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i
CONTROL OF SOLID OXIDE FUEL CELL (SOFC) SYSTEMS
IN STAND-ALONE AND GRID CONNECTED MODES
A thesis submitted in partial fulfillment of the requirements for
the award of degree of
MASTER OF TECHNOLOGY in
ENERGY STUDIES
by
K. LAKSHMANA RAO
2007JES2855
Under the guidance of Under the guidance of
Prof. R. BALA SUBRAMANIAN Dr. K. GADGIL
CENTRE FOR ENERGY STUDIES
INDIAN INSTITUTE OF TECHNOLOGY DELHI
HAUZ KHAS, NEW DELHI-110016
MAY 2009
ii
CERTIFICATE
This is to certify that the present work entitled "CONTROL OF SOLID OXIDE FUEL
CELL (SOFC) SYSTEMS IN STAND-ALONE AND GRID CONNECTED MODES",
submitted by Mr. K. LAKSHMANA RAO (2007JES2855) in partial fulfillment of the
requirements for the award of degree of Master of Technology, is a record of his original work
carried out by him. He has worked under my supervision and has fulfilled the requirement for the
submission of this report. The results presented in this work have not been submitted in part or
full to any other university for award of degree/diploma.
Signature of supervisor Signature of supervisor
Prof. R. BALASUBRAMANIAN Dr. K. GADGIL
Centre for Energy Studies
Indian Institute of Technology Delhi
Hauz Khas, New Delhi-110016
Place: IIT Delhi
Date: 27-05-2009.
iii
ACKNOWLEDGEMENT
I am extremely grateful to my supervisor Prof. R. Balasubramanian & Dr.K.Gadgil for
their invaluable guidance and co-operation throughout the project and for providing me their
personal books and technical papers whenever needed. Without their help, encouragement and
generous counsel, it would have been impossible for me to carry out my project work. They were
a constant source of inspiration right from the beginning and at every stage of this project. I am
very much thankful to them for extending maximum possible help at times of need.
I express my indebtedness to Prof. S.C. Kaushik, Prof. T.S. Bhatti, Prof. S.C. Mullick,
Prof. A. Chandra, Prof. M.G. Dastidar and Dr. K.A. Subramanian for their valuable technical
suggestions.
I would like to thank to V.L Narayana, D.Chandra Sekhar, N.V.Harsha, V.R.S.Satish,
Pradeep Reddy, K.Rambabu, D.Kiran Kumar, P.P.T.Naidu, Rajgopal, Purnendra and my family
members for their constant emotional and moral assistance throughout my work.
Place: IIT Delhi K.LAKSHMANA RAO
Date: 27-05-09 (2007JES2855)
iv
ABSTRACT
As energy consumption rises, one must find suitable alternative means of generation to
supplement conventional existing generation facilities. In this regard, distributed generation
(DG) will continue to play a critical role in the energy supply demand realm. The common
technologies available as DG are micro-turbines, solar, photovoltaic systems, fuel cells stack and
wind energy systems.
In this project, dynamic model of solid oxide fuel cell (SOFC) is done. Fuel cells operate
at low voltages and hence fuel cells need to be boosted and inverted in order to connect to the
utility grid. A DC-DC converter and a DC-AC inverter were used for interfacing SOFC with the
grid. These models are built in MATLAB/SIMULINK.
The power characteristics of the fuel cell, DC-DC converter, DC-AC inverter are plotted
for reference real power of 50kW for standalone applications. The power characteristics of the
DC-AC inverter are plotted for 30kW, 50kW, 70kW of load and also for step change in load for
grid connected applications.
v
CONTENTS
CERTIFICATE ............................................................................................................................... ii
ACKNOWLEDGEMENT ............................................................................................................. iii
ABSTRACT ................................................................................................................................... iv
LIST OF FIGURES ..................................................................................................................... viii
LIST OF TABLES .......................................................................................................................... x
CHAPTER I .................................................................................................................................... 1
INTRODUCTION .......................................................................................................................... 1
1.1. DISTRIBUTED GENERATION ......................................................................................... 1
1.2. FUEL CELL ......................................................................................................................... 1
1.2.1 OPERATING PRINCIPLE: ........................................................................................... 2
1.2.2. TYPES OF FUEL CELLS: ........................................................................................... 3
1.2.3. SOLID OXIDE FUEL CELL (SOFC) .......................................................................... 5
1.2.4. ADVANTAGES – DISADVANTAGES OF FUEL CELL: ........................................ 7
1.3. FUEL CELL APPLICATIONS ............................................................................................ 8
1.4 FUEL CELL PLANT DESCRIPTION ................................................................................. 9
1.5. OBJECTIVE ....................................................................................................................... 11
1.6 OUTLINE OF THE THESIS .............................................................................................. 12
CHAPTER II ................................................................................................................................. 13
LITERATURE REVIEW.............................................................................................................. 13
CHAPTER III ............................................................................................................................... 15
POWER CONDITIONING UNIT ................................................................................................ 15
3.1 DC-DC CONVERTER CONTROL LOOP: ....................................................................... 16
3.2 DC/AC CONVERTER (INVERTER) CONTROL LOOP: ................................................ 17
vi
CHAPTER IV ............................................................................................................................... 18
SOFC SYSTEM IN STANDALONE MODE .............................................................................. 18
4.1 MODELING OF SOFC: ..................................................................................................... 18
4.2 MODELLING OF DC/DC CONVERTER ......................................................................... 21
4.3. SIMULATION MODEL OF FUEL CELL (SOFC) .......................................................... 22
4.4. SIMULATION MODEL OF DC/DC CONVERTER ........................................................ 23
4.5. SIMULATION MODEL OF SOFC IN STANDALONE MODE ..................................... 24
4.6 RESULTS AND DISCUSSIONS ....................................................................................... 25
4.6.1. HYDROGEN FLOW OF SOFC: ................................................................................ 25
4.6.2. OXYGEN FLOW OF SOFC: ..................................................................................... 26
4.6.3. VOLTAGE WAVE FORM OF SOFC: ...................................................................... 27
4.6.4 OUTPUT VOLTAGE WAVE FORM OF DC/DC CONVERTER: ........................... 28
4.6.5. DUTY RATIO OF DC/DC CONVERTER: ............................................................... 29
4.6.6. OUTPUT CURRENT WAVE FORM OF INVERTER ............................................. 30
4.6.7. OUTPUT VOLTAGE WAVE FORM ACROSS THE LOAD: ................................. 31
CHAPTER V ................................................................................................................................. 33
GRID CONNECTED APPLICATIONS: ..................................................................................... 33
5.1. DATA FOR THE INVERTER MODELING: ................................................................... 33
5.2. INVERTER SWITCHING MODEL WITH RL LOAD AND GRID: .............................. 35
5.3. CONTROL STRATEGY FOR GRID CONNECTED INVERTERS: .............................. 36
5.3.1 CONSTANT CURRENT CONTROL: ........................................................................ 36
5.3.2 CONSTANT POWER CONTROL: ............................................................................ 37
5.4 SIMULATION MODELS: .................................................................................................. 39
5.4.1. SIMULATION MODEL OF SOFC FOR GRID CONNECTED APPLICATIONS . 39
5.4.2. SIMULATION MODEL OF POWER REGULATOR .............................................. 40
vii
5.4.3. SIMULATION MODEL OF CURRENT REGULATOR .......................................... 41
5.5. SIMULATION RESULTS FOR GRID CONNECTED APPLICATIONS: ..................... 42
5.5.1 RESPONSE FOR 50KW OF LOAD: .......................................................................... 42
5.5.3 RESPONSE FOR 70KW OF LOAD: .......................................................................... 46
5.5.4 RESPONSE FOR STEP CHANGE IN LOAD: .......................................................... 48
