PERFORMANCE ASSESSMENT OF PHOSPHORIC ACID FUEL CELL THERMOELECTRIC GENERATOR HYBRID SYSTEM WITH ECONOMIC ASPECT

Purpose of this paper is to evaluate phosphoric acid fuel cell (PAFC) - thermoelectric generator hybrid system with economic and thermoeconomic point of view. Firstly, basic equations of PAFC, thermoelectric generator and hybrid system are described. Secondly, basic performance parameters like power output, energy efficiency, exergy efficiency and exergy destruction rates are investigated. Finally, cost equations are set up to determine economic results of the considered system, in addition to that, these system are considered by using EXCEM analysis. According to results, the maximum total cost of the hybrid system is obtained j= 10900 am -2 , exergy loss ratio to capital cost ( ec ) of the hybrid system increases dramatically after the point where is j= 11000 am -2 . Maximum power density, maximum energy efficiency and of the hybrid system are 8735.340 wm -2 , 81.35% and 86.6% respectively.


INTRODUCTION
Fuel cell technology is the conspicuous technology because of their nearly harmless to environment, relatively higher efficiency and their flexible fuel option. Nowadays, one of the most important problem of engineers and scientists are design to systems that convert to energy as most efficiently that enable us environmental friendly usage of them. Efficiency of a heat engine are restricted by the Carnot efficiency, however, this limitations is not valid for fuel cells. Because, fuel cell generates electricity in fuel cell by electrochemical reaction. Irreversible fuel cells including Solid oxide fuel cells (SOFC), molten carbonate fuel cell (MOFC), proton exchange membrane (PEM) fuel cell, phosphoric acid fuel cell (PAFC) and direct carbon fuel cell (DCFC) are investigated [1][2][3][4][5]. Zhang et al. considered PAFC in [5], they investigated cell voltage for different parameters including temperature, resistances, power and efficiency of the fuel cell according to current density, load resistance and mole fraction. They defined the optimum operating conditions. Another opportunity offered by fuel cells are that heat rejected by the fuel cell can be used in another process and fuel cell -heat engine/refrigeration hybrid systems may be designed. In last decade, irreversible fuel cell and hybrid systems have been gained attention. In ref. [6], a hybrid PAFC-absorption refrigerator system was investigated. Power densities, efficiencies are studied under different conditions like temperature, pressure and phosphoric acid mole fraction. General performance characteristics and optimum criteria of the hybrid system are shown. PAFC-heat driven refrigerator cycle was taken into account in ref. [7]. System was researched for power density and efficiency and variable parameters were defined according to current density and refrigeration temperature, finally optimum conditions and performance characteristics were obtained. Performance of different fuel cell hybrid systems can be found literature; in refs. [8][9][10] fuel cell-Stirling, in refs. [11][12][13][14][15] fuel cellheat engine, in refs. [16][17][18][19][20][21][22][23][24][25] fuel cell-Brayton, in refs. [26,27] fuel cell-Braysson hybrid systems were investigated for different conditions and performance criteria. In addition, novel hybrid systems including fuel cell-thermionic generator and fuel cell -Super critical CO2 -Organic Rankine cycle can be seen in refs. [28,29].
Thermoelectric generators may be an alternative for creating hybrid system with fuel cells. They have several advantageous like; they don't have moving part, noiseless and they are not required maintenance 30 frequently. A thermoelectric generator is used heat to generate electricity based on the Seebeck effect and similarly they can be utilized as cooler on the principle of the Peltier effect. Some authors have been researched about optimization of thermoelectric devices [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45].In the open literature, one can find papers about fuel cellthermoelectric generators hybrid systems. Chen et al, analyzed PAFC-thermoelectric hybrid system for the maximum power output conditions [46]. Zhao et. al. investigated direct carbon fuel cell-thermoelectric generator hybrid system [47]. Chen et al. analyzed a PEM-thermoelectric hybrid system in terms of power output and efficiency [48]. Another alternative to evaluate and design thermal cycles is finite time thermodynamics and constructional optimization. Some example of these may be found in [49][50][51][52][53] and these methods can be applied for the fuel cell hybrid systems widely.
In the open literature, authors are no aware of any study about PAFC-thermoelectric hybrid system in terms of economical and thermoeconomic aspects. Such techniques seek to determine of the appropriate allocation of economic resources so as to optimize the design and/or operation of a system; and/or the economic feasibility and profitability of a system [54]. In this paper, this shortage is tried to be completed. Firstly, thermodynamic relations are expressed for the fuel cell and thermoelectric generator. Secondly, PAFCthermoelectric generator hybrid system is analyzed with regard to power output, energy efficiency, exergy efficiency and exergy destruction rate. After these, cost of the hybrid system and thermoeconomic analysis are performed. EXCEM method [54] is chosen for the thermoeconomic evaluation. Results are obtained numerically, some important outcomes are discussed and suggestions are made.

