Optimization of the variable refrigerant flow systems by use of genetic algorithm and energy exergy

Abstract

Keywords: Exergy; Evaporator; VRF; COP; Cost

Introduction

The systems with VRF were first designed and built about 20 years ago, in Japan. Although today, these systems are being used in many countries, still many experts do not have enough information about this system. These systems were first used in Europe in 1987. It should be noted that nowadays in Japan, 50% of air conditioning used by the medium commercial buildings (buildings up to 70000ft2 [6500m2] of the area) and one-third of the large commercial buildings (more than 70000ft2 [6500m2] of the area) are of this type. The VRF systems are also, actually a type of channel-less multi-part air conditioning systems which have additional capabilities. The structure of VRF systems are a little more complicated and have the capability of connecting to channel fan coil units. These systems are more complicated than the multi-part air conditioning systems and consist of several compressors and evaporators. Also, their control system is more complicated than that of the multi-part air conditioning systems. The rationale behind naming these systems as the “systems with variable refrigerant flow” of the “VRF” systems is that these systems can control the amount of the refrigerant input from each evaporator. Controlling the input refrigerant from each evaporator is a characteristic specific to VRF systems, by the use of which, a large number of the evaporators with different capacities and structures can be simultaneously used for supplying cooling and heating in different areas, with the capability of independent and regional controlling of the room’s internal conditions. In these systems, the recovery of heat from another area is also viable. This characteristic significantly reduces the energy consumption. The VRF systems are modular and have a low weight, as in these systems, each module can be easily carried to the place of mounting, and they can be sent up and down a building through an elevator. Besides, in these systems, by putting some modules together, high cooling capabilities can also be obtained. The structure of VRF systems is such that each module (each dual set of modules) forms an independent and complete refrigeration cycle, but these modules all operate under the command of a central control system. The modularity of these systems also has other capabilities such as step-by-step and region-to-region controlling. For example, if a part of a large building has no residents, the VRF systems such as variable volume can be used for supplying the cooling, only for the parts with residents. The relatively low weight of VRF’s enables them to be used without any specific construct constructs and the reinforcements[1, 2]. 1

Department of Energy system, South Tehran Branch, Islamic Azad University, Tehran, Iran Department of Mechanical Engineering, K.N.Toosi, University of Technology, Iran 3 Department of Mechanical Engineering, Pardis Branch, Islamic Azad University, Pardis new city, Iran *E-mail address: aliehyaei@yahoo.com Tel:+98-9123478028 Orcid id: https://orcid.org/0000-0002-0856-1262 Manuscript Received 8 April 2018, Accepted 25 May 2018 2

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 There have been a several studies conducted on the VRF systems and applications in residential building. Aynor et al. in 2010, dealt with evaluation and review of the works done in terms of the VRF systems regarding their structure, performance, and application [3]. Kwon et al. in 2014, evaluated the use of a VRF system for an educational unit in the heating mode. The results showed that the system’s performance can be improved by the use of a heat exchanger [4]. Zhu et al. in 2014 investigated a VRF system with the enthalpy wheel system to meet the heating load. They showed this system could cover all zones with specified set-point [5]. Meng et al. in 2015 investigated experimentally cooling performance of a VRF system. They employed micro channel heat exchanger. This system has a better performance in heat season [6]. Yu et al. in 2016 investigated a comparative study between VRF and VAV systems in two different climate conditions. The VRF systems consumed 40-53% less energy rather than VAV systems. This saving energy is depended upon many factors such as operating mode and set point temperature [7]. Kim et al. in 2018 investigated a VRF system with dedicated outdoor system in small office building located in USA. They conclude that by using this system, energy saving is about 78.8 (kWh) or 109% [8]. Kani-Sanchez in 2017 investigated energy saving of the VRF heat pump systems with heat recovery to meet heating and cooling loads of office building located south western Ontario (Canada). They developed many design optimization methods. They showed that appropriate size of equipment led to 16% of energy saving [9]. Li et al. in 2017 proposed a new model included the VRF system with split type air condition system. They developed a model for this system. With this system energy losses were reduced. Energy saving values were 12.1%, 11.6% and 11.6% for a one floor residential building in Beijing, Shanghai and Guangzhou, Respectively [10]. Several papers have been investigated the modeling of the room air conditioner and VRF system. These model were bases on energy analysis and building energy consumption. These models were divided to three groups: steady state, transient and dynamic models [11-13]. Also, several papers have been published about the application of this method in several systems especially power plant and dispersed power generation [14-29]. Reviewing the previous works, it can be concluded that there have been no comprehensive studies conducted on the VRF’s energy, exergy, and economic modelling and the effects of different refrigerants such as R11, R22, and R134a. Firstly, the introduction of the VRF system, its components, and the factors effective on its performance, are dealt with. Then, through the mathematical modelling and modeling of the basic cycle of this system, the thermodynamic specifications of the refrigerants R11, R22, and R134a at different points of the cycle were calculated, and the impacts of the factors effective on the cycle’s COP were evaluated. After the exergy and economic analysis of the cycle, the VRF system’s cycle is optimized by the use of the multi-purpose genetic algorithm. The innovations of the current study are:  The comprehensive energy, exergy, and economic analysis of the VRF cycle  Proposing a new method for calculation of the cooling load cost  Calculation of energy and exergy efficiency, entropy production, and cooling generation costs for the three refrigerants R11, R22, and R134a  Optimization of the VRF cycle by the multi-purpose genetic algorithm for the three types of refrigerant fluids (R11, R22 and R134a)  Analysis of the above cycle’s sensitivity to its key parameters.