5.5.5 RESPONSE FOR OCCURRENCE OF FAULT IN LOAD: ....................................... 50
5.5.6. RESPONSE OF REACTIVE POWER FLOW: ......................................................... 52
CHAPTER VI ............................................................................................................................... 54
CONCLUSIONS AND FUTURE WORK ................................................................................... 54
6.1. CONCLUSIONS ................................................................................................................ 54
6.2. FUTURE WORK ............................................................................................................... 55
REFERENCES .............................................................................................................................. 56
APPENDIX ................................................................................................................................... 59
SYSTEM DATA ........................................................................................................................... 60
BIODATA ..................................................................................................................................... 61
viii
LIST OF FIGURES
FIGURE 1. SCHEMATIC OF AN INDIVIDUAL FUEL CELL................................................... 2
FIGURE 2. COMPONENTS OF FUEL CELL STACK ................................................................ 3
FIGURE 3. VOLT-AMP CHARACTERISTICS SOFC ................................................................ 6
FIGURE 4. BLOCK DIAGRAM OF A FUEL CELL POWER SYSTEM .................................. 10
FIGURE 5. POWER CONDITIONING SYSTEM ...................................................................... 15
FIGURE 6. DC/DC CONVERTER CONTROL LOOP ............................................................... 16
FIGURE 7. DC/AC CONVERTER CONTROL LOOP ............................................................... 17
FIGURE 8. BLOCK DIAGRAM FOR DYNAMIC MODEL OF SOFC .................................... 20
FIGURE 9. CIRCUIT DIAGRAM OF DC/DC CONVERTER ................................................... 21
FIGURE 10. SIMULATION CIRCUIT OF SOFC ...................................................................... 22
FIGURE 11. SIMULATION MODEL OF DC/DC CONVERTER ............................................. 23
FIGURE 12. SIMULATION CIRCUIT FOR STANDALONE APPLICATIONS ..................... 24
FIGURE 13. HYDROGEN FLOW OF SOFC ............................................................................. 25
FIGURE 14. OXYGEN FLOW OF SOFC ................................................................................... 26
FIGURE 15. VOLTAGE WAVEFORM OF SOFC ..................................................................... 27
FIGURE 16. OUTPUT VOLTAGE WAVEFORM OF DC/DC CONVERTER ......................... 28
FIGURE 17. DUTY RATIO OF DC/DC CONVERTER ............................................................. 29
FIGURE 18. OUTPUT CURRENT WAVEFORM OF INVERTER ........................................... 30
FIGURE 19. OUTPUT VOLTAGE WAVEFORM ACROSS THE LOAD ................................ 31
FIGURE 20. OUTPUT CURRENT WAVEFORM THROUGH THE LOAD ............................ 32
FIGURE 21. BLOCK DIAGRAM OF DG CONNECTED TO GRID ........................................ 33
FIGURE 22. INVERTER SWITCHING MODEL WITH RL LOAD AND GRID ..................... 36
FIGURE 23. BLOCK DIAGRAM OF CONSTANT CURRENT-CONTROL INVERTER ...... 37
FIGURE 24. BLOCK DIAGRAM OF CONSTANT-POWER-CONTROLLED INVERTER ... 38
FIGURE 25 SIMULATION MODEL FOR GRID CONNECTED APPLICATIONS ................ 39
FIGURE 26 SIMULATION MODEL OF POWER REGULATOR ............................................ 40
FIGURE 27. SIMULATION MODEL OF CURRENT REGULATOR ...................................... 41
FIGURE 28. POWER RESPONSE FOR 50KW OF LOAD ........................................................ 42
FIGURE 29. CURRENT RESPONSE FOR 50KW OF LOAD ................................................... 43
FIGURE 30. POWER RESPONSE FOR 50KW OF LOAD ........................................................ 44
ix
FIGURE 31. CURRENT RESPONSE FOR 30KW OF LOAD ................................................... 45
FIGURE 32. POWER RESPONSE FOR 70KW OF LOAD ........................................................ 46
FIGURE 33. CURRENT RESPONSE FOR 70KW OF LOAD ................................................... 47
FIGURE 34. RESPONSE OF POWER FOR STEP CHANGE IN LOAD .................................. 48
FIGURE 35. RESPONSE OF CURRENT FOR STEP CHANGE IN LOAD ............................. 49
FIGURE 36. RESPONSE OF POWER FLOW DURING FAULTS IN LOAD .......................... 50
FIGURE 37. RESPONSE OF CURRENT FLOW DURING FAULTS IN LOAD ..................... 51
FIGURE 38. RESPONSE OF REACTIVE POWER FLOW OF 200 VAR ................................ 52
FIGURE 39. RESPONSE OF REACTIVE POWER FLOW FOR STEP CHANGE ................. 53
x
LIST OF TABLES
Table 1. SUMMARY OF FUEL CELLS ........................................................................................ 4
Table 2. DATA FOR THE INVERTER/RL LOAD/GRID .......................................................... 34
Table 3. PARAMETERS IN SOFC MODEL ............................................................................... 59
Table 4. PARAMETERS IN BOOST DC-DC CONVERTER .................................................... 60
Table 5. Kp & Ki VALUES OF DC-DC CONVERTER ............................................................. 60
Table 6. Kp & Ki VALUES OF DC-AC CONVERTER FOR STANDALONE ......................... 60
Table 7. Kp & Ki VALUES OF DC-AC CONVERTER FOR GRID .......................................... 60
1
CHAPTER I
INTRODUCTION
1.1. DISTRIBUTED GENERATION
The centralized and regulated electric utilities have always been the major source of
electric power production and supply. However, the increase in demand for electric power has
led to the development of distributed generation (DG) which can complement the central power
by providing additional capacity to the users. These are small generating units which can be
located at the consumer end or anywhere within the distribution system.
DG can be beneficial to the consumers as well as the utility. Consumers are interested in
DG due to the various benefits associated with it: cost saving during peak demand charges,
higher power quality and increased energy efficiency. The utilities can also benefit as it generally
eliminates the cost needed for laying new transmission/distribution lines.
Distributed generation employs alternate resources such as micro-turbines, solar
photovoltaic systems, fuel cells and wind energy systems. This thesis lays emphasis on the fuel
cell technology and its integration with the utility grid.
1.2. FUEL CELL
A fuel cell is an electro chemical device that converts the chemical energy of the fuel
(hydrogen) into electrical energy. It is centered on a chemical reaction between fuel and the
oxidant (generally oxygen) to produce electricity where water and heat are byproducts. This
conversion of the fuel into energy takes place without combustion. The efficiency of the fuel
cells ranges from 40-60% and can be improved to 80-90% in cogeneration applications [3]-[5].
Fuel cell technology is a relatively new energy-saving technology that has the potential to
compete with the conventional existing generation facilities. Among the various DG
technologies available, fuel cells are being considered as a potential source of electricity because
they have no geographic limitations and can be placed anywhere on a distribution system. Fuel
cells have numerous benefits which make them superior compared to the other technologies.
Benefits include high efficiency, high power quality and service reliability, few or no moving
parts which leads to low noise, fuel flexibility, modularity and low maintenance[6].
2
1.2.1 OPERATING PRINCIPLE:
The structure and the functioning of a fuel cell is similar to that of a battery except that
the fuel can be continuously fed into the cell. The cell consists of two electrodes, anode (negative
electrode) and cathode (positive electrode) separated by an electrolyte. Fuel is fed into the anode
where electrochemical oxidation takes place and the oxidant is fed into the cathode where
electrochemical reduction takes place to produce electric current and water is the primary
product of the cell reaction.
Figure 1. Schematic of an individual fuel cell
The typical anode and cathode reactions for a hydrogen fuel cell are given by Equations
(1) and (2), respectively.
H2 2H+ +2e
- (1)
½ O2 + 2H+ +2e
- H2O (2)
An individual fuel cell produces less than a volt of electric potential. A large number of
cells are stacked on top of each other and connected in series (with bipolar connects) to produce
higher voltages. Figure shows cell stacks which consists of repeating units, each comprising an
3
anode, cathode, electrolyte and a bipolar separator plate. The number of cells depends on the
desired power output [5].
Figure 2. Components of fuel cell stack
1.2.2. TYPES OF FUEL CELLS:
Fuel cells are classified according to the type of electrolyte used. There are various fuel
cell types at different stages of development. The various types of fuel cells in the increasing
order of their operating temperature are [18].
