decision parameters and our problem condition. Scaling value ‘sl’ adjusts using following equation vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !þffi u 9 u X slðt þ 1Þ ¼ t Eik ðt þ 1Þ10i ð1Þiþ1 ,

k¼1

i¼1

ð102Þ  Eik ðt þ 1Þ ¼ Eik ðtÞ þ i Rik ðtÞ  Eik ðtÞ

ð103Þ

where i represents the number of variable in each solution. Eik ð0Þ initialized with some small random values. Conscience mechanism is applied in order to revive the dead units (weights) in neuron center.30 Dead unit is a term that refers to weights with a trivial chance of learning and adaption during the progress. The policy of repairing these units is often called conscience

In this section, pseudo code and the schematic flowchart of proposed method will be given, respectively: . Step 0. Define algorithm initial parameters such as mutation probability (Pmut ), number of neurons (NuGA and NuABC ) in SOM center for each phase, sharing factor (), pool size, number of generation, population size (Ps ), descending constant (sf ), ,  and stopping criterion. Set n ¼ 1 and start the process. . Step 1. Randomly generate Ps solution for the initial population P1 . . Step 2. Share (shuffle) the solutions into ABC phase and NSGA-II phase due to the sharing factor ().  is a random number from a uniform distribution. Lead (1  )*Ps of solutions in ABC operator phase (PABC ) and the rest of them in genetic operator (PGA ). . Step 3. Evaluate the fitness of ABC solutions (foods) in PABC and rank them based on none dominate sorting and crowding distance. . Step 4. Define random weight vectors for SOM unit center in ABC operator phase (NuABC ) in a uniform stochastic distribution manner spanning to problem solution space. Evaluate the fitness of weight vectors.

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. Step 5. Train the weight vectors in SOM center (Wnj , j ¼ 1, 2, . . . , NuABC ) using obtained non-dominate solutions (elite bees) in the current nth generation. . Step 6. Generate new weight vector Wnþ1 , using j equation (98). . Step 7. If the new weights dominated old ones, replace old ones with new ones. In other words, move the SOM mobile units toward better area. If they do not dominate each other, save the new nondominate weights in external archive. . Step 8. Apply the employed bees for neighbor search (as agents that perform near the PABC ) . Step 9. Evaluate the fitness of new obtained solutions. . Step 10. Sort the new solutions based on none dominate sorting and crowding distance to evaluate their fitness. . Step 11. Select a food source (solution) and employed the onlooker bees in order to perform a neighbor search near the chosen solution and a greedy selection based on the evaluated fitness. . Step 12. If all of the onlooker agents contribute in searching go to the next step, otherwise return to step 11. . Step 13. Export the obtained solutions in ABC phase to the collection site. . Step 14. Evaluate the fitness of GA solutions (chromosomes) in PGA and rank them based on none dominate sorting and crowding distance. . Step 15. Perform a same treat for SOM center in GA phase. In other words, regard NuGA instead of NuABC and repeat steps 4 to 7, respectively. . Step 16. Generate a random number with uniform distribution. If the random number is less than Pmutation produce children using mutation operator, else produce children using crossover due to the pool size. . Step 17. Evaluate the fitness of produced solutions and combine them with old population. Rank all of the solutions using non-dominate sorting and crowd distance. . Step 18. Select *Ps best solutions from current population. . Step 19. Export the obtained solutions in GA phase to the collection site. . Step 20. If the stopping criterion is satisfied, go to step 21, otherwise go to step 3. . Step 21. Latest population, the weight vectors in both SOM centers and also the recorded solutions (Archived ones) are considered as the final solution. . Step 22. Stop. Figure 4 indicates the flowchart of the SPSSOPSA.

Controlling the power plant using Matlab-Simulink software Matlab-Simulink is a well-known controlling software that is applied to simulate the interaction of interconnected components and consequently the total behavior of a complex engineering system. The Simulink software consumes the operating parameters and mathematical relation (governing equations) of the system components (known as blocks) and yields the correspond values of objective functions (qualities) respecting to the governing constraints. One of the other major applications of Simulink software is to control the feasibility of operating parameters of simulated system. In this article, Matlab-Simulink software is applied for simulating and controlling the interaction between Damavand’s components and also to indicate the relation between operating variables and the governing objective functions. Each plant’s component is modeled as a single block that simulates the thermodynamic processes occur inside the blocks, e.g. conservation law and between the blocks, e.g. energy flow and the exergy stream. Figure 5 represents the Simulink model of Damavand power plant.