Mathematical Modelling Of VRF Cycle

Figure 1 shows a schematic diagram of the VRF system. In this figure, the direction of the arrows shows the direction of the refrigerants movement. As it is seen in the figure, the cycle consists of a compressor, a condenser, evaporator, 5 strangle valves, and two separators. In this system, controlling the refrigerant fluid is one of the most important design parameters. The refrigerant flow output from the evaporators 1 and 2, enters the expansion valves to have the same pressure as the evaporator (3), and to maintain the pressure balance at the inlet of the compressor. The refrigerant obtained from the mixing of the three evaporators is collected at point (1), and then, its pressure is increased in the compressor (point 2). In the condenser, the refrigerant gives its energy to the surrounding environment and arrives at the point 3. In this point, the refrigerant is divided to three pressure levels for the evaporator (1), (2), (3) and enters the three evaporators. The mathematical modelling hypotheses are as follows: 1) The pipes pressure drop has been assumed to be about 3%. 382

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 2) 3)

The efficiency of the condenser is 85%. The heat dissipation to the environment is ignored.

Figure1. A schematic diagram of the VRF system The heat exchange amount in the evaporators 1, 2, and three are calculated as follows [30]:

In which Q̇ Evap1 , Q̇ Evap2 , Q̇ Evap3 are the heat exchange rates in the evaporators 9( kW), ṁ4 , ṁ7 , ṁ10 are the mass discharge of the evaporators 1, 2, and 3 (kg/s), and h4 , h5 , h7 , h8 , h10 , h11 are the enthalpies at the marked points (kJ/kg). The law of conservation of mass for the evaporators 1, 2, and 3 are as follows:

In which ṁ5 , ṁ8 , ṁ10 are the mass discharge of the evaporators 1, 2, and 3 (kg/s). The equations of mass and energy conservation in the mixing chamber are as follows [30]:

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 In which m ̇ṁ6 , ṁ9 are mass discharge after the strangulation valve, ṁ11 is the mass discharge after evaporator 3, ṁ1 is the mass discharge of the compressor 9 (kg/s), and h1 , h9 , h6 , h11 are the enthalpies at different points of the cycle (kJ/kg). The work needed for the compressor can be calculated as follows [30]:

In the above equation, m ̇_1 is the mass discharge of the compressor (kg/s), WComp and h2 are the compressor output and input enthalpy (kJ/kg). The heat exchange between the condenser and environment can be calculated by the following equation [30]: (10)

In the above equation, ṁ2 is the mass discharge passing through the condenser (kg/s), and h2 and h3 are the enthalpies of the points 2 and 3 (kJ/kg). The laws of conservation of mass and energy for separation are as follows [30]: (11) 𝑚̇14 + 𝑚̇13 = 𝑚̇12 + 𝑚̇3

For exergy analysis, potential exergy, kinetic exergy, and chemical exergy components have been ignored in all processes. The flow’s exergy is equal to the equation 1 [30]:

By ignoring the kinetic and potential exergy, the equation will be as follows [30]: (14)