• Proton exchange membrane fuel cell (PEMFC-175o F)
• Phosphoric acid fuel cell (PAFC-400o F)
• Molten carbonate fuel cell (MCFC-1250o F)
• Solid oxide fuel cell (SOFC-1800o F) .Each of these fuel cell types differ in the electrolyte and
fuel used, operating temperature and pressure, construction materials, power density and
4
efficiency. Table 1 gives a basic summary of the characteristics and requirements of the fuel cell
types mentioned above.
Table 1. SUMMARY OF FUEL CELLS
Fuel Cell
Type PEMFC AFC PAFC MCFC SOFC
Electrolyte Solid polymer
(Nafion) KOH
Phosphoric
acid
Lithium and
potassium
carbonate
Solid oxide
electrolyte (yttria,
zirconia)
Charge
Carrier H+ OH
- H
+ CO3
2- O
2-
Fuel
Pure H2
(tolerates
CO2)
Pure H2
Pure H2
(tolerates CO2,
approx. 1%
CO)
H2, CO, CH4,
other
hydrocarbons
(tolerates
CO2)
H2, CO, CH4,
other
hydrocarbons
(tolerates CO2)
Catalyst Platinum Platinum Platinum Nickel Perovskites
Operation
Temperature 50–100°C 60–120°C ~220°C ~650°C ~1000°C
External
Reformer
For CH4
Yes Yes Yes No No
Product
Water
Management
Evaporative Evaporative Evaporative Gaseous
Product Gaseous Product
Product Heat
Management
Process Gas +
Independent
Cooling
Medium
Process Gas +
Electrolyte
Circulation
Process Gas +
Independent
Cooling
Medium
Internal
Reforming +
Process Gas
Internal
Reforming +
Process Gas
Power Range
/Application
Automotive,
CHP (5–
250kW),
portable
<5 kW,
military,
space
CHP (200
kW)
200 kW–MW
range, CHP
and
standalone
2 kW–MW range,
CHP and
standalone
5
1.2.3. SOLID OXIDE FUEL CELL (SOFC)
The SOFC is a high-temperature operating fuel cell which has high potential in stationary
applications. The efficiency of SOFC is in the range of 45-50% and when integrated with a gas
turbine, it reaches a high efficiency of 70-75%. It is a solid-state device that uses an oxide ion-
conducting non-porous ceramic material as an electrolyte. Since the electrolyte is a solid, the
cells do not have to be constructed in the plate-like configuration typical of other fuel cell types.
Corrosion is less compared to MCFC and no water management problems as in PEMFCs due to
the solid electrolyte. High temperature operation removes the need for a precious-metal catalyst,
thereby reducing the cost. It also allows SOFCs to reform fuels internally, which enables the use
of a variety of fuels and reduces the cost associated with adding a reformer to the system.
The electrolyte used is a ceramic oxide (yttria stabilized zirconia). The anode used is
nickel-zirconia cermets and the cathode is a strontium doped lanthanum manganite. The use of
ceramic materials increases the cost of SOFCs. High operating temperature requires stringent
materials to be used which further drives up the cost. Research is being carried out to reduce the
operating temperature and use less stringent materials Reduction of temperature improves the
starting time, cheaper materials can be used, durability and robustness can be increased.
Intermediate-temperature SOFCs cannot be used for all applications. Higher temperature is
required for fuel cell micro-turbine hybrid systems. However, for smaller systems intermediate
temperature SOFCs would be ideal [9].
Since SOFCs have fuel-flexibility, the input to the anode can be hydrogen, carbon
monoxide or methane. Hydrogen or carbon monoxide may enter the anode. At the cathode,
electrochemical reduction takes place to obtain oxide ions. These ions pass through the
electrolyte layer to the anode where hydrogen is oxidized to obtain water. In case of carbon
monoxide, it is oxidized to carbon dioxide.
6
In this analysis, a reduced model of the fuel cell has been taken into account, neglecting
the activation and concentration losses as well as the double charging effect. The loss due to
internal resistance of the stack is basically due to the resistance to the flow of ions in the
electrolyte as well as the material of the electrode.
In general, it is mainly caused by the electrolyte. Figure shows the typical volt-amp
characteristics of SOFC. Fuel cells have drooping voltage characteristics: an increase in the load
current causes a decrease in the stack voltage. The number of cells is taken to be 450 and the
standard cell potential is 1.18V. Hence the open circuit voltage (OCV) is 531V which decreases
as the load current increases as seen in Figure. The drop is fairly linear in the middle region,
known as region of ohmic polarization. This is the operating region for the fuel cell. The voltage
varies rapidly at lower and higher currents
0 100 200 300 400 500 600 700
100
150
200
250
300
350
400
450
500
550
Voltage [Volts]
Current [Amp]
Figure 3. Volt-amp characteristics SOFC
7
1.2.4. ADVANTAGES – DISADVANTAGES OF FUEL CELL:
Fuel cells have various advantages compared to conventional power sources, such as
internal combustion engines or batteries. Although some of the fuel cells’ attributes are only
valid for some applications, most advantages are more general. However, there are some
disadvantages facing developers and the commercialization of fuel cells as well.
Advantages
Fuel cells eliminate pollution caused by burning fossil fuels; the only byproduct is water.
Since hydrogen can be produced anywhere where there is water and electricity,
production of potential fuel can be distributed.
Installation of smaller stationary fuel cells leads to a more stabilized and decentralized
power grid.
Fuel cells have a higher efficiency than diesel or gas engines.
Most fuel cells operate noise less, compared to internal combustion engines.
Low temperature fuel cells (PEM, DMFC) have low heat transmission which makes them
ideal for military applications.
Earning of carbon credits by using this fuel-cell technology.
Disadvantages
Fuelling fuel cells is still a problem since the production, transportation, distribution and
storage of hydrogen is difficult.
Reforming hydrocarbons via reformer to produce hydrogen is technically
challenging and not clearly environmentally friendly.
Fuel cells are in general slightly bigger than comparable batteries or engines. However,
the size of the units is decreasing.
Some fuel cells use expensive materials.
8
1.3. FUEL CELL APPLICATIONS
Presently there are many uses for fuel cells; for example all of the major automakers are
working to commercialize a fuel cell car. Fuel cells are powering buses, boats, trains, plains,
scooters, and even bicycles. There is a variety of commonly used machines powered by fuel
cells, such as vending machines, vacuum cleaners, and high road signs. Miniature fuel cells for
cellular phones, laptop computers and portable electronics are on their way to the market.
Hospitals, credit card centers, police stations, and banks are all using fuel cells to provide power
for their facilities. Wastewater treatment plants and landfills are using fuel cells to convert the
methane gas they produce into electricity. The possibilities are endless. Main fuel cells
applications can be divided into the following categories:
- stationary,
- residential,
- transportation,
- portable power,
- landfill/wastewater treatment.
More than 2500 fuel cell stationary systems have been installed all over the world — in
hospitals, nursing homes, hotels, office buildings, schools, utility power plants, and airport
terminals, providing primary power or backup. In has been estimated that in large-scale building
systems, fuel cells can reduce facility energy service costs by 20% to 40% over conventional
energy service.
Fuel cells are ideal for residential power generation, either connected to the electric grid to
provide supplemental power and backup assurance for critical areas, or installed as grid-
independent generators for on-site service in areas that are inaccessible by power lines. Since
fuel cells operate silently, they reduce noise pollution as well as air pollution and the waste heat
from a fuel cell can be used to provide hot water or space heating for a house. Many of the
prototypes being tested and demonstrated for residential use extract hydrogen from propane or
natural gas.
All major automotive manufacturers have a fuel cell vehicle either in development or in
testing right now, and Honda and Toyota have already begun leasing vehicles in California and
Japan. Automakers and experts speculate that the fuel cell vehicle will not be commercialized
9
until at least 2010; nevertheless, manufacturers started incorporating fuel cells into buses,
locomotives, airplanes, scooters and golf carts.
Miniature fuel cells, once available to the commercial market, will help consumers talk for
up to a month on a cellular phone without recharging. Fuel cells will change the telecommuting
world, powering laptops and palm pilots hours longer than present day batteries. Other
applications for micro fuel cells include pagers, video recorders, portable power tools, and low
power remote devices such as hearing aids, smoke detectors, burglary alarms, hotel locks, and
meter readers. These miniature fuel cells generally run on methanol, an inexpensive wood
alcohol.
