OPTIMAL LOCATION OF ELECTRICAL ENERGY STORAGE IN A POWER SYSTEM
WITH WIND ENERGY
A Dissertation by
Yi Xu
Master of Science, Pittsburg State University, 2009
Bachelor of Science, Taiyuan University of Technology, 2006
Submitted to the Department of Electrical Engineering and Computer Science
and the faculty of the Graduate School of
Wichita State University
in partial fulfillment of
the requirements for the degree of
Doctor of Philosophy
July 2014
© Copyright 2014 by Yi Xu
All Rights Reserved
OPTIMAL LOCATION OF ELECTRICAL ENERGY STORAGE IN A POWER SYSTEM
WITH WIND ENERGY
The following faculty members have examined the final copy of this dissertation for form and
content, and recommend that it be accepted in partial fulfillment of the requirement for the
degree of Doctor of Philosophy with a major in Electrical Engineering.
________________________________________
Ward T. Jewell, Committee Chair
________________________________________
Chengzong Pang, Committee Member
________________________________________
John Watkins, Committee Member
________________________________________
Pingfeng Wang, Committee Member
________________________________________
Visvakumar Aravinthan, Committee Member
Accepted for the College of Engineering
_______________________________________
Royce Bowden, Dean
Accepted for the Graduate School
_______________________________________
Abu S. M. Masud, Interim Dean
iii
DEDICATION
To my parents and my dear friends
iv
ACKNOWLEDGMENTS
I would like to express my deepest gratitude to my adviser, Dr. Ward T. Jewell, for his
many years of thoughtful, patient guidance and encouragement. His valuable teaching and
inspiration led me to explore the field of electrical power systems, which will continuously
benefit my future career. Thanks are also due to my co-adviser, Dr. Chengzong Pang, for his
advice on my dissertation. I also express gratitude to my dissertation committee members, Dr.
John Watkins, Dr. Pingfeng Wang, and Dr. Visvakumar Aravinthan, whom I thank for their
valuable suggestions and instruction.
In addition, I acknowledge my former colleague and friend, Zhouxing Hu, for his
suggestions and help. I also thank my colleagues—Trevor Hardy, Haneen Aburub, and Saurav
Basnet—who provided me with an outstanding academic environment in the power laboratory at
Wichita State University.
Last, special gratitude goes to my parents for their endless support and unconditional love.
v
ABSTRACT
Providing reliable and clean electricity is an essential responsibility for the entire
electrical industry. With the many concerns relative to environmental issues, the applications of
renewable energy are being paid more attention, and the replacement of fossil fuels is recognized
as an inevitable trend in the future power grid. Renewable energy is friendly to the environment;
however, its uncertainty remains a challenge to the power system.
Energy storage devices can provide a satisfactory solution to many aspects of the power
system, especially their coordination with renewables. The development of storage and material
technologies can mean that various energy storages with different properties will be invented and
could be deployed based on the purpose of the application. To fully utilize storage in a power
system with renewable energy, it is necessary to do some investigation. The deployment of
storage devices is one issue that needs considerable discussion.
This dissertation provides a general procedure to optimize the location of electric energy
storage (EES) units in a power system with renewable energy. The core optimization problem is
accomplished by the simulation tool MATPOWER. At the same time, a stochastic, pointestimation method is applied. The performances of storage devices in different situations are
presented though several cases.
vi
TABLE OF CONTENTS
Chapter
1.
INTRODUCTION .............................................................................................................. 1
1.1
1.2
1.3
2.
Modeling and Scheduling of Bulk Energy Storage .............................................. 12
Probabilistic Optimal Power Flow ........................................................................ 13
Location of Energy Storage .................................................................................. 15
Simulation Tool .................................................................................................... 15
MODELING AND METHODOLOGY ........................................................................... 17
3.1
3.2
3.3
3.4
3.5
3.6
3.7
4.
Renewable Energy .................................................................................................. 1
1.1.1 Renewable Energy Policies......................................................................... 1
1.1.2 Wind Energy ............................................................................................... 4
1.1.3 Electrical Energy Storage ........................................................................... 6
Objective and Scope of This Work ......................................................................... 9
Organization of Dissertation ................................................................................. 10
LITERATURE STUDY ................................................................................................... 12
2.1
2.2
2.3
2.4
3.
Page
Test System ........................................................................................................... 17
Operating Cost ...................................................................................................... 19
3.2.1 Traditional Generator Unit ........................................................................ 19
3.2.2 Renewable Generation .............................................................................. 20
Objective Function ................................................................................................ 21
General Procedure ................................................................................................. 21
Modeling of Wind Energy .................................................................................... 22
Probabilistic Optimal Power flow ......................................................................... 23
3.6.1 Point Estimation ........................................................................................ 23
3.6.2 Modified Two-Point Estimation ............................................................... 25
3.6.3 Implementation Point Estimation Method ................................................ 26
Genetic Algorithm ................................................................................................ 27
SIMULATION AND RESULTS I ................................................................................... 30
4.1
4.2
4.3
Case 1: Basic Case ................................................................................................ 30
4.1.1 Basic Case Information ............................................................................. 30
4.1.2 Basic Case Results and Analysis .............................................................. 32
Case 2: Limited Capacity ...................................................................................... 35
4.2.1 Limited Capacity Case Information .......................................................... 35
4.2.2 Limited Capacity Results and Analysis .................................................... 36
Case 3: Multiple Wind Plant ................................................................................. 44
4.3.1 Multiple Wind Plant Case Information ..................................................... 44
vii
TABLE OF CONTENTS (continued)
Chapter
Page
4.3.2 Multiple Wind Plant Results and Analysis ............................................... 46
5.