𝛹 = (ℎ − ℎ0 ) − 𝑇0 (𝑠 − 𝑠0 ) In which h and S are the enthalpy and entropy, and h0 and s0 are the thermodynamic specifications in the reference mode (kJ/kgK). Since the condenser is in the ambient temperature, V is the fluid’s speed (m/s), g is the gravity velocity (m/s2), and z is the reference height (m). The condenser’s temperature is considered to be equal to the reference temperature (40 oC). Usually, the irreversibility is defined as the difference between the reversible work and actual work. If we want to write this definition in general terms and the form of the intensity equations, taking into account more than one mass and more than one heat transfer, we will have [30]:

İw is the reversibility (kW), ṁc and ṁe are the input and output mass discharges (kg/s), Ψe and Ψi are the input and output flow exergies (kJ/kg), Tj is the reference temperature (kW), Q̇ cvj is the heat exchange (kW), and Ẇcv is the amount of work production of the control volume (kW). The irreversibility rate for the compressor is as equation (16) [30]: 384

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̇ 𝐼𝐶𝑜𝑚𝑝 = 𝑚̇1 (𝛹1 − 𝛹2 ) + 𝑊̇𝐶𝑜𝑚𝑝 Ψ1 𝑎𝑛𝑑 Ψ2 are the rates of energy before and after compressor (kJ/kg).

The irreversibility in the condenser, regarding cooling it by the ambient weather which is in the reference temperature, is as follows [30]:

Ψ3 is the exergy rate after condenser (kJ/kg). The evaporator irreversibility, regarding the heat exchange in an environment other than reference environment, is as follows [30]:

In the above equation, Ψ7 , Ψ10 , Ψ11 , Ψ8 , Ψ5 , Ψ4 are the input and output exergies of the evaporators 1, 2, and 3 (kJ/kg). Since there is no heat exchange and work in the strangulation process, the energy loss is as follows [30]:

Which is as follow for the strangulation valves 1, 2, 3, 4, and 5 [30]:

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Since like strangulation valve, there is no heat exchange and work in the divider, the exergy loss is as follows [30]:

The exergy efficiency or the efficiency of the second law of thermodynamic is as follows [30]:

In the refrigeration cycle, the exergy input from the outside of the system is only the electrical energy of compressor. Therefore, the cost of the exergy from outside of the system is the very cost of the electrical energy unit, and the initial investment costs include the costs of the compressor, heat exchangers, expansion valves, strangulation valve, electric motor, and the dividers. The costs of the dividers have been ignored. The product of the system is also just the cooling capacity. The objective function for calculation of the cooling produced by the VRF system is as follows [31-33]: (34) 𝐶𝑄 = 𝐶1 + 𝐶𝑜 + 𝐶𝐸 In the above equation, 𝐶𝑄 is the cooling costs ($/kWh), 𝐶1 is the initial mounting costs ($/kWh), 𝐶𝑜 is maintenance costs ($/kWh), and 𝐶𝐸 is the cost of the electricity consumed ($/kWh). The advantage of this proposed method is the calculation of the costs per each kilowatt of the produced electricity. Besides, by changing the parameters and conditions, the final cost of the produced cooling can be calculate 386

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 The cooling costs about the initial mounting costs can be calculated as follows [31-33]:

In which C is initial mounting costs ($), and I is the initial costs profit. The initial costs profit can be calculated as follows [31-33]:

In the above equation, L is the equipment lifespan (Year), and i is the interest rate. The maintenance costs are considered to be 4% of the initial mounting costs. The costs of electricity can be calculated as follows [31-33]:

The electricity cost has been considered to be 0.071(US$/kWh) [31-33]. The initial costs of the compressor can be calculated as follows [34]:

Genetic Algorithm

This algorithm is a random method, based on the genetics and natural evolution processes, for responding to the complicated problems of optimization. It was first created by professor Holland, based on the random global search inspired by natural structures. The most important points in each numerical algorithm are: 1- Generalizability, 2Convergence speed, and 3- Accuracy of the answer. In the genetic algorithm, the first item is desirable, however the items 2 and 3 are contrary, and improvement of one of them leads to the drop in the other. The genetic algorithm is initiated with a primary population, which is totally randomly chosen, and starts a global search. The population size depends on the specifications of the problem. In this algorithm, the genetics terms are used as key definitions. Each strand of the population is like a chromosome, and each binary section (bit) of each strand is like a gene. The strands are the updated values of the design identifiers. From the evolution of the initial population, a new population is created based on the following factors [35]: 1Reproduction 2Crossover 3Mutation In the reproduction phase, the best chromosomes of the previous iteration have higher chances for being in the next iteration. In the crossover phase, some of the genes of the two select chromosomes replace each other. In the mutation, a series of genes are randomly chosen and changed into other genes through the number associated with mutation. One of the most important parameters in convergence speed and the algorithm precision is the mutation. Without mutation, the convergence speed is high, however, the precision of the answer is low. On the other hand, if the mutation is applied, the answer precision will be highly desirable, however, the number of repetitions for achieving an answer will be high. The most important stage in genetic algorithm is determination of the objective function. This function should be defined in a way to satisfy the optimization conditions of the problem. At the end of optimization by this algorithm, a chromosome is selected as the best chromosome, which is the most desirable response to the problem. Figure 2 shows the flowchart showing how the genetic algorithm works [35].

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Results And Discussion

The VRF cycle designing conditions are shown in table 1. The thermodynamic specifications of the three fluids R11, R22, and R134a are shown in table 2. In tables 3 to 5, the thermodynamic specifications of different points in the VRF cycle for the refrigerants R11, R22, and R134a are presented. Table 1. The VRF cycle designing conditions

2416(kPa) 904.2 (kPa) 797.8 (kPa) 701.2 (kPa) 0.07662 (kg/s) 0.07717 (kg/s) 0.07777 (kg/s) %70

Table 2. The thermodynamic specifications of the three fluids R11, R22, and R134a Coolant R11 R22 R134a

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 Table 3. The thermodynamic specifications of different points in the VRF cycle for the refrigerants R11 P(kPa)

Table 4. The thermodynamic specifications of different points in the VRF cycle for the refrigerants R22 P(kPa)

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 Table 5. The thermodynamic specifications of different points in the VRF cycle for the refrigerants R134a P(kPa)

Figure 3 shows the VRF equipment’s COP for the three refrigerants R11, R22, and R134a. By changing the refrigerant from R11 to R22 and R134a, the COP of the equipment is increased from 3.2 to 3.8, and 3.6, respectively.

Figure 3. The VRF equipment’s COP for the three refrigerants R11, R22, and R134a Figure 4 shows the efficiency of the second law of thermodynamics of VRF equipment for the three refrigerants R11, R22, and R134a. It is clear from the figure that by changing the refrigerant from R11 to R22 and R134a, the efficiency of the second law of thermodynamics for the VRF cycle is increased from 11% to 19.1% and 23.8%, respectively. Figure 5 sows the value of VRF cycle per refrigerants R11, R22, and R134a. By changing the 391

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 refrigerant from R11 to R22 and R134a, the exergy loss is decreased. This change is more evident in changing the refrigerant from R22 to R134a. Figure 6 shows the cost of the cooling produced by the VRF cycle per refrigerants R11, R22, and R134a. By changing the refrigerant from R11 to R134a, the costs of the produced cooling is decreased. 30 23,8

Figure 4. The efficiency of the second law of thermodynamics of VRF equipment for the three refrigerants R11, R22, and R134a

Figure 5. The exergy loss of the VRF cycle per the tree refrigerants R11, R22, and R134a

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Figure 6. The cost of the cooling produced by the VRF cycle per refrigerants R11, R22, and R134a Figure 7 shows the exergy loss in different components of the VRF equipment for the refrigerant R11. The lowest exergy loss belongs to the mixture6, and the strangulation valves 3, 4, and 5 after it. The highest exergy loss belongs to the condenser, mixture 6, and evaporators 1, 2, and 3, respectively. Figure 8 shows the exergy loss in different components of VRF equipment for the refrigerant R22. The highest exergy loss, like the R11, belongs to the condenser. The lowest exergy loss also belongs to the mixture6. The exergy loss in different components of the VRF equipment for R22 is lower than R11. Figure 9 shows the exergy loss in different components of the VRF equipment for R134a. Like the previous refrigerant, the highest exergy loss belongs to the condenser, and the lowest loss belongs to the Mixture6. 9435,30

Figure 7. The exergy loss in different components of the VRF equipment for the refrigerant R11 393

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Figure 8. The exergy loss in different components of the VRF equipment for the refrigerant R22 6000,00 5045,40 5000,00

Figure 9. The exergy loss in different components of the VRF equipment for the refrigerant R134a The dual-purpose genetic algorithm is used for optimization of the system. Table 6 shows the specifications of the dual-purpose genetic algorithm used in the current study.