Applying back propagation neural network for predicting the dynamic specific heat ratio during the process ANN is a computational system that simulates the microstructure of biological neurons. It mimics the learning process of a natural brain, organizes itself to gain knowledge from given examples, and applies the knowledge to solve new problems. The important advantage of ANNs compared to classical methods is speed, simplicity, and capability to learn from examples. It operates like a ‘black box’, only cares about the inputs and outputs, and requires no detailed information about the system. ANN is able to handle noisy systems and tasks involving incomplete data sets, fuzzy or incomplete information and for highly complex cases such as non-linear and ill-defined problems. Once it is trained, it can perform prediction at high speed, just as humans usually decide on an intuitional basis. Because of its advantages, ANN has been widely used in diverse applications such as classification, forecasting, control systems, optimization, and decision making. The ANN consists of many units that represent neurons. Each neuron is a basic unit of the information process. Units are interconnected via links that contain weight values. Weight values help the neural network to learn and express special knowledge. Each input is multiplied by a connection weight and summed and passes through a transfer function to generate a result, and finally, the proper output is obtained.

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Start

Parameters Definition: Nu1 ,Nu 2,Ps,Pmutation ,S f ,…. Randomly Generation First population and SOM units weight vector Perform Truncation due to sharing factor ( Rank ( (1 −

)

× Ps) artificial bees

Rank ( Record Non-dominated Solution in Archive

Calculate Learning Ratio and train

× Ps) chromosomes

Calculate Learning Ratio and train

SOM’s units using None-dominate

SOM’s units using None-dominate

artificial bees

chromosomes

Moving Neuron Center toward Non-

Moving Neuron Center toward Non-

dominate artificial bees

dominate chromosomes

Evaluate new weight vectors

Evaluate new weight vectors

NO

New weigh vectors dominate previous

Record Non-dominated weights of SOM

NO

New weigh vectors dominate previous ones?

ones?

Yes

Yes Replace previous weight vectors by

Replace previous weight vectors by

new ones

new ones

Determine neighbors of solutions

Produce a random number from

using employed bees

uniform distribution

Evaluate Nectar amount

Yes Produce children using

Rand
mutation

mutation Rank new solutions

NO Produce children using crossover

Selection

Evaluate and rank new chromosomes NO

All onlookers

Determine a neighbor of chosen food using

distributed?

onlooker bee

Select (

× Ps) best solutions based

on their rank for next population

Yes Collect solutions

NO

Stopping criteria

Yes

met?

Latest population and the SOM’s unit weight vectors and the archived ones are the final solution

Stop

Figure 4. The flowchart of SPSSOPSA. SOM: self-organizing map.

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Cond

ST

+ +

Air

AC

+ +

AP

+ +

HRSG

CC

HRSG

+ +

GT

GT

+ +

CC

+ +

Electrical Power

AP

+ +

AC

Air

F1

Fuel

Fuel costs

F2

Fuel costs

Fuel costs

F3

Fuel costs

Fuel

Figure 5. Simulink model of Damavand power plant. AC: air compressor; AP: air preheater; CC: combustion chamber; GT: gas turbine; HRSG: heat recovery steam generator; SOM: self-organizing map.

x1

y1

Target

l1 x2

y2 l2

input

xi

yi

Neural network including connection (called weights) between neurons

compare

li output xk

yn Input layer

lm hidden layer

Adjust weight

output layer

Figure 7. Schematic of BP process. Figure 6. Architecture of MLFF ANN.