SIMULATION AND RESULTS II .................................................................................. 52
5.1
5.2
5.3
Case 4: Typical Week ........................................................................................... 52
5.1.1 Typical Week Case Information ............................................................... 52
5.1.2 Typical Week Results and Analysis ......................................................... 53
Case 5: Typical Year ............................................................................................. 59
5.2.1 Typical Year Case Information ................................................................. 59
5.2.2 Typical Year Results and Analysis ........................................................... 60
Case 6: Market Factor ........................................................................................... 63
5.3.1 Market Factor Case Information ............................................................... 63
5.3.2 Market Factor Results and Analysis ......................................................... 65
CHAPTER 6 ................................................................................................................................. 67
6.1
6.2
Conclusions ........................................................................................................... 67
Future Work .......................................................................................................... 68
REFERENCES ............................................................................................................................. 70
APPENDIXES...............................................................................................................................77
A. Operating Cost Figures for Limited Capacity Case ..................................................... 78
B. Charging Energy Figures for Limited Capacity Case .................................................. 82
C. Operating Cost Figures for Multiple Wind Plant Case ................................................ 86
D. Charging Energy Figures for Multiple Wind Plant Case ............................................. 88
E. Operating Cost Figures for Typical Week Case ........................................................... 90
viii
LIST OF TABLES
Table
Page
3.1
Average CO2 Emissions Factors ....................................................................................... 20
4.1
Results Summary for Basic Case ...................................................................................... 33
4.2
EES Parameters for Limited Capacity Case [26] .............................................................. 36
4.3
EES Location Record for Limited Capacity Case ............................................................ 44
5.1
EES Location Record for Typical Year Case ................................................................... 63
5.2
Discharging Times for Market Factor Case ...................................................................... 64
iii
LIST OF FIGURES
Figure
Page
1.1. Comparison of regional non-hydropower renewable electricity generation in 2011
and 2040 (billion kilowatt hours) [5] ...................................................................................... 3
1.2. Renewable electricity generation by type, 2008–2040 (billion kilowatt hours) [5] ................ 3
1.3. Total U.S. greenhouse gas emissions by economic sector in 2012 [6] .................................... 4
1.4. Relative contribution of generation types in annual capacity additions [8]............................. 5
1.5. Daily renewable watch for 05/28/2014 (top) and 05/29/2014 (bottom) [10] .......................... 6
1.6. Positioning of energy storage technologies [15]...................................................................... 9
1.7. Rated power of U.S. grid storage projects (including announced projects) [18] ..................... 9
3.1. IEEE 24-bus RTS ................................................................................................................... 18
3.2. Generation capacity distribution of modified IEEE 24-bus RTS .......................................... 19
3.3. Optimization flow chart ......................................................................................................... 22
3.4. Point estimation explanation [61] .......................................................................................... 24
3.5. Implementation steps for 2m+1 PE scheme........................................................................... 27
3.6. Genetic algorithm flow chart ................................................................................................. 28
4.1. EES working pattern for basic case ....................................................................................... 31
4.2. Load information for basic case ............................................................................................. 32
4.3. Results curves for basic case.................................................................................................. 33
4.4. Comparison of operating costs in basic case ......................................................................... 34
4.5. Comparison of CO2 emissions in basic case .......................................................................... 35
4.6. Comparison of operating costs in limited capacity case ........................................................ 37
4.7. Decreasing rates in limited capacity case .............................................................................. 38
iv
LIST OF FIGURES (continued)
Figure
Page
4.8. Operating costs (wind rating of 40 MW) in limited capacity case ........................................ 39
4.9. Operating costs (wind rating of 50 MW) in limited capacity case ........................................ 39
4.10. Comparison of CO2 emissions in limited capacity case ...................................................... 40
4.11. Charging energy in limited capacity case ............................................................................ 41
4.12. Charging rates (80 MWh of storage) in limited capacity case............................................. 42
4.13. Charging rates for different capacities in limited capacity case .......................................... 42
4.14. Charging energy (wind rating of 40 MW) in limited capacity case .................................... 43
4.15. Implementation steps of 2m+1 PE scheme with multiple variables .................................... 45
4.16. Operating costs in multiple wind plant case ........................................................................ 46
4.17. Decreasing rates in multiple wind plant case ....................................................................... 47
4.18. Operating costs (wind rating is 40 MW) for multiple wind plant case ................................ 48
4.19. Comparison of CO2 emissions in multiple wind plant case ................................................. 49
4.20. Charging energy in multiple wind plant case ...................................................................... 50
4.21. Charging energy (wind rating is 40 MW) in multiple wind plant case ............................... 51
5.1. SPP for one week in typical week case .................................................................................. 53
5.2. Load data for typical week case ............................................................................................. 53
5.3. Comparison of operating costs in typical week case ............................................................. 54
5.4. Operating costs (wind rating is 90 MW) in typical week case .............................................. 55
5.5. Comparison of CO2 emissions in typical week case .............................................................. 56
5.6. CO2 emissions in charging periods in typical week case ....................................................... 57
5.7. CO2 emissions in discharging periods in typical week case .................................................. 57
v
LIST OF FIGURES (continued)
Figure
Page
5.8. Comparison of charging and discharging CO2 emissions in typical week case .................... 58
5.9. Comparison of charging energy in typical week case ........................................................... 59
5.10. Load data for typical year case ............................................................................................ 60
5.11. Comparison of operating costs in typical year case ............................................................. 61
5.12. Comparison of CO2 emissions in typical year case ............................................................. 62
5.13. Comparison of charging energy in typical year case ........................................................... 62
5.14. Settlement point prices and bounded line in market factor case .......................................... 64
5.15. Operating costs (wind 90 MW and storage 100 MWh) in market factor case .................... 65
5.16. Operating costs (wind 100 MW and storage 110 MWh) in market factor case .................. 66
A.1. Wind rating of 60 MW .......................................................................................................... 78
A.2. Wind rating of 70 MW .......................................................................................................... 78
A.3. Wind rating of 80 MW .......................................................................................................... 78
A.4. Wind rating of 90 MW .......................................................................................................... 78
A.5. Wind rating of 100 MW ........................................................................................................ 79
A.6. Wind rating of 110 MW ........................................................................................................ 79
A.7.Wind rating of 120 MW ......................................................................................................... 79
A.8. Wind rating of 130 MW ........................................................................................................ 79
A.9. Wind rating of 140 MW ........................................................................................................ 80
A.10. Wind rating of 150 MW ...................................................................................................... 80
A.11. Wind rating of 160 MW ...................................................................................................... 80
A.12. Wind rating of 170 MW ...................................................................................................... 80
vi
LIST OF FIGURES (continued)
Figure
Page
A.13. Wind rating of 180 MW ...................................................................................................... 81
