Mechanics, Materials Science & Engineering, January 2016 – ISSN 2412-5954
Performance Optimization of a Gas Turbine Power Plant Based on Energy and Exergy Analysis Ghamami M.1, a, Fayazi Barjin A.1, Behbahani S.1 1 – Department of Mechanical Engineering, Isfahan University Technology, Isfahan, Iran a – Mghamazi@ut.ac.ir
Keywords: Gas turbine, Exergy, Multi-objective, optimization, Fireflies algorithm, thermoflow.
Abstract. The purpose of this study is energetic and exergetic analysis of combined cycle power plant, study of the variables that affect the efficiency and performance and provide a solution to improve the efficiency and performance of the gas turbine. Therefore, after modeling gas cycle, the impact of environmental conditions and performance of gas turbine cycle will be checked, eventually we achieve two objective optimization of gas cycle that optimized by firefly algorithm in six cold months of the year. The objective functions are exergy efficiency and cost of the gas cycle maintenance, fuel cost and destroyed exergy cost. The proposed optimized result show increase in net output power of the gas cycle, energy and exergy efficiency and decrease in air pollution amount.
Introduction. Gas turbine is one of the power generating machines that have been widely used in various industries such as power plants, refineries and oil and gas industries. Since a high percentage of the power requirements of the country, is provided in the gas power plants and due to the fact that fossil fuels are the energy requirements of these power plants, thus the performance improvement of these power plants is very important. From about 70 years before gas turbines have been used to generate electricity, in the last twenty years the production of these type of turbines has increased by twenty times. Thermodynamic Simulator of gas cycle and combined cycle, is a useful tool to predict the behavior of each components of the cycle, by which the basic parameters of the processes in the cycle can be obtained. Exergy analysis is a good way to evaluate the quality of the energy with the aid of laws of conservation of mass and the first law of thermodynamics, and is on the basis of the second law of thermodynamics. The tool is used for design, analysis and optimization of thermal systems. The main objective of exergy analysis, finding solutions to eliminate or reduce thermodynamic defects in the processes. We can reduced exergy destruction by identifying the irreversibility factors and situation. Many studies have been done in this field, research done in this field can be mentioned the following: Siddiqui et al. [1] In their article they simulated a 100 MW gas cycle of one of the power plants in Iran is hot and dry regions ,by thermoflow software ,and investigated the effect of steam injection into the combustion chamber based on the exergy concept in order to improving gas turbine cycle. Sadeghi et al. [2] they studied and simulated the effects of light and heavy fuel on operational parameters of the gas turbine and combined cycle in Kazeroon power plant. Kim and Hwang [3] examined the performance of a gas turbine with recovery in half-load situation, by considering and comparing different mechanisms to control the turbine. Salary et al. [4] have studied exergy analysis of 112 MW Power Plant in Ahvaz Zergan. They optimized the cycle by increasing the turbine inlet temperature in terms of energy and exergy. Abdul Khaliq [5], used exergy method to analyze gas turbine cycle with inlet air cooling and has shown that most exergy destruction occurs in the combustion chamber, he also showed that by use of cooling the compressor inlet air, energy efficiency and the cycle Exergy will be increased. Ehyaei et al. [6] at the same time studied exergic, economic and enviromental analysis affected by Fog cooling system in the gas cycle of Rajayee power plant. Sanaye and Jafari [7] work in optimizing field, they have examined effect of inlet air cooling in gas turbine cycle by absorption refrigeration. The two-
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Mechanics, Materials Science & Engineering, January 2016 – ISSN 2412-5954
objective optimization of the system is done by the genetic algorithm. kaviri et al. [8] have done thermodynamic modeling and two-objective optimization of a combined cycle power plant. Ahmadi [9] study on thermodynamic analysis of a gas cycle power plant and obtained best design parameters by using multi-objective optimization. In this study, energetic and exergetic analysis of gas turbine power plants have done and solutions to improve efficiency and performance of gas turbine are suggested. Factors affecting the efficiency of power plants have been studied and finally variables to improve the efficiency of power plants have been selected. Exergy (or ability to perform work). The maximum work that a system may do during a reversible process from initial state to reach a dead end is called exergy. Exergy of a system in a given state depends on environmental conditions and system properties, and for a control volume, it’s equal to or reversible work with a dead end. Exergy has potential, physical and chemical components. For the steady flow devices, kinetic and potential exergy can be assumed to be zero. The sum of physical and chemical exergy, is called thermal exergy [10].
