OPTIMIZATION OF A NEW CONFIGURATION OF POWER TRI-GENERATION CYCLE BY THE USE OF A MULTI-PURPOSE GENETIC ALGORITHM

In the current study, a new configuration of power tri-generation cycle was suggested. In this cycle, the energy of hot gases output from the gas cycle in the heat recovery steam generator (HRSG), and the waste energy of the condenser in the steam cycle were recovered in the Organic Rankine Cycle (ORC). After the energy, exergy, and economic modeling of the cycle, the optimization of this cycle by the use of multipurpose genetic algorithm was performed. The objective functions were the electricity cost and the second law efficiency of thermodynamics. The variables chosen for optimization were the air to fuel molar ratio, the compression, and expansion ratio of the compressor and turbine of the gas cycle, the mass flow rate of water steam and refrigerant in steam cycles and ORC, the Pinch points between the gas cycle and steam, and steam cycles and ORC, and the maximum temperatures of the steam and ORC cycles. The optimization results showed that by choosing the optimal values of variables, the efficiency of the first and second thermodynamic laws, and the produced entropy would be 67.3%, 68.9%, and 3342.5 kW/K. Also, the generated electricity cost was reduced to 0.049 $ US

They concluded that the best choice is the ORC with heat recovery [11]. Pierobon et al. in 2013 found an optimal design of MW-sized ORC's by the use of multi-purpose optimization with the genetic algorithm. They considered three objective functions: thermal efficiency, the total system volume, and the Net Present Value. The optimization variables were the working fluid, the turbine inlet heat pressure, and the condensed heat of compression points of fluid velocity in heat exchangers. They used this method to recover the waste heat from the SGI-500 gas turbine installed on Draugen oil and gas platform, in the North Sea. The two optimal working fluids are Acetone and Cyclopentane, and the thermal efficiency and Net Present Value for cyclopentane were higher than Acetone [12]. Wang et al. in 2013, used the genetic algorithm as the optimization method, in a comparative study on an ORC with R-134a working fluid, for recovering the low-heat waste. Exergy efficiency and total investment cost were considered as two objective functions to be optimized under certain waste heat conditions. The Pareto limit obtained shows that the increase in exergy efficiency can lead to the increase in total investment costs of ORC [13].Tanczuk & Ulbrich in 2013, dealt with the investigation of the combined gas-fueled internal combustion engine, gas boilers, and ORC system. The results showed that this system is economic in Germany. However, it is not economic in the Netherlands. The Payback Period for Germany and Netherlands were 9.2 and 15 years, respectively [14]. Clemente et al. in 2013, dealt with the investigation of the combined thermodynamic cycle of the gas power plant with organic Rankine cycle. In the above analysis, the gas power plant had a gas turbine with heat recovery and nominal power of 100kW. The gas turbine outlet gases are recovered in an ORC. In this analysis, six working fluids and four types of ORC were studied [15]. Darvish et al. in 2015,simulated the thermodynamic performance of a regenerative ORC which used a low-temperature heat source to help with the selection of proper organic working fluid. They use the thermodynamic models to investigate thermodynamic parameters such as ORC's output power and energy efficiency. Also, in this study, the electricity costs were estimated by the exergy-economic analysis. The working fluid was considered as a part of the investigation to determine the highest output power and energy efficiency in the system condition. The energy and rate of electricity cost were used as the objective functions for system optimization, and each fluid is evaluated based on optimal operational conditions. The high temperature and pressure rate are the independent variables of optimization [1]. Carcasci and Winchler, in 2016, dealt with the investigation of an ORC for recovery of compressor outlet air heat. The two high-and low-pressure compressors were used in this analysis which was cooled between two compressing stages. The heat recovered from the air was used as the heat source of ORC thermal cycle. The results showed that through this method, the system efficiency is increased by about 10% [16]. Cao & Dai, in 2017, investigated the efficiency of a combined cycle of gas turbine and ORC in different working conditions. Their results showed that ORC's with variable pressure have better performance compared to the ORC's with constant pressure [17]. Khaljani et al. in 2015 investigated the exergy and economic analysis of the combined cycle of gas turbine and ORC cycle. In this research, steam produced in HRSG is transferred directly to the evaporator of ORC cycle, which is different from cycle configuration of this paper. In this paper, the heat exhausted from the condenser in steam cycle, can be recovered in ORC's evaporator [18]. Carcasci et al.in 2014 also proposed a Thermodynamic analysis of an organic Rankine cycle for waste heat recovery from gas turbines their investigate showed cyclohexane is the best fluid for low oil temperature, benzene is the best choice for medium oil temperature and toluene should be used for high oil temperature. Configurations of cycle proposed are totally different from cycle configuration of this research [19].