A.14. Wind rating of 190 MW ...................................................................................................... 81
A.15. Wind rating of 200 MW ...................................................................................................... 81
B.1.Wind rating of 50 MW ........................................................................................................... 82
B.2. Wind rating of 60 MW .......................................................................................................... 82
B.3. Wind rating of 70 MW .......................................................................................................... 82
B.4. Wind rating of 80 MW .......................................................................................................... 82
B.5. Wind rating of 90 MW .......................................................................................................... 83
B.6. Wind rating of 100 MW ........................................................................................................ 83
B.7. Wind rating of 110 MW ........................................................................................................ 83
B.8. Wind rating of 120 MW ........................................................................................................ 83
B.9. Wind rating of 130 MW ........................................................................................................ 84
B.10. Wind rating of 140 MW ...................................................................................................... 84
B.11. Wind rating of 150 MW ...................................................................................................... 84
B.12. Wind rating of 160 MW ...................................................................................................... 84
B.13. Wind rating of 170 MW ...................................................................................................... 85
B.14. Wind rating of 180 MW ...................................................................................................... 85
B.15. Wind rating of 190 MW ...................................................................................................... 85
B.16. Wind rating of 200 MW ...................................................................................................... 85
C.1. Wind rating of 50 MW .......................................................................................................... 86
C.2. Wind rating of 60 MW .......................................................................................................... 86
vii
LIST OF FIGURES (continued)
Figure
Page
C.3. Wind rating of 70 MW .......................................................................................................... 86
C.4. Wind rating of 80 MW .......................................................................................................... 86
C.5. Wind rating of 90 MW .......................................................................................................... 87
C.6. Wind rating of 100 MW ........................................................................................................ 87
C.7. Wind rating of 110 MW ........................................................................................................ 87
C.8. Wind rating of 120 MW ........................................................................................................ 87
D.1. Wind rating of 50 MW .......................................................................................................... 88
D.2. Wind rating of 60 MW .......................................................................................................... 88
D.3. Wind rating of 70 MW .......................................................................................................... 88
D.4. Wind rating of 80 MW .......................................................................................................... 88
D.5. Wind rating of 90 MW .......................................................................................................... 89
D.6. Wind rating of 100 MW ........................................................................................................ 89
D.7. Wind rating of 110 MW ........................................................................................................ 89
D.8. Wind rating of 120 MW ........................................................................................................ 89
E.1. Wind rating of 90 MW .......................................................................................................... 90
E.2. Wind rating of 100 MW ........................................................................................................ 90
E.3. Wind rating of 110 MW ........................................................................................................ 90
E.4. Wind rating of 120 MW ........................................................................................................ 90
viii
LIST OF ABBREVIATIONS
AA-CAES
Advanced Adiabatic Compressed Air Energy Storage
AB
Assembly Bill
AC
Alternate Current
ACR
Annual Capital Recovery
AMT
Alternative Minimum Tax
CAES
Compressed Air Energy Storage
CAISO
California Independent System Operator
CAMX
California-Mexico
CO2
Carbon Dioxide
CRF
Capital Recovery Factor
DC
Direct Current
DOE
Department of Energy
EES
Electrical Energy Storage
EIA
U.S. Energy Information Administration
ERCOT
Electric Reliability Council of Texas
FF
Fitness Function
FFT
Fast Fourier Transform
FOSMM
First-Order Second-Moment Method
GA
Genetic Algorithm
GHG
Greenhouse Gas
GW
Gigawatt(s)
GWh
Gigawatt Hour(s)
ix
LIST OF ABBREVIATIONS (continued)
ICB
Iron-Chromium
ITC
Investment Tax Credit
KV
Kilovolt(s)
kWh
Kilowatt Hour(s)
LAES
Liquid Air Energy Storage
Li-ion
Lithium Ion
LMP
Locational Marginal Pricing
LP
Linear Programming
MBTu
Million British Thermal Unit
MC
Monte Carlo
MIPS
MATLAB Interior Point Solver
MW
Megawatt(s)
NAS
Sodium Sulfur
NI-CD
Nickel-Cadmium
OCC
Overnight Capital Cost
OPF
Optimal Power Flow
O&M
Operation and Maintenance
PDF
Probability Density Function
PE
Point Estimation
PHES
Pumped Heat Electrical Storage
POPF
Probabilistic Optimal Power Flow
PTC
Production Tax Credit
x
LIST OF ABBREVIATIONS (continued)
RPS
Renewable Portfolio Standard
RTS
Reliability Test System
SPP
Settlement Point Price
VRB
Vanadium Redox
WECC
Western Electric Coordinating Council
ZNBR
Zinc-Bromine
xi
LIST OF NOMENCLATURE
ef
Emission Factor
f(x)
Cost Function
f(w)
Wind Distribution Function
fu
User-Defined Cost Function
pl
Input Random Variable
vi
Cut-In Wind Speed
vo
Cut-Out Wind Speed
vr
Rated Wind Speed
θ
Voltage Angle
λ
Standard Central Moment
μ
Mean Value
ξ
Standard Location
ω
Weight
σ
Standard Deviation
Vm
Voltage Magnitude
Pg
Real Power
Qg
Reactive Power
Ffuel
Fuel Cost Function
Fco2
CO2 Emissions Amount
Ftotal
Total Operation Cost
C
Fuel Cost
Cco2
CO2 Cost
xii
LIST OF NOMENCLATURE (continued)
Gwr
Wind Rating Power
Gw
Wind Generation Power
Z
Output
xiii
CHAPTER 1
INTRODUCTION
This chapter briefly introduces the research background of this dissertation. Section 1.1
explains the impact of the energy policy, the development of renewable energy, and the benefits
of energy storage. The research objective of this dissertation is explained in Section 1.2, and the
organization of this dissertation is described in Section 1.3.
1.1
Renewable Energy
1.1.1
Renewable Energy Policies
With environmental issues becoming increasingly prominent, people in the world attach
more importance to using clean energy, especially wind and solar. The wide use of renewable
energy has reached a broad consensus. Renewable energy brings significant benefits, and
meanwhile the efforts to enhance its reliability, efficiency, and availability are under way. The
relevant issues of renewable energy are becoming hot topics. Researchers are making great
strides toward improving the overall performance of renewables; nevertheless, wind, solar, and
others forms of renewable energy are not gaining an economically overwhelming advantage over
traditional sources, such as coal and natural gas. The policy stimulus becomes a necessary tool to
promote the use of alternate energy sources. Take, for example, the federal business energy
investment tax credit (ITC) [1], which was expanded significantly by the Energy Improvement
and Extension Act of 2008 (H.R. 1424) and enacted in October 2008. This law extends the
duration, by eight years, of existing credits for solar energy, fuel cells and micro-turbines, and
increases the amount of credit for fuel cells, etc. It allows tax payers to take a credit against the
alternative minimum tax (AMT). This policy encourages utilities to use renewable energy.
1
In addition, other policies and regulations have been enacted in different states and
regions in order to promote the employment of renewable energy. In early 2006, the passage of
Assembly Bill (AB) 32 [2], the global warming solution act, by the California government
accelerated the process of clear energy usage. AB 32 includes several requirements, which are
compelled to reduce greenhouse gas (GHG) emissions state wide. One of the most important
requirements is to limit the state’s GHG emission level to the 1990’s level by 2020. This law
hastens the replacement of fossil fuels (coal, natural gas, and oil) with renewable energy (wind,
solar, biomass, geothermal, and hydro). It also sets an example for other states. Meanwhile, most
states [3] have set a regulatory mandate to increase production of energy from renewable sources
such as wind, solar, biomass and other alternatives to fossil and nuclear electric generation.
Referred to as the Renewable Portfolio Standard (RPS), this mandate is most successful in
driving renewable energy projects when combined with the federal production tax credit (PTC).
There can be multiple goals for an RPS, and some states aim for a broader set of goals and
objectives, such as environmental benefits, economic development, and advancing specific
technologies. The California’s RPS, as one of the most ambitious renewable energy standards in
the country, requires investor-owned utilities, electric service providers, and community choice
aggregators to increase their eligible renewable energy resources to 33% of total procurement by
2020 [4]. Under the promotion of the RPS, the U.S. Energy Information Administration (EIA)
has projected the highest level of non-hydro-electric renewable generation in 2040, at 104 billion
kWh, will occur in the Western Electric Coordinating Council (WECC) California-Mexico
(CAMX) region [5], as shown in Figure 1.1. It has also projected that renewable generation will
increase from 524 billion kilowatt hours (kWh) in 2011 to 858 billion kWh in 2040 [5], as shown
in Figure 1.2. Wind, solar, and biomass renewable energy account for most of this growth.
