gas turbine hybrid power plant

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 7 0 2 e1 7 0 9

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Thermo-economic optimization of an indirectly coupled solid oxide fuel cell/gas turbine hybrid power plant Denver F. Cheddie* Centre for Engineering Systems, University of Trinidad and Tobago, Point Lisas Campus, Esperanza Road, Brechin Castle, Couva, Trinidad and Tobago

article info

abstract

Article history:

Power generation using gas turbine (GT) power plants operating on the Brayton cycle

Received 24 August 2010

suffers from low efficiencies, resulting in poor fuel to power conversion. A solid oxide fuel

Received in revised form

cell (SOFC) is proposed for integration into a 10-MW GT power plant, operating at 30%

25 October 2010

efficiency, in order to improve system efficiencies and economics. The SOFC system is

Accepted 26 October 2010

indirectly coupled to the GT, in order to minimize the disruption to the GT operation. A

Available online 27 November 2010

thermo-economic model is developed to simulate the hybrid power plant and to optimize its performance using the method of Lagrange Multipliers. It predicts an optimized power

Keywords:

output of 18.9 MW at 48.5% efficiency, and a breakeven per-unit energy cost of USD 4.54 ¢

Thermo-economic model

kW h
1 for the hybrid system based on futuristic mass generation SOFC costs.

Power plant optimization

ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

Solid oxide fuel cell Gas turbine Indirect coupling Lagrange Multipliers

1.

Introduction

Fuel cells are electrochemical devices that convert the chemical energy in a fuel into electricity without direct combustion. As a result, they avoid many of the limitations of combustion engines, providing more energetically and exergetically efficient fuel to power conversion. Solid oxide fuel cells (SOFC) are best suited for distributed power generation. They operate at temperatures between 600 and 1100  C and have been tested at operating pressures up to 1.52 MPA (15 atm.) [1]. Because of their high temperature and pressure exhaust, SOFCs are considered ideal for integration in hybrid power generating systems, where they are coupled with gas turbines (GT) to produce additional power. SOFC hybrid power systems have received considerable interest in the literature over the past 5e10 years [2e25],

which is reviewed more comprehensively in Refs. [26e28]. Zhang et al. [2] discussed strategies for integrating SOFCs with other power generating components, which can be categorized as direct thermal coupling, indirect thermal coupling, and fuel coupling. Direct thermal coupling involves two or more power systems sharing the same working fluid. In indirect thermal coupling, different working fluids are kept separate; only heat is transferred between the two power systems via heat exchangers. Fuel coupling schemes involve the configuring of the integration system to include hydrogen production or fuel reforming. Most of the SOFCeGT schemes presented in the literature involve direct thermal coupling, mainly because the focus has been on designing new micropower plants for small scale distributed power generation (<1 MW). However, there are GT power plants already in existence that operate at relatively

* Tel.: þ1 868 343 5014; fax: þ1 868 636 3339. E-mail address: [email protected]. 0360-3199/$ e see front matter ª 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2010.10.089

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 7 0 2 e1 7 0 9

low efficiencies. These power plants can be retrofitted using SOFC technology to improve their performance. In such cases, special care has to be taken to ensure that the addition of the SOFC system does not interfere with the operation of the GT power plant. For this reason, indirect coupling is more feasible for such applications. Further, the existing GT power plants in question are larger in scale than those presently used in SOFCeGT hybrids, and thus would require larger scale SOFCs for effective coupling. Most existing SOFCeGT hybrid plants are in the kW range [3e5], however, larger plants have been modeled in the literature. Chan et al. [22] considered a 1.3-MW plant, which consisted of a SOFC stack with 40,000 tubular cells. Arsalis [19] considered SOFC stacks up to 8.5 MW for a SOFCeGTeST hybrid system. They also discussed the inherent difficulty in selecting a micro-gas turbine for small scale operation since their efficiencies decrease as the system scales down. One of the advantages of large scale operation is that, in theory, SOFC technology can readily be scaled up by adding more stacks. Despite the practical hurdles that must be overcome, Singhal and Kendall [24] and Larminie and Dicks [25] predict that practical SOFC systems will be scaled up from 100 kW to 10 MW prior to commercialization of the technology [21]. The present work builds on our previous studies [26e28], which presented thermo-economic models for various hybrid power plant configurations. In this work, the focus is on optimization. A 10-MW gas turbine power plant, which entails a compression ratio of 10 and a turbine inlet temperature of 1400 K, is considered. A thermo-economic model for indirectly coupled SOFC/GT hybrid systems was developed in ref. [27], which is now used to generate data and develop multivariate correlations between power plant performance measures and