ex ex Ph ex Ch
(1)
Physical exergy is defined by Equation 2.
ex Ph ( h ho ) T o (s s o )
(2)
Chemical exergy of mixtures is obtained from equation (3) [11]. =∑
+( ×
× =
)∑
× ln( ),
(3) (4)
Exergy analysis by using of the first and second laws of thermodynamics on the components of a system, makes it possible to identify the place and production of irreversibility and unfavorable thermodynamic process of the system, In this way, in addition to evaluate the different components of thermodynamic cycle, approaches to increase efficiency and output are identified [13]. Efficiency of Thermodynamic Second Law (Exergic efficiency). The first law efficiency is defined by an ideal isentropic process that never happens in practice. It makes no mention of the best case, and isn't sufficient to measure the actual system performance alone. To assess the deviation from the best possible processes, second law efficiency is defined. The second law efficiency determines how much work ability or potential used in a process [11]. In fact, it determines how much of exergy given to the system, by a process is achieved and how much of it is wasted in the form of irreversibility. The second law efficiency is defined the ratio of useful exergy to exergy input and output intensity of irreversibility is defined as (5) the difference between output exergy and input exergy [13]. = ̇=
̇
,
− ̇
(5) ,
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(6)
Mechanics, Materials Science & Engineering, January 2016 – ISSN 2412-5954
Thermodynamic Modeling of gas cycle and power plant. Thermodynamic modeling of gas cycle power plant have been done by using thermodynamic relations. Plant that studied in this paper, included 4 gas unit manufactured by Mitsubishi Japan MW-701D models with nominal capacity of each is 128.5 MW and in total 514 megawatts. By installation of 4 retriever boilers and two steam turbo generator that each has nominal capacity of 100 MW, power plant Transformed to combined cycle power plant. In order to simulate the combined cycle power plant, we set the data related to environmental conditions (Table 1). Table 1. Environmental condition in power plant Environmental condition
Value
Temperature
31 centigrade
Pressure
0.8964 bar
Relative humidity
RH=29%
Above sea level
1022 meter
Thermoflow software is one of the most powerful software in design and analysis of power plant cycles, which is capable to model various stages of the power plant, including thermodynamic analysis, engineering design and simulating equipment. Combined cycle block consists of two gas turbines, two recovery boilers and a steam turbine. By choosing Siemens W701 D engine which is available in the software engines, combined cycle block is simulated in normal loads and in software. Table 2 shows the software output. Table 2. Power plant output in normal times (90%) Type of gaseous fuel cycle
Natural gas
Gas oil
Net power output of the plant (kW)
526576
520844
Plant heat rate (kJ/kWh)
7894
7948
Plant thermal efficiency (%)
45.6
45.3
In order to verify the results of the software simulation, the values obtained from the simulation and actual data are compared in Table 3.
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Fig. 1. Operating parameters plant in case of 90% load
Fig. 2. Performance and placement components of HRSG plant in case of 90% load
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Fig. 3. Diagram of Energy flow (input and output plant power) Figure 3 shows the flow of incoming and outgoing energy to one block in combined cycle of power plant, also, it shows where the input fuel energy is intended in terms of heat value of fuel. Input energy consists of latent and sensible energy of air and chemical energy of fuel. Most thermal losses is related to the condenser, because discharges the heat taken from the cooling water to the environment. After condenser most heat losses is related to the exhaust flue gas that is at about 118 Celsius degrees, which enters too much heat into the environment without using them. Table 3. Data comparing of power plant in case of 90% load Parameter
Software simulation
Power plant
Net power output
532250
526576
Heat Rate
7883
7894
-0.14
Thermal efficiency (%)
45.67
45.6
+0.15
Fuel flow
6.361
6.35
+0.11
Air flow
339.1
338
0.11
The compressor pressure ratio
12.27
12.2
0.57
Turbine pressure ratio
11.29
11.2
0.8
Turbine inlet gas temperature (K)
1387.9
1385
0.21
Error (%) +1.08
In tables 3, net output power is expressed in kilowatts (kW) scale and heat rate is expressed in kJ / kWh scale. The rate is expressed on a scale of kilograms per second (kg/s). By comparing the study results provided by the simulation and power plant results it can be seen that there is a good MMSE Journal. Open Access www.mmse.xyz
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Mass flow rate of air entering the compressor [kg/s]
adaption between the results. In six cold months (October to the end of April), due to a dramatic reduction in household electricity consumption compared with six warm months of the years, the demand for electricity from power plants in the country declined. The main priority in the six cold months, is increase in exergy efficiency of gas cycle and reduce the annual cost. With the increase in air temperature, the gas turbine and the compressor's power reduces, due to the more steep decline of power in gas turbine compared with the compressor, the net output power of the gas cycle is reduced. With the increase in air temperature, mass flow of gas turbine exhaust gases reduces, less steam is produced in the recovery boiler and there will be a total loss in power of steam turbine. By reducing the power of steam-gas cycle, the net output of power plant appear with declined more sharply. For one degree Celsius rise in ambient air temperature, pure output power of the gas cycle, steam turbine and power plant will averagely reduce 0.63 and 0.27 and 0.53, respectively. Comparison between output powers with respect to temperature is shown in Figure 4.
