4E analysis and multi objective optimization of a micro gas turbine and solid oxide fuel cell hybrid combined heat and power system

doi:10.1016/j.jpowsour.2013.08.065

Journal of Power Sources

Volume 247, 1 February 2014, Pages 294-306

https://doi.org/10.1016/j.jpowsour.2013.08.065 Get rights and content

Highlights

•
Energy, exergy, economic and environmental (4E) modeling of SOFC–MGT CHP system.
•
Obtaining optimal values of design parameters by defining new objective functions.
•
Performing sensitivity analysis with variation of fuel cost and capital investment.

Abstract

Energy, exergy, economic and environmental (4E) analysis and optimization of a hybrid solid oxide fuel cell and micro gas turbine (SOFC–MGT) system for use as combined generation of heat and power (CHP) is investigated in this paper. The hybrid system is modeled and performance related results are validated using available data in literature. Then a multi-objective optimization approach based on genetic algorithm is incorporated. Eight system design parameters are selected for the optimization procedure. System exergy efficiency and total cost rate (including capital or investment cost, operational cost and penalty cost of environmental emissions) are the two objectives. The effects of fuel unit cost, capital investment and system power output on optimum design parameters are also investigated. It is observed that the most sensitive and important design parameter in the hybrid system is fuel cell current density which has a significant effect on the balance between system cost and efficiency. The selected design point from the Pareto distribution of optimization results indicates a total system exergy efficiency of 60.7%, with estimated electrical energy cost 0.057 $kW⁻¹ h⁻¹, and payback period of about 6.3 years for the investment.

Introduction

The world's increasing energy demand and the environmental impacts of fossil fuel utilization in conventional power plants have attracted much interest to the development of clean and high efficiency energy systems. Still majorly relying on fossil fuels, fuel cells stand as the most promising technology for their ability to avoid combustion emissions due to the fact that they directly convert the chemical energy of fuel into electricity. High efficiency, clean operation and fuel flexibility of fuel cells has made them a very attractive choice [1] for energy specialists. The solid oxide fuel cell has advantages such as increasing power output and efficiency over other types of fuel cells in power generation industries when they are used as a bottoming cycle with a gas turbine. The resulted hybrid system can reach the first law efficiency levels more than 60% and overall thermal efficiency more than 80% [2]. This system is applicable for small scale plants by coupling with micro gas turbines (MGTs) for distributed generation. Modeling and optimizing the hybrid SOFC–micro gas turbine system is a subject of interest. Lubelli and Massardo [3] performed a comprehensive study on different layouts of hybrid SOFC–GT systems for the atmospheric and pressurized configurations and studied their performance under the effects of different parameters. Campanari [4] and Costamagna [5] predicted the performance of a hybrid MGT–SOFC system in both full load and part load conditions for mode and speed control. Chan et al. [6], [7], [8], [9], [10] proposed an accurate model for the electrochemical behavior of the fuel cell and studied the effects of various parameters on the simple and hybrid SOFC systems in full and part loads which provided a means for sizing the system. Massardo and Magistri [11] performed an exergy analysis on the hybrid system and carried out a thermo-economic study on this system by proposing cost models. Bavarsad [12] investigated the hybrid system from the second law viewpoint as well as effects of various parameters on the exergy destruction in system components. Calise et al. [13], [14], [15], [16] modeled and analyzed the hybrid system from energy, exergy and economic aspects and performed a single level thermo-economic optimization analysis. Autissier et al. [17] used an optimization approach to design the hybrid system for two objectives of efficiency and cost. Duan et al. [18] performed a parametric optimization of the hybrid SOFC-MGT system.

However, in the most of above research works the first law efficiency was applied as the criteria for evaluating the system performance, this paper proposes four E (energy, exergy, economic, environmental) analysis and multi-objective optimization for estimating the values of interested design parameters (decision variables) of a hybrid SOFC and micro gas turbine CHP system. Two objective functions used in optimization procedure were the exergy efficiency and system total cost rate. The environmental penalty cost caused by CO₂ emissions was also added to the total cost. An optimization procedure based on genetic algorithm has been incorporated to reach the optimum design parameters with regard to a set of constraints. The results were discussed and an optimum solution point was selected from the Pareto front. The exergy destruction in system components and effects of optimization on the exergy destruction has been studied, in a next step the sensitivity analysis of the optimum solutions to different parameters were performed. The followings are the contribution of this paper into the subject:

•
Simultaneous energy, exergy, economic and environmental (4E) modeling and analysis of the hybrid SOFC–MGT CHP system was performed to predict the system performance, for generating combined heat and power.
•
The optimal values of system design parameters were estimated using new objective functions, new design parameters and a list of constraints.
•
Performing sensitivity analysis of the system to study the change in optimum values of design parameters with variation of fuel cost as well as the capital investment and system power output.