2
Figure 1.1. Comparison of regional non-hydropower renewable electricity generation in 2011
and 2040 (billion kilowatt hours) [5]
Figure 1.2. Renewable electricity generation by type, 2008–2040 (billion kilowatt hours) [5]
Limiting GHG emissions has been adopted widely by many state and regional policies.
Carbon dioxide (CO2), as one of the most important GHG emissions [6], is also restricted
directly. And most CO2 emissions come from the electricity-generation and transportation
sectors, as shown in Figure 1.3 [6]. With the electric vehicle being widely used in the next few
3
years, electric consumption will increase quickly. However, if most of the energy comes from
fossil fuel plants, then CO2 emission will increase. Therefore, it is necessary to consider the CO2
emissions effect in a power system study. A straightforward method that incorporates the cost of
CO2 emissions into the generator heat rate function [7] has been introduced.
Figure 1.3. Total U.S. greenhouse gas emissions by economic sector in 2012 [6]
1.1.2
Wind Energy
Wind energy, as one of the important renewable energies, has been paid more attention
and shown explosive development. In 2012, wind power was the largest source of new
generation capacity added to the U.S. electrical grid, contributing up to 43% of all U.S.
generation capacity additions, which is much greater than the sum of other renewable energy [8].
Figure 1.4 shows the relative contribution of different types of energy generation from 2000 to
2012 and, in particular, the remarkable growth of wind power, which increased sharply from
2004 to 2012, up to about 150,000 gigawatt hours (GWh) in 2012 [9].
4
Figure 1.4. Relative contribution of generation types in annual capacity additions [8]
The most disadvantageous property of wind energy is its uncertainty and intermittency. It
poses a major challenge relative to planning and dispatching for the system and market operators,
especially with the increasing penetration level of renewable energy. Wind energy is limited by
the availability of wind; thus, the location of the wind plant is restricted by the wind resource.
Generally, the wind plant is a distance from the load center. Wind power, as a renewable energy,
has a higher priority than traditional generation and must be dispatched by a system operator.
Transmission congestion and operation reliability become the major limiting factors of a power
system with renewable energy.
Two samples of hourly average breakdown of renewable resources observed by the
California Independent System Operator (CAISO) on two different days in 2014, May 28 and 29
[10], are shown in Figure 1.5. Comparing these samples, the production from geothermal,
biomass, biogas, and small hydro are relatively constant and steady, whereas wind power
experienced great variation. The wind profile in the first sample varied from 3,900 megawatts
(MW) to 2,000 MW, while it dropped below 500 MW around noon time in the second sample,
where demand usually peaks from around 10 am to 12 pm. It is required that the system have
enough reserve as backup for wind power.
5
Figure 1.5. Daily renewable watch for 05/28/2014 (top) and 05/29/2014 (bottom) [10]
1.1.3
Electrical Energy Storage
Electrical energy storage (EES) has many advantages. When facing an unpredictable
decrease in renewable generation or an increase in energy demands in a power grid with high
renewable penetration, the performance of an EES system is considered an effective way to deal
with this variability. Compared to the working pattern of traditional large pumped-hydro plants
6
coordinating with other thermal units, known as a peak shaving operation [11], EES has a more
flexible schedule. In addition, for renewable penetration, EES can reduce the variability, control
ramping time, and shift load time. For transmission and distribution, EES can provide line and
transformer deferral, and voltage and frequency regulation [12]. Scheduling EES for energy
arbitrage will make the power grid more economical and reduce the locational marginal pricing
(LMP). Transmission loss and congestion must be considered for energy-storage scheduling [13].
Moreover, EES could provide ancillary services, such as ramp requirements, voltage support,
and so on.
For many years, the energy storage industry has continued to evolve from different types
of technologies and to adapt to new challenges. These technologies, which have been adopted
and deployed around the world, can be divided into six main categories [14]:

Solid State Batteries: A range of electrochemical storage solutions, including advanced
chemistry batteries and capacitors, for example, electrochemical capacitors, lithium ion
(Li-ion) batteries, nickel-cadmium (NI-CD) batteries, and sodium sulfur (NAS) batteries.

Flow Batteries: Batteries in which energy is stored directly in an electrolyte solution for
longer cycle life and quick response times. For example, redox flow batteries, ironchromium (ICB) flow batteries, vanadium redox (VRB) flow batteries, and zinc-bromine
(ZNBR) flow batteries.

Flywheels: Mechanical devices that harness rotational energy to deliver instantaneous
electricity.

Compressed Air Energy Storage (CAES): Utilization of compressed air to create a potent
energy reserve, for example, advanced adiabatic compressed air energy storage (AACAES) and isothermal CAES
7

Thermal: The capture of heat and cold to create energy on demand, for example, pumped
heat electrical storage (PHES), hydrogen energy storage, and liquid air energy storage
(LAES)

Pumped Hydro-Power: The creation of large-scale reservoirs of energy using water, for
example, pumped hydroelectric storage, sub-surface pumped hydroelectric storage,
surface reservoir pumped hydroelectric storage, and variable speed pumped hydroelectric
storage.
Different types of EES have diverse characteristics in terms of capital cost, size,
operation and maintenance (O&M), efficiency, ramp rate, and so on. Figure 1.6 illustrates the
power and energy relationships of these technologies [15]. It can be seen that CAES and pumped
hydro have the ability to discharge in several hours, with correspondingly high values that reach
1,000 MW. In contrast, the other two technologies, flywheels and electrochemical batteries, have
the ability to provide lower power and shorter discharge times. The choice of EES device
depends on the specific situation and requirements. The application of EES can be divided into
three groups based mainly on the discharging time capability: power quality, bridging power,
and energy management [16].
As of May 2014, the interactive database [17] created and maintained by the U.S.
Department of Energy (DOE), reported 333 storage system deployments in the U.S., with a
capability of more than 26 gigawatts (GW). Figure 1.7 shows the contribution of each
technology to the overall capability [18]. Pumped hydro obviously dominates at 95 percent
because of its larger unit size and longer history. Other storage technologies, such as CAES,
thermal energy storage, batteries, and flywheel, account for the other 5 percent.
8
Figure 1.6. Positioning of energy storage technologies [15]
Figure 1.7. Rated power of U.S. grid storage projects (including announced projects) [18]
1.2
Objective and Scope of This Work
The main objective of this dissertation is to develop a general procedure to optimize the
location of the EES unit in a power system with high renewable penetration. This research also
analyzes the results through two group cases. The outcome of this research, a proposed method
and results, could be utilized to analyze other power systems with renewable energy and provide
some suggestions on the location issue. The general conclusions from the case studies may
provide limited references to planning engineers and system operators.
9
The objectives of this research include the following:

Identify and analyze the prime effects of EES on a power system with renewable energy.