Several papers have been investigated about the exergy, economic and environment analysis of gas turbine power plant, various methods of gas turbine cycle inlet air cooler, dispersed power generation systems have been published by the author of this paper [20][21][22][23][24][25][26][27][28][29][30][31]. A. Abbassi and M. Aliehyaei in 2004 investigated Exergy method of optimization of a wavy plate indirect evaporative cooler they understated although the exery analysis has high efficiency for thermal systems at a high temperature difference , nevertheless the present result show that this method may also be applied for systems with high fraction pressure loss and low temperature difference by this method can increase energy efficiency by up to 65% [32].
E.Ghasemian and M. Aliehyaei in 2017worked on Evaluation and optimization of organic Rankine cycle (ORC) with algorithms NSGA-II, MOPSO, and MOEA for eight coolant fluids their result showed The selection of the optimization method depends on the desired objective of optimizing and the selected fluid. For optimization, the MOPSO method shows the best performance in terms of exergy and thermal efficiency; however, in terms of the costs, the three methods show different performance in different fluids [33]. Kazemi, and, Ehyaei, in 2018 investigated exergy, and economic analysis of a geothermal power plant, they coupled geothermal power planet cycle with ORC cycle in the next step exergy, and economic analysis were made, their results determined The highest and lowest amounts of the costs of exergy waste in the ORC with geothermal heat source were 78.1 and1.2 (US$), for the turbine and pump [34].
Regarding the studies conducted so far, it can be found that no studies have been done on heat recovery from recovery boiler system condenser (HRSG). Also, there has been no newtri-generation system and its optimization through multi-purpose genetic algorithm proposed, so far. In the current study, the energy, exergy, and economic modeling of the gas turbine, recovery boiler, and ORC triple system. In fact, the proposed system is formed between the two stages of heat recovery. In the first stage, the heat energy of the gas turbine outlet gases is recovered, and the water is converted to high-pressure steam in the recovery boiler. In the second stage, the energy of steam turbine outlet low-pressure steam is transferred to the ORC working fluid and converts it to the super-heat steam. After the energy, exergy, and economic modeling of the mentioned system, based on the constrains on the system, the objective function is defined, and the tri-generation system is optimized through the use of the multi-purpose genetic algorithm. The innovations of the current study are as follows: -Proposition of a new thermodynamic cycle for recovery of as much energy as possible -Energy, exergy, and economic modeling of tri-generation system for the first time -Definition of the constrains and objective function of the cycle for optimization -Optimization of the cycle by the use of multi-purpose genetic algorithm -Complete sensitivity analysis of calculated optimal values by the optimization algorithm Figure 1 shows the gas, steam, and ORC triple cycle system. Figure 1. The gas, steam, and ORC triple cycle system

MATHEMATICAL MODELING
In the system of figure 1, the air is entered at the point one in the environment condition, and it is condensed by the compressor (point 2). The condensed air at the pint 2, reacts with the fuel condensed in the compressor booster (point 19), in the combustion chamber (cc), and the fuel is combusted. The gases produced by the combustion are entered into gas turbine (point 3). This gas is expanded in the gas turbine and then generates power (point 4). This gas is entered into Heat recovery steam generation (HRSG) and converts the pump outlet water (point 9) into super-heat steam (point 12). The HRSG includes three parts namely the economizer, drum, and super heater. In the Economizer, the pump outlet condensed water converts into the saturated fluid (point 10). In the Drum, the saturated fluid converts into saturated steam (point 11). And in the super heater, the saturated steam converts into super-heat (point 12). The points 5, 6, and 7 show the gases outlet from super heater, Drum, and Economizer, respectively. The super-heat steam is expanded in the gas turbine and generates power (point 13). The steam expanded in the steam cycle condenser transfers its heat to the ORC operator (point 8). In the ORC, the In modeling the cycle of figure 1, the following assumptions have been considered: 1. The "steady state" conditions have been presumed. 