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decision variables that affect the performance. The multivariate correlations are then used to optimize the power plant performance using the method of Lagrange Multipliers [29]. The goal is to optimally size the SOFC stack and to determine the ideal operating conditions required to obtain the most cost effective performance of the system, subject to necessary constraints. These constraints include limitations on the turbine inlet temperature, ensuring that sufficient steam is provided for reformation within the SOFC anode, and ensuring that the SOFC does not overheat.

2.

Model development

2.1.

Schematic

The existing power plant (hereafter referred to as the standard plant) is based on the standard Brayton cycle using natural gas to provide heat input. In this paper, natural gas is considered to be mostly methane with other components providing negligible contribution. It utilizes a compression ratio of 10, followed by combustion of natural gas (methane) to provide sufficient heat to achieve a turbine inlet temperature of 1400 K. The products of combustion are then expanded in the turbine back down to atmospheric pressure. Methane is consumed at a rate of 41.7 mol s
1 in the combustion processes, while oxygen is consumed at the rate of 252 mol s
1. The isentropic efficiencies (82.3% and 86.0% for the compressor and turbine, respectively) and combustion efficiency (98.9%) are determined from experimental data. At the time the measurements were taken, the plant was operating at full load, producing 10.0 MW of net power at a thermal efficiency of 30.0% and

Fig. 1 e Hybrid schematic using indirect coupling with anode recycle.

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second law thermodynamic efficiency of 28.9%. This plant presently produces power at a breakeven cost of 5.46 ¢ kW h
1. Fig. 1 shows the proposed hybrid configuration intended to improve performance of the existing power plant. In this configuration, the goal is to couple the SOFC to the GT power plant in a way that minimizes the disruption to normal operation. The fuel cell and the gas turbine operate with different fluid streams and thus characterized as indirect coupling. The outlet from the turbine is used to preheat the fuel cell reactants, while the outlet from the fuel cell is used to preheat the compressed gases entering the turbine. Preheating the fuel cell inlet gases results in a higher fuel cell operating temperature and hence better performance. Preheating the turbine inlet gases reduces the amount of combustion required in the GT power plant. So this way, the SOFC and GT improve each other’s performance. In addition, no external water is supplied to the fuel cell. Instead, a fraction of the anode outlet is recycled to provide steam for reformation of the methane. Since the fuel cell does not operate at 100% fuel utilization, an afterburner is needed to combust excess fuel. The output from the afterburner is then used to preheat the air entering the fuel cell. This heat exchanger is equipped with a control mechanism that regulates the flow rates such that the SOFC outlet temperature is maintained at 1373 K. In this work, the cell voltage is externally controlled and maintained at 0.5 V, while the current depends on the IeV curve.



 Ji ¼ hi
hi;0
T0 si
si;0 þ e0i þ RT0 lnðxi Þ

The first and second laws of thermodynamic efficiencies are defined in equations (3) and (4). The enthalpy and entropy values of each gas species as a function of temperature are determined from coefficients used in reference [31]. hI ¼

Wnet Q in

(3)

hII ¼

Wnet E xin

(4)

2.3.1.

Combustor, mixer and heat exchangers

In the combustion chamber, only the heat transfers need to be considered. The heat of reaction is already incorporated in the outlet enthalpy values. The outlet composition is determined from a molar balance assuming complete combustion of methane and hydrogen. CH4 þ 2O2 /CO2 þ 2H2 O

(5)

2H2 þ O2 /2H2 O

(6)

For known inlet conditions, the combustion outlet temperature is determined so as to ensure Equation (1) is satisfied. An iterative approach based on the NewtoneRaphson method, is used in this work to accomplish this goal.  X ni hTi

out

2.2.