365 360 355 350 345 340 335 330 325 320 315 5
8,5
12
15,5 19 22,5 26 29,5 Environment temperature [C]
33
36,5
40
Fig. 4. Special compressor pressure ratio and can shift with ambient temperature Optimization. After reviewing the parameters affecting the performance of plants, defining optimization problem based on target functions and parameters can be done. Optimization problem in finding answers or solutions on a set of possible options aimed at improving the standard or standards of the issue. Multi-objective optimization problem arise from the decision-making methods in the real world that one decision maker faces a set of contradictory and conflicting objectives and criteria. In these types of issues, unlike the single-objective optimization problems and because of the multi-purpose (often conflicting), rather than just a solution optimized set of questions arises. In the multi-objective optimization, after the introduction of design variables and determine the objective functions, optimal points are determined and the impact of design on objective functions are provided. Many factors affect the performance of gas turbine, therefore, gas turbine cycle has many ways to improve the performance of the industry. Each of these methods has different effects on output power, efficiency and specific consumption of fuel. The selection of a particular method according to plant type, climatic conditions, work area, how it affects the performance of the project cycle, and measures will be considered. Some of the most important factors affecting the operation of the gas turbine are: • Pressure ratio • Compressor inlet temperature • Compressor efficiency
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Mechanics, Materials Science & Engineering, January 2016 – ISSN 2412-5954
• The compressor intake • Turbine inlet temperature • Turbine efficiency • Output power of turbine • Fuel air ratio • Mass flow rate As can be seen in Figure 5, with increasing ambient air temperature, compressor pressure ratio reduces. As well as the temperature increases, air density decreases, resulting in a greater volume of air should be particularly dense, and the special power of compressor will increase.
Special power
Compressor pressure ratio
13,2
380 375 370 365 360 355 350 345 340 335 330
13 12,8 12,6 12,4 12,2 12 11,8 11,6 11,4 5
8,5
Special power compressors [kW / kg / s]
Pressure ratio
12 15,5 19 22,5 26 29,5 33 36,5 40 Environment temperature [C]
Fig. 5. Change in net output power cycle gas and steam turbine power plants with ambient temperature For one degree Celsius increase in temperature, compressor pressure ratio and special averaged power increases 0.24 percent and 0.25 percent respectively. Gas turbine is power generation system at constant volume. By increasing the ambient air temperature and constant air pressure in a fixed volume, density and mass flow rate of air flow is reduced, resulting in reduced compressor inlet mass. Figure 6 shows the compressor inlet air mass flow changes to show the changes in ambient temperature. For one degree Celsius rise in temperature, compressor inlet air flow is reduced by an average of 0.24 per cent.
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TET
1119
550 548
1118
546 544
1117 1116
542 540 538
1115 1114 1113
536 534
1112 1111
532 530
1110 5
8,5
12
15,5 19 22,5 26 29,5 Environment temperature [C]
33
36,5
40
Exhaust turbine gas temperature [C]
Turbine inlet gas temperature [C]
TIT
Fig. 6. Chart compressor inlet air mass flow changes with temperature With the increase in air temperature, gas turbine inlet gas temperature increases due to the reduced amount of fuel and increase in air to fuel ratio. With increasing temperature due to increased temperature of the exhaust gases from the gas turbine inlet air temperature for cooling turbine blades increases. For one degree Celsius rise in temperature ambient air, intake and exhaust gas temperature of the turbine by an average of 0.4 degrees Celsius, respectively 0.17 ° C decrease and increase. Figure 7 shows the change in gas turbine inlet and outlet gas temperature than the ambient temperature shows.