2. The temperature and inlet air pressure have been presumed as 288 K and 101.3kPa. 3. The air compressor pressure ratio and efficiency are presumed to be 10 and 85%. 4. The temperature and pressure of natural gas input to the compressor booster are presumed to be 283 K and 250kPa. 5. The compressor booster pressure ratio and efficiency are presumed to be 5 and 80%. 6. The molar ratio of fuel mixture components is accordance table (1). 7. The gas turbine pressure ratio and efficiency are presumed to be 11 and 80%. 8. The air-to-fuel molar ratio in the gas turbine is 2.5. 9. The pressure drop in the steam cycle and ORC is about 2 and 3%. 10. The mass discharge of steam in the steam cycle is 78.9kg/sec. 11. The pressure at the top and bottom of the steam cycle is 4000, and 300kPa, respectively. 12. The steam cycle pinch point (TPP,st) is presumed to be 313 K. 13. The HRSG's efficiency is considered to be 95%. 14. The pump and steam turbine efficiency are considered to be 85%. 15. The mass discharge of the coolant in the ORC is 47.5 kg/s. 16. The pressure at the top and bottom of the ORC is 300, and 70 kPa, respectively. 17. The ORC pinch point (TPP,ORCt) is presumed to be 293 K. 18. The pump and turbine efficiency in the ORC are considered to be 85%.
The mass and energy balance equation are shown in Table 1. For investigation and designing the combustion chamber, the gas analysis is needed, which is done based on

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For calculation of the temperature and combustion output, the below equation can be considered. The combustion process has been assumed to be the equilibrium: In which: a r is the air-to-fuel molar ratio, a', b', c', d', e', f', g' are the equation coefficients in the equation (7) which are calculated based on mass conservation. Regarding the following equilibrium equations: In which, CO K is the equilibrium constant of the equation 2, NO K is the equilibrium constant of the equation 3, 2 P is the pressure before to entering the combustion chamber (kPa), 3 P is the combustion pressure (kPa), and a, b, c, d, e, f, g are the coefficients of equation 2 and 3.
The combustion process in the combustion system is also considered as follows [38]: In which, P m  is the mass flow of the products (kg/s), and r m  is the mass flow of the reactants (kg/s). cc η is the combustion efficiency, h is the enthalpy (kJ/kg),  h is the enthalpy at the reference temperature (kJ/kg), and  f h is the enthalpy of formation (kJ/kg). Based on the equations 1 to 4, and solving them, the combustion temperature and the products can be calculated.
the system first law efficiency is defined as: The exergy of the points 1 to 7, and 18 and 19 (gas turbine cycle) can be calculated from the following equation [38]: In the above equation, ph e and ch e are the physical and chemical exergy, respectively (kJ/kg).
The exergy of the steam cycle and ORC can be calculated from the following equation [35,36].
The entropy production in the gas cycle and for the compressor, compressor's booster, combustion chamber, and the gas turbine are shown in table 3. Table 3. The entropy production in the gas cycle In the table 2 gen S  is the entropy production (kW/K). The bc,g, cc,g, c,g, t,g subscripts represent compressor booster, combustion chamber, and gas compressor, gas turbine, respectively. The entropy production in the Economizer, Drum, Super Heater, Steam Turbine, and Condenser is shown in table 4.
