MULTI-OBJECTIVE OPTIMIZATION OF A VEHICULAR PEM FUEL CELL SYSTEM SEMINAR REPORT

Submitted byNIDHIN.BS7 Mechanical, 27227ToThe University of KeralaIn partial fulfillment of the requirements for the award of the degreeOfBachelor of Technology in Mechanical Engineering

DEPARTMENT OF MECHANICAL ENGINEERINGCOLLEGE OF ENGINEERINGTHIRUVANANTHAPURAM-162011

DEPARTMENT OF MECHANICAL ENGINEERINGCOLLEGE OF ENGINEERINGTHIRUVANANTHAPURAM 16

CERTIFICATE

This is to certify that the report entitled MULTI-OBJECTIVE OPTIMIZATION OF A VEHICULAR PEM FUEL CELL, submitted by NIDHIN.B, 7th semester, Roll no: 08400070 to the university of kerala in partial fulfillment of the requirements for the award of the degree of bachelor of technology in mechanical engineering is a bonafide record of the seminar presented by him.

Prof. MANOHARAN ACHARYAsst. Prof. T.N RAVI Department of Mechanical Engineering Department of Mechanical Engineering Asst. Prof. R.R. AJITHAsst. Prof. V.B. SURESHKUMAR Department of Mechanical EngineeringDepartment of Mechanical Engineering

Prof. E ABDUL RASHEEDHead of Department Dept. of Mechanical Engineering

ACKNOWLEDGMENT The preparation of this seminar report has been a thoroughly enlightening experience for me. I take this opportunity to thank God almighty for bestowing His blessings on me during the course of completion of this report. Further, I wish to place on record the assistance rendered by Prof. MANOHARAN ACHARY, Asst. Prof. R.R.AJITH, Asst. Prof. T.N.RAVI and Asst. Prof. V.B. SURESHKUMAR in completing this seminar report. Their suggestions and advices were invaluable. I express my sincere thanks to Prof. E.ABDUL RASHEED, Head of Department, Mechanical Engineering, for his inputs, facilitating the timely completion of this report. Had it not been for my faculty, this report would never have been a reality. I would also wish to record my great fullness to all my friends and classmates for their help and support in carrying out this work successfully. Last but not the least, I wish to express my heartfelt gratitude to the Mechanical Engineering Department.

NIDHIN.B

ABSTRACT

The multi-objective optimization of a vehicular fuel cell system was conducted in this study with the objective functions for maximizing the power output, both energy and exergy efficiencies, and minimizing cost generation (through exergoeconomics). The cases were investigated parametrically using varying operating conditions, such as temperature, pressure, surrounding temperature and pressure, current density, humidity and membrane thickness.

A computer program was developed (MULOPe The Multi-Objective Optimizer) and a genetic algorithm based solver was applied to the program for dealing with the multi-objective problems. It was seen that the variation of the cost and work values at the same work, energy, and exergy fractions are in opposite directions. This study not only calculates the minimum result of cost and maximum results of work, energy and exergy efficiencies, but also improves the computer program for solving general multi-objective optimization problems.

The selection of the optimum value depends on the requirements of the system that will be used The Pareto solution values of the multi-objective problem are 3.31 $/GW, 118 kW, 0.49 and 0.55 from the cost, work, energy efficiency and exergy efficiency points of views respectively.

INDEX OF CONTENTSTITLE PAGE NO:

1. INTRODUCTION6.2. THE VEHICULAR PEM FUEL CELL SYSTEM 6. 3.MODELING 8.

4.THE MULTI-OBJECTIVE OPTIMIZATION 25.

5.THE MULTI-OBJECTIVE OPTIMIZATION OF A PEM FUEL 27. CELL

6.EVALUATION OF RESULTS 29.

7.CONCLUSIONS35.

8.REFERENCES37.

