A Review on Modeling of Hybrid Solid Oxide Fuel Cell Systems

Abstract

Over the past 2 decades, there has been tremendous progress on numerical and computational tools for fuel cells and energy systems based on them. The purpose of this work is to summarize the current status of hybrid solid oxide fuel cell (SOFC) cycles and identify areas that require further studies. In this review paper, a comprehensive literature survey on different types of SOFC hybrid systems modeling is presented. The paper has three parts. First, it describes the importance of the fuel cells modeling especially in SOFC hybrid cycles. Key features of the fuel cell models are highlighted and model selection criteria are explained. In the second part, the models in the open literature are categorized and discussed. It includes discussion on a detail example of SOFC-gas turbine cycle model, description of early models, models with different objectives such as parametric analysis, comparison of configurations, exergy analysis, optimization, non-stationary power generation applications, transient and off-design analysis, thermoeconomic analysis and so on. Finally, in the last section, key features of selected models are summarized and suggestions for areas that require further studies are presented. In this paper, a hybrid cycle can be any combination of SOFC and gas turbine, steam turbine, coal integrated gasification, and application in combined heat and power cycle.

Full text

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Farshid Zabihian, Alan Fung

International Journal of Engineering (IJE), Volume (3) : Issue (2)

85
A Review on
Modeling of Hybrid Solid Oxide Fuel Cell Systems


Farshid Zabihian
Department of Mechanical and Industrial Engineering
Ryerson University
Toronto, M5B 2K3, Canada

Alan Fung
Department of Mechanical and Industrial Engineering
Ryerson University
Toronto, M5B 2K3, Canada
farshid.zabihian@ryerson.ca
alanfung@ryerson.ca

ABSTRACT

Over the past 2 decades, there has been tremendous progress on numerical and
computational tools for fuel cells and energy systems based on them. The
purpose of this work is to summarize the current status of hybrid solid oxide fuel
cell (SOFC) cycles and identify areas that require further studies.

In this review paper, a comprehensive literature survey on different types of
SOFC hybrid systems modeling is presented. The paper has three parts. First, it
describes the importance of the fuel cells modeling especially in SOFC hybrid
cycles. Key features of the fuel cell models are highlighted and model selection
criteria are explained. In the second part, the models in the open literature are
categorized and discussed. It includes discussion on a detail example of SOFC-
gas turbine cycle model, description of early models, models with different
objectives such as parametric analysis, comparison of configurations, exergy
analysis, optimization, non-stationary power generation applications, transient
and off-design analysis, thermoeconomic analysis and so on. Finally, in the last
section, key features of selected models are summarized and suggestions for
areas that require further studies are presented. In this paper, a hybrid cycle can
be any combination of SOFC and gas turbine, steam turbine, coal integrated
gasification, and application in combined heat and power cycle.

Keywords: Solid Oxide Fuel Cells, SOFC, Hybrid Energy Systems, Steady State and Dynamic Modeling.

1. INTRODUCTION
We owe our sophisticated society and current standard of living to energy infrastructure
development and its consequences in the last century. But, global climate change and natural
resources pollution cause significant worldwide concerns about current trend in energy systems
development. According to the World Energy Outlook published by the International Energy
Agency (IEA) [1], the world’s total electricity consumption would be doubled between 2003 and
2030. This report predicted that the share of fossil fuels as energy supplies for electricity
generation will remain constant at nearly 65%. Power generation is responsible for half of the
increase in global greenhouse gas emissions over the projection period. As a result of all these
problems, sustainability considerations should be involved in all major energy development plans

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all over the world. There are various definitions for sustainability. Probably the simplest one is that
sustainable activities are the activities that help existing generation to meet their needs without
destroying the ability of future generations to meet theirs [2].