The multi-layer feed forward (MLFF) neural network is the foremost network utilized by researchers because of its wide applicability in various types of real-life problems. An MLFF neural network typically employs three or more layers for the architecture: an input layer, an output layer, and at least one hidden layer. Figure 6 shows the architecture of MLFF neural network. In this type of networks, neurons are arranged in layers with connectivity between the neurons of different layers. The layer that receives inputs is called the input layer, and the layer that gives the output is called the output layer. Other layers, as they do not receive

any direct input or contribute to output directly, are called hidden layers. The transfer function that used in MLFF can be linear (which used in perceptron networks) or non-linear. Logistic sigmoid (logsig) transfer function and tangent hyperbolic (tanh) are the most transfer functions which used by researchers. ANN can be trained to approximate peculiar complex functions by adapting the weights between the nodes (neurons). After training the ANN, a particular input leads to a specific target output. Figure 7 indicates the schematic of training procedure. The adapting process will be continued, based on a comparison of the output and the target, until the actual

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outputs and expected outputs (targets) reach to a minimum difference. Many input/target pairs are needed to train a network efficiently. Batch training of a network proceeds by making weight and bias changes based on an entire set (batch) of input vectors. Incremental training changes the weights and biases of a network as needed after presentation of each individual input vector. Incremental training is sometimes referred to as ‘online’ or ‘adaptive’ training. Back propagation (BP) algorithm is one of the most popular methods among the learning techniques which possess different variants. Standard BP is a gradient descent algorithm. It tries to enhance the performance of the ANN by reducing the total error by modifying the weights along its gradient and these changes are stored as knowledge in network. These networks learn the mapping from input data spaces to target spaces by hiring supervised learning. These models are so versatile and can be used for data modeling, classification, control, forecasting, and pattern recognition. In this article, the authors utilize an MLFF network fused with BP algorithm in order to approximate the variable specific heat.

Results and discussion Analyzing the effect of turbine inlet temperature on the power plants operating parameters Deriving to an optimal turbine inlet temperature is one of the most crucial parameters that should be considered. This is because of the high impact of GTs internal interaction on the power plant exergy destruction, total investment cost, monetary flows, exergetic efficiency, net power output, etc. Hence, a proper analysis of the power plants behavior under dynamic turbine inlet temperature is required. In this article, SPSSOPSA is applied to find the relation of operating parameters through optimal Pareto fronts. Figure 8 depicts the effect of turbine inlet temperature on the constructive components of Damavand power plant. Figure 8(a) to (d) represents the relation of turbine inlet temperature and the capital investment of different components. According to Figure 8(a), increasing in the turbine inlet temperature has not an obvious impact on the capital investment of AC. Figure 8(b) and (c) suggests an increase in the capital investment of CC and GT for sustaining the optimal performance of power plant. However, in the real world, it is not acceptable to increase the capital investment of power plant components. Figure 8(d) shows a decrement of HRSG capital investment under high turbine inlet temperature. Figure 8(e) shows the consequent relation between turbine inlet temperature and the power plant cost. It is obvious that an increment in

turbine inlet temperature leads to an exponential increase in the total cost of power plant. Hence, in the range of high turbine inlet temperature (1430–1500 K), the obtained solutions have no practical interest because of the prohibitive cost. Figure 8(f) to (l) investigates the exergetic relations of turbine inlet temperature and the power plant’s operating parameters. As it is shown in Figure 8(f), an increase in the turbine inlet temperature leads to higher amounts of energetic and exergetic efficiencies. However, in higher turbine inlet temperature (1390–1440 K), there is a slight difference between amounts of efficiencies. As it is shown in Figure 8(g), the compressor pressure ratio rises from 8.8 to 19 when the turbine inlet temperature reaches to 1440 K. Figure 8(h) and (i) suggests an increasing in compressor and GT isentropic efficiency (from 0.81 to 0.92 for AC and 0.83 to 0.96 for GT) for retaining the optimal performance. However, utilizing a compressor with higher isentropic efficiency requires more initial investment. Besides, the amount of variations in isentropic efficiencies can be neglected in higher temperatures (between 1400 and 1450 K; Figure 8(h) and (i)). According to Figure 8(j), the AP effectiveness decreases exponentially from 0.96 to 0.75 which is one of the most promising elements, as a view of monetary providence, that suggests applying higher turbine inlet temperature during the process. This is because of the high price of AP in industry. Figure 8(k) indicates the monotonic increasing of CC efficiency from 0.62 to 0.98. Generally, CC’s efficiency depends on different parameters and it is an acceptable economical policy to utilize a CC with higher quality in power plants. Figure 8(l) evidences the approximate independency of turbine inlet temperature and the HRSG efficiency. Figure 8(m) to (r) analyzes the impact of turbine inlet temperature variation on mass flow rates, AP temperatures, and exhaust gas temperature. According to equation (48), in order to promote the exergetic efficiency at an acceptable cost rate for a fixed production, both air and fuel mass flow rate should be decreased. Besides, due to equation (30), a lower fuel mass flow rate decreases the fuel cost rate and a lower air (gases) mass flow rate decreases the investment cost rates and suggest a lower total cost. According to obtained plots, it will be a good idea to control the injected fuel in the range 8.37–9.1 and the air mass flow rate spanning to 440 and 500. It is important to mention that Figure 8(o) does not show a Pareto front and just derived by analyzing the effect of variable fuel and air mass flow during the process.