Fuel cells currently operate at landfills and wastewater treatment plants across the country,
proving to be the valid technology for reducing pollution emission and generating power from
the methane gas they produce.
1.4 FUEL CELL PLANT DESCRIPTION
Fuel cells produce DC power, water and heat from the combination of hydrogen
produced from the fuel and oxygen from the air. In procedures where CO and CH4 react in the
cell to produce hydrogen, CO2 is also a co-product. Reactions in fuel cells depend substantially
on the temperature and pressure inside the cell. A system must be built around the fuel cell to
supply air and clean fuel, convert the energy to a more usable form such as grid quality ac
power, and remove the depleted reactants and heat that are produced by the reactions in the
cells. Figure 4 shows the basic structure of a fuel cell power plant.
10
Figure 4. Block diagram of a fuel cell power system
First stage of a fuel cell power system plant is a fuel processing unit where a conventional
fuel (natural gas, methanol, coil, naphtha, or other gaseous hydrocarbon) is purified into a gas
containing hydrogen. The following stage converts chemical energy to DC electricity using the
stacks of individual fuel cells. Number of stacks used in the power producing section unit
depends on the specific power application. Finally, power conditioner converts DC power
generated by the fuel cell stacks into the regulated AC or DC power suitable for customer usage.
11
1.5. OBJECTIVE
High-temperature fuel cells such as solid oxide fuel cells (SOFC) have potential for
centralized power generation as well as combined heat and power. Compared to other fuel cells,
SOFC’s are capable of handling more convenient forms of hydro carbons fuels where they are
highly efficient and tolerant to impurities and its high temperature enables internal reforming
[1].This thesis employs a dynamic model of SOFC presented in[2]
The DC-DC converter boosts the low voltage of the fuel cell as well as regulates the
voltage. The boost converter with a conventional PI controller has been used for the converter
control [6]. In this thesis, boost converter with a PWM closed loop control has been employed.
The DC-AC inverter plays a key role in making the fuel cell DC power available for
standalone applications as well as grid connected applications. This thesis focuses on the
interfacing of the fuel cell system with the utility grid. The duty cycles given to the inverter is
controlled by constant power control scheme for grid connected applications.
In this thesis, MATLAB/SIMULINK has been used to model the dynamic system of
SOFC, DC-DC converter, DC-AC inverter with controllers.
12
1.6 OUTLINE OF THE THESIS
Chapter I of the thesis devoted to an in depth explanation of different fuel cell technologies and
their most important characteristics overview of the fuel cell systems and applications. It briefly
describes typical fuel cell plants and their constituent parts such as fuel processors, power
conversion stages, and conditioners. A comparison between the various fuel cell types is made.
Chapter II presents an overview of the literature review for standalone and grid connected
systems.
Chapter III presents power conditioning system and detailed explanation on closed loop control
of DC-DC Converter and closed loop control of DC-AC converter.
Chapter IV involves the design and modeling of fuel cell, DC-DC converter, DC-AC converter
and constant voltage control strategy for standalone applications. Power, voltage, current
characteristics of fuel cell &DC/DC converter &DC/AC converter are plotted for reference real
power of 50kW.
Chapter V presents constant power control strategy for DC-AC converter for grid connected
applications and it also presents the simulation results of voltage, current, power for DC-AC
converter, for grid and for load at different loading conditions.
Chapter VI presents detailed conclusions on results for standalone and grid connected
applications and also presents future scope of work.
13
CHAPTER II
LITERATURE REVIEW The fuel cell is a fast growing technology and much research has been going on in this
decade. Fuel cells are gaining much attention because of their light weight, compact size, low
maintenance, and low acoustic and chemical emissions. They can serve as a potential source for
electric power generation for stand-alone as well as for grid-tied applications. Reference [1]
provides a basic approach for fuel cell modeling suitable for distributed generation. A model for
the proton exchange membrane fuel cell (PEMFC) has been developed by various researchers in
[2]-[4] taking its thermodynamic effect into consideration.
Simulation Model of the SOFC is developed using the Reference [5]-[7]. SOFC based
fuel cells for load following stationary applications and control of fuel cell power is studied
elaborately with the References [8]-[10]. buck-boost DC-DC converter with a closed loop PWM
(pulse width Modulation) control strategy as described in Reference [11]-[12] has been
employed. Control Strategy for Grid-Connected DC-AC Converters with Load Power Factor
Correction and A New Power Inverter for Fuel Cells has been studied from [13]-[15].
DC-AC inverter converts the DC power of the fuel cell system into AC power for stand
alone as well as grid connected applications. The voltage source inverter (VSI) plays a vital role
in interfacing the fuel cell-DC-DC system with the utility grid is studied from [16]-[17].
Dynamic model of solid oxide fuel cell (SOFC) developed & this model is used to
investigate the short-time overloading capability of the SOFC. Then, the application of this
model in distributed generation (DG) system studies is explored. Controller design
methodologies are also presented for grid-connected SOFC (DG) power conditioning units to
control power flow from the SOFC (DG) to the utility grid [18].
A grid connected fuel-cell plant consists of the fuel cell and the voltage source inverter.
The flux-vector control is used very effectively for the control of this inverter, where the space-
vector pulse width modulation is implemented by artificial neural networks [19].
Control of inverters in distributed source environments such as in isolated ac systems,
large and distributed uninterruptible power supply (UPS) systems are explained in [20].
Maximizing performance of a grid-connected PV-fuel cell hybrid system by use of a two-
loop controller was discussed. One loop is a neural network controller for maximum power point
tracking, which extracts maximum available solar power from PV arrays under varying
14
conditions of isolation, Temperature, and system load. A real/reactive power controller (RRPC)
is the other loop. The RRPC meets the system’s requirement for real and reactive powers by
controlling incoming fuel to fuel cell stacks as well as switching control signals to a power
conditioning subsystem was studied in [21].
Distributed resources (DR) include a variety of energy sources, such as micro-turbines,
photovoltaic’s, fuel cells, and storage devices, with capacities in the 1 kW to 10 MW range.
Deployment of DR on distribution networks could potentially increase their reliability and lower
the cost of power delivery by placing energy sources nearer to the demand centers. By providing
a way to by-pass conventional power delivery systems, DR could also offer additional supply
flexibility is explained in detail in [22].
The overall configuration of the PEMFC DG system is given, dynamic models for the
PEMFC power plant and its power electronic interfacing are briefly described, and controller
design methodologies for the power conditioning units to control the power flow from the fuel
cell power plant to the utility grid are presented in [23].
Three-phase grid-connected inverter modeling is done and these models include average
and switching models, and this demonstrates that the schemes work for any multi-phase
inverters, including three-phase and single-phase inverters and it evaluates and validates the
proposed schemes under conditions of practical applications are explained in detail [24].
Distributed Generation will play an increasing role in the electric power system of the
near future. It includes a variety of technologies, such as fuel cells, wind turbines etc in the
power range between 10kW and 100 MW. Control system for the integration of a fuel cell and a
wind turbine generating system has been proposed in this paper [25].
The physical model of the fuel cell stack is described, to properly represent the slow
dynamics associated with the gas flows and the fuel processor operation. Then, suitable control
architecture is presented for the overall system, its objective being to regulate the input fuel flow
in order to meet a desirable output power demand. Then, the power conditioning system,
including the DC/DC and DC/AC converters are presented in [26].
15
CHAPTER III
POWER CONDITIONING UNIT
The power conditioning system provides regulated dc or ac power appropriate for the
application. It is the major component of an FC system. The output of the FC is an unregulated
dc voltage and it needs to be conditioned in order to be of practical use. The power conditioner
section converts the raw power into useable power for different applications. The power
conditioning unit also controls electricity’s frequency and maintains harmonics to an acceptable
level. The purpose of conditioners is to adapt the electrical current from FC to suit the electrical
needs of the application.
The general configuration of the system will be the FC followed by a boost converter
followed by an inverter. In general, the load for the boost stage is a filter and the inverter system
(for stand-alone purpose a purely resistive and a reactive load might be considered). The boost
converters for the FC will be operated in the voltage control mode. The boost converter is ideally
suited for interfacing the inverter system with the FC.