Fuel cells are very interesting alternative for conventional power generation technologies because
of their high efficiency and very low environmental effects. In conventional power generation
systems, fuel should be combusted to generate heat and then heat should be converted to
mechanical energy, before it can be used to produce electrical energy. The maximum efficiency
that a thermal engine can achieve is when it operates at Carnot cycle. The efficiency of this cycle
is related to the ratio of the heat source and sink absolute temperature. However, fuel cells
operation is based on electrochemical reactions and not fuel combustion; therefore, their
efficiency is not limited by the thermodynamics laws and Carnot cycle. Instead, their efficiency is
limited by the ratio of released Gibbs free energy to the inlet fuel heating value. It is interesting to
note that this maximum efficiency is equal to the Carnot efficiency calculated at the temperature
at which the combustion is reversible [3]. Furthermore, since there is no combustion, none of the
pollutants, commonly produced by fuel combustors, is emitted.

In this review paper, a comprehensive literature survey on different types of SOFC hybrid
systems modeling is presented. It begins with a general discussion on roles of fuel cell and SOFC
hybrid systems modeling and importance of review papers in this field. Then, key features of the
fuel cell models are highlighted and model selection criteria are explained. In the second part, the
models in the open literature are categorized and discussed based on selected criteria. Finally, in
the last section, key features of selected models are summarized and suggestions for areas that
require further studies are presented.

2. FUEL CELL MODELING
Simulation and mathematical models are certainly helpful for development of various power
generation technologies; however, they are probably more important for fuel cell development.
This is due to complexity of fuel cells and systems based on them, and the difficulty in
experimentally characterizing their internal operation. This complexity can be explained based on
the fact that within the fuel cell, tightly coupled electrochemical reactions, electrical conduction,
ionic conduction, and heat transfer take place simultaneously. That is why a comprehensive study
of fuel cells needs a multidisciplinary approach. Modeling can help to understand what is really
happening within the fuel cells [4].

Understanding the internal physics and chemistry of fuel cells are often difficult. This is because
of great number of physical and chemical processes in the fuel cells, difficulty in independent
controlling of the fuel cells parameters, and access limitations to inside of the fuel cells [5].

In addition, fuel cells simulation can help to focus experimental researches and to improve
accuracy of interpolations and extrapolations of the results. Furthermore, mathematical models
can serve as valuable tools to design and optimize fuel cell systems. On the other hand, dynamic
models can be used to design and test fuel cell systems’ control algorithms. Finally, models can
be developed to evaluate whether characteristics of specific type of fuel cell can meet the
requirements of an application and its cost-effectiveness [4].

Due to its importance, in the past 2 decades there has been tremendous progress on numerical
and computational tools for fuel cells and energy systems based on them, and virtually unlimited
number of papers has been published on fuel cells modeling and simulation. With this large
amount of literature, it is very difficult to keep track of the developments in the field. This problem
can be intensified for new researchers as they can be easily overwhelmed by this sheer volume
of resources. As such, review papers can be very useful. That is why there have been many
review papers on modeling of different types of fuel cells especially for modeling and simulation of
Proton Exchange Membrane Fuel Cells (PEMFC) [6, 7, 8, 9, 10, 11], Solid Oxide Fuel Cells

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(SOFC) [10, 11, 12, 13, 14] and to a lesser extent, Molten Carbonate Fuel Cells (MCFC) [15]. In
addition, review papers can be helpful to summarize the current status of global research efforts
so that unresolved problems can be identified and addressed in future works.

3. SOFC HYBRID CYCLES
Among different types of fuel cells, high temperature fuel cells, namely, SOFC and MCFC, are
very interesting. Because of high operating temperature, their application can lead to some
advantages, such as:

 ability to incorporate bottoming cycles to generate further power from high temperature
exhaust stream,
 ability to reform hydrocarbons which results in fuel flexibility,
 capability to consume CO as fuel,
 no need for noble metal, such as platinum, as electro-catalysts,

And in case of SOFC:

 high oxide-ion conductivity,
 high energy conversion efficiency due to high rate of reaction kinetics
 solid electrolyte and existence of only solid and gas phases result in:
 simplicity in concept,
 ability to be casted into various shapes (that is why wide range of cell and stack
geometries have been proposed for SOFC),
 accurate and appropriate design of the three-phase boundary,
 no electrolyte management constraints.