Assumptions

Steady state full load conditions are studied in this paper. The schematic shown in Fig. 1 applies for full load operating point conditions. There are numerous practical contingencies that are deliberately not shown to avoid complicating the figure. Full combustion is also assumed. Combustion efficiency is taken to mean that 100% oxidation of the fuel occurs, however, some of the heat of combustion is “lost” to the environment. Direct internal reforming SOFCs are considered in this paper, however, the thermodynamic analysis would still apply if an external reformer were used since the thermodynamic analysis of the fuel cell presented in this paper applies to the entire fuel cell system. The only factor that would be affected is the additional capital cost. It is also assumed that complete reformation of methane takes place in the reforming section of the SOFC, and that only hydrogen, carbon dioxide and water vapor exist in the anode section of the SOFC.

2.3.

Equations

The model equations presented in this section are the same as ref [27]. A lumped approach is used to analyze each component of the plant. Mass and energy balances are considered across each component, the first and second laws of thermodynamics are applied to determine outlet states and exergy destruction. Q
W ¼ DH

(1)

The total exergy (physical þ chemical) for each component i is given by Equation (2), where e0 is the standard chemical exergy for each substance [30],

(2)

¼
Q

loss

þ

 X ni hTi

in

(7)

Mixing processes are treated in an identical manner, except that the outlet composition is merely the algebraic sum of all inlet compositions. The heat exchangers also employ energy conservation, the difference being that the hot and cold streams are not mixed, hence they maintain a given composition. There are two outlet streams, hence two outlet temperatures need to be determined. The effectiveness-NTU [32] method is used to determine the actual temperature changes to both the cold and hot fluid, based on the heat exchanger type, effective heat transfer coefficient and surface area.

2.3.2.

Compressors and turbine

In the present power plant, the compressors and turbine already exist, so the only interest is in retrofitting the existing plant to replace as much combustion with fuel cell processes. Thus it is desired to maintain “normal” operation of the compressor and turbine. As a result, the inlet conditions to the turbine and compressor, as well as their respective isentropic efficiencies are already given. The only minor difference is that a different amount of fuel will be handled in the hybrid plant than in the standard plant, which is assumed to not significantly affect its isentropic efficiency. W ¼
DH

 hs ¼

2.3.3.

W for turbine Ws Ws for compress W

(8)

(9)

Solid oxide fuel cell

The SOFC produces DC power via electrochemical processes. The methane is reformed inside the anode compartment, producing hydrogen which is electrolyzed in the SOFC. The

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following reformation, shift and half cell reactions take place at the respective electrodes.

Table 1 e Model parameters used in SOFC and turbomachinery calculations.

CH4 þ H2 O/CO þ 3H2

(10)

Quantity

Value at 1373 K

CO þ H2 O/CO2 þ H2

(11)

H2 þ O2
/H2 O þ 2e


(12)

1 O2 þ 2e
/O2
2

(13)

Rohm Eact,an Eact,ca ganode gcathode Turbine isentropic efficiency Compressor isentropic efficiency Combustion efficiency

2.488  10
6 U.m2 140  103 J mol
1 137  103 J mol
1 6.54  1011 A m
2 2.35  1011 A m
2 86.0% 82.3% 98.9%

The operating cell voltage is determined from subtracting all overpotentials (activation, ohmic and concentration) from the standard Nernst potential at the given temperature and pressure. sffiffiffiffiffiffiffiffiffiffi1 G0 RT B PH2 PO2 C E ¼
þ log@ A 2F 2F PH2 O Patm 0

production costs when the technology matures [19]. These projected capital costs are shown below.