Develop a general procedure to optimize the location of EES units in a power system
with renewable energy.

Illustrate the importance and diversity of scheduling EES and the impact on a power
system with renewable energy.

Investigate a method to efficiently simulate wind energy’s variability.

Investigate how the proposed approach will impact the location of EESs in different
scenarios.

Analyze the possible location of an EES unit in a power system with renewable energy
under different situations.

Illustrate the main limiting factors in deploying an EES unit in an existing power system
with renewable energy.
This dissertation focuses on optimizing the location of an EES unit in a power system
with wind energy. Other types of renewable energy are not considered. However, it is possible to
consider other renewables by modifying the relative parameters and input data. Only two of the
regulatory policies—CO2 emissions and renewable incentive—are considered. More polices may
be incorporated into this model by making appropriate modifications.
1.3
Organization of Dissertation
The main body of this dissertation consists of six chapters. The first chapter introduces
the impact of renewable energy regulatory policies, wind energy, and general information of the
EES. Chapter 2 reviews existing algorithms of EES modeling and optimization and simulation
platforms. Chapter 3 discusses the modeling and methodology. Chapters 4 and 5 present two
10
groups of case simulations and results in this research. Chapter 6 presents some general
conclusions and future work.
11
CHAPTER 2
LITERATURE STUDY
This chapter reviews the literature related to energy storage modeling, scheduling,
probabilistic optimal power flow (OPF), and simulation tools. Section 2.1 explains the methods
used in modeling and scheduling of EES. Three categories of methods that are used for solving
the probabilistic power flow problem are discussed and compared in Section 2.2. Section 2.3
reviews some of the research on location issues involving EES. Section 2.4 explains the
simulation tool, MATPOWER, used in this research.
2.1
Modeling and Scheduling of Bulk Energy Storage
Research on EES systems has been ongoing for many years, beginning with a study on
hydrothermal coordination in 1963 [19]. Studies on hydropower and pumped storages show
several algorithms involving the coordination with thermal plants, such as gradient method [11],
λ-γ iteration, and dynamic programming [20]. Hydropower, as a form of energy storage, has
limitations based on geographical location as well as seasonal variation and other factors.
However, it plays a unique role in utilizing renewable energy efficiently. These algorithms are
not suitable for application on a power system with multiple types of renewables and energy
storage, since they are based on cubic or quadratic heat rate curves.
With the application of different storage forms in a power system, such as flywheels,
CAES, batteries, and so on, the EES system is recognized as having the ability to improve the
efficiency and reliability of an electrical system by appropriate scheduling. The coordination
should accommodate the features of a future power system, which has a high renewable
penetration, and it should consider the transmission system constraints. The cost and cycle
efficiency of storage, transmission limits, and power losses in the system are major restrictions
12
for large-scale energy storage becoming economically feasible in the power system [21]. One
observation of a power system with wind energy for a short period of time shows a large
variation of locational marginal pricing [22]. This illustrates the potential capability of how an
EES works in an energy arbitrage function by alleviating the variation of wind production and
LMP to a certain extent. To relieve transmission congestion, the scheduling of EES will be more
economically reflected by the LMP at the storage location [21]. An EES system can profit
considerably, not only though energy arbitrage or congestion relief but also through ancillary
services [23]. In addition, other algorithms have been recently developed for optimizing the
planning work of EES coordinate with renewables. A multi-period optimization approach was
proposed [24] [25] to optimize the operation and planning of EES coordination with renewables.
Hu and Jewell [26] also applied a multi-period optimization method in their research and
provided valuable conclusions about the generation expansion in the future power system
integration with renewables and the EES system. In their research, the optimization work is
based on the linear lossless direct current (DC) OPF method in order to reduce the complexity in
a long-term planning study. For long-term planning work, some researchers [24] [27] use a
stochastic model, which focuses on the price and investment rate of an EES system, while others
[25] [28] use a deterministic model. The employment of EES needs to consider power flow,
energy, location, investment, and other factors.
2.2
Probabilistic Optimal Power Flow
In order to fully consider the uncertainty factor and other aspects associated with
renewable energies, power flow studies use probabilistic methods, in which the variables in the
power flow become random. To deal with these problems of uncertainty, some technologies,
such as Monte Carlo (MC) simulation [29], analytical methods, and approximate methods are
13
applied. The MC method, which is widely used [30] [31], generates a large number of values
randomly as input data; however, its disadvantage is that the computation is very inefficient.
Analytical methods, which are applied to some mathematical technologies, transformation skills,
and appropriate assumptions, are much improved in terms of computational efficiency; however,
it is difficult to simplify a complex problem with this method. In the case of specific analytical
methods, a linearized method for a multilinear model has been developed [32] [33] [34] to deal
with the nonlinear problem. Also, the probabilistic cumulated method has been used to solve a
power flow problem [35]. The fast Fourier transform (FFT) has also been applied on a
probabilistic power flow issue [36] [37]. A combination of two analytical methods, cumulants
and Gram-Charlier expansion, were developed [38] [39] in order to estimate the probability
function of random variables. Finally, the approximate method utilizes the statistical properties
of random variables, the first-order second-moment method (FOSMM) [40], and point
estimation method to solve the probabilistic power flow. The point estimation (PE) method is
applied in this research.
Compared with other methods, there are some definite advantages for using the point
estimation method to solve the probabilistic power flow. First, this method has much higher
computational efficiency than the MC method, which needs a great number of values. Second,
for the analytical method, the probability functions are approximated and some predefined
assumptions are applied, thus making it less than perfect. The point estimation method does not
have high data requirements. Lastly, the point estimation method takes full advantage of existing
data and statistical properties to solve the probabilistic power flow.
14
2.3
Location of Energy Storage
Recently, most research related to EES involves scheduling and coordination with other
plants. However, some research focuses on the issue of optimal location of the EES system in a
power system with renewable energy [41] [42] [43] [44] [45]. All of these studies consider this
issue in the distribution system. The situation in a distribution system is different from the
situation in a transmission system. Several studies deal with this issue in the transmission system
[46] [47] [48]. However, two of them [47] [48] are based on deterministic models, which lack
consideration for the properties of renewable energy, and the accuracy of one of them [46] that
uses the 2m point estimation method with multiple variables is doubted. Furthermore, all of them
do not fully consider a deregulated market structure for the power system. In addition, with
increased attention on environment issues, none of this research considers the price of CO2 as an
important factor.
2.4
Simulation Tool
In order to solve the core part of the proposed method for the alternate current (AC) OPF
problem, MATPOWER [49] is used as the simulation tool, providing users more flexibility to
modify or augment the problem formulation based on the standard OPF formulation.