Based on the load conditions, the boost stage can be commanded to draw a specific
amount of current from the FC with a ripple well defined by the frequency, size of the inductor,
and duty ratio. Similarly, the inverter is used for the interfacing of the FC system to the load to
provide the load with voltage/current with proper frequency phase and magnitude where the
input for the inverter comes from the boost converter stage and the inverter (with the filter)
becomes the load for the boost converter. The power conditioner is also used for the grid
connection of the FC. An electrical power-generating system that uses FC as the primary source
of electricity generation and is intended to operate synchronously, and in parallel with the
electric utility network is a grid-connected FC system [3–5].
POWER
CONDITIONING
UNIT
FUEL CELL
(SOFC)
LOAD
Figure 5. Power conditioning system
16
3.1 DC-DC CONVERTER CONTROL LOOP:
The output voltage of FC at the series of the stacks is uncontrolled dc voltage which
fluctuates with load variations. This raw voltage, which is unregulated and uncontrolled, is
regulated to an average value with help of dc/dc converter. The controlled voltage thus obtained
is fed to the dc/ac inverter after it is filtered. The power obtained from this inverter is added to
the grid. This system can be used as a standalone after the dc/dc converter stage if dc power is
needed or after the dc/ac stage if ac power is needed.
This unregulated voltage has to be adjusted to a constant average value (regulated dc
voltage) by adjusting the duty ratio to the required value. The voltage is boosted depending upon
the duty ratio. The duty ratio of the boost converter is adjusted with the help of a PI controller
The duty ratio is set at a particular value for the converter to provide desired average value of
voltage at the output, and any fluctuation in the FC voltage due to change in fuel flow, in the
load or in the characteristics of FC due to the chemistry involved takes the output voltage away
from the desired average value of the voltage.
The PI controller changes the duty ratio properly to get the desired average value. The
duty ratio of the converter is changed by changing the pulses fed to the switch in the dc/dc
converter circuit by the PWM generator.
FUEL
CELL
LOAD/GRID DC/DC
CONVERTER
PWM
GENERATOR
PI CONTROLLER
Figure 6. DC/DC converter control loop
17
3.2 DC/AC CONVERTER (INVERTER) CONTROL LOOP:
Inverters are devices that change the dc electricity produced by FC into ac electricity.
Utility – interactive inverters are used in systems connected to a utility power line. The inverters
produce ac electricity in synchronization with the power line, and of a quality acceptable to the
utility company once the control strategy is implemented.
The inverter output voltage (i.e. load voltage) will be compared every time with the ref
voltage. The change in the output (due to change in the load) and grid voltage is given as inputs
to the PI controller, and the output of the PI controller is given to the PWM generator and this
generator will generate 6 pulses.
These pulses will be given to the switches of the inverter which will change the duty
ratio of the inverter. Due to this change in duty ratio the output voltage will be maintained
constant during the loading conditions.
DC/DC
CONVERER
DC/AC
CONVERER
LC
FILTER LOAD
/GRID
PWM
GENERATOR
PI
CONTROLLER
Figure 7. DC/AC converter control loop
18
CHAPTER IV
SOFC SYSTEM IN STANDALONE MODE
4.1 MODELING OF SOFC:
The modeling of SOFC is based on the following assumptions
The fuel cell temperature is assumed to be constant.
The fuel cell gasses are ideal.
Nernst’s equation applicable.
By Nernst’s equation dc voltage fcV across stack of the fuel cell at current I is given by the
following equation.
(3)
fcV – Operating dc voltage (V)
E0 – Standard reversible cell potential (V)
pi – Partial pressure of species i (Pa)
r – Internal resistance of stack (Ω)
I – Stack current (A)
N0 – Number of cells in stack
R – Universal gas constant (J/ mol K)
T – Stack temperature (K)
F – Faraday’s constant (C/mol)
fcfc rIopH
pOpH
F
RTENV −
+=
2
5.0
2200 ln2
19
The main equations describing the slow dynamics of a SOFC can be written as follows.
(4)
(5)
!"# !$%
&'() (6)
*
+
$
, !"# 2./ (7)
*0
+0
1 $0
2 0
!"# 2.3 (8)
*4
+4
5 !$%$4
(9)
qH2 – Fuel flow (mol/s)
qO2 – Oxygen flow (mol/s)
KH2 – Valve molar constant for hydrogen (kmol/s atm)
KO2 – Valve molar constant for oxygen (kmol/s atm)
KH2O – Valve molar constant for water (kmol/s atm)
τH2 – Response time for hydrogen (s)
τO2 – Response time for oxygen (s)
τH2O – Response time for water (s)
20
τe – Electrical response time (s)
τf– Fuel response time (s)
Uopt – Optimum fuel utilization
rHO – Ratio of hydrogen to oxygen
Kr – Constant (kmol/s A)
Pref – Reference power (kW)
The block diagram representation of the SOFC dynamic model is shown in the Fig
Figure 8. Block diagram for dynamic model of SOFC
21
4.2 MODELLING OF DC/DC CONVERTER
Figure 9. Circuit diagram of DC/DC Converter
"# " " (10)
" 6 (11)
7 1 9'9 (12)
For continuous conduction the designed values of L, C, R is
: 9'' (13)
; (9<)(=) (14)
> (9'<)(?=9@) (15)
22
4.3. SIMULATION MODEL OF FUEL CELL (SOFC)
By taking the dynamic model equations of the SOFC and relative data (in appendix) and
simulated it in MATLAB/SIMULINK which was shown in Figure10.
Figure 10. Simulation circuit of SOFC
23
4.4. SIMULATION MODEL OF DC/DC CONVERTER
The DC/DC converter boosts the low unregulated voltage to a desired regulated
voltage. The input for the DC/DC converter is the fuel cell voltage and output of the DC/DC
converter is connected to the inverter circuit which was shown in Figure 11.
Figure 11. Simulation model of DC/DC converter
4
- FC
3
+ FC
2
-
1
+
v+
-
v+
-
1
0.001s+1
Transfer Fcn
t18
t17 t16
t13
t15
t14
L
Ec dc
Duty Cycles
UBus
UrefEc
i+
-
700
Constant
Duty Cycle
+
-
A
Chopper
CBus
<IGBT 2>
24
4.5. SIMULATION MODEL OF SOFC IN STANDALONE MODE
Infinite Bus
Continuous
powergui
Vabc
Iabc
PQ
Vabc
Iabc
PQ
meas FC
dq0
sin_cos
abc
dq0_to_abc Transformation
abc
sin_cos
dq0
abc_to_dq0
Transformation2
abc
sin_cos
dq0
abc_to_dq0 Transformation
0
z
1
t8
t7
t6
t5t4
t3
t1
t2
t19
t
A
B
C
a
b
c Three-Phase Breaker
Vabc
Iabc
A
B
C a
b
c
VabcA B C
a
b
c
VabcA
B
C
a
b
c
Vabc
Iabc
A
B
C
a
b
c
Vabc
Iabc A
B
C
a
b
c
A B C
A B C
A
B
C
A
B
C
A B C
A
B
C
A B C
Three-Phase
R Load
A B C Three-Phase
R Load
Terminator4
Terminator1
Conn1
Conn2
Subsystem
Scope6
Scope11
Scope10
Scope
g
A
B
C
+
-
Inverter
[Vq] Goto9
[Vd] Goto8
[Vabc]
Goto7
Vabc_grid
[PWM]
Goto18
[Vq_grid] Goto13
[Vd_grid] Goto12
[sin]
Goto1
[Vd] From9
Vabc_grid From8
[Vq_grid] From7
[Vd_grid]
From6
[sin] From5
[sin]
From3
[Vabc]
From2
[sin]
From16
[Vq]
From12
[PWM]
Freq Sin_Cos
wt
Discrete
Virtual PLL
Uref Pulses
Discrete
PWM GeneratorPI
Discrete
PI Controller2
PI Discrete
PI Controller1
Clock
Figure 12. Simulation circuit for standalone applications
25
4.6 RESULTS AND DISCUSSIONS
4.6.1. HYDROGEN FLOW OF SOFC:
By equating the equation (7) to zero for calculating the initial value of the
hydrogen flow, while taking the initial current as 100 Amperes, the value of hydrogen flow
obtained theoretically at t=0 is qH2 =0.274(mol/s). The same value is obtained practically while
simulating the SOFC which was shown in Fig12. SOFC is loaded to 50 kW at t=0, the hydrogen
flow corresponding to this point of operation is 0.345 (mol/s), which was verified theoretically.