In the above table, ex8 to ex13isthe exergy of the points given in figure 1 (kJ/kg), and the TEco,TDrum,TSH and TCo are the temperatures of the Economizer, Drum, Super Heater, and Condenser in the steam cycle (K), The objective equation for calculation of the cost of power generated by the gas turbine is defined as the following equation: Journal of Thermal Engineering, Research Article, Vol. 6, No. 2, Special Issue 11, pp. 65-91, March, 2020

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In the above equation, E C is the power cost ($/kWh), 1 C is the initial installation costs ($/kWh), O C is the maintenance costs ($/kWh), and F C is the fuel costs ($/kWh).
The advantage of this method is the calculation of the costs based on each kilowatt of power production. Also, the cost of power can be calculated with the changes in parameters and conditions. The electricity cost related to the initial installation can be calculated by the following equation: In which, C is the initial installation costs ($), and I is the profits from the initial costs.
The profits from the initial costs can be calculated as follows [39]: In the above equation, L is the equipment life span (year), and i is the interest rate. The maintenance costs were considered as 4% of the initial installation costs.
The fuel costs can be calculated from the following equation [39]: The fuel cost is equal to 0.0296 (US$/kWh) [39]. Table 5 shows the equations for compressor, combustion chamber, and gas turbine equipment costs [40] .   (10) Table 6 shows the costs of the pump, HRSG, steam turbine, and condenser, in the steam cycle, the following equations can be used [41].

GENETIC ALGORITHM
The genetic algorithm is an optimization method inspired by the creatures' nature. This algorithm is based on iteration, and its principles are derived from the genetic science. In the genetic algorithm, the exploration methods act based on the selection mechanism and natural genetics. These algorithms select the most suitable threads from organized random information. In each generation, a new group of threads is formed by the best parts of the previous iterations, and a new random part is created for a suitable response. These threads efficiently explore the past information in the search space to advance to the new exploration point with better responses [45] .In general mode, when a genetic algorithm is applied, the following cycle is passed: Firstly, a primary population of people is selected randomly and without any specific criteria. For all the chromosomes (people) of the generation zero, the fitness value is determined based on the Fitness Function (objective function) which can be very simple, or complex. Then, through the different defined mechanisms for selection operator, a subset of the primary population will be selected. Afterwards, the crossover and mutations operations will be applied to the selected people, based on the problem statement. Now, these people on whom the genetic algorithm mechanisms were applied, should be compared to those of the primary population (generation zero), regarding to fitness value. (Definitely, we would expect the generation one's people have more fitness, regarding the application of the genetic algorithm operations on them. But it is not necessarily true). Anyways, there would remain some people with the highest fitness. These people, as a collection, will act as the primary population for the next stage.
The general design of an algorithm is as follows: 1) Initiation: create an n-chromosome population, randomly (the suitable solutions to the problem).

RESULTS AND DISCUSSION
For modeling the combinational cycle (GT+HRSG+ORC), an M-File has been written in MATLAB Software. The written M-Files Xsteam and Refprop were used for thermodynamic specifications of the steam and working fluids of the cycle [47] .For validation of the model, since the cycle proposed in the current study have not been presented in any other studies so far, the gas turbine cycle and the single-pressure HRSG are investigated. The specifications of the combined cycle presented in the reference [48] are input into the written code, and the results of the modeling are compared to the results of that reference. Regarding the evaluations, the highest error in the gas cycle first law efficiency is about 5.6%, and in the steam cycle, it is 7.1%.For system second law efficiency this difference is higher. For gas turbine is about 6.8% and for the steam cycle is about 8.6%.