(14)

CSOFC ¼ ASOFC ð2:96TSOFC
1907Þ

Vcell ¼ E
ðhactivation þ hohmic þ hconcetration Þ

(15)

Cinverter ¼ 105





 nF nF i ¼ i0 exp a hact
exp
ð1
aÞ hact RT RT

(16)

0:78 AHX CHX ¼ 130 0:093

(23)

(17)

CSOFC;aux ¼ 0:1ðCSOFC Þ

(24)

CGT ¼ WGT ½1318:5
98:328lnðWGT Þ

(25)

Wcomp 0:67 Ccomp ¼ 91562 445

(26)

i0;anode ¼ ganode

pH2 pH2 O Eact;an exp
pref pref RT

i0;cathode ¼ gcathode

hconc

pO2 pref

!1=4



Eact;ca exp
RT

RT i ¼ log 1
2F ilim

(18)

(19)

Constants for the ohmic and activation parameters are given in ref [33]. The work or power output from the SOFC is the product of total current and cell voltage. The SOFC produces DC power which must be inverted to an AC output. An inverter efficiency of 98% is assumed in this work. Applying the first law of thermodynamics to the entire fuel cell system, the following equation applies. WSOFC ¼ iVcell ASOFC ¼
DHSOFC

(20)

The fuel cell operating temperature in a lumped parameter model is typically taken as the outlet temperature [7] since the inlet gas streams are preheated inside the fuel. This is especially the case in injection tube SOFCs. The SOFC stack is typically designed in such a way as to minimize temperature gradients and hence thermal shock. Thus a fairly uniform spatial temperature distribution is actually achieved in SOFC design. As a result, the outlet temperature (assumed common for both anode and cathode) can be taken as the operating cell temperature. Equation (20) is used to determine the inlet air temperature required to maintain the predetermined SOFC temperature. Table 1 shows the critical parameters of the SOFC and turbomachinery.

2.3.4.

Cost functions

The economic analysis of the plant entails the capital costs associated with the SOFC and other related equipment. Presently the cost of SOFC technology is prohibitive, however, the cost analysis in this work is based on projected mass



0:7 WSOFC 500

(21)

(22)

The cost analysis is based on an assumed natural gas cost of US $0.124/m3 (US $3.50 per thousand cubic feet), and a 10-year lifecycle (95% operational time) with a 9% rate of interest. The capital costs as well as annual costs are used to determine the lifecycle breakeven per-unit energy cost (USD $kW h
1). Minimizing this energy cost is the design objective in this work. The enthalpy and entropy equations for each species are programmed as user defined functions into MATLAB. Subroutines for each component as well as cost functions are then written in MATLAB’s programming language. These subroutines iteratively determine the outlet conditions (temperature and composition) of each component given the inlet conditions. When inlet conditions are unknown, the outlet conditions are initially guessed and iteratively determined. All sub-routines are combined into one plant algorithm which is used to determine all state properties, and hence optimize the hybrid power plant.

3.

Results and discussion

3.1.

Model validation

The SOFC model is validated using experimental data published in references [21,33,34]. Experimental data are based on 89% H2 and 11% H2O as the anode fuel, and operation at 1000  C and 101.3 kPa (1 atm.). The model predictions for this hydrogen cell are within 2.3% of the experimental data, as detailed in ref. [27].

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3.2.

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Power plant optimization

The optimization objective is to size the SOFC and find the operating conditions which minimize the lifecycle per-unit energy cost of the power plant. The decision variables which affect the performance of the plant are the size of the SOFC denoted by its active surface area, the molar flow rate of methane into the GT, the molar flow rate of methane into the SOFC, the molar flow rate of oxygen into the SOFC, and the fraction of the SOFC anode outlet recycled back to the inlet; respectively, ASOFC, XCH4 ; YCH4 ; YO2 , YREC. The molar flow rate of air into the GT is already established to be 252 mol s
1 so this is left unaltered. The power plant is also subject to various constraints. The GT was designed to operate best at its maximum permissible temperature of 1400 K. The SOFC anode recycle fraction must be sufficiently high so that there is sufficient steam for full reformation of the methane. Also the purpose of the SOFC inlet heat exchanger is to preheat the air stream in order to regulate the SOFC temperature. Under normal operation, T19 should be higher than T20. If any configuration produces the result, T20 > T19, then this is interpreted to mean that this heat exchanger cannot prevent the fuel cell from overheating, and this configuration is deemed unacceptable. These constraints are listed in equations (27)e(29). T7
1400 ¼ 0