Now the load is increased to 100 kW, for meeting this load the hydrogen flow rate has to be
increased from 0.345 to 0.69(mol/s) in 0.15s. This time period depends upon the reformer time
constant which was taken as 0.03s. At 5 times of this reformer time constant the steady state is
reached in the simulation which was shown in Figure 13.
Figure 13. Hydrogen flow of SOFC
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
TIME (S)
HYDROGEN FLOW (m
ol/s)
HYDROGEN FLOW (qH2)
26
4.6.2. OXYGEN FLOW OF SOFC:
Figure 14 shows the oxygen flow of SOFC,The oxygen flow can be obtained
by dividing the hydrogen flow with hydrogen to oxygen ratio. In the data the ratio has been taken
as 1.145. At t=0 the required oxygen flow rate is found to be 0.2395 (mol/s) obtained by
theoretically calculations.
Figure 14. Oxygen flow of SOFC
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
TIME (S)
OXYGEN F
LOW
(mol/s)
VARIATION OF OXYGEN FLOW WITH LOAD (qO2)
27
4.6.3. VOLTAGE WAVE FORM OF SOFC:
From the equation (3) the fuel cell voltage can be obtained, here the
number of cells connected in series is taken as 450 from the data (appendix). Initially for a
50 kW of load the calculated SOFC voltage is 403V,while increasing the load its value is
coming down to 385V due to the drop in the internal resistance when the load is increased
from 50 kW to 100 kW which was shown in Figure 15.
Figure 15. Voltage waveform of SOFC
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
50
100
150
200
250
300
350
400
450
TIME (S)
VOLTAGE (V)
FUEL CELL VOLTAGE(V)
28
4.6.4 OUTPUT VOLTAGE WAVE FORM OF DC/DC CONVERTER:
The output voltage of the DC/DC converter is maintained almost constant at 700V
throughout the loading conditions. This is achieved by using a PI controller along with the
DC/DC converter. The function of the PI controller is to reduce the change in error obtained
during the loading. This error will be minimized by choosing the appropriate KP and KI values of
the PI controller. The appropriate values of the KP and KI are 0.0005 and 0.15 respectively which
was shown in Figure 16.
Figure 16. Output voltage waveform of DC/DC Converter
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
500
600
700
800
900
1000output voltage of the DC/DC converter
time (s)
voltage (v)
29
4.6.5. DUTY RATIO OF DC/DC CONVERTER:
During the loading conditions output voltage will be changed due to the change in
current according to the equation (3). But we require a desired constant output voltage and this is
possible by changing the duty ratio (DR) of the converter appropriately. Initially DR=0.4242 for
50 kW load and it is increased to 0.4514 in order to make the output voltage constant. According
to this DR, the gate pulses will be generated and the output voltage will be controlled which was
shown in Figure 17.
Figure 17. Duty ratio of DC/DC Converter
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
TIME
DUTY RATIO
BOOST CONVERTER DUTY RATIO VARIATION WITH LOAD
30
4.6.6. OUTPUT CURRENT WAVE FORM OF INVERTER
The current is get inverted from DC to AC by an inverter. The three phase instantaneous
line-line current is 96.42 Ampere’s for 50 kW of load and it is increased to 192.45 Ampere’s for
100 kW of load. This current waveform contains some odd harmonics which can be filtered by
using a LC filter which was shown in Figure 18.
Figure 18. Output current waveform of inverter
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-500
-400
-300
-200
-100
0
100
200
300
400
500INVERTER CURRENT
TIME
CURRENT
31
4.6.7. OUTPUT VOLTAGE WAVE FORM ACROSS THE LOAD:
The voltage across the load is maintained constant and ripple free for varying loading
conditions by the action of the PI controller. This three phase voltage waveform is first converted
into dq0 form, where the controlling is much easier due to the constant values obtained in dq0
form. These dq0 components of voltage compared with the grid voltage and the error is given to
the PI controller and these PI controller output is then given to the PWM generator which in turn
generates the pulses and these pulses given to the inverter which in turn produces a constant
voltage for all loading conditions. The instantaneous L-L voltage value is 615V and the RMS
value is around 434.8V which was shown in Figure 19.
Figure 19. Output voltage waveform across the load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-800
-600
-400
-200
0
200
400
600
800INSTANTANEOUS L-L VOLTAGE ACROSS THE LOAD
TIME
VOLTAGE
32
4.6.8 OUTPUT CURRENT WAVEFORM THROUGH THE LOAD:
The three phase instantaneous L-L current wave form through the load is having the
value of 96.22 and 192.45 Ampere’s for 50 kW and 100 kW of load respectively. This smooth
increment is achieved by tuning the parameters of the PI controller which was shown in Figure
20.
Figure 20. Output current waveform through the load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
-150
-100
-50
0
50
100
150
200
TIME
CURRENT
INSTANTANEOUS L-L CURRENT THROUGH LOAD
33
CHAPTER V
GRID CONNECTED APPLICATIONS:
Figure 21 shows the block diagram of DG connected to load and grid. Although there are
many types of DG, including traditional reciprocating engines, small gas turbines, as well as
emerging technologies such as fuel cells, micro turbines, sterling engines, PV, wind turbines,
etc., basically there are two interfaces for grid interconnection: One is rotating machines,
including synchronous machines and induction machines and the other is inverters—as part of
the overall power conditioning system, inverters convert variable frequency, variable voltage AC
sources or DC sources to regulated frequency/voltage AC sources that can be interconnected to
the grid.
Figure 21. Block diagram of DG connected to Grid
5.1. DATA FOR THE INVERTER MODELING:
The specifications of the three-phase inverter being modeled are listed in Table 2. The
inverter is based on a GE (General Electrical) Grid-Connected Inverter product platform used for
sterling engines and fuel cells. The majority of grid-connected inverters were single-phase,
mainly for PV applications, more and more new DGs tend to use three-phase inverters as grid
interface. Therefore, the technology for three-phase inverter is gaining more and more practical
value.
34
Table 2. DATA FOR THE INVERTER/RL LOAD/GRID
INVERTER
fs 8000 HZ Switching frequency
Vdc 700 V Dc voltage
Lf 2.1E-3 H Filter inductance
Vl-l 440 V Line-line voltage
Vl-n 254 V Line-neutral voltage
P 50000 W Rated power
PF 1 power factor
P 50000 W Active power output
Q 0 VAR Reactive power output
RL LOAD
R 2.304 Ohm Resistance
L 3.395E-3 H Inductance
fload 50 HZ Load frequency
GRID
f 50 HZ Grid frequency
Vl-l 440 V Line-line voltage
Vl-n 254 V Line-neutral voltage
Lgrid 3.056E-4 H Grid Inductance
Rgrid 0.012 Ohm Grid Resistance
35
Generally, the overall power-conditioning system includes front-end conversion and
regulation, for example, DC/DC conversion for prime movers with DC output (e.g., fuel cell,
PV, Battery), or AC/DC conversion for prime movers with AC output (e.g. micro turbines,
sterling engines). They may have an energy-management system, such as a battery charger, at
the DC bus. In either case, the input to the inverter is a regulated DC source.
In this model, the input to the inverter is simplified as a DC voltage source. Another
simplification is the inverter output filters, which could have different variations in practical
applications; for example, the output filter could include L, or LCL, or LC plus a transformer,
with or without harmonic filters, etc. To simplify the analysis here, only an L (inductor) filter is
considered.
5.2. INVERTER SWITCHING MODEL WITH RL LOAD AND GRID:
Figure 22 shows the inverter-, load- and grid-system diagram with the inverter being
modeled as a switching model. The switching devices used for the inverter are insulated gate
bipolar transistors (IGBTs).