THERMODYNAMIC ANALYSIS
PAFC is made of phosphoric acid as electrolyte and two electrodes which are anode and cathode. Air is provided to cathode and hydrogen is provided to anode and electrochemical reaction occurred in the fuel cell is H2+1/2 O2 H2O + heat + electricity. This produced heat resulted from the electrochemical reaction that can be used in another process. Operating temperature of PACF is about 150-200 o C which can be used in cogeneration applications for buildings and low temperature processes. Schematic of the hybrid system is shown in fig.1. In this paper, PAFC -thermoelectric hybrid system is analyzed in terms of economical aspect. Firstly, equations for fuel cell are presented. Maximum theoretical potential or Nernst equation is [ Overpotentials cause the irreversible losses. These are activation overpotential described as activation overpotential, concentration overpotential and ohmic overpotential are shown in eqs. (2-4) respectively [5].
where j is operating current density, jo is exchange current density, R is the universal gas constant, α is the charge transfer coefficient, ne number of electrons and F is the Faraday's constant, T is the operating temperature of the fuel cell, m and n are two constant, tele is the thickness of the electrode and κ is the conductivity of phosphoric acid solution. The Output voltage of the PAFC is expressed as [5]: where A is the polar plate area,  H  is the total energy provided to fuel cell per unit time and Δh is the molar enthalpy change at the operating temperature.  H  is described in eq. (8) [5]: where  G  Gibbs energy change per unit time and g  is the molar Gibbs energy change.  G  is defined as 32 Exergy destruction rate of the fuel cell is [3]: (11) Heat transfer occurred in the regenerator is [6]: where θ heat conductance, εr, regenerator effectiveness and To is the ambient temperature. Heat released from the fuel cell is: Secondly analysis of the thermoelectric generator must be performed. Heat input of thermoelectric generator can be defined in eqs. (14) and (16) [36]. These are equal as well as heat rejected from the PAFC in eq. (13). Heat rejected form the thermoelectric generator is shown in eqs. (15) and (17) [36].
Power supplied from the thermoelectric generator is: where β is Seebeck coefficient, T1 is the temperature of the hot junction, T2 is the temperature of the cold junction, N is the number of thermoelectric units, I is the electrical current generating in semi-conductor couple, r is the electrical resistance, K is the thermal conductance of the semi-conductance couple, kH and kL are the heat transfer coefficients and at is the heat transfer area of the heat exchangers. In this study, calculations are conducted for maximum power output of the thermoelectric generator. Optimum electrical current for maximum power can be defined as [36]: Number of modules required to heat input can be calculated by equalizing eqs. (14) and (16): Journal of Thermal Engineering, Research Article, Vol. 5, No. 2, Special Issue 9, pp. 29-45, February, 2019 Similarly T2 is solved by equalizing eqs. (15) and (17) and result is: Finally,T1 is defined as using (13) and (16) Thermoelectric properties depending on temperature are shown in (23) where Tm is the mean temperature, L1 is the length of p type material, L2 is the length of n type material and, similarly, A1 is the area of p type material, A2 is the length of n type material. Efficiency and reversible power of the thermoelectric generator are shown in eqs. (29) and (30) respectively.
Finally, thermodynamic parameters for PAFC-thermoelectric generator is shown in (33) - (36). These are power output, efficiency, exergy efficiency and exergy destruction rate respectively.
Firstly, hybrid system is investigated by using thermoeconomic method called EXCEM [54] where EC is ratio of thermodynamic loss rate (in this paper exergy loss rate, which is described as is ratio of rate, which is difference of exergy output from the exergy input, is considered) to capital cost [54].
Where Z is the capital cost of the system and it is calculated by multiplying unit cost (c) for per kW and power output of the considered system: Journal of Thermal Engineering, Research Article, Vol. 5, No. 2, Special Issue 9, pp. 29-45, February, 2019

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Another economic evaluation criteria is the total cost of the system and it is defined as [55]: where k Z is capital cost to per unit of time [55]: where CRF is the capital recovery factor,  is the maintenance factor and N is the operating hours in a year [55].