(27)


 YREC 1 þ Uf
1  0

(28)

T19
T20  0

(29)

The model is used to generate data for a wide range of operating conditions, from which multivariate regression models can be developed for various output variables. The regression models are of the form, Y ¼ að0Þ þ

X

ð1Þ

ð2Þ

ai Xi þ ai X2i

(30)

i

where Y is the dependent variable and Xi are the independent (or decision) variables. The regression model finds the best quadratic multivariate fit. Based on a sample of generated data, the best fit coefficients are obtained using SPSS and shown in Table 2. The dependent variables shown are the

breakeven energy cost, the first law efficiency, the fuel utilization factor, the turbine inlet temperature T7, as well as the inlet and outlet temperatures of the SOFC inlet heat exchanger, T19 and T20. The regression coefficients are also shown, and for each case this value is very close to 1 indicating that the quadratic models produce a very good fit to the generated data. The values in the Table 2 are the best fit coefficients for each dependent variable, analyzed separately. For example,
 Cpower ¼ 9:429 þ 3:694  10
5 ASOFC
 2 þ 6:653  10
9 A2SOFC þ . þ ð1:623ÞYREC

(31)

The regression models are then used to optimize the energy cost. This is done using the method of Lagrange Multipliers [29]. The energy cost, Cpower is to be minimized subject to the constraints given by equations (27)e(29). The first constraint sets the desired temperature of the turbine inlet, the second one ensures that the anode recycle fraction is sufficiently high to provide sufficient steam for reformation, and the third ensures that the SOFC does not overheat. Since the last two constraints contain inequalities, they are more difficult to handle. The method of Lagrange Multipliers was first implemented with only the first constraint, however, it was found that the optimized results violated the last two constraints. This meant that the optimized results should be expected at the equality limit of the last two constraints. The method was then reapplied holding the last two constraints as equalities rather than inequalities, and satisfactory results were obtained. Using the Lagrange Multiplier method, the function to be optimized is,


H ¼ Cpower
l1 fT7
1400g
l2 fT19
T20 g
l3 yrec 1þUf
1:05 (32) where the ls are the Lagrange Multipliers which allow for variable optimization subject to the constraints. The last term allows for 5% excess steam in the anode inlet. The method of Lagrange Multipliers requires that, VH ¼ 0

(33) 

where V ¼

v

vASOFC

;

v v v v v v v ; ; ; ; ; ; vXCH4 vYCH4 vYO2 vYREC vl1 vl2 vl3

 (34)

Table 2 e Best fit coefficient for quadratic regression model.

Constant ASOFC (ASOFC)2 XCH4 ðXCH4 Þ2 YCH4 ðYCH4 Þ2 YO 2 ðYO2 Þ2 YREC ðYREC Þ2 R2 Factor

Cpower

h

Uf

T7

T19

T20

9.429 3.694E-05 6.653E-09
17.543 65.597
38.296 80.152
2.082 2.755
1.527 1.623 0.995

23.261 2.291E-03
1.014E-07 4.320
94.449 101.810
234.192 23.489
30.466 15.014
16.579 0.996

0.487 1.236E-04
5.463E-09
1.944E-04 1.852E-03
5.020 8.078 0.279
0.180 0.813
0.897 1

626.650
5.509E-02 2.423E-06 6498.613
5285.375 4601.489 2255.529 496.049
758.424
363.094 401.326 0.999

1767.081
0.113 5.860E-06
8.819E-02 0.792 4114.177
4081.806
618.302 250.386 172.348
271.286 0.978

1480.377
9.494E-02 4.157E-06 2797.744
1166.190 16469.687
26490.896
3323.643 1355.107
624.928 693.072 0.999

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Table 3 e Optimized parameters. Quantity