In a fuel cell hybrid cycle both SOFC and MCFC can be utilized in fuel cell part, but the focus of
this paper is only on SOFC hybrid cycles. An excellent historical and technical review of SOFCs
can be found in [16], and also in [17, 18, 19, 20]. Moreover, Dokiya [21] studied materials and
fabrication technologies deployed for manufacturing of different cell components, investigated the
performance of the fuel cells manufactured using these materials, and reviewed efforts to reduce
fuel cell costs.

As mentioned, high temperature of fuel cell product provides very good opportunity for hybrid high
temperature fuel cell systems especially for distributed generation (DG). Rajashekara [22]
classified the hybrid fuel-cell systems as Type-1 and Type-2 systems. They are mainly suited for
combined cycles power generation and backup or peak shaving power systems, respectively. An
example of Type–1 hybrid systems is hybrid fuel cell and GT cycle, where high temperature of
fuel cell off-gas is used in GT to increase the efficiency of combined system. Another example of
this type of combined cycle is designs that combine different fuel cell technologies. Examples of
Type–2 hybrid systems are designs that combine a fuel cell with wind or solar power generation
systems which integrate the operating characteristics of the individual units, such as their
availability of power.

By definition, proposed by Winkler et al. [23], any combination of a fuel cell and a heat engine
can be considered as fuel cell hybrid system. In these combinations, the heat energy of the fuel
cell off-gas is used to generate further electricity in the heat engine. Here, we extend this
definition to include combined heat and power systems to make this review paper extensive and
exhaustive. Therefore, in this paper, a hybrid cycle can be any combination of SOFC and gas
turbine (GT), steam and gas turbine combined cycle (CC), steam turbine, coal integrated
gasification (IG), and integrated gasification combined cycle (IGCC) and application in combined
heat and power (CHP) cycle.

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In Type–1 hybrid systems, if the fuel cell is operated at atmospheric pressure, the exhaust gases
can be passed through series of heat exchangers to generate either hot water and low-pressure
steam for industrial applications [24] or high-pressure steam for a Rankine power plant. The latter
scheme was proposed as early as 1990 [25].

The fuel cell may also operate at high pressure. In this case, the pressurized hot combustion
gases exiting combustor at the bottom of SOFC can be used to drive a gas turbine with or without
a bottoming steam cycle. This scheme was proposed in 1991 [26].

Among the various hybrid schemes proposed for pressurized fuel cells, probably SOFC-GT
hybrid cycles are the most popular systems being studied theoretically and the only one being
studied experimentally. There are two main designs to combine SOFC and GT. The difference
between these designs is how they extract heat from fuel cell exhaust. In the first design, fuel cell
off-gas directly passes through GT. That means the gas turbine combustor is replaced by the fuel
cell stack. But in the second scheme, the fuel cell off-gas passes through high temperature
recuperator which, in fact, replaces the combustor of the gas turbine cycle [27].

From operational point of view, these designs are distinguished by the operating pressure of the
fuel cell. Their operating pressure is equal to operating pressure of the gas turbine and slightly
above atmospheric pressure, respectively. It should be mentioned that in all cases a steam cycle
[28] and CHP plants can be integrated to the hybrid system to recover more energy from exhaust.

So far, to the authors’ best knowledge, there have been three proof-of-concept and
demonstration SOFC-GT power plants installed in the world. Siemens claimed that it successfully
demonstrated its pressurised SOFC-GT hybrid system and has two units; a 220 kW at the
University of California, Irvine and a 300 kW unit in Pittsburgh [29, 30]. Also, in 2006 Mitsubishi
Heavy Industries, Ltd. (MHI, Japan) claimed that it succeeded in verification testing of a 75 kW
SOFC-MGT hybrid cycle [31].