1. INTRODUCTION

The phenomena of fuel cell systems are complicated due to the fuel cell elements and reactions. Therefore, their modeling and optimization is essential for better performance. Nowadays with an increase in pollution and the decrease of fossil fuel resources a movement has begun towards more environmentally benign and more efficient power production. This has shifted the priority from conventional fuels and internal combustion engines and increased the interest for alternative fuels and power sources. In this study, the optimization problem includes cost, produced work, and efficiency objectives in a multi-objective manner. The aim of this study is to apply a multi-objective optimization scheme to a PEM fuel cell system used for transportation purposes. Fuel cells are considered as one of the most promising alternative power sources especially for sub-megawatt scale applications like light-duty transportation. Fuel cells convert chemical energy into electrical energy by a well known electrochemical process. Since the electrochemical processes are not governed by Carnots law, relatively low operating temperatures do not lead to efficiency losses. Furthermore, contrary to internal combustion engines, the efficiency of fuel cells is not strongly dependent on the operating power. Fuel cells have an increasing demand with their high efficiency and one used in many areas including transportation applications, domestic uses, heat production, etc.

2. THE VEHICULAR PEM FUEL CELL SYSTEM

For this investigation The Ballards Xcellsis_ HY-80 Fuel Cell Engine was used (Fig. 1). Since the Xcellsis_ HY-80 fits beneath the floor of the vehicle, the size of the passenger compartment is not affected. The engine is a lightweight, 68 kW hydrogen-fueled, fuel cell engine. The hydrogen is stored in a tank at 10 atm at 298 K. After pressure regulation, depending on the system pressure, the hydrogen is fed to the system. The fuel cell stack is composed of 97 cells each having a 900 cm2active surface area. The cooling system is used in order to maintain a constant operating temperature inside the fuel cell stack.

Figure 1: A vehicular PEM fuel cell system

2.1. Working of a PEM fuel cell

Hydrogen fuel is channelled through the field flow plates at the anode on one side of the fuel cell while the oxidant (oxygen or air) is channelled to the cathode at the other side of the fuel cell. Now platinum catalyst at the cathode causes the hydrogen atoms to split into positively charged hydrogen ions or protons and negatively charged electrons. Now the proton exchange membrane (PEM) or the polymer electrolyte membrane only allows positive ions or protons to pass through it and reach the cathode. Now the electrons are forced to pass through the external circuit to reach cathode producing electricity. At cathode the protons and electrons combine with oxygen to form water which is flown out of the system. The unreacted hydrogen is recycled for further power production. The cell reaction is exothermic and the waste heat is radiated using a radiator and a cooling system is employed to keep the fuel cell stack at constant operating temperature with water or glycerine as coolant. The working of a simple PEM fuel cell is shown in fig 2.

Figure 2: Working of a simple PEM fuel cell.

3. MODELLING

3.1. Reversible cell voltage

The maximum voltage that can be produced by a cell without any irreversibility is called the reversible cell voltage. A form of the Nernst equation was used since it allows us to investigate the performance at temperature, system pressure, and the partial pressures of both hydrogen and oxygen points of view

Where, the hydrogen and oxygen partial pressures may be calculated as,

Where, XH2O is the water mole fraction that is Psat/P respectively both for the anode and cathode. XA and XC are the anode and cathode dry gas mole fractions respectively and XA and XC are anode and cathode stoichiometric ratios respectively.

3.2. Operating cell voltage

The operating cell voltage is less than the reversible cell voltage because of the irreversibility and over-potentials. Since the overpotentials depend on the system operating parameters the operating cell voltage is not constant while the reversible cell voltage is constant for general cases. The operating cell voltage may be expressed by;

Activation losses, ohmic losses, mass transport or concentration losses are the over-potentials that are taken to account in this study.

After calculating the irreversibilities the power produced by the stack is calculated via,

Where, ncell is the number of fuel cells inside the stack; Acell is the area of the each cell; and i is the current density.

3.3. Exergoeconomic analysis and efficiency

Exergoeconomic analysis covers the economic concerns with exergy analysis, equipment costs, and related thermodynamic irreversibilities through the system. The overall exergy balance is;

The following equations are used to formulate the net work output, energy, and exergy efficiencies for the entire system :

Where, Ein is calculated from the exergy of the inlet streams of the system. The overall exergetic cost balance equation is;

Where; the Ein,i, Eout,i, Cin,i and Cout,i is the exergies and exergy costs of the streams entering and leaving the control volume respectively. Ztot is the annualized cost of the total system inside the control volume. Cw is the cost of the work or the power of the equipment. The cost balance is applied to the overall system to calculate the cost of the produced power by the fuel cell system.