The specifications of the coolant fluid employed in this study are presented in Table 8 [47]. The multi-purpose algorithm genetic was used for optimization of the system. The variables defined for optimization and their change range are as follows:  , and the y-axis is the efficiency of the second law of thermodynamics. The trend of the shown graph is descending, i.e., by the decrease in the efficiency of the second law of thermodynamics, the cost of the power generated by the cycle is increased, and vice versa. The specifications of the dual-purpose genetic algorithm for the Pareto graph in figure 3 are shown in table 9. Table10shows the values of the variables, the efficiency of first and second laws of thermodynamics, the entropy production, and electricity cost before and after optimization.
Based on the values in table 10, it can be concluded that optimization of the cycle has led to the increase in efficiency of the first and second laws of thermodynamics from 52.1% and 53.4%, to 67.3% and 68.9%. However, this increase in the efficiency has led to the rise in entropy production from 3062.2 (kW/K) to 3342.5 (kW/K). From another aspect, in general, the cost of the electricity generated by the tri-generation cycle has been reduced from  Figure 4 shows the optimal value of the efficiency of the second law of the thermodynamics in the cycle per different populations of genetic algorithms. It is obvious in the figure that from the pairs above 200, the optimal response is constant. Therefore, the evaluation of the optimal responses of the population was also done, in order not to affect the optimal response.  Figure 5 shows the changes in the efficiency of the second law of thermodynamics in tri-generation cycle per air-to-fuel molar ratio (ra) and different pressure ratios of the compressor. From the changes in the figure, it can be concluded that by the increase in pressure ratio of the compressor to the air-to-fuel molar ratio, the efficiency of the second law of thermodynamics in the tri-generation cycle is decreased. By the increase in the air-to-fuel molar ratio, considering that the gas turbine outlet temperature is decreased, the efficiency of the steam cycles and ORC is also reduced, which lead to the subsequent decrease in overall efficiency of the cycle. From another point of view, by the increase in the air compressor pressure ratio, two opposite effects can be observed: 1) increase in the compressor consumed power, and 2) increase in the compressor outlet temperature as a result of which, the combustion occurs in a higher temperature. This increase in combustion temperature would subsequently increase the efficiency of the steam cycles and ORC. Based on the changes in the graph, it is clear that the first effect dominates the second one. Figure 6 shows the changes in the efficiency of the first law of thermodynamics for the tri-generation cycle per air-to-fuel molar ratio (ra), and in different pressure ratios of the air compressor. The process changes of figure 6 are similar to figure 5. It should be noted that in the figures 5 and 6, all the values except the air-to-fuel molar ratio (ra) and compressor pressure ratio (rc), have been chosen as optimal. Figure 7 shows the efficiency of the second law of thermodynamics for a gas cycle, gas cycle with steam and gas, steam, and ORC triple cycle, per air-to-fuel ratio. It indicates that by the increase in the air-to-fuel molar ratio, the efficiency of the second law of thermodynamics is reduced for all the three cycles; the efficiency range of the gas cycle is from 26 to 23%, for the gas and steam combined cycle, it is from 65 to 52%, and for the tri-generation cycle, it is from 70 to 56%. It should be noted that in figure 7, all the optimal values of the changes which have been calculated by the dual-purpose genetic algorithm, are entered into the software as input.

Figure 7.