MATPOWER’s extensible standard OPF structure [50] is shown as follows:
Objective Function:
min
,
( )+
( , )
(2.1)
Constraints:
( )=0
(2.2)
ℎ( ) ≤ 0
(2.3)
≤
≤
15
(2.4)
≤A
≤
≤
(2.5)
≤
(2.6)
The term ( ) stands for the cost function, and is the summation of real and reactive power
rejections of all generators. The term
( , ), the user-defined cost function, could be defined by
users and is optional. The optimization vector
voltage angle θ, voltage magnitude
for the standard AC OPF problem consists of
, real power injection
, and reactive power injection
.
Equation (2.2) involves a set of equations and represents the nodal power balance. Equation (2.3)
entails a set of inequalities and constrains the power flow for each transmission line. Equation
(2.4) shows the bounded variables θ,
,
, and
. Equations (2.5) and (2.6) construct the
additional variables and constraints associated with the user-defined function.
Compared with the commercial software simulator PowerWorld, MATPOWER, which is
as an open source tool, has more advantages. It employ a powerful nonlinear solver, MATLAB
Interior Point Solver (MIPS) [51], as a default setting, which can be utilized to solve both AC
OPF and DC OPF. It also has the ability to invoke other powerful nonlinear programming and
quadratic programming solvers, for example, MINOPF [52], TSPOPF [53], BPMPD [54],
MOSEK [55], CPLEX [56], GUROBI [57], etc., according to different types of optimization
models. While the PowerWorld default solver setting is primary linear programming (LP) OPF
[58], this method shortens the solving time by sacrificing accuracy. In additional, the bounded
value setting for the voltage limits cannot be applied on PowerWorld’s LP model. Moreover,
with the predefined function and other constrains, PowerWorld loses more flexibility than that of
MATPOWER. However, the disadvantages of MATPOWER are obvious. There is no one-line
diagram or connection map available, which can give users a clear and general view. In addition,
no friendly interface easily makes the tool tedious to use.
16
CHAPTER 3
MODELING AND METHODOLOGY
This chapter investigates the issues relative to modeling and methodology that are used in
this research. Section 3.1 introduces the basic information about the test system, a modified
IEEE 24-bus system. The operation cost incorporated with the CO2 emissions cost is described in
Section 3.2. Section 3.3 shows the objective function used in this research. Section 3.4 illustrates
the general procedures to optimally locate the EES. The method for modeling the wind plant by
using the Weibull distribution is discussed in Section 3.5. Section 3.6 analyzes details of the
probabilistic OPF. It contains information about point estimation, details of the modified twopoint estimation scheme, and the implementation steps. Section 3.7 introduces the genetic
algorithm used in this research.
3.1
Test System
In this dissertation, the modified IEEE 24-bus reliability test system (RTS) is used to
illustrate the methodology. As shown in Figure 3.1, the IEEE 24-bus RTS [59], was first
developed by the IEEE Application of Probability Methods Subcommittee in 1979 and updated
in 1986 and 1996. The total load, in the original IEEE 24-bus RTS is 2,850 MW, and the total
generation is 3,405 MW. The test system has two voltage levels: 138 kilovolts (KV) and 300 KV.
Bus No. 1 to Bus No. 10 are in low voltage level, and the remaining buses are in a high voltage
level. The reference bus is Bus No. 13.
17
Figure 3.1. IEEE 24-bus RTS
In this research, the type of generation for the modified IEEE 24-bus RTS includes
nuclear, coal, oil, natural gas, hydro, and wind energy. Later on in different case studies, wind
power with different generating capacity will be added into this system. The generating capacity
of all types of resources of the modified IEEE 24-bus RTS is shown in Figure 3.2.
18
2% 0%
Coal
24%
37%
Gas
Hydro
Nuclear
9%
Oil
Wind
28%
Figure 3.2. Generation capacity distribution of modified IEEE 24-bus RTS
3.2
Operating Cost
Operating cost is the expense to operate equipment, a generator, or existing generators. It
does not include the capital cost for any generator.
3.2.1 Traditional Generator Unit
The operating cost for a fossil-fuel fired generator includes the cost of fuel and cost of
CO2 emissions. Both of them have a relationship with real power output, depending on the
characteristics of each generator. Fuel cost is the product of fuel price and a heat rate function, as
shown in equation (3.1). The amount of CO2 emissions is the product of an emission factor and
the heat rate function, as shown in equation (3.2). The CO2 emissions cost is the product of the
CO2 price and the amount of CO2, as shown in equation (3.3). The operating cost for each single
generator is shown in equation (3.4).
_
( )=
( )=
_
(
(
( )=
+
+
+
+
×
19
)
)
( )
(3.1)
(3.2)
(3.3)
_
where
_
( )=(
+
×
)× (
+
+
)
is the fuel cost function of the fossil-fuel-fired generator using fuel
( ) is the amount of CO2 emissions from generator using fuel in ton/h;
emissions cost of generator using fuel in $/h;
using fuel in $/h;
_
,
, and
_
in $/h;
is the CO2
is the operating cost of generator
is the given price of fuel in $/MBTu;
is the CO2 emission factor of fuel in ton/MBTu;
and
(3.4)
is the price of
in $/ton;
is the real power of generator in MW;
are coefficients of the polynomial heat rate.
To simulate a power system with CO2 emissions regulation, the emissions cost along with
the unit of $/MWh is added to each fossil-fuel-fired generator model. According to the
emissions-incorporated OPF algorithm developed by Shao [7], the CO2 emission factor is
combined with the heat rate function and considered together. The average CO2 emission rate is
listed in Table 3.1.
TABLE 3.1
AVERAGE CO2 EMISSION FACTORS
Emission Factor
(ton/MBTu)
0.0938
0.052
0.0741
Generator Type
Coal
Natural Gas
Oil
3.2.2
Renewable Generation
Renewable energy plants tend to have very low operating costs in comparison with fossil
fuel generators. The fuel is from a natural source, wind or solar, and is free. And there is no
emissions cost, since renewable generation does not produce CO2 during its operation.
20
3.3
Objective Function
The main purpose of optimal power flow is to minimize the objective function and satisfy
a set of relative constraints by adjusting the control variables. The objective function in this
research is to minimize the system operating cost while incorporating the CO2 emissions cost, as
shown in equation (3.5):
∑
where
3.4
(
+
×
)× (
+
+
)
(3.5)
is the total number of fossil-fuel-fired generators in the system.
General Procedure
The main purpose of this research is to optimize the location of EES in a power system.
Figure 3.3 briefly depicts this general procedure to find the right location of EES. The input data
includes wind and load data, which are seen as the variables of probabilistic optimal power flow
(POPF). And initialize the first population, which will be used in the POPF part. There are two
main functions of POPF: to minimize the operating cost for every hour of the system, and to
fully consider the uncertainty property of wind in the OPF calculation. The genetic algorithm
(GA) here has the function of finding the desired location for the EES system. Then to determine
whether these results meet the criteria, which is defined by the fitness function. If it is not meet
the criteria, the next generation will be produced and rerun the POPF part.
21
Input Data and
Initialize variables
t=1
Probabilistic OPF
New Generation
t=t+1
Y
t≤T
N
Genetic Algorithm
N
Meet
criteria?