3.4. Thermodynamic analysis of a PEM fuel cell power system

Automobiles using fossil fuel are the major source of harmful air pollutants. Automobiles contribute significantly to the growing environmental concerns such as greenhouse effect, regional acidification and climate change. In addition to these environmental concerns, depletion of fossil fuel reserves and increasing oil prices have generated the need for alternative fuels and energy conversion technologies with minimum environmental impact which can provide energy security, economic growth and sustainable development. The energy conversion technology which receives considerable attention recently is the proton exchange membrane(PEM) fuel cell, a potential replacement for the conventional internal combustion engine (ICE) in transportation applications. PEM fuel cell is an electrochemical energy conversion device, which converts the chemical energy of hydrogen and oxygen directly and efficiently into electrical energy, with waste heat and liquid water as by-products. A PEM fuel cell powered automobiles using hydrogen offer several advantages, such as energy efficient and environmentally benign low temperature operation, quick start-up, compatible with renewable energy sources and can obtain a power density competitive with the internal combustion engine. However, the major barriers which are hindering the commercialization of PEM fuel cell powered automobiles are cost and hydrogen infrastructure.

One of the means of reducing the cost of PEM fuel cell powered automobile is by improving the performance of PEM fuel cell itself. A proven method of enhancing the performance of energy systems is thermodynamic second law analysis or exergy analysis , which is considered to be a primary tool in addressing the impact of energy resource utilization on the environment. In contrast to various studies on exergy analysis of high temperature solid oxide fuel cell for stationary power generation applications, e.g., there are only a few studies on exergy analysis that were performed for low temperature PEM fuel cell for transportation applications. Cowndenet al performed exergy analysis of hydrogen fuel cell power system for bus transportation. Their work showed the usefulness of thermodynamic analysis in determining the irreversibilities in different system components, but did not rigorously address the operating characteristics of PEM fuel cell which helps in minimizing irreversibilities and maximizing the performance of the system. Recently, Kazim has conducted exergy analysis of a PEM fuel cell at specifiedoperating voltages of 0.5 and 0.6 V. Exergy efficiency of the PEM fuel cell at different operating conditions were reported; however, the second law characteristic such as irreversibility within the cell was not evaluated since the analysis was performed at specified operating voltages. Additionally, the auxiliary components or balance-of-plant were not included in his study.

Thus, in the present study, thermodynamic analysis of a PEM fuel cell power system for light-duty fuel cell vehicle is conducted, which consists of two major modules: PEM fuel cell stack module and system module, and a cooling pump. System module includes air compressor, heat exchanger, humidifier and the cooling loop. The analysis is completed using a PEM fuel cell performance model developed by two of the authors. Moreover, a parametric study is conducted to investigate the effect of operating conditions on the performance of the system.

3.4.1. Thermodynamic analysis

3.4.1.1 Exergetic aspects

Exergy method of analyzing energy systems integrates the first and second law of thermodynamics and reference environmental conditions. Exergy is defined as the maximum amount of work which can be obtained from a system or a flow of matter when it is brought reversibly to equilibrium with the reference environment. Every substance or system not in equilibrium with its reference environment has some quantity of exergy, while a substance or system in equilibrium with its reference environment has no exergy since it has no ability to cause any change with respect to its reference environment. The exergy consumption during a process is proportional to the entropy production due to irreversibilities. It is a useful tool for furthering the goal of more efficient energy use, as it enables the determination of the location, type and true magnitude of energy wastes and losses in a system. Exergy of a stream of matter can be divided into different components. In the absence of nuclear, magnetism, electricity and surface tension effects, the specific total exergy is the sum of:ex = exke + expe +extm +exchWhere, exke, expe, extm and exch are the kinetic exergy, potential exergy, thermomechanical exergy and chemical exergy, respectively. Since the changes in the kinetic and gravitational potential energies are considered to be negligible in the present study, physical exergy, which is the sum of kinetic, potential and thermomechanical exergies, reduces to thermomechanical exergy only.

The specific thermomechanical exergy at a given state is defined as follows:extm = (h h0)T0(s s0)Where, h and s refer to specific enthalpy and entropy, respectively, at a given state. The subscript 0 represents the conditions of the reference environment (restricted). The chemical exergy is a result of compositional imbalance between a substance and its reference environment. On a molar basis, the specific chemical exergy of a substance can be written as follows:

Where, xj is the mole fraction of the species j in the flow, j0 is the chemical potential of species j in the flow evaluated at T0 and P0 and j00 is the chemical potential of species j in the flow evaluated in the reference environment (unrestricted).