The changes in efficiency of the second law of thermodynamics for gas cycle, dual cycle, and trigeneration cycle per air-to-fuel molar ratio (ra) Figure 8 shows the changes in the efficiency of the second law of thermodynamics for tri-generation cycle per gas turbine expansion ratio. In this figure, all the optimal values obtained from the dual-purpose genetic algorithm, except the gas turbine expansion ratio (rt), have been selected. The trend of the graph changes shows that change in gas turbine expansion ratio from 6 to 13, would lead to the increase in efficiency of the second law of thermodynamics from 68.5 to 69%. It can be concluded that the changes in gas turbine expansion coefficient have no significant effects on the efficiency of the second law of thermodynamics in tri-generation cycle. In general, the increase in gas turbine expansion ratio has the following effects: 1) Increase in the gas turbine output power due to the rise in the gas turbine expansion ratio 2) Decrease in the gas turbine outlet temperature that is subsequently effective on the steam output from HRSG. From the graph change trend, it can be concluded that the first effect dominates the second one. However, in general, the change in the gas turbine expansion coefficient has no significant effects on the efficiency of the second law of thermodynamics in the tri-generation cycle.  Figure 9 shows the changes in the efficiency of the second law of the thermodynamics in tri-generation cycle per Pinch Point (PP1) between the combustion output gases of gas turbine and HRSG's steam at the point 12 in figure 1. According to the graph, by the increase in PP1, the efficiency of the second law of thermodynamics in the tri-generation cycle is decreased. The reason behind this phenomenon is the increase in the wastages and irreversibility due to the increase in temperature difference between the hot gas and HRSG steam.  Figure 10 shows the changes in the cost of electricity generated by the tri-generation cycle per air-to-fuel ratio, and in different density ratios of the gas cycle air compressor. In this figure, the residuals of the variable have been considered to be the optimal values of table 10. Figure 10 shows that by the increase in air-to-fuel molar ratio, as well as the compressor's pressure ratio, the cost of the electricity generated by the tri-generation cycle would increase. Figure 10. The cost of electricity generated by the tri-generation cycle per air-to-fuel ratio(ra) Figure 11 shows the changes in the initial equipment costs (CI) per air-to-fuel molar ratio. In this figure, all the values except the air-to-fuel molar ratio, have been assumed to be optimal values in the table10. In fact, in this figure, the share of the initial equipment costs (CI) in the electricity costs and its changes based on the air-to-fuel molar ratio has been investigated. By the increase in the air-to-fuel molar ratio, though the tri-generation cycle output power is increased, the equipment purchase costs are also increased. As a result, the cost of electricity related to the initial equipment costs is increased by the rise in the air-to-duel molar ratio. Figure 11. The changes in the cost of electricity in the initial equipment costs (CI) per air-to-fuel molar ratio Figure 12 shows the changes in the cost of electricity generated by the tri-generation cycle per Pinch Point (PP1) between the gas cycle output and HRSG's steam. It can be understood from the figure that by the increase in (PP1), the electricity cost is increased. In fact, by the increase in (PP1), two effects can be observed: 1) the decrease in the cycle efficiency that leads to the increase in electricity cost, 2) increasing the heat exchange level between the gas fluid and steam in the HRSG exchanger that leads to the increase in initial equipment costs and subsequent rise in the electricity cost. Regarding the above mentioned two effects, by the increase in (PP1), the rise in the electricity cost seems logical. Figure 13 shows the changes in costs of electricity generated by the cycle in three modes as gas turbine cycle, dual gas and steam cycle, and tri-generation cycle of gas, steam, and ORC. The overall trend of the figure shows that converting the cycle from the gas mode to the dual gas and steam mode would lead to the decrease in the electricity cost by about 50%.