Section snippets

Plant description

The SOFC–MGT system layout is depicted in Fig. 1. This configuration includes all critical thermal processes of a direct coupled internal reforming SOFC–MGT hybrid system in a simplified manner and is close to the first real constructed system of its kind [2], [4].

The system consists of the following processes:

Air (point 1) and CH₄ fuel (point 9) at known inlet conditions pass through compressors (AC and FC). These streams (points 2 and 10) are preheated in recuperator (REC) and fuel preheater

Thermal modeling

For thermal modeling of the system in steady state condition the average values of the thermodynamic parameters at each component were applied. In this model the gradients of temperature and pressure in the fuel cell as well as other components were neglected and the equilibrium outlet temperature of fuel cell stack was considered as its working temperature. For thermo-physical properties of gases, a temperature dependent specific heat model based on empirical polynomials for ideal gas was

Exergy analysis

The rate of exergy was found in all flow lines of the system from known thermodynamic states and molar compositions by relative chemical and physical equations. The rate of exergy destruction in a component was then computed from the respective exergy balance equations. $\sum {\dot{E}}_{in} = {\dot{E}}_{d} + \sum {\dot{E}}_{out} + {\dot{W}}_{out}$

Or in terms of fuel and product exergy streams and definition of exergy efficiency, we get ${\dot{E}}_{fuel} = {\dot{E}}_{product} + {\dot{E}}_{destructed}$ $η_{ex} = \frac{{\dot{E}}_{product}}{{\dot{E}}_{fuel}}$

The relations for fuel and product exergy values are listed in Table 1

Economic analysis

Both thermodynamic and economic aspects are important in analysis and optimization of energy systems. Several methods were proposed for the thermo-economic assessment of energy systems. However, the first and second law of thermodynamics in conjunction with economic factors provided us a very powerful tool for the optimization of energy systems. The system total cost in this paper is one of objective functions which should be minimized. The total cost included capital and maintenance expenses,

Environmental analysis

Environmental impact is one of the major concerns in analysis of energy systems which is covered in the present study through the optimization of the hybrid SOFC–MGT system. As a general principle, an increase in thermal efficiency of a plant (which provides a specific power output), lowers fuel consumption and decreases emission products such as CO₂. Fuel cells are definitely in a superior situation over the conventional power plants in terms of higher efficiency and lower emissions.

Objective functions

In order to find the optimum set of design parameters that provide a trade-off between the cost and performance of hybrid SOFC–MGT system with minimized environmental impacts, a multi objective optimization problem was defined. The first objective function to be maximized was the total exergy efficiency of the system. $Obj .Func .I = η_{ex, plant} = \frac{{\dot{W}}_{net, out}}{{\dot{m}}_{{CH}_{4}, in} e_{{CH}_{4}}}$ The second objective function to be minimized simultaneously was the total cost of the system. This objective function included the

Case study

The hybrid SOFC–MGT system shown in Fig. 1 with 260 kW power and 100 kW heat output (as 80 °C hot water) in full load operation was our case study for the system optimization in the present paper. This configuration is similar to the pressurized hybrid system pioneered by Siemens-Westinghouse in 2000 [28]. For the economic modeling φ = 1.08 and N = 8000 h, the interest rate I = 14% and the unit cost of electricity c_elec = 0.06 $kW⁻¹ h⁻¹ were selected for use in Eqs. (20.2), (20.1), (21), (22),

Model verification

In order to validate the modeling output results, the operating parameters were compared with the corresponding data reported in Ref. [4] for the same input parameters. Table 5 compares two above groups of data and their corresponding differences in percentage. Results show that the model was capable of predicting the thermal performance of the system quite precisely.

Pareto front

Two objective functions were defined for the optimization procedure. Maximizing the total exergy efficiency and minimizing the

Conclusions

A hybrid SOFC–MGT system was modeled and optimized for various power outputs (sizes) using multi-objective genetic algorithm optimization. The objective functions were selected as the total exergy efficiency and the system total cost. To consider the environmental effects, a term was added to the total cost. It was observed that among design parameters of the system, the cell current density had varying nature in the allowable range of variation. This parameter played the main role in

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4E analysis and multi objective optimization of a micro gas turbine and solid oxide fuel cell hybrid combined heat and power system

Highlights

Abstract

Introduction

Section snippets

Plant description

Thermal modeling

Exergy analysis

Economic analysis

Environmental analysis

Objective functions

Case study

Model verification

Pareto front

Conclusions

J. Power Sources

J. Power Sources

J. Power Sources

J. Power Sources

Int. J. Hydrogen Energy

J. Power Sources

Int. J. Hydrogen Energy

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J. Power Sources

J. Power Sources

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Appl. Energy

Appl. Therm. Eng.

Appl. Energy

Energy

Fuel Cell Systems Explained