As mentioned, although both SOFC and MCFC can be used in hybrid cycle, due to the cell
reactions and the molten nature of the electrolyte and lower efficiency of MCFC [32] vast majority
of research in this field are in SOFC hybrid cycles. There are some steady state [33, 34, 35, 36]
and dynamic [37] modeling on the hybrid MCFC-GT cycles. However, the number of papers and
diversity of such are not comparable with papers on SOFC hybrid cycle modeling.

The complex nature of interaction between the already complicated fuel cell and bottoming cycle
make simulation and modeling an essential tool for researchers in this field. In the next section
the ways to categorize SOFC hybrid cycles will be discussed.

4. SOFC HYBRID SYSTEMS MODELING CATEGORIZATION
Haraldsson and Wipke [7] summarized the key features of the fuel cells models as follows:

 modeling approach (theoretical, semi-empirical)
 model state (steady state, transient)
 system boundary (atomic/molecular, cell, stack, and system)
 spatial dimension (zero to three dimensions)
 complexity/details (electrochemical, thermodynamic, fluid dynamic relationships)
 speed, accuracy, and flexibility
 source code (open, proprietary)
 graphical representation of model
 library of models, components, and thermodynamic properties
 validation

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Although they provided this for PEMFC, it could be equally applied for SOFC modeling. They
described the approach of a model as being either theoretical (mechanistic) or semi-empirical.
The mechanistic models are based upon electrochemical, thermodynamic, and fluid dynamic
relationships, whereas, the semi-empirical models use experimental data to predict system
behaviors.

The state of the model, either steady state or transient, shows whether the model can simulate
system only at single operating condition or it can be used in dynamic conditions, including start-
up, shut-down and load changes, too.

Spatial dimension of a model can be zero to three dimensions. Zero-dimension models only
consider current-voltage (I-V) curves whereas mechanistic approaches that address governing
laws including mass, momentum, and energy balances, and the electrochemical reactions need
the explicit treatment of geometry [38]. This will be explained in detail later on.

It is noteworthy that the novel central part of the hybrid system is SOFC, so the categorization is
mainly based on this component, although well established bottoming cycle can be considered as
well.

Singhal and Kendall [16] categorized the resolution of SOFC models in four levels:
atomic/molecular, cell, stack, and system. As Singhal and Kendall pointed out, “the appropriate
level of modeling resolution and approach depended upon the objectives of the modeling
exercise”. For instance, recommended approach for IEA Annex 42, model specifications for a fuel
cell cogeneration device, was system level approach. Because the Annex 42 cogeneration
models included the models of associated plant components, such as hot-water storage, peak-
load boilers and heaters, pumps, fans, and heat exchangers. In addition, the systems models
should be able to couple to the building models. These models simulate the building to predict its
thermal and electrical demands [38].

On the other hand, the models can be categorized based on their SOFC type rather than
modeling approach. For instance,

 Fuel cell type :
 Planar
 Tubular
 Monolithic (MSOFC)
 Integrated Planar (IP-SOFC)
 Cell and stack design (anode-, cathode-, electrolyte-supported and co-, cross-, and
counter- flow types)
 Temperature level:
 Low temperature (LT-SOFC, 500–650 ̊ C)
 Intermediate temperature (IT-SOFC, 650–800 ̊ C)
 High temperature (HT-SOFC, 800–1000 ̊ C)
 Fuel reforming type
 External steam reforming
 Internal steam reforming
 Partial oxidation (POX)
 Anode recirculation
 Fuel type

They can even be categorized by the cycles that used to form hybrid system with SOFC, such as
GT, CC, IGCC, and CHP. Alternatively, purpose of the modeling like parametric sensitivity
analysis, optimization, exergy analysis, economical analysis, configuration analysis, feasibility
studies, partial load and transient conditions analysis can be considered for categorizing SOFC