3.4.1.2. The reference environment

Exergy analysis cannot be performed without defining the reference environment. Moreover, in dealing with reacting systems, two forms of equilibrium has to be defined, the environmental (restricted) state and the dead (unrestricted) state. The environmental state is a restricted equilibrium where the conditions of mechanical (P ) and thermal (T ) are satisfied. The dead state is an unrestricted equilibrium where the conditions of mechanical (P ), thermal (T ) and chemical potential () are satisfied.

In the present study, restricted dead state is defined as STP condition (298 K and 1 atm), whereas the unrestricted dead state is defined (Table 1) as the composition of wet atmospheric air with relative humidity of 57.5%, which can betaken as a typical annual average.

3.4.1.3. Fuel cell power system

The PEM fuel cell power system considered in the present study is based on Ballards fuel cell engine for light-duty vehicles and is shown in Fig. 1. The power system consists of two modules: the PEM fuel cell stack module and system module, and a cooling pump. The main components of the system module are air compressor, heat exchanger, humidifier and the cooling loop.

The PEM fuel cell stack module is the heart of the power system where pressurized, humidified air and hydrogen are supplied from the system module. This is the place where electrical power is produced through electrochemical reaction of hydrogen and oxygen as follows:H2(g) + (1/2) O2(g) H2O(l) +electrical power+waste heatHere, the waste heat produced in the stack module is removed through the cooling loop. The air compressor component of the system module provides pressurized oxygen in the form of air, to the stack. The pressurized air is cooled down in a heat exchanger and humidified in a humidifier before being fed to the stack. Similarly, compressed hydrogen stored on-board is humidified in a humidifier before feeding to the stack. Humidification of inlet streams is necessary to prevent dehydration of the membranes in the fuel cell stack. Not all the hydrogen supplied to the fuel cell is consumed by the fuel cell stack, and therefore the unreacted hydrogen leaving the stack is recirculated. The purpose of the cooling loop is to remove the heat produced by the exothermic reaction of hydrogen and oxygen.

The cooling loop consists of a radiator, cooling pump, radiator fan. The cooling pump directs coolant (water/glycol) through the stack to remove the waste heat via radiator.

3.4.1.4. PEM fuel cell performance model

Here, the PEM fuel cell performance model developed by Baschuk and Li is used to simulate the fuel cell stack. The model predicts the voltage of a single cell at any specified operating conditions. The voltage of the entire stack is then obtained by multiplying the single cell potential with the number of cells in the stack. The output voltage of a fuel cell can be represented as,E(I ) = Er EirrWhere, Er is the reversible voltage of the cell and Eirr is the irreversible voltage loss or overpotential due to catalyst layers, electron migration in the bipolar plates and electrode backing, and proton migration in the polymer electrolyte membrane.

Figure 3: Schematics of a PEM fuel cell system

Table 1: Mole fraction and chemical energy of components at dead state.

3.4.1.4.1. Reversible cell voltage (Er )

The reversible cell voltage is the cell potential obtained at thermodynamic reversible condition. It is given by the following expression:

3.4.1.4.2. Irreversible cell voltage loss or overpotential (Eirr)

Irreversible cell voltage loss or overpotential is composed of activation overpotential (act) due to catalyst layers, ohmic overpotential (ohmic) due to electron migration in the bipolar plates and electrode backing, and proton migration in the polymer electrolyte membrane, and concentration overpotential (con) due to the mass transfer limitations at higher current densities.Eirr = act +ohmic +con

3.4.1.4.3. Activation overpotential (act)

Activation overpotential is due to the catalyst layers. It takes into account the electrochemical kinetics, and electron and proton migration, and is composed of both the anode and cathodecatalyst layer activation overpotentials:

where a(act) and c(act) are the activation overpotentials in the anode and cathode catalysts layers, respectively.

3.4.1.4.4. Ohmic overpotential (ohmic)

The ohmic overpotential is given by the following expression:

Where, a(bp) and c(bp) are the ohmic losses of the anode and cathode bipolar plates, respectively. The ohmic losses of the anode and cathode electrode backing layers are denoted by a e and c e . The overpotential due to the polymer electrolyte membrane is m. The detailed descriptions and expressions for these overpotentials can be found elsewhere.