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 Table 6. The specifications of the genetic algorithm Parameters Population Initial range

the second law of thermodynamics). The variables considered for the optimization are as follows: 0.07>ṁ4>0.1)kg/s( 0.07>ṁ7>0.1)kg/s(

Figure 10 shows the Pareto graph of the VRF cycle for the refrigerant R11. By the change in cycle’s exergy efficiency from 10 to 16, the cost of the cooling is decreased from 0.233 (

of the variables are shown in table 7. Figure 11 shows the changes in the efficiency of the second law of thermodynamics for the VRF cycle per mass discharge of evaporator 1, for the refrigerant R11. By the increase in evaporator 1’s mass discharge from 0.07 to 0.1 (kg/s), the cycle’s exergy is decreased from 14.1 to 13.9%.

Figure 10. Pareto graph of VRF cycle for R11 Table 7. The optimal values of the VRF cycle variables for R11 ṁ4(kg/s) ṁ7(kg/s) P2(kPa)

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ṁ4(kg/s) Figure 11. The changes in efficiency of the second law of thermodynamics for the VRF cycle per mass discharge of evaporator 1, for the refrigerant R11 Figure 12 shows the changes in COP of the system per condenser pressure for refrigerant R11. The COP changes of the cycle is descending with the increase in condenser pressure. Figure 13 shows the changes in the efficiency of the second law of thermodynamics for the VRF system per evaporator 1’s pressure. By the increase in evaporator 1’s pressure from 900 (kPa) to 1100 (kPa), the efficiency of the second law of thermodynamics for the VRF cycle is decreased from 16.4 to 15.6%. Therefore, it can be concluded that the changes in evaporator 1’s pressure have no significant effects on the efficiency of the second law of thermodynamics for the VRF system. 3,56

p2(kPa) Figure 12. The changes in COP of the system per condenser pressure for refrigerant R11

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p4(kPa) Figure 13. The changes in efficiency of the second law of thermodynamics for the VRF system per evaporator 1’s pressure Figure 14 shows the Pareto graph of the refrigerant R22 and VRF equipment. The trend of the changes is similar to that of R11, i.e., by the increase in efficiency of the second law of thermodynamics, the cooling costs of the VRF equipment are decreased. However, it should be noted that the values of the second law of thermodynamics and cooling costs for the R22 refrigerant are different from those of R11. By the increase in efficiency of the second law of thermodynamics from 13 to 29%, the cost of the cooling produced by the VRF is decreased from 0.0188 (

). Table 8 shows the optimal values VRF equipment variables for the refrigerant R22.

Figure 14. Pareto graph of the refrigerant R22 and VRF equipment

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 Table 8. The optimal values VRF equipment variables for the refrigerant R22 ṁ4(kg/s) ṁ7(kg/s) P2(kPa) P4(kPa) P7(kPa) P10(kPa)

If the values of table 8 are compared with those of table 7, it can be concluded that the optimal values are almost in the same range with no significant difference. Therefore, changing the refrigerant R11 to R22 has no significant effects on the optimal values of the cycle. Figure 15 shows the changes in the efficiency of the second law of thermodynamics for VRF equipment per mass discharge of the evaporator 1’s refrigerant, for R22. It can be seen in the figure that by the increase in the mass discharge of evaporator 1 from 0.07 to 0.1kg/s, the efficiency of the second law of thermodynamics is decreased from 29.2 to 28%. Through comparison of the above figure with figure 11, it can be known that the trends of the changes in the efficiency of the second law of thermodynamics for the VRF equipment, or mass discharge of evaporator 1, are similar for the refrigerants R11 and R22, i.e., for both refrigerants, the trend is descending. 29,4