Table 5 e Cost breakdown for the optimized hybrid plant. Optimized value 2

ASOFC XCH4 (GT) XO2 (SOFC) YCH4 (SOFC) YO2 (SOFC) YREC Steam/carbon Fuel utilization, Uf Cpower Efficiency (I) Efficiency (II) Pnet PSOFC TIT, T7 T19 T20

4761 m 8.5 mol s
1 252 mol s
1 40.0 mol s
1 136.5 mol s
1 0.654 2.1 0.6 4.54 ¢ kW h
1 48.5% 46.7% 18.9 MW 9.3 MW 1404 K 1659 K 1650 K

This yields a system of 8 equations and 8 unknowns, the solution of which is the power plant configuration that minimizes the energy cost while adhering to the necessary constraints. This system of equations is solved using Maple, and the results are shown in Table 3. A minimum breakeven energy cost of 4.54 ¢ kW h
1 is observed when a 9.3 MW SOFC is utilized with 65.4% anode recycle and an SOFC oxygen/methane molar ratio of 3.41 (70% excess air). The fuel utilization factor turns out to be fairly low (60%), but this allows more fuel to be combusted in the afterburner resulting in a hotter fluid stream to preheat the GT inlet gases. The 60% utilization factor allows for a steam to carbon ratio of 2.1. Overall the plant produces 18.9 MW of power at a first law efficiency of 48.5% and a second law efficiency of 46.7%. The amount of fuel supplied to the GT (8.5 mol s
1) is significantly reduced from that of the standard plant (41.7 mol s
1), mainly because most of the heating of the GT inlet gases are accomplished by heat exchangers. Compared to the standard plant, the total methane usage is increased by 17% (48.5 vs. 41.7 mol s
1) with a concomitant power increase of 89%. This accounts for a 62% improvement in plant efficiency. In our previous work [27] dealing with the identical indirectly coupled system layout discussed in this paper, an optimum energy cost of 4.65 ¢ kW h
1 was obtained. This, however, assumed a fuel utilization of 75%. A 70e75% fuel utilization is commonly reported in the literature as ideal for directly coupled SOFC/GT hybrids. The results of this work,

Table 4 e Exergy destruction in the standard and hybrid plants (MW). Process Combustion Fuel cell Compression Expansion Heat exchange/mixing Total exergy destruction Total plant power

Standard plant

Hybrid plant

11.1

3.5 4.4 1.1 1.2 3.9 14.1 18.9

NA 1.1 1.3 NA 13.5 10.0

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System

Cost (USD $M)

Gas turbine power plant SOFC Heat exchange Gas cost Break even electricity cost

8.28 12.17 1.60 4.08 4.54 ¢ kW h
1

Type Capital Capital Capital Annual

however, have shown that the optimum operation for indirectly coupled systems occurs for much lower fuel utilization factors (in this case, 60%). It is also noted that the turbine inlet temperature is not exactly 1400 K, while T19 and T20 are not exactly equal to each other. This is because of slight errors in developing the regression models. Nevertheless, the constraints are observed. A turbine inlet temperature of 1404 K is not considered to be a significant problem.

3.3.

Exergy and economic analyses

For the optimized operating conditions, the exergy and cost breakdown are shown in Tables 4 and 5. The exergy destruction associated with combustion in the hybrid plant processes amounts to 3.5 MW for 18.9 MW of total power, compared with 11.1 MW for 10 MW of total power for the standard power plant. However, the SOFC accounts for 4.4 MW, and the heat exchange and mixing introduced by the coupling accounts for 3.9 MW. The total exergy destruction is 14.1 MW of the total plant power compared with 11.1 MW for the standard plant, in addition to the fact that the hybrid plant produces 89% more power. For the hybrid plant, the exergy destruction is distributed among the various components, unlike the standard plant where the combustion device dominates the exergy destruction. These results mean that the indirect coupling of the SOFC significantly improves the second law performance of the power plant. The result is that the second law thermal efficiency increases from 28.9% for the standard plant to 46.7% for the hybrid. Table 5 shows a breakdown of the projected capital and operating costs of the optimized hybrid power plant. The existing GT components (turbine, compressors and combustor) incur a capital cost of $8.28M. The cost of the SOFC system is $12.17M, while the heat exchangers add a relatively small cost of $1.60M. Operating costs include the annual cost of natural gas, estimated at $4.08M. Maintenance costs are included in the capital cost of each component. The break even energy cost is 4.54 ¢ kW h
1, which is considerably less than the 5.46 ¢ kW h
1 energy cost associated with the standard plant, indicating that the hybrid plant produces power in a more cost effective manner than the standard plant.