3.4.1.4.5. Concentration overpotential (con)

It is due to mass transfer limitations at higher current densities, and is composed of both the anode and cathode concentration overpotentials:con = a(con) + c(con)where a(con) and c(con) are the anode and cathode concentration overpotential, respectively.

3.4.1.4.6. Stack power ( Wstack)

The power produced by a single cell is given as:Wcell = E(I )I AcellWhere, I is the current density and Acell is the geometric area of the cell.

The stack power is then obtained by multiplying the single cell power with number of cells in the stack, which can be written as:Wstack = nfc WcellWhere, nfc is the number of fuel cells in the stack. In the present power system, we consider 97 cells of 900 cm2 geometric area in the stack producing net system power of 68 kW at I=1.15 Acm2 and E = 0.78 V.

3.4.1.5. Assumptions

The assumptions considered in the analysis are as follows: The hydrogen storage cylinder or tank is at a constant pressure of 10 bar and temperature of 298 K. Isentropic efficiencies of compressor, cooling pump and radiator fan are assumed to be 70%. 20% of the total heat produced by the fuel cell stack is assumed to be lost due to convection and radiation [9]. The temperatures at the inlet and outlet of the coolant circulation pump are assumed to be equal. The environmental (restricted) state is at STP conditions, i.e., 298 K and 1 atm. Wet atmospheric air with the composition given in Table 1 is used as dead (unrestricted) state.

The net system power produced by the fuel cell power system is obtained by deducting the parasitic loads from the gross stack power. For the present system, net system power becomesWnet = Wstack Wac Wcp WrfWhere, Wstack, Wac, Wcp and Wrf denotes stack power, power input to air compressor, cooling pump and radiator fan, respectively. The governing thermodynamic first and second law equations are combined for the system as well as for individual components to obtain the exergy balance equation for the system and its components. The exergy balance equation for the system and energy and exergy efficiencies for the system are presented below.

3.4.1.6. Overall system

The exergy balance equation for the overall system can be written as:

Where, subscripts 1, 2, 14, and 18 stand for the states of the system shown in Fig. 3. Qstack and Qradiator are the rate of heat produced by the stack and rate of heat loss by the radiator to the environment, respectively. Also, Isystem is the internal rate of exergy destruction or irreversibility for the overall system. It should be noted that in deriving all exergy balance equations, we assumed the kinetic and potential energies to be negligible and system as well as its components to be at steady state so that time derivatives are zero. The energy and exergy efficiencies of the system are defined as follows:

The analysis presented above is integrated with the fuel cell performance model developed by Baschuk and Li, and applied to the system with the fuel cell stack operating at varying temperatures, pressures and air stoichiometric ratios. The base-case operating conditions of the system are listed in Table 3.

The variation of net system and gross stack power with current density at base-case operating conditions is shown in Fig. 5. At a current density of 1.15 Acm2, the net power produced by the system is around 68 kW. It can be observed from the figure that, with the increase of current density in other words, the external load, the difference between the gross stack power and the net system power increases, which is due to the increase in parasitic loads with the increase of external load.

Table 3: Base-case operating conditions

The variation of system energy and exergy efficiencies with current density at base-case operating conditions listed in Table 3 is shown in Fig. 6. The maximum system energy and exergy efficiencies are obtained as 42.32 and 49.59% respectively, at a current density of 0.42 Acm2. The system energy and exergy efficiencies at a typical cell voltage of 0.78 V and current density of 1.15 Acm2 are found to be 37.72 and 44.20% respectively. From the figure, it can be seen that both system energy and exergy efficiencies initially increases at lower current densities reaching their peaks and finally decreases with the increase of current density. Since at lower current densities, the molar flow rate of fuel consumed by the stack is less and the power required by the auxiliary devices is low, both energy and exergy efficiencies increases until reaches their threshold values at a current density of 0.42 Acm2 and finally decreases with the increase of current density, which is due to the increase in parasitic load and molar consumption of fuel. Exergy efficiencies are higher than energy efficiency, which is due to lower exergy values at states 1 and 9 corresponding to the enthalpy values. Figs. 7 and 8 show the energy and exergy efficiencies of the system at different operating temperatures of the fuel cell stack. The operating pressure was set as 3 atm, and air and fuel stoichiometries were kept constant at 1.1 and 2.0, respectively. It can be seen that both energy and exergy efficiencies of the system increase with the increase of temperature.