36
Figure 22. Inverter Switching Model with RL Load and Grid
5.3. CONTROL STRATEGY FOR GRID CONNECTED INVERTERS:
There are two basic control modes for the grid-connected inverters. One is constant-
current control and the other is constant-power control. It is still arguable whether an inverter
should be allowed to regulate voltage during grid-connected operation. The current IEEE
standard does not allow DG to actively regulate voltage, but some people in the industry suggest
that DG voltage regulation may have some positive impact on the grid.
In this study, only constant-current and power-controlled inverters are considered. In
detailed analysis, constant-current controlled inverters are used as an example to demonstrate the
concepts, which can be easily extended to constant-power controlled inverters.
The control design for a three-phase inverter can be realized either in ABC (stationary) or
in DQ (rotating) frames. The latter is more popular in modern digitally controlled inverters.
5.3.1 CONSTANT CURRENT CONTROL:
Figure 23 shows the inverter with constant current control. The inverter output currents
are regulated to the given current references. The controller is greatly simplified with a few key
functional blocks like ABC/DQ transformation, DQ phase-lock loop, summing function, linear
regulator (proportional-integral) and DQ/ABC transformation. Many functions to deal with
37
practical issues are not modeled, e.g. negative sequence regulation, DQ decoupling, device
protection, etc.
Figure 23. Block diagram of constant current-control inverter
5.3.2 CONSTANT POWER CONTROL:
Figure 24 shows the inverter with constant power control. There are two key concepts in
the DQ implementation. First, the active power is proportional to the D-axis components, and the
reactive power is proportional to the Q-axis components. Therefore, the active and reactive-
power commands should feed into the D-axis and Q-axis, respectively. Second, since the overall
vector (voltage or current) is the synthesis of the D and Q axes, changing one axis not only
changes the magnitude of the vector, but also changes the angle between the D and Q axes. The
angle change will result in frequency change, because frequency is the derivative of the angle.
38
Figure 24. Block diagram of constant-power-controlled inverter
Here the inverter output power is compared with the reference power and the error is
given to the PI controller, the output of the PI controller represents direct axis current component
(D-axis), similarly by comparing the reactive powers, quadrature axis current component (Q-
axis) component is obtained. These current components is compared with the inverter output
currents and the error is given to the PI controllers, the output of the PI controller is current
signals which in turn given to the PWM generator and generate the pulses at switching frequency
and then fed to the inverter switches.
39
5.4 SIMULATION MODELS:
The SIMULINK model of inverter, current regulator, and power regulator for grid
connected applications and its results are presented below.
5.4.1. SIMULATION MODEL OF SOFC FOR GRID CONNECTED APPLICATIONS
Figure 25 Simulation model for GRID connected applications
40
5.4.2. SIMULATION MODEL OF POWER REGULATOR
Figure 26 Simulation model of power regulator
41
5.4.3. SIMULATION MODEL OF CURRENT REGULATOR
Figure 27. Simulation model of current regulator
42
5.5. SIMULATION RESULTS FOR GRID CONNECTED APPLICATIONS:
In this grid connected application, SOFC will produce constant (reference) power of
50kW at all loading conditions. Depends upon any particular loading condition for this
centralized application, grid will take power from the fuel cell (SOFC) or it will give power to
the load.
5.5.1 RESPONSE FOR 50KW OF LOAD:
CONDITION 1: 61A< ?BC
At this condition, power supplied to the grid is zero at steady state. In the transient
condition, the grid is giving the power (negative) because due to the slow response of fuel cell
power which was shown in Figure 28.
Figure 28. Power response for 50kW of load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000LOAD POWER 50KW
Vinv(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
x 104
Pinv(W)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
x 104
Pload(W)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4-20246x 10
4
Pgrid(W)
time
43
For 50kW of load the current flowing through the load is 92.78 amps which is coming
from the fuel cell system (i.e. from inverter) and the current flowing through the grid is zero at
steady state. In this simulation for grid connected application, the voltage is maintained constant
value L-L 440Vrms (440√2 =622V peak value) for all loading conditions which was shown in Figure 29.
Figure 29. Current response for 50kW of load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000LOAD POWER 50KW
Vinv(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
I inv(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100
0
100
I load(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-200
0
200
I grid(A)
time
44
5.5.2 RESPONSE FOR 30KW OF LOAD:
CONDITION 2: 61A< E ?BC
At this condition, power supplied to the grid will be?BC 61A<. If power is taken by the grid, then F" is considered as positive otherwise negative. The positive value of F"
in the below plot indicates that grid is taking the remaining power from the fuel cell system (i.e.
from inverter) after supplying to the load. At this loading condition also voltage at the inverter,
load is maintained constant which was shown in Figure 30.
Figure 30. Power response for 50kW of load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000LOAD POWER 30KW
Vinv(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
x 104
Pinv(W
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
2
4x 10
4
Pload(W
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4-20246x 10
4
Pgrid(W
)
time
45
The current flowing from the inverter is 92.78 amps (peak) which is constant for the
reference power of 50kW. For 30kW of loading condition, the current flowing through the load
is 55.67(peak) amps which is coming from the fuel cell system (i.e. from inverter) and the
remaining current 37.11 amps (peak) flowing through the grid which is shown in Figure 31.
Figure 31. Current response for 30kW of load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000LOAD POWER 30KW
Vinv(V
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
I inv(A
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-100
0
100
I load(A
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-200
0
200
I grid(A
)
time
46
5.5.3 RESPONSE FOR 70KW OF LOAD:
CONDITION 3: 61A< G ?BC
At this condition, power supplied to the grid will be?BC 61A< which is a negative value i.e. grid (F" ) is supplying the power to the load according to its requirement.
For 70kW of load, fuel cell system is supplying 50kW (reference power) and remaining 20kW is
supplied from the grid which is shown in Figure 32.
Figure 32. Power response for 70kW of load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000LOAD POWER 70KW
Vinv(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
x 104
Pinv(W
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10x 10
4
Pload(W
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4-20246x 10
4
Pgrid(W
)
time
47
For 70kW of loading condition, the current flowing through the load is 129.89 (peak)
amps and the current coming from the fuel cell system (i.e. from inverter) is 92.78 amps (peak)
which is constant for the reference power of 50kW and the remaining current 37.11 amps (peak)
is coming from the grid which is shown in Figure 33.
Figure 33. Current response for 70kW of load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000LOAD POWER 70KW
Vinv(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
I inv(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
I load(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-200
0
200
I grid(A)
time
48
5.5.4 RESPONSE FOR STEP CHANGE IN LOAD:
CONDITION 4: STEP CHANGE IN LOAD FROM 40KW TO 80KW AT 0.5 SEC
When there is a sudden change in the load from 40kw to 80kw, both the power taken by
the grid and power given to the grid is possible. Up to 0.5 sec the load is 40kW so remaining
10kW of power is given to the grid. After 0.5 sec the load is 80kW, so the grid will supply
30kWof power to the load which was shown in Figure 34.
Figure 34. Response of power for step change in load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000STEP CHANGE IN LOAD POWER FROM 40KW TO 80KW
Vinv(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
x 104
Pinv(W
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10x 10
4
Pload(W
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4-20246x 10
4
Pgrid(W
)
time
49
For step change in load, the current flowing through the load below 0.5sec is 74.22 (peak)
amps and the current coming from the fuel cell system (i.e. from inverter) is 92.78 amps (peak)
which is constant for the reference power of 50kW and the remaining current 18.55 amps (peak)
is going to the grid. After 0.5 sec load is 80kW ,so the current flowing through the load is
148.45 (peak) amps and the current coming from the fuel cell system (i.e. from inverter) is 92.78
amps (peak) and the remaining current 55.69 amps (peak) is coming from the grid which is
shown in Figure 35.
Figure 35. Response of current for step change in load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000STEP CHANGE IN LOAD POWER FROM 40KW TO 80KW
Vinv(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
I inv(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
I load(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-200
0
200
I grid(A)
time
50
5.5.5 RESPONSE FOR OCCURRENCE OF FAULT IN LOAD:
CONDITION 5: OCCUREANCE OF FAULT IN THE LOAD
Response of power flow as shown in Fig 36, when phases of the load are switched off
due to the fault (L-N, L-L) occurred in load or due to any other non-technical problems. In the
Fig 36 up to 0.2 sec all the phases are switched off, then the entire power of fuel cell system will
go to grid. Between 0.2s and 0.4s, one phase is switched on and between 0.4 to 0.6 one more
phase is switched on and at 0.6 all phases became healthy and at 0.7 sec there is a step change in
load and corresponding power flows for all above conditions are shown in Figure 36.