Acceptable analytical constraints By considering the obtained economic and exergetic analytical results altogether, it will be a good idea to

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Figure 8. Obtained Pareto fronts represent the behavior of different operating parameters as a function of turbine inlet temperature under optimal condition.

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Figure 9. Obtained Pareto fronts for different unit cost of fuel.

retain the power plants operating parameters in following spans: . . . . . . . . .

turbine’s inlet temperature: 13904T5 , T14 41445; air mass flow rate: 4404mai 4500, i ¼ 1, 2; fuel mass flow rate: 84mfi 49:5, i ¼ 1, 2; turbine isentropic efficiency: 0:834T 40:96; C isentropic efficiency: 0:814C 40:92; P isentropic effectiveness: 0:754AP 40:96; CC isentropic efficiency: 0:624CC 40:98; HRSG efficiency: 04HRSG 41; exhaust gas temperature: 378:154T170 , T17 .

Verifying the effect of different unit costs of fuel on the optimum Pareto front of cost-exergetic efficiency After obtaining acceptable engineering conditions, additional runs are performed using SPSSOPSA to find the influence of unit cost of fuel on the optimum Pareto front. Proposed algorithm yields promising results about the total effect of fuel unit cost on the performance of Damavand power plant. Figure 9 compares the obtained Pareto front with different unit costs of fuel.

It is obvious that for the higher amount of fuel cost (k ¼ 0.000008), the Pareto front begins form higher exergetic efficiency; however, consuming a fuel with higher unit cost leads to higher total cost of product. In our case, for the fuel with higher price, the exergetic efficiency varies from 50% to 54% and the cost of product ranges from 5($/S) to 8 ($/S). For the medium amount of fuel cost (k ¼ 0.000006), the exergetic efficiency spanning between 48% and 52%, which is inferior than the fuel with higher quality; however, the results illustrate that consuming this type of fuel is more acceptable as a view of thermoeconomic.24 For the fuel with k ¼ 0.000004, the exergetic efficiency varies from 46% to 50% and the total cost of product ranges from 2($/S) to 5 ($/S) which is superior, as a view of thermoeconomic, comparing to other cited fuels. Since decreasing the cost of an operating system is one of the most important elements in industry, it is a wise choice to consume a fuel with lower cost.

Validation of results To the author’s knowledge, there are no experimental data for Damavand cycle available to verify the quality of obtained results. However, for validating the obtained results, the properties of some components

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Table 1. Comparing the net exergy flow rates and exergy destruction of power plant at rated condition. Ebadi and Gorji-Bandpy23

Obtained results

Component

E_ w

E_ CHE

E_ T

E_ MEC

E_ D

E_ w

E_ CHE

E_ T

E_ MEC

E_ D

AC AP CC GT Total plant

154.814 0.000 0.000 267.824 116.010

0.000 0.000 508.566 0.000 508.566

47.034 4.295 233.545 192.585 88.699

91.318 3.534 3.863 88.402 4.481

13.462 7.829 278.88 13.163 313.338

134.966 0.000 0.000 307.082 172.11

0.000 0.000 508.566 0.000 508.566

41.700 3.045 261.15 224.484 75.32

81.590 3.158 1.435 79.218 2.21

11.676 6.203 248.85 3.383 270.11

AC: air compressor; AP: air preheater; CC: combustion chamber; GT: gas turbine. Note: Data in bold represent the optimum operating parameters.