This is in fact due to the decrease in irreversible losses (irreversibility) of the fuel cell stack with the increase of temperature, which in turn reduces the irreversibility of the system and hence results in increase of both energy and exergy efficiencies.

Figs. 9 and 10 show the variation of energy and exergy efficiencies of the system with current densities at different operating pressures of the stack. The operating temperature was 80 C and air and fuel stoichiometries were set.

With the increase of pressure, both the energy and exergy efficiencies of the system increases. This is due to significant increase in the gross stack power as a result of decrease in irreversible losses, especially anode and cathode overpotentials, with the increase of pressure. With the increase of pressure, concentration of the reactants at the reaction sites increases, as a result the irreversible losses in the form of anode and cathode overpotentials decreases, which in turn enhances the performance of the fuel cell stack. Although, high pressure operation requires pressurization of inlet streams, which means more parasitic load in the form of power input to the compressor, but the net power produced by the system increases with the increase of pressure. Therefore, energy and exergy efficiencies of the system increase with the increase of pressure.

Fig. 12. Exergy flow diagram of the system at base-case operating conditions, I = 0.938 Acm2 and V = 0.466 V. Bold value in each component denotes irreversibility rate.( All units are in kW)

The variations of energy and exergy efficiencies of the system at different air stoichiometries are shown in Figs. 8 and 9. The operating temperature and pressure were set as 80 C and 3 atm with a fuel stoichiometry of 1.1. From the figures, it can be observed there is no appreciable increase in energy and exergy efficiencies with the increase of stoichiometry of air. With the increase of air stoichiometry, molar flow rate of air increases resulting in the decrease of cathode overpotential and hence gross power produced by the stack increases. Although the gross power produced by the stack increases with the increase of air stoichiometry, but the increase in net power produced by system is not significant. Increasing the air stoichiometry from 3.0 to 4.0 has almost no increase in net power produced by the system. This is again due to increase in parasitic load which is offsetting the increase in gross stack power with air stoichiometry, resulting no significant increase in energy and exergy efficiencies with increase in air stoichiometry. Fig. 12 shows the exergy flow diagram of the system at a particular operating condition. The bold values inside each component of the system denote the irreversibility rate.

The system energy and exergy efficiencies are found to be 37.72 and 44.20% respectively. The largest irreversibility rate was found in fuel cell stack. The other major irreversibility rate was found in fuel humidifier, where hydrogen from the storage cylinder and exhaust hydrogen not utilized in the fuel cell stack are mixed and humidified before being fed into the stack. The performance of the system can be enhanced by minimizing the irreversibility rate in the fuel cell stack, which in turn reduces the cost and helps in commercialization of fuel cell power system in transportation applications.

A thermodynamic modeling based on energy and exergy analysis of a PEM fuel cell power system for light-duty vehicle has been carried out. In addition, a parametric study is conducted to examine the effect of varying operating conditions on the energy and exergy efficiencies of the system. It was found that, with the increase of external load (current density), the difference between the gross stack power and net system power increases as a result of increase in parasitic loads. Both energy and exergy efficiencies of the system increase with the increase of stack operating temperature.

Although the high pressure operation increases the parasitic load in the form of power input to the compressor, but the net power produced by the system increases with the increase of pressure, which results in increase of energy and exergy efficiencies of the system with pressure. No appreciable increase in energy and exergy efficiencies was found with the increase of air stoichiometry. The largest irreversibility rate takes place in fuel cell stack. Thus, minimizing the irreversibility rates in the fuel cell stack results in enhancing the performance of the system, which in turn reduces the cost and helps in commercialization of fuel cell power system for transportation applications.

4. MULTI-OBJECTIVE OPTIMIZATION

Multi-objective optimization seeks the solution to a problem that has two or more objectives simultaneously. Objectives of the problem may be conflicting with each other such as the search for the best performance and least cost . The nature of this type of problem is generally complicated and because of the various alternative possibilities about the optimum, shows the problem in a more complex structure from the solution point of view.

There is not a single solution to a multi-objective optimization, where as, there are a set of solutions that one called the Pareto Solution. So it is obvious that a decision maker is necessary in order to make the correct choice from the Pareto Solutions. The selection of the solution depends on a trade off over the multi-objective solution space.