Figure 36. Response of power flow during faults in load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000LOAD POWER 40KW
Vinv(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
x 104
Pinv(W
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
x 104
Pload(W
)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4-20246x 10
4
Pgrid(W
)
time
51
In Fig 37, the current flow through the load upto 0.2 sec is zero i.e. all the phases are switched
off and between 0.2 and 0.4 sec, only one phase current is flowing in the load and between 0.4
and 0.6sec, current flow takes place in two phases and after 0.6 sec current flow through load
will be in all the three phases i.e. load became healthy at 0.6 sec. and after 0.7 sec load is
increased from 40kW to 80kW and respective current flows are shown in Figure 37.
Figure 37. Response of current flow during faults in load
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1000
0
1000LOAD POWER 40KW
Vinv(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
I inv(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200
0
200
I load(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-200
0
200
I grid(A)
time
52
5.5.6. RESPONSE OF REACTIVE POWER FLOW:
Fig 38 shows the reactive power flow in the load and grid. Q ref injected into the grid from
the inverter is taken as zero, if load demand 200 VAR inductive reactive power then it will be
supplied by the grid which is shown in Figure 38. Negative sign in the grid plot indicates that
grid is supplying inductive reactive power to the load.
Figure 38. Response of Reactive Power Flow of 200 VAR
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.1
0
0.1REACTIVE POWER FLOW IN GRID COONECTED MODE
QINV (VAR)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-200
0
200
QLOAD (VAR)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-500
0
500
QGRID (VAR)
time
53
For a step change in inductive reactive power flow, the load inductive reactive power is
200 VAR until 0.5 sec and after 0.5 sec, it increases to 400 VAR. Grid supplies this increased
inductive reactive power which is shown in Figure 39. Q ref injected into the grid is zero for all
loading conditions.
Figure 39. Response of Reactive power Flow for step change
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.1
0
0.1ACTIVE & REACTIVE POWER FLOW IN GRID COONECTED MODE
QINV (VAR)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-2000
200400
QLOAD (VAR)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-500
0
500
QGRID (VAR)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
x 104
PLOAD (WATTS)
time
54
CHAPTER VI
CONCLUSIONS AND FUTURE WORK
6.1. CONCLUSIONS
A dynamic model of the solid oxide fuel cell (SOFC) was developed in this project in
MATLAB environment setup.
A DC-DC boost converter topology and its closed loop control feedback system have been built.
A three phase inverter has been modeled and connected between the SOFC-DC-DC system on
the one side and the utility grid on the other side. A control strategy for the inverter switching
signals has been discussed and modeled successfully.
The fuel cell, the converter and the inverter characteristics were obtained for a reference
real power of 50kW.The slow response of the fuel cell is due to the slow and gradual change in
the fuel flow which is proportional to the stack current. The interconnection of the fuel cell with
the converter boosts the stack voltages and also regulates it for varying load current conditions.
The fuel cell stack voltage drops to zero for discontinuous current and the system shuts down.
The fuel cell unit shuts off for real power above the maximum limit. Additional power at the
converter is provided by the inductor, connected in series with the equivalent load which acts as
an energy storage. The inductor can be replaced by any energy storage device such as a capacitor
or a battery for providing additional power during load transients.
The inverter control scheme uses a constant power control strategy for grid connected
applications and a constant voltage control strategy for standalone applications to control the
voltage across inverter and current flowing through the load. The characteristics for the system
have been obtained. The inverter voltage, current, power waveform have been plotted. The real
power injection into the grid takes less than 0.1s to reach the commanded value of 50kW. The
reactive power injection has been assumed to be zero and was evident from the simulation
results. The maximum power limit on the fuel cell is 400kW. For any reference power beyond
this limit, the fuel cell loses stability and drops to zero. This limit has been set by the parameters
considered for the fuel cell data. Higher power can be commanded by either increasing the
number of the cells, increasing the reversible standard potential or by decreasing the fuel cell
resistance.
55
The system was then subjected to a step change in the reference real power from 40 to
80kW.The fuel cell, the converter and the inverter responses were obtained. The characteristics
of the fuel cell (voltage, current and power) have a slower gradual change at the instant of step
change. The DC link voltage was maintained at the reference value by the closed loop control
system. Step change in the reference power from 40 to 80kW has been considered in order to
observe the sharing of power from inverter to grid and from grid to the load of the fuel cell. The
reactive power was zero until the step change and after the step change, oscillations were
observed in the reactive power as well. Voltage, current, power characteristics of inverter, load
and grid as been plotted for various conditions of load.
6.2. FUTURE WORK
The fuel cell system developed in this thesis can be modified for improving the
applicability of the system. In this thesis, the thermodynamic effect of the fuel cell has not been
considered. Future work can involve inclusion of thermodynamic equations. The performance of
the stack voltage with and without the temperature effect can be obtained and its overall effect on
the load.
The work can be further extended for simulating the hybrid system i.e. wind & fuel cell,
PV & fuel cell and it can further be extended for simulating the power train. Different
placements of the fuel cell unit can be studied and analyzed. The performance of multiple units
at multiple locations can also be studied. The performance of the fuel cell can also be tested by
carrying out short circuit studies.
56
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59
APPENDIX
Table 3. PARAMETERS IN SOFC MODEL
Variable Representation Value
T Absolute temperature 1273K
F Faraday’s constant 96487C/mol
R Universal gas constant 8314J/(Kmol K)
oE Standard reversible cell potential 1.18V
N Number of cells in stack 450
rK Constant rK =N/4F .996* 610 − Kmol/(s A)
maxU Maximum fuel utilization 0.9
minU Minimum fuel utilization 0.8
optU Optimum fuel ratio 0.85
2HK Value molar constant for hydrogen 8.43* 410 − Kmol/(s atm)
2KO Value molar constant for oxygen 2.81* 410 − Kmol/(s atm)
OKH 2 Value molar constant for water 2.52* 310 − Kmol/(s atm)
2Hτ Response time for hydrogen flow 26.1s
OH 2τ Response time for water flow 78.3s
2Oτ Response time for oxygen flow 2.91s
R Ohmic loss 0.126
eT Electric response time 0.8s
fT Fuel processor response time 0.03s
HOr Ratio of hydrogen to oxygen 1.145
Ω
60
SYSTEM DATA
Table 4. PARAMETERS IN BOOST DC-DC CONVERTER
L 0.0005H
C 7500µF
rc 0.2ohm
SWITHCHIG FREQUENCY 8KHz
Table 5. Kp & Ki VALUES OF DC-DC CONVERTER
Kp 0.0005
Ki 0.15
Table 6. Kp & Ki VALUES OF DC-AC CONVERTER FOR STANDALONE
Kp 0.4
Ki 500
Table 7. Kp & Ki VALUES OF DC-AC CONVERTER FOR GRID
POWER REGULATOR CURRENT REGULATOR
Kp 0.4 1.5
Ki 3000 4000
61
BIODATA
NAME: KOSURU LAKSHMANA RAO
EDUCATIONAL QUALIFICATIONS:
QUALIFICATION INSTITUTE
M.TECH (ENERGY STUDIES) IIT DELHI
B.TECH (ELECTRICAL AND ELECTRONICS) GAYATRI VIDYA PARISHAD
COLLEGE OF ENGINEERING,
VISAKHAPATNAM.
PRESENT ADDRESS:
KOSURU LAKSHMANA RAO,
ROOM N0: A-46,
NLGIRI HOSTEL,
IIT DELHI
HAUZ KHAS,
NEW DELHI -110016.
EMAIL:[email protected],
ALTERNATE EMAIL: kosuru23@ gmail.com,
PERMANENT ADDRESS
KOSURU LAKSHMANA RAO,
C/O K.NAGESWARA RAO,
D.NO:33-14-284,
ALLIPURAM MAIN ROAD,
VISAKHAPATNAM,
ANDHRA PRADESH-530004.
62