Table 2. Comparing the initial investments, monetary flow rates, and capital cost rates under full load condition. Ebadi and Gorji-Bandpy23

Obtained results

Component

PEC ð106 Þ

C_ ð106 Þ

Z_ ð104 Þ

PEC ð106 Þ

 C_ 106

Z_ ð104 Þ

AC AP CC GT

9.69 0.7 0.97 39.17

2.36 0.171 0.236 9.56

869 63 87 3519

7.99 0.22 1.35 33.24

1.95 0.054 0.330 8.820

746 21 126 3023

AC: air compressor; AP: air preheater; CC: combustion chamber; GT: gas turbine. Note: Data in bold represent the optimum operating parameters.

Table 3. Comparing the exergoeconomic parameters of GT components. Ebadi and Gorji-Bandpy23

Obtained results

Component

cp ½$ GJ1 

cf ½$ GJ1 

C_ D ½$ s1 

fk ½%

cp ½$ GJ1 

cf ½$ GJ1 

C_ D ½$ s1 

fk ½%

AC AP CC GT

5.808 6.012 4.461 4.628

4.628 4.461 2.399 4.461

0.0623 0.0349 0.6692 0.0587

58.24 15.29 1.28 85.7

4.824 5.023 2.927 3.853

3.853 2.927 1.305 2.927

0.0449 0.0181 0.3247 0.0099

62.42 10.39 3.73 96.82

AC: air compressor; AP: air preheater; CC: combustion chamber; GT: gas turbine. Note: Data in bold represent the optimum operating parameters.

Table 4. Comparison of the decision variables. Decision variables

ma

mf

rp

T

C

T1

T2

T3

T5

Ebadi and Gorji-Bandpy23 Obtained results

497.0 442.2

10.09 8.8

10.26 9.96

88 90

85 81

299.15 300.4

603.02 604.4

796.91 770.8

1320.0 1443.5

are compared to available data.23 Since the GTs possess similar properties, we can check the obtained properties for one GT. Tables 1 to 4 compare the properties of obtained data with available data. Advantages of applying Simulink, neural network, and SPSSOPSA in analyzing, controlling, and optimizing Damavand power plant can briefly expressed as follows. 1. According to above tables, by applying neural network for predicting variable specific heat, the authors derive to more precise results.

2. By analyzing the effect of turbine inlet temperature on the power plant components, more precise spans for operating parameters are derived which play an important role in the quality and speed of optimizing and also on the robustness of algorithm. 3. By applying the Matlab-Simulink software for Damavand power plant, it is more convenient to control the validity of input decision variables (checking the constraints) and obtained results. 4. Theoretical results suggest the potential of 2964 MW power for the power plant which is an

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explicit improvement as a view of power plant’s performance management. 5. Applying the self-organizing map in the SPSSOPSA leads the optimizing model to archive higher amount of non-dominated solutions with an acceptable diversity. In our case, proposed algorithm has found 411 non-dominated solutions in its obtained Pareto front.

Conclusion Combining the second law of thermodynamics with economics, i.e. thermoeconomics using availability of energy and exergy for cost purposes provides a powerful tool for systematic study and optimization of complex energy systems like power plants. In this article, the maximum energetic/exergoeconomic potential of Damavand power plant has been investigated using a novel multi-objective optimizing algorithm based on synthesizing the artificial bees and chromosomes simultaneously. Also, it was indicated that an efficient optimizing of the operating parameters requires a complex multi-objective and multi-modal simulated functions that makes the decision making process really complicate. Hence, some of the common controlling models such as Simulink software and neural network have been utilized to overcome these crucial problems. The results confirm that proposed model is a predominance optimizing method in analyzing and optimizing real-life engineering complex systems. Funding This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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Appendix Notation CHE

chemical properties

C_ K

component cost

CP E_ k hK m m_ a m_ f MEC n PK Pref rp SV T Tref T1 T2 T3 T5 W Z_ K

specific heat ratio exergy stream for Kth component enthalpy of Kth component material air mass flow rate fuel mass flow rate mechanical properties time period pressure of Kth component standard state pressure compressor pressure ratio salvage value thermal properties standard state temperature compressor input temperature compressor output temperature combustion inlet temperature combustion product temperature work or electricity capital investments rate for Kth component

T c CC HRSG T I ;k " _ W _ Q S_

mean logarithmic temperature difference compressor isentropic efficiency CC efficiency HRSG efficiency turbine isentropic efficiency first law of thermodynamic efficiency maintenance cost rate for Kth component exergetic efficiency power output heat transfer rate entropy flow rate

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