RESULTS AND DISCUSSION
Results obtained from calculations are shown in figs. 2-10. Parameters used in the calculations are listed in table 1 and 2 which is given from the refs. [5][6][7][35][36][37]. Results are presented as power density (p = P/A) and exergy destruction density (exd= Exd/A) for power output and exergy rate. One can be seen the change of power densities with current density in fig 2. As it is shown, all power outputs have an optimum (maximum) point. Power density of hybrid system reaches its maximum at j= 10200 Am -2 and it is equal to 8735.340 Wm -2 . When investigating power densities for PAFC and thermoelectric generator, it is seen that they have optimum points too. These points are provided at j = 10100 Am -2 with 8538.440 Wm -2 for PAFC and at j = 12500 Am -2 with 351.036 Wm -2 value for TEG. Changes of hybrid system and PAFC are parabolic, however, TEG increases nearly linear about j=8500 Am -2 after this point it changes logarithmically and reaches its optimum. In figure 3 energy efficiencies are illustrated. As it is seen that they have no optimum point, their maximum values are obtained at minimum current density. Maximum efficiencies of hybrid system, PAFC and TEG are 81.35%, 81.28% and 5.51% respectively. Effect of TEG on the hybrid system increases at higher current densities, however, average effect of it on the hybrid system is about 2%.
Variation of exergy efficiencies are in fig. 4. Curves in the fig 4. is very similar in fig.3. Maximum exergy efficiencies are obtained at minimum current density and the bigger current density means the lower exergy efficiency. Maximum exergy efficiency of hybrid system is 86.6%, 86.5% for the PAFC and 14.9% for the TEG. Comparing results of energy and exergy efficiencies, it can be seen that exergy efficiencies bigger than energy efficiencies. However, effect of the TEG on the hybrid system in terms of the exergy efficiency is same with effect of the energy efficiency.
Exergy destruction densities changes are shown in fig.5. All exergy densities grow up with current density and this change nearly linear until j = 10000 Am -2 , after this point they increase dramatically. Their maximums, which are at j = 12900 Am -2 , 21473 Wm -2 for the hybrid system, 15925 Wm -2 for the PAFC and 5548 Wm -2 for the TEG.
Total cost rate of the hybrid system, PAFC and TEG are indicated in fig. 6. Total cost rates of hybrid system and PAFC have an critical (maximum point) contrast to TEG. Total cost of hybrid system and PAFC increase until their critical point and then they begin to decrease. Their critical point are obtained at j = 10900    p-η-φ curves is shown in fig. 8. This chart may be called as performance curve. In this graphic, energy and exergy efficiencies of hybrid system are investigated according to power density. In there, pmax, pη, pφ, ηmax, ηp,φmax, φp mean maximum power density, power density at the maximum energy efficiency, power density at maximum exergy efficiency, maximum energy efficiency, energy efficiency at maximum power density, maximum exergy efficiency and exergy efficiency at the maximum power density. ηp and φp are equal to 67.9%  p-C -EC curves can be shown in fig.9 where pC, pEC, max C , p C , ECmax, ECp represent to power density at total cost rate, power density at EC, maximum total cost rate, total cost rate at power density, maximum exergy loss rate and EC at maximum power density respectively. pC is equal to 8485.99 Wm -2 which is 97.1% of the maximum power density and pEC is 8397.20 Wm -2 which is equal to 96.1% of the maximum power density.  Similarly, p C , is 0.620 and it is 98% of the maximum total capital cost rate and ECp is equal to 0.0917 W$ -1 which is only 3.3% of the maximum EC.
Finally, η--C -EC chart is indicated in fig.10 where ηC, ηEC, max C , C  , ECmax, ECη are energy efficiency at the maximum total capital cost rate, energy efficiency at the maximum EC, maximum total capital cost rate, total capital cost rate at the maximum energy efficiency, maximum EC and EC the maximum energy efficiency respectively. ηC and ηEC are 61.7% and 4.1%, these values correspond to 75.8% and 5% of the maximum efficiency. In addition to that C  and ECη are 0.013 $h -1 and 0.039 W$ -1 , these values are 2% and 1.4% of their maximum.

CONCLUDING REMARKS
In this paper, a PAFC-TEG hybrid system is investigated in terms of its performance, economical and thermoeconomic aspects. Some important results are listed follows: -Maximum power density of the hybrid system is 8735.340 Wm -2 at j= 10200 Am -2 -Maximum energy efficiency of the hybrid system is 81.35% at low current densities, effect of TEG on the hybrid system 2% on average. Maximum exergy efficiency of the hybrid system is 86.6%, and it is obtained at low current densities similar to energy efficiency.
-The maximum total cost of the hybrid system is obtained j= 10900 Am -2 and this cost is equal to 0.633 $h -1 -The maximum EC of hybrid system is 10.922 W$ -1 .
-Exergy loss rate of the hybrid system increases dramatically at j= 11000 Am -2 and it is equal to 15925 Wm -2 .
As it is shown where the maximum power density, the total cost rate is maximum too, until 11000 Am -2 exergy lost rate does not change so importantly. In addition to these, energy efficiency, exergy efficiency and exergy destruction rate are high and the total cost rate, exergy loss rate have low values at the small current densities. According to these results, current densities should be chosen as low as possible in terms of economic aspects, economical and thermoeconomic analyses are recommended to be conducted for fuel cell hybrid systems.