Therefore, it can be concluded that the initial equipment costs of the steam cycle are ignorable, considering the rise in efficiency and the reduction in fuel consumption. However, for the tri-generation cycle (GT+HRSG+ORC), this decrease in the electricity costs is about 5%, which is negligible. Figure 12. The cost of electricity generated by the tri-generation cycle per (PP1) Figure 13. The cost of electricity generated by the (GT,GT+HRSG,GT+HRSG+ORC) cycles per air-to-fuel molar ratio (ra) Figure 14 shows the changes in costs of the electricity generated by the tri-generation cycle, per different values of gas turbine expansion ratio. It is clear from the figure that the effects of the gas turbine expansion coefficients changes on the cost of electricity generated by the tri-generation cycle are negligible.  Figure 15 shows the efficiency of the first law of thermodynamics for gas turbine cycle (GT), gas and steam cycle (GT+HRSG), and tri-generation cycle (GT+HRSG+ORC), before and after optimization by the dualpurpose genetic algorithm. Regarding the values of the efficiency of the first law of thermodynamics before and after optimization, it can be concluded that optimization in GT, GT+HRSG, and tri-generation cycle leads to the increase in efficiency of the first law of thermodynamics by 41.5%, 29.9%, and 29.2%, respectively. Figure 16 shows the efficiency of the second law of thermodynamics for the (GT, GT+HRSG,GT+HRSG+ORC) cycles, before and after optimization. This optimization leads to increase in the second law of thermodynamics by 41.7%, 30%, and 29.3% for the GT cycle, GT+HRSG, and GT+HRSG+GT+HRSG+ORC, respectively. Figure 17 shows the entropy production by the GT cycle, GT+HRSG, and GT+HRSG+GT+HRSG+ORC, before and after optimization. It can be read from the values in the figure that despite the increase in the first and second laws of the thermodynamics after optimization, the entropy production is also increased for all three cycles.  Figure 18 shows the cost of electricity generated by the GT,GT+HRSG, and GT+HRSG+ORC, pre-and afteroptimization. The figure shows that the although the energy recycling in each cycle leads to higher costs of new equipment and initial cost, the electricity cost is reduced, considering the cycles efficiency and decrease in the fuel consumption in a constant amount power generation. On the other hand, application of optimization on the cycles also leads to the decrease in power generation costs, in a way that the cost is reduced by 30, 22, and 22% respectively, for the GT, GT+HRSG, and GT+HRSG+ORC cycles, compared to pre-optimization. Figure 18. The cost of the electricity generated by the GT, GT+HRSG, and GT+HRSG+ORC cycles, before and after optimization

CONCLUSION
The current study dealt with the energy, exergy, and economic modeling of a tri-generation cycle. In this cycle, the energy of gas turbine outlet hot gases was used for the production of steam and power in the steam cycle. Also, the steam cycle condenser waste energy was used for the production of the organic fluid steam and power in the ORC. After the above modeling was done, the multi-purpose genetic algorithm was used for optimization. The objective functions were the cost of the electricity generated by the cycle and the efficiency of the second law of thermodynamics. The variables investigated in optimization include the air-to-fuel molar ratio, the compressor and gas cycle turbine density and expansion ratio, mass discharge of the water and coolant, the Pinch Points between the gas and steam cycles, and steam cycle and ORC, and the maximum temperatures of the steam cycle and ORC.
The results of the current study are as follows: • The convergence of the multi-purpose genetic algorithm for tri-generation power cycle with 200 iterations was performed. • By the increase in the air-to-fuel ratio, the efficiency of the second law of the thermodynamics is decreased.
By the increase in air compressor density ratio, a similar effect can be observed. • By the increase in air-to-fuel ratio, the efficiency of the first law of thermodynamics in the tri-generation cycle is decreased. By the increase in air compressor density ratio, a similar effect can be observed. • By adding the steam cycle to the gas cycle for increasing the efficiency, the efficiency of the second law of thermodynamics is increased up to 2.5 times. • By adding the ORC to the GT+HRSG cycle, the efficiency is increased by about 7%.
• The change in gas turbine expansion coefficient has no significant effects on the efficiency of the second law of thermodynamics in tri-generation cycle, e.g., by the increase in gas turbine expansion coefficient from 6 to 13, the efficiency of the second law of thermodynamics is only increased from 68.5% to 69%. • The increase in air-to-fuel ratio and compressor density would lead to the increase in the cost of the electricity generated by the tri-generation cycle. • The increase in Pinch Point between hot gas and super-heat steam would lead to the increase in electricity cost. • The GT, GT+HRSG, and GT+HRSG+ORC would lead to the increase in the first law of thermodynamics by 41.5%, 29.9%, and 29.2%, and the increase in the second law of thermodynamics by 41.7%, 30%, and 29.3%, respectively.
• The optimization of the power generation cycle from the gas cycle to the gas and steam cycle, and the trigeneration cycle would lead to the increase in entropy, in all modes.
• In general, by the optimization of the mentioned tri-generation cycle, the electricity cost is reduced from