GT GrossPower
ST Gross Power 111 108 105 102 99 96 93 90 87 84 81 78 75
Net power output (Plant) MW
310 300 290 280 270 260 250 240 5
8,5
12
15,5
19
22,5
26
29,5
33
36,5
Net power output (GT-ST) MW
Plant Net Power
40
Environment temperature [C]
Fig. 7. Gas turbine exhaust gas temperature changes graph input and ambient temperature Differences between the energy and exergy system can be expressed as follows [12].
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Mechanics, Materials Science & Engineering, January 2016 – ISSN 2412-5954
1. Energy just relates to the system condition and the mass flow but exergy in addition to those conditions is dependent on environmental conditions. 2. The amount of energy in the dead system may also have an amount, but the exergy in a dead system is always zero. 3. Energy for all the processes are subject to the law of survival, and is stated in the form of the first law of thermodynamics but exergy is subject to survival only in reversible processes. In irreversible processes, always exergy a destroyed. Exergy, applies a combination of the first and second laws of thermodynamics to the review process. 4. Energy is only a quantitative measure for evaluating processes but exergy is both quantitative and qualitative measure. 5. Energy can be calculated with respect to each case assumptions but exergy basis mode is determined by environmental conditions. After reading the parameters and variables on power plant performance optimization, optimization process takes place. Because of the simultaneous search of multiple points, no need for an explicit mathematical relationship between objective functions, the need for direct measurement and mathematical calculations needed to optimize the methods of analysis and generalization of random search algorithms, optimization of problem is done by random search algorithms. The objective function. To compare the achieved considerable optimization problems we need to have a selection criterion. Such a measure, which plan is optimized and is a function of design variables, standard function, is called advantage function or objective function. In this study, the objective functions, exergy efficiency and costs related to gas cycle, and the optimal points represent the highest efficiency and lowest costs. Relation 6 and 7 show the first and second objective function, respectively.
OF1:Max η = OF2: Min Ċ Ẇ ̇
= η = ̇
̇ ̇
(7)
= Ċ + Ċ + Ż × Ẇ − Ẇ ×
, η
,
(8) = 0.985 = 46254
(9)
(10)
Net Output power of the gas cycle can be obtained as above. Decision variables. Thermodynamic modeling inputs are decision variables and numbers represent degrees of freedom of the system. Decision variables change during the optimization process, but the parameters are fixed, but some parameters, are dependent parameters which is determined on the amount of basis of the decision variables. The variables which are specified in Table 4, are selected as the decision variables. In order to stay in the recovery boiler circuit, the gas turbine load is considered higher than 55%. Using thermoflow and EES software and range change in environmental conditions, according to the decision of the six variables in Table 1 and also taking into account the load percentage of the gas turbine in the range of 55 to 100% has been obtained. Firefly algorithm. Firefly optimization algorithm or FA for short is inspired of the natural behavior of fireflies which live together in large collections, and was introduced for the first time in late 2008 by Xin-She Yang [14], this multi-agent algorithms can be a solution of hard optimization problem and it is a very efficient algorithm for solving combinatorial optimization problems. In summary, the performance of the algorithm is that the number of artificial fireflies (initial population) are randomly distributed in the range and then emits light of a firefly which intensity is MMSE Journal. Open Access www.mmse.xyz
Mechanics, Materials Science & Engineering, January 2016 – ISSN 2412-5954
proportional to the amount of optimality point Firefly is that it is located. The light intensity of each firefly regularly intensity compared to other fireflies and fireflies brighter too faint to be absorbed. At the same time the brightest fireflies also aims to increase the chances of finding the optimal solution is the global accidentally move. In this algorithm, exchange information with each other through the light emission occurs. The composition of this combined action makes the overall trend towards a more efficient is fireflies. Table 4. Optimization variables and their ranges Variable interval
Variable
Compressor pressure ratio
10 <
< 14.3
Isentropic efficiency turbine
0.88 <
< 0.91
Isentropic efficiency compressor
0.79 <
< 0.86
288 < Ě&#x2021; < 400
Compressor inlet mass flow rate (kg/s) The output of the gas turbine combustion pressure (bar) Gas turbine inlet temperature (K)
0.92 < 1290 <
< 0.94 ( ) < 1390
(Millions of dollars) costs
Optimization Results. Given the equations required optimization objective functions according to the decision made and the six variables in MATLAB fireflies algorithm code was used to optimize the objective function. The primary population for the first generation is considered 200. In the multi-objective optimization instead of an optimal point, we have an optimal solution that is optimized to the famous pareto point and the set of these points are called pareto front. Figure 8 shows the pareto front of the optimization objective functions, including optimal points. As can be seen by increasing the efficiency of the gas cycle exergy, it also increases annual costs.