Y
Output
Figure 3.3. Optimization flow chart
3.5
Modeling of Wind Energy
The wind generation output converts from the historical data of wind speed. Wind speed
is modeled as a two-factor Weibull distribution. Its probability density function (PDF) is given as
equation (3.6). The curve-fitting method is utilized to maximally estimate the Weibull
distribution parameters. The output of the wind generator is relative to the wind speed [60],
22
,
which is shown as equation (3.7). The output of wind generation is zero when the wind speed is
lower than the cut-in wind speed or greater than the cut-out wind speed. The wind generation
output is its rating value when the wind speed is greater than the rated wind speed and smaller
than the cut-out speed. The output wind generation is a proportion of its rating power when the
wind speed is between the cut-in wind speed and rated wind speed.
( ⁄ )
( )=
0,
,
where
speed,
≤
is the wind rating power,
is the cut-out wind speed,
≤∞
(3.6)
≤ , ≥
≤ ≤
,
=
0≤
(3.7)
≤
is the wind generation output,
is the rated wind speed, and
and
is the cut-in wind
are factors of the
Weibull distribution.
3.6
Probabilistic Optimal Power flow
The POPF approach, which considers uncertainty factors from different sources, provides
more realistic results than traditional methods. Several techniques, such as MC simulation,
analytical method, and approximate method, are developed. The point estimation method, which
calculates the moments of a random variable, is used in this research. Hong’s point estimation
method [61], one of the PE methods, is better than other methods by Li [62] and Harr [63] to
solve the power flow problem. Especially, the 2m+1 scheme is more accurate than the 2m
scheme and more efficient than the 3m scheme.
3.6.1
Point Estimation
The first few central moments of an input random variable on K points for each variable
are called concentrations. The PE method mainly utilizes that information, or concentrations, to
23
solve the problem. These K points combined with the nonlinear function F together provide clues
to obtain outputs of the problem with uncertainty.
For a random input variable
, its th concentration (
plane, as shown in Figure 3.4 [61]. The location value of
,
,
,
,
) is a coordinate on the
and the weight value
,
are
considered together as the th concentration. From the point estimation explanation shown in
Figure 3.4, the location value
,
is the
th value of input variable
as the horizontal
coordinates. The weight value
,
is a weighting factor. It is part of the input variable’s
concentration and also part of the estimated output. Total K points mean that K points are
selected for each input variable
. In other words, the function F is going to be evaluated K
times for each input variable
, in order to obtain those concentration values and other
parameters. The number of K depends on the scheme adopted. For example, the K value of a
two-point estimation scheme is two. Therefore, the total number of evaluations for function F is
K × m. The value m is the number of input variables.
Figure 3.4. Point estimation explanation [61]
Specifically, the location value
,
is determined by
24
=
,
where the value
,
+
is the standard location,
deviation of the input variable
(3.8)
,
is the mean value, and
is the standard
.
Other values, such as the standard location
and weight
,
,
, are obtained by solving
the following nonlinear equations:
∑
∑
(
,
,
,
) =
,
=
,
(3.9)
= 1, … ,2
,
−1
(3.10)
( )
(
( )=∫ (
where
=
(3.11)
)
−
)
(3.12)
is the jth standard central moment of the input random variable, m is the amount of
input variables, and
is zero and the value
is the probability density function for
,
. At the same time, the value
is one. The third standard central moment
variable
is called skewness. The fourth standard central moment
variable
is called kurtosis.
After all concentrations (
,
,
,
,
,
,
of the input random
of the input random
) are obtained, output variables ( , ) will result from
the evaluation of function F. Finally, weighting factors
,
and output variables ( , ) are used
to calculate the jth moment of output variables by equation (3.13).
≅ ∑
3.6.2
∑
,
( ( , ))
(3.13)
Modified Two-Point Estimation
The modified two-point estimation, 2m+1 scheme, is used in this research because of its
advantages mentioned previously. Briefly, this scheme is more efficient, has a lower
computational burden, and has accepted accuracy.
25
This 2m+1 scheme can be seen as a 2m scheme with one additional evaluation of
function F, or as a 3m scheme with one of the three standard locations already fixed. Based on
this view, some values are set as K equals three and
equals zero. Under these settings, the
,
other parameters are obtained and shown in equations (3.14) to (3.16):
=
,
,
+ (− 1)
,
=
,
(
−
,
)
,
( ,
,
=
,
= 1, 2
)
= 1, 2
(3.14)
(3.15)
(3.16)
,
,
These equations show that the standard location value
,
in the 2m+1 scheme does not have any
relationship with the number of input variables. At the same time, it also shows that the
improved two-point estimation method is more accurate than the 2m scheme, since it takes into
account the kurtosis value
3.6.3
,
of the input variables.
Implementation Point Estimation Method
Based on information presented previously, the 2m+1 PE scheme is implemented by
several steps, as shown in Figure 3.5. The first step is to prepare the input random variables and
initialize the relative variables. Then, the second step is to calculate standard central moments
,
, standard locations
,
, and weights
,
. The third step is to determine the location
according to equation (3.8). The fourth step is to solve the deterministic power flow by using the
above values. The fifth step aims to check whether all evaluation work on the deterministic
system is finished. If not, then it will go back to the third step. If it is finished, then it will update
the variables according to equation (3.13). The third step to the fifth step is a loop to finish
evaluating the power system. Once the evaluation work is finished, it will jump out of this loop.
Finally, in the last step, all output data will be obtained.
26
Input random variable
Computation:
standard central moments
standard locations
weights
Select the point location
Solve deterministic system
Update variables
Outputs
Figure 3.5. Implementation steps for 2m+1 PE scheme
3.7
Genetic Algorithm
The aim of the GA is to find the desired location for the EES system based on the fitness
function. In this research, the criterion is to find a location where more energy can go into the
EES. Then the mission of the GA is to maximize the fitness function (FF), as shown in equation
(3.17).
27
∑
∑
,
−∑
∑
(
)
(3.17)
,
where D is the demand from the loads, P is the real power coming from all resources, and
is
the bus number that the EES system located in the power system. The fitness function means the
amount of energy charged into the EES system.
Figure 3.6 shows the flow chart of the genetic algorithm. At first, a random initial
population, composed of a number of individuals, is created. The second step is to determine
whether this population satisfies the fitness function. If yes, then it will show the results. If no,
then it will produce the next generation by selecting a group of individuals in the current
population and making the evaluation of the fitness function the same as the previous time. The
process of producing the next generation is implemented by three steps: selection, crossover, and
mutation.
Initial
Y
New Generation
Results
Evaluate FF
N
Selection
Crossover
Mutation
Figure 3.6. Genetic algorithm flow chart
28
The new generation will be used in POPF part, which also shown in Figure 3.3. Then the
outputs from POPF part will again be evaluated by the fitness function till find the satisfied
solution. The dashed line shown in Figure 3.6 describes that the new generation will be used in
POPF to obtain the results and then to be evaluated.