4.

Conclusions

A thermo-economic model was developed to simulate and optimize an indirectly coupled SOFCeGT hybrid power plant using the method of Lagrange Multipliers. Indirect coupling was utilized because it offers the most practical coupling of

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SOFCs to existing GT power plants. Results show that the overall thermal efficiency can be increased from 30% to 48.5% while the cost of producing power can be reduced from 5.46 to 4.54 ¢ kW h
1 as a result of the coupling. The most optimum performance was observed when a 9.3-MW SOFC was used for a total power output of 18.9 MW. For indirect coupling, the optimum performance is obtained with 60% fuel utilization, 65.3% anode recycling and an SOFC oxygen/methane molar ratio of 3.41 (70% excess air).

Nomenclature

A C e E F H h i I p Q R S s T U V W X Y h j

area, m2 cost, USD standard chemical exergy, J mol
1 potential, V Faraday constant, 96485 C mol
1 enthalpy, W molar enthalpy, J mol
1 current density, A m
2 irreversibility, W pressure, Pa heat, W universal gas constant, 8.3143 J mol
1 K
1 entropy, W K
1 molar entropy, J mol
1 K
1 temperature, K utilization factor potential, V work, W molar flow rate, mol s
1 molar flow rate, mol s
1 efficiency, %, overpotential, V exergy, W

Abbreviations AB after burner AC air compressor FC fuel compressor GT gas turbine HX heat exchanger MX mixer PR pre-reformer SOFC solid oxide fuel cell TIT turbine inlet temperature

references

[1] EG&G Technical Services. Fuel cell handbook. 7th ed. Morgantown, WV: US Department of Energy; 2003. [2] Zhang X, Chan SH, Li G, Ho HK, Li J, Feng Z. A review of integration strategies for solid oxide fuel cells. J Power Sources 2010;195:685e702. [3] KP Litzinger. Comparative evaluation of SOFC gas turbine hybrid options. In: Proceedings of the ASME Turbo Expo Conference, Reno, NV, June 2005.