6,8 6,6 6,4 6,2 6 5,8 5,6 5,4 5,2 5 4,8 4,6 4,4 4,2 4
C
B A
0,26
0,27
0,28
0,29
0,3
0,31
0,32
Exergy efficiency (%)
Fig. 8. Pareto Front of the first objective functions (cost) for six months MMSE Journal. Open Access www.mmse.xyz
0,33
0,34
0,35
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Selection the desired optimization of energy systems based on multi-objective optimization decision-making ideas happen after the search. Each individual decision-maker may be due to considerations in mind, their own scenario is to select the optimal point. Pareto front of the optimization objective function shows that the costs for the six months is considered. The results, show minimal costs during the year should be paid for a certain exergy efficiency, and most exergy efficiency that can be achieved for a certain fee during the year. Figure 9 shows the net profit for the six months according to exergy efficiency. Net profit, the difference between the proceeds from the sale of electricity and the cost of the cycle ( Cď&#x20AC;Ś Tot ) is obtained. The price of electricity purchased from power plants 0.15 Dollar/kWh is considered [13]. Pareto front of net profit of the previous stage results are plotted in Figure 9.
(Millions of dollars) net profit
1,2
B
1 0,8
C
0,6 0,4
A
0,2 0 0,26
0,27
0,28
0,29
0,3
0,31
0,32
0,33
0,34
0,35
Exergy efficiency (%)
Fig. 9. The change in net profit with electricity prices 0.15 Dollar / kWh In Figure 10, the net profit in the six months according to exergy efficiency has been showed in gas cycle power plant. The price of electricity purchased from power plants is intended 0.3 Dollar /kWh. (Millions of dollars) net profit
10 9
C B
8 7
A
6 5 4 3 0,26
0,27
0,28
0,29
0,3
0,31
0,32
0,33
Exergy efficiency (%)
Fig. 10. The change in net profit with electricity prices 0.3 Dollar / kWh
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0,34
0,35
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Table 5 Three optimal point A, B and C compared with each other. Given the priority of each objective function optimal point can be selected. Table 5. Comparison of the optimum Point A
Point B
Point C
Exergy efficiency (%)
26.7
31.3
34.5
Efficiency (%)
27.5
32.5
34.9
Net output power
68
90.7
114
Price Six months (millions of dollars)
4.3
4.9
6.4
Exergy destroyed
104
120
141
Net profit price of electricity: 0.3
0.05
0.9
0.9
Net profit price of electricity: 0.15
4.4
6.7
8.3
In table 5, net output power and destroyed exergy are in megawatts scale (MW) and amounted net profit is expressed in millions of dollars scale for both 0.15 and 0.3 dollar per Kilowatt hours (dollar/kWh) of generated electricity. Summary. The main goal of this study was to evaluate and improve the performance of gas cycle power plant in different environmental conditions. The analysis results show that the greatest destruction exergy of gas cycle power plant is happening in the combustion chamber. That reason is high temperature difference between the temperature of the flame and fluid. Much of this destruction exergy is inevitable that cannot be reduced, so exergy efficiency of power plants has been studied and other ways use to reduce the exergy destruction. Firefly algorithm has been optimization algorithm in gas cycle power plant. Objective functions are exergy efficiency and cost, cost include the gas cycle maintenance costs, fuel cost and the cost of exergy demolition, highest efficiency exergy and lowest cost are requirements. The results show that by increasing the efficiency of the gas cycle exergy, its cost also increased. Lower temperature reduces emissions and steam quality in the recovery boiler and steam turbine power output is reduced as a result. To remedy this problem, the use of gas turbine exhaust duct burner is recommended. In this case, the temperature of the exhaust gas from the turbine should exceed the temperature of HRSG design. The study achievements can be cite to use of meta-heuristic algorithm in large search space, nonlinear variables and objective functions such as firefly algorithm. Because that limited studies have been done for examine ability and capabilities of this algorithms, this study is an opportunity to investigate the algorithm and its ability. Multi-objective optimization