ṁ4(kg/s) Figure 15. The changes in the efficiency of the second law of thermodynamics for VRF equipment per mass discharge of the evaporator 1’s refrigerant, for R22 Figure 16 shows the changes in COP per condenser pressure for the refrigerant R22. The trend of the changes is similar to that of figure 12. Figure 17 shows the changes in the efficiency of the second law of thermodynamics for refrigerant R22 per evaporator 1’s pressure. By changing the evaporator’s pressure from 900 (kPa) to 1100 (kPa), the efficiency of the second law of thermodynamics is decreased from 29.7 to 25.9%. Figure 18 shows the costs of the cooling produced by the VRF system per evaporator 1’s pressure, for refrigerant R22. The increase in pressure from 900 (kPa) to 1100 (kPa), leads to the increase in the cooling costs from 0.0169 (

shows the Pareto graph of R134a and VRF equipment. By the increase in efficiency of the second law of thermodynamics from 18 to 34%, the cost of cooling is decreased from 0.0186 to 0.0166 (

Journal of Thermal Engineering, Research Article, Vol. 6, No. 3, pp. 381-404, April, 2020 optimal values of the VRF cycle with R134a refrigerant. Comparing the table 9 with tables 7 and 8, it can found out that changing the refrigerant from R11 to R22 and R134a does not significantly affect the optimal values of the cycle. 4,35 4,3

Figure 16. The changes in COP per condenser pressure for the refrigerant R22 30 29,5 29 28,5 28 27,5 27 26,5 26 25,5 900

p4(kPa) Figure 17. The changes in efficiency of the second law of thermodynamics for refrigerant R22 per evaporator 1’s pressure 0,0172

p4(kPa) Figure 18. The costs of the cooling produced by the VRF system per evaporator 1’s pressure, for refrigerant R22 399

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Figure 19. Pareto graph of R134a and VRF equipment Table 9. The optimal values of the VRF cycle with R134a refrigerant ṁ4(kg/s) ṁ7(kg/s) P2(kPa) P4(kPa) P7(kPa) P10(kPa)

Figure 20 shows the changes in the efficiency of the second law of thermodynamics for VRF cycle per condenser pressure for R134a. By the change in condenser pressure from 2300 to 2500 (kPa), the exergy efficiency is increased from 3.8 to 4.4%. It should be noted that the condenser pressure for the refrigerant R134a does not significantly affect the efficiency of the second law of thermodynamic for VRF cycle. Figure 21 shows the effects of the condenser pressure on the cost of cooling produced by VRF cycle, for the refrigerant R134a. By the increase in condenser pressure, the cost of the cooling has an ascending trend. 34,5

p2(kPa) Figure 20. The changes in efficiency of the second law of thermodynamics for VRF cycle per condenser pressure for R134a

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p2(kPa) Figure 21. The effects of the condenser pressure on the cost of cooling produced by VRF cycle, for the refrigerant R134a

Conclusion

The current study aimed at energy, exergy, and economic analysis of the VRF cycle. This VRF cycle has 3 evaporators, 2 mixers, 5 expansion valves, one compressor, and one condenser. The three refrigerants R11, R22, and R134a were considered. The multi-purpose genetic algorithm was used for optimization of this system. The objective functions were cooling costs and second law efficiency. The variables considered for the optimization were condenser and evaporators 1, 2, and 3 pressure, mass discharge of the evaporators 1 and 2, and the mass discharge of the condenser, respectively. The results of the current study are as follows: -The highest COP and efficiency of second law of thermodynamics is for the R134a, and second and third to it are R22 and R11. -The lowest exergy loss and cooling costs belonged is for the R134a, with R22 and R11 being second and third. -The change in the refrigerant type does not significantly affect the optimal values obtained by the dual-purpose genetic algorithm. -The sensitivity analysis shows that by the increase in the mass discharge of refrigerant inside the evaporator, the efficiency of the second law of thermodynamics of the VRF cycle for all the three refrigerants is reduced. NOMENCLATURE: A US$ C( ) kWh COP m g( 2)

I İ(kW) K L kg ṁ( ) S P(kW) Q̇(kW) T(K) m V( ) S Ẇ(kW) z(m)

Interest rate Irrerorsibility Coefficient Equipment life Mass flow rate Power of electric motor Heat transfer rate Temperature Speed

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Subscripts 1,2,3,4,5,6,7,8,9,10,,11,12,13,14 Comp Cond CV 0 E Elec Evap 1 , 2 , 3 Exp E I I O Q Sep

Number in Figure (1) Compressor Condenser Control volume Standard condition Exit Electrical Evaporators 1 ,2 , 3 Expansion valve Exit Intel Initial Operation and maintenance Cooling Separator

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