[4] DGD Agnew, The design and integration of the Rolls Royce fuel cell systems 1MW SOFC. In: Proceedings of the ASME Turbo Expo Conference, Reno, NV, June 2005. [5] A Traverso, M Pascenti, ML Ferrari, R Bertone, L Magistri, Hybrid simulation facility based on commercial 100 kWe micro-gas turbine. In: Proceedings of the ASME Fuel Cell Conference, Irvine, CA, June 2007. [6] Massardo AF, Lubelli F. Internal reforming solid oxide fuel cellegas turbine combined cycles (IRSOFCeGT): Part Adcell model and cycle thermodynamic analysis. J Eng Gas Turbines Power 2000;122:27e35. [7] Chan SH, Low CF, Ding OL. Energy and exergy analysis of a simple SOFC power system. J Power Sources 2002;103: 188e200. [8] Bavarsad PG. Energy and exergy analysis of internal reforming solid oxide fuel cellegas turbine hybrid system. Int J Hydrogen Energy 2007;32:4591e9. [9] Calise F, d’Accadia MD, Palombo A, Vanoli L. Simulation and exergy analysis of a hybrid solid oxide fuel cell (SOFC)egas turbine system. Energy 2006;31:3278e99. [10] Song TW, Sohn JL, Kim TS, Ro ST. Performance characteristics of a MW-class SOFC/GT hybrid system based on a commercially available gas turbine. J Power Sources 2006;158:361e7. [11] Akkaya AV, Sahin B, Erdem HH. Thermodynamic model for exergetic performance of a tubular SOFC module. Renew Energ 2009;34:1863e70. [12] Haseli Y, Dincer I, Naterer GF. Thermodynamic modeling of a gas turbine cycle combined with a solid oxide fuel cell. Int J Hydrogen Energy 2008;33:5811e22. [13] Haseli Y, Dincer I, Naterer GF. Thermodynamic analysis of a combined gas turbine power system with a solid oxide fuel cell through exergy. Thermochim Acta 2008;480:1e9. [14] Akkaya AV, Sahin B, Erdem HH. An analysis of SOFC/GT CHP system based on exergetic performance criteria. Int J Hydrogen Energy 2008;33:2566e77. [15] Burbank Jr W, Witmer D, Holcomb F. Model of a novel pressurized solid oxide fuel cell gas turbine hybrid engine. J Power Sources 2009;193:656e64. [16] Calise F, Palombo A, Vanoli L. Design and partial load exergy analysis of hybrid SOFCeGT power plant. J Power Sources 2006;158:225e44. [17] Franzoni A, Magistri L, Traverso A, Massardo AF. Thermoeconomic analysis of pressurized hybrid SOFC systems with CO2 separation. Energy 2008;33:311e20. [18] Palazzi F, Autissier N, Marechal FMA, Favrat MD. A methodology for thermo-economic modeling and optimization of solid oxide fuel cell systems. Appl Thermal Eng 2007;27:2703e12. [19] Arsalis AM. Thermoeconomic modeling and parametric study of hybrid SOFCegas turbineesteam turbine power plants ranging from 1.5 to 10 MWe. J Power Sources 2008;181: 313e26. [20] Santin M, Traverso A, Magistri L, Massardo AF. Thermoeconomic analysis of SOFCeGT hybrid systems fed by liquid fuels. Energy 2010;35:1077e83. [21] Calise F, d’Accadia MD, Vanoli L, von Spakovsky MR. Singlelevel optimization of a hybrid SOFCeGT power plant. J Power Sources 2006;159:1169e85. [22] Chan SH, Ho HK, Tian T. Multi-level modeling of SOFCegas turbine hybrid system. Int J Hydrogen Energy 2003;28:889e900. [23] Bao C, Shi Y, Li C, Cai N, Su Q. Multi-level simulation platform of SOFCeGT hybrid generation system. Int J Hydrogen Energy 2010;35:2894e9. [24] Singhal SC, Kendall K. High temperature solid oxide fuel cells. London, UK: Elsevier; 2003. [25] Larminie J, Dicks A. Fuel cell systems explained. Chichester, UK: John Wiley and Sons; 2003.

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[26] Cheddie D. Integration of a solid oxide fuel cell into a 10 MW gas turbine power plant. Energies 2010;3:754e69. [27] Cheddie D, Murray R. Thermo-economic modeling of an indirectly coupled solid oxide fuel cell/gas turbine hybrid power plant. J Power Sources 2010;195:8134e40. [28] Cheddie D, Murray R. Thermo-economic modeling of a SOFCeGT hybrid power plant with semi-direct coupling and anode recycle. Int J Hydrogen Energy 2010;35:11208e15. [29] Vapnyarski IB. Lagrange multipliers. In: Hazewinkel M, editor. Encyclopaedia of mathematics. Springer Dordrecht, Netherlands; 2001.

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[30] Dincer I, Rosen MA. Exergy: energy, environment and sustainable development. Oxford, UK: Elsevier Science; 2007. [31] Winterbone J. Advanced thermodynamics for engineers. Oxford, UK: ButterswortheHeinemann; 1996. [32] Incroperra FP, DeWitt DP. Fundamentals of heat and mass transfer. Hoboken, NJ: John Wiley and Sons; 2006. [33] Akkaya AV. Electrochemical model for performance analysis of a tubular SOFC. Int J Energy Res 2007;31:79e98. [34] SC Singhal. Recent progress in tubular solid oxide fuel cell technology In: Fifth International Symposium on Solid Oxide Fuel Cells, Aachen, Germany, June 1997.