The multi-objective optimization problem can be defined as:

Where fi(x) is the i-th objective function, g(x) and h(x) are the inequality and equality constraints, respectively, and x is the vector of continuous or decision variables.

4.1. Solution methods

The alternative solutions to the multi-objective problem generally are in a conflict with some of the objectives. It is very hard to find a solution that fits all the objectives well. The Pareto set is the set of solutions that has minimum conflict. The Weighing Sum of Objectives Method was used in this study. The multiple objective functions are combined in one function as;

by changing the corresponding weight (wi) the importance given to a objective can be changed easily. On the other hand, weighting all the objectives can cause the waste of a lot of information. With the help of this method it is possible to investigate a broad range of feasible solution sets from the different importance given to various objectives. It is also possible to give some weights that are totally illogical with the studied optimization problem.

4.2. Genetic algorithms

Figure 13 :Genetic algorithm A genetic algorithm (GA) is a search technique used in computing to find exact or approximate solutions to optimization and search problems based on mechanics of genetics and natural selection inspired by evolutionary biology (Fig. 2). In a genetic algorithm a randomly populated set of solutions (population) is used iteratively to reach a solution. In each solution the candidate solutions (chromosomes) are used to find the objective function value (fitness value) and then depending on some criteria a new population is formed. There are several methods to generate new population, such as mutation and crossover.

The most important step in GA is to define the fitness function which shows the direct representation of the solution and then, GA seeks a probabilistic method to reach the final objective function value.

5. MULTI-OBJECTIVE OPTIMIZATION OF A PEM FUEL CELL

In order to apply a multi-objective optimization technique to the derived model an objective function is to be prepared for the solution. In this study, a weighing method is used to form the objective function that is a weighing factor is given to the objective function parameters which are the produced work (WFC), enefficiency hsys,energy, exergy efficiency hsys,exergy, and the cost of produced work CW. It must also be considered that CW must be minimized where as, the other parameters have to be maximized in the search for the optimum condition.

Table 4: The ranges for parametric investigation

A selection for the weighing factors is not made, instead a parametric study for different weighting factors is applied and the multi-objective problem is separately solved for each case. So the results were attempted tried to be discussed in light of this parametric study.

Figure 14: MULOP (MULti OPtimizer)

The fitness function is formed depending on the objective function derived. The main problem for optimizing this objective function is the difference in the scales of the parameters. The values of WFC lies between 0 and 120 kW, on the other hand, the values of Cw lies between 2 to 6*10^-3 $/kW. So if the problem is solved without manipulating these conditions the results will always seek the maximum work without giving importance to the cost of production regardless of which weight factor is given to the parameters. To avoid this situation the parameters are normalized to form the fitness function between 0 and 1. The normalization is done by dividing each parameter with its maximum value which is obtained by single optimization of that parameter by using the developed computer program MULOP. So the fitness function is changed as shown in equation;

The multi-objective optimization procedure covers a search for optimum values over the range given in the Table 4.

6. EVLUATION OF RESULTS

Table 5: Simulated results

Fig. 15. The variation of produced work and efficiencies with respect to the weight of work in the objective function.

Fig. 16. The variation of produced work and cost with respect to the weight of work in the objective function.

Fig. 17. The Variation of produced work and cost with respect to the weight of energy eff. in the objective function.

Fig. 18. The variation of produced work and efficiencies with respect to the weight of energy eff. in the objective function.

Fig. 19. The variation of produced work and efficiencies with respect to the weight of exergy eff. in the objective function.

Fig. 20. The Variation of produced work and cost with respect to the weight of exergy eff. in the objective function.

Fig. 21. The Variation of produced work and cost with respect to the weight of cost in the objective function.

Fig. 22. The variation of produced work and efficiencies with respect to the weight of cost in the objective function. For understanding the behavior of the multi-objective structure of the PEM fuel cell system 48 different sets with different weights were calculated using MULOP the computer program developed for the solution.

In Fig. 15 the change of produced work and energy and exergy efficiencies with respect to the weight of work in the objective function is seen. It is seen that the work and efficiencies are proportional with each other which is an expected result since these values are all maximized. It is seen that the best values for efficiencies lies in the lower values of contribution but, in these values the produced work values are low since the values between 0.5 and 0.6 is much more acceptable.