process has its own challenges and advantages. In the multi-objective optimization not only efficiency but also exergy cycle costs, including the cost of repair and maintenance, the cost of fuel and the cost of destruction exergy have been studied. Time-consuming optimization process is very important. Less computational time and iteration means less computational cost, by using of the optimal response of optimization algorithm, the net power output of the gas cycle power plants by as much as 11.15 and 8.08 percent, energy efficiency and exergy cycle gas 3.64 and 3.61 respectively percent and air emissions, 0.77 percent decrease. This study also examines changes in environmental conditions and levels of load on the gas cycle power plant, Technical and economic assessment, energy and exergy analysis using the
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first and second law of thermodynamics can be mentioned. As well as alternative ways to reduce destruction exergy and increase exergy efficiency are reviewed. Thermoflow Software can calculate the pollutions of the turbine gas output. It is suggested that the impact of changing load levels and the effect of cooling system of air entering to compressor will be investigated in order to predict exhaust pollutions of gas turbines. Reference [1] Siddiqi H, Bayati Gh,Tvakoli A, Fotoohi D, "simulated cycle 100 MW gas and steam injection into the combustion chamber 'exergetic analysis and energetic", conferences energy efficiency, conferences Institute of Technology, Tehran, (2010). [2] Sadeghi H, Haghighi khoshkhor V, Tanasan M, Moosavian M, "Simulation of the thermodynamic effects of non-gaseous fuels on the performance and efficiency of combined cycle power plant", the twenty-seventh International Conference on Electric Power Research Institute, Inc. Tavanir, Tehran, (2012). [3] Kim T, Hwang S.H, “Part load performance analysis of recuperated gas turbines considering engine configuration and operation strategy”, J.of.Energy, 31, pp. 260-277, (2006), doi: 10.1016/j.energy.2005.01.014 [4] Salari M, Hashemi Sh, Zayer noori M, "Exergy and Exergy Economic Analysis Zargan Gas Power Plant in Ahvaz", the first International Conference on Energy Planning and Management, Institute for Research in Energy Planning and Management, Faculty of Tehran University,(2006). [5] Khaliq A. and Dincer I, “Energetic and exergetic performance analyses of a combined heat and powerplant with absorption inlet cooling and evaporative aftercooling”, J.of.Energy, 36, pp. 2662-2670, (2011). doi:10.1016/j.energy.2011.02.007 [6] Ehyaei M. and Mozafari A. and Alibiglou M, “Exergy, economic & environmental (3E) analysis of inlet fogging for gas turbinepower plant”, J.of. Energy, 36, pp. 6851-6861, (2011), doi:10.1016/j.energy.2011.10.011 [7] Sanaye S, Jafari s, "Optimizing the objective cycle gas turbine inlet air cooling by absorption chiller", Second International Conference of chiller and cooling tower, energy Ham Andyshan Kimia, Tehran, (2011). [8] Kaviri A. and Jaafar M. and Lazim th, “Modeling and multi-objective exergy based optimization of a combined cycle power plant using a genetic algorithm”, J.of.Energy Conversion and Management, 58, pp. 94-103, (2012), doi:10.1016/j.enconman.2012.01.002 [9] Ahmadi P. and Dincer I, “Thermodynamic and exergoenvironmental analyses, and multi-objective optimization of a gas turbine power plant”, J.of.Applied Thermal Engineering, 31, pp. 2529-2540, (2011), doi:10.1016/j.applthermaleng.2011.04.018 [10] Cengel Y. and Boles M, “Thermodynamics an Engineering Approach”, Vol. 5, McGrawHill, (2005). [11] Bejan A. and Tsatsaronis G. and Moran M, “Thermal Design and Optimization”, Vol. 1, Wiley-Interscience, (1995). [12] Shapiro H. and Munson B. and Moran D, “Introduction to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, and Heat Transfer”, Vol. 1, Wiley, (2002).
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[13] Power Research Institute, Deputy optimize energy consumption, and productivity studies office productivity sources of energy organization of Iran (SABA), the archives information plant. [14] Yang, X-S., “Nature-Inspired Metaheuristic Algorithm”, Luniver Press, (2008).
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