Differing from Figs.15 and 16 represents one maximization and one minimization objective which is produced work and cost of production respectively. It is seen that when the produced work amount increases the cost of production decreases, that is also an expected result where the optimum values in the figure are seen between 0.5 and 0.6 which is in harmony with the efficiency values.

When the variation of the energy efficiency objective weight is considered Fig. 17 and Fig. 18 must be investigated. As in the other figures it is seen that when the weight of an objective increased it does not guarantee a better result for that objective particularly because of the dynamics and complexity of the problem. The optimum results for these sets lie in 0.7 weight of the energy efficiency which has the minimum cost and meaningful efficiency and produced work results.

The results for the exergy efficiency objective are similar to the values of the energy efficiency as seen in Fig. 19 and Fig. 20. The result for this situation is in accordance with these efficiency values and both values depend on the performance of the fuel cell system tested. The variation of the work, efficiencies, and cost with respect to the weight of cost of the production objective function is seen in Fig. 21 and Fig. 22. Surprisingly it is seen that the 0.6 value both the work, efficiencies and cost has the smallest values differing from the other sets. Besides, the optimum results seem to lie between 0.8 and 0.9 from, the cost and produced work point of view. If the efficiencies are considered, the best optimum value seems to be the values between 0.3 and 0.4 weights.

Table 5 presents the optimum cases for the investigation. The best values for the efficiencies, cost and the work values (see the highlighted data) lie at high values of the work fraction as expected at 0.9, which is taken as the maximum fraction given to the work in this study. The cost of production is inversely proportional to the maximum produced work, and the selection of the optimum value depends on the needs of the system, in which the fuel cell system will be used according to Figs. 4. So, the best value from the cost point of view is 3.31 $/GW at 0.6 work fraction.

7. CONCLUSION

In this paper, the multi-objective optimization of a typical vehicular PEM fuel cell was carried out using a Genetic Algorithm. The phenomena of fuel cell systems are complicated due to the fuel cell elements and reactions, and their modeling and optimization is essential for better performance. In this study, the optimization problem includes more than one objective function which are one minimum and three maximum functions. If the objective functions of this study are written one by one, these are minimum cost and maximum produced work, maximum energy efficiency and maximum exergy efficiency. This study covers a multi objective optimization scheme for a PEM fuel cell system used for transportation purposes.

Moreover, the optimization of this system was performed to find the Pareto optimal solutions. The modified objective function is constructed using the linearized weight factors given in Table 2 and multi-objectives are the summation of the product of linearized weight factors and related objectives. The constraints are the mass, energy and exergy balance, and design equations of the vehicular PEM fuel cell model. Additionally, operating conditions of this PEM fuel cell are the bounds of this modified model. The computer program MULOP was developed to solve this type of problems based on a hybrid genetic algorithm. The results of the parametric investigation are mostly expected when the tendencies of the variables and objectives are investigated. In order to determine a certain optimum working condition further studies that include optimization of the weighting factors in addition to the objective parameters need to be studied.

As a result of the studies it is seen that cost of production is inversely proportional to the maximum produced work, and the selection of the optimum value depends on the needs of the system in which the fuel cell system will be used, the best value from cost point of view is 3.31 $/GW at 0.6 cost fraction, from work point of view 118 kW at 0.9 work fraction, and from the efficiencies point of view 0.49 and 0.55 at a 0.33 efficiency fraction.

When the results and the corresponding weights are investigated it is also seen that the increase in a weight factor of an objective leads to a better solution from that objective while the other objectives are drastically degraded. It is also seen that there is an extreme point in all of the parametric investigation that in some given weights, the solution surprisingly departed from the general tendency of the solution set. But it is also concluded that this situation arises from the complex structure of the model and the nature of the problem that includes a comprehensive exergo economic analysis.

In summary, from this solution it was concluded that the importance of one of the objectives guarantees high weight factors. According to the tendency of the weight factors, the optimum solution set could be changed.

8. REFERENCES

1. Multi-objective optimization of a vehicular PEM fuel cell system. Suha Orun Mert, Zehra zelik , Yavuz zelik , Ibrahim Diner .

2. Thermodynamic analysis of a PEM fuel cell power system . M.M. Hussain , J.J. Baschuk, X. Li , I. Dincer.

3. A grid based multi-objective evolutionary algorithm for the optimization of power plants. J. Dipama , A. Teyssedou , F. Aub , L. Lizon-A-Lugrin.

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