In order to have an accurate result, the parameter setting work is critical in the GA
process. A large size, but appropriate, population has the ability to improve the probability of
convergence. The population is composed by an array of individuals, which are the points that
can be applied to the fitness function. Some amount of children as the elitism, those are the
individuals with better fitness value in the current generation, keep the calculation goes the right
and fast way. A large penalty factor is necessary to eliminate the unsuitable solution during the
calculation.
29
CHAPTER 4
SIMULATION AND RESULTS I
In this chapter, the first group study of three cases is presented. Section 4.1 shows the
simplest case involving one wind plant and one EES unit in the test system for one day. Section
4.2 discusses a limited capacity case, considering the cost and capacity of the EES unit. Section
4.3 involves two wind plants and considers one more variable input data in the calculation.
4.1
Case 1: Basic Case
4.1.1
Basic Case Information
The first case study, the basic case, is a simple one and does not consider constraints of
the EES unit, such as price and capacity. It provides an example by using a special working
scheme of the EES unit to explain how to optimize its location. In this case, the wind plant is
located on the 19th bus, since usually the wind plant is a distance from the load center.
The working pattern of the EES system specifies on what situation the EES is charging
and discharging electricity. It is critical to set the EES system working pattern because it will
directly influence the results. The EES working pattern depends on the research purpose;
generally, it will coordinate with the renewable resource. In this case study, the EES unit works
with the wind plant and absorbs wind energy that is generated in excess of the load. The wind
plant gives first priority to the loads around it, which means first supplying power to the load
directly connected to itself. Then the extra wind power is used to charge EES system. If the wind
plant cannot supply enough power to supply the nearby loads, then the EES system begins to
discharge. Figure 4.1 illustrates the EES working pattern of this basic case. On each hour, the
first step is to compare the sum of minimum generators outputs and wind output with the total
load. If the former value is greater, the excess amount of wind energy is used to charge the
30
storage. The function of this step is to make sure that all other type of resources is working in a
less cost status. If not, the wind plant and storage are coordinate with each other based on the
above priority rule.
Wind and Load Data
Y
∑Pmin + Pwind > ∑D
Charge
N
Y
Pwind > ∑Daround
Charge
N
Discharge
Figure 4.1. EES working pattern for basic case
The load profile for this case is from the Electric Reliability Council of Texas (ERCOT)
official website, hourly load data archives [64], from March 1, 2013, and then scaled down to the
system load of the IEEE RTS. The wind speed data is from an environmental issues website [65].
Figure 4.2 shows the total load information and the loads surrounding the wind plant in one day.
31
It is obvious that the system peak hour is around 8 am and the lowest loads occurred at midnight.
Demond (MW)
Loads around the wind plant experience a similar situation.
2000
200
1800
180
1600
160
1400
140
1200
120
1000
100
800
80
600
60
400
40
200
20
0
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Time (Hour)
Load infromation
load_surround Wind plant
Figure 4.2. Load information for basic case
4.1.2
Basic Case Results and Analysis
This basic case has one wind plant and one unlimited capacity storage in the test system,
and the simulation period is one day. Table 4.1 provides a summary of the results. Different
wind-plant ratings are shown in the first column, and optimal buses are listed in the second
column. The charge energy, shown in the third column, means the amount of energy used to
charge the EES, and the utilization, shown in the fourth column, shows the percentage used to
account for the wind energy. This information indicates that EES units are likely to be located
near the load center when the wind rating is very high. And the EES unit is preferred in a highvoltage-level bus when the wind rating is between 100 MW and 160 MW, since high-voltage
transmission lines have a larger capacity than low-voltage transmission lines, which means fewer
32
chances of producing congestion. Figure 4.3 shows that the charge energy and utilization
increase with the increase in wind rating.
TABLE 4.1
RESULTS SUMMARY FOR BASIC CASE
Energy (MWh)
Wind Rating
(MW)
80
90
100
110
120
130
140
150
160
170
180
190
200
Charge Energy
(MWh)
23.95
89.11
150.31
160.97
199.16
239.56
294.36
370.67
437.37
567.42
740.55
890.79
1113.77
Bus No.
7
7
23
18
21
24
14
10
10
2
2
2
2
Utilization
(%)
1.2
4.1
6.3
6.1
6.9
7.7
8.8
10.3
11.4
13.9
17.1
19.5
23.2
1200.00
25.0%
1000.00
20.0%
800.00
15.0%
600.00
10.0%
400.00
5.0%
200.00
0.00
0.0%
80 90 100 110 120 130 140 150 160 170 180 190 200
Wind Rating (MW)
Charge energy
Utilization
Figure 4.3. Results curves for basic case
33
Figure 4.4 shows the operating cost comparison between test systems with and without
storage. It is clearly illustrated that the system with storage has a much lower operating cost than
that without storage. With the increasing wind plant output, the operating cost goes down, as
shown by the blue line. The red line, indicating the system with storage, goes up more sharply
when the wind output is about 160 MW, since there is rarely a chance for the storage to
discharge, and more traditional generators would have to increase their output to satisfy the
demands with a higher price. It is suggested that this working scheme may change into another
more efficient way to coordinate with the renewables and achieve a better performance of the
test system in the future. It is easy to assume that these two lines may converge at some point
with the current trend; however, they would not, because of line congestion. The potential value
Thousands
Operating Cost ($)
of storage can be explored by carefully analyzing the data and condition of the existing system.
2120
2115
2110
2105
2100
2095
2090
2085
2080
2075
2070
80
90 100 110 120 130 140 150 160 170 180 190 200
Wind Rating (MW)
without storage
with storage
Figure 4.4. Comparison of operating costs in basic case
Figure 4.5 shows a comparison of CO2 emissions between the test systems with and
without storage. The characteristics here are similar to those in Figure 4.4, for the same reasons
explained previously.
34
Co2 emission (ton)
18500
18000
17500
17000
80
90 100 110 120 130 140 150 160 170 180 190 200
Wind Rating (MW)
without storage
with storage
Figure 4.5. Comparison of CO2 emissions in basic case
4.2
Case 2: Limited Capacity
4.2.1
Limited Capacity Case Information
This case considers the parameters of the EES unit, including cost and efficiency. There
is one wind plant and one storage in the system. The performance of the system is presented
under different wind ratings and storage capacities.
According to Hu and Jewell [26], the EES unit in this research uses the best type of
CAES, where the cost of EES unit comes from the overnight capital cost (OCC) and then is
broken down into the annual capital recovery (ACR) for both power and energy of the storage.
The ACR is the product of the OCC and the capital recovery factor (CRF), which is expressed as
=
where
stands for the number of years, and
(
(
)
)
(4.1)
is the interest rate.
Parameters of the EES and calculated cost for this limited capacity case are listed in
Table 4.2 [26]. The storage working scheme here is different from the first case. This time the
storage discharges during peak hours and charges during off-peak hours. As shown previously in
35
Figure 4.2, the discharge time is at hour 8–9 (8–9 am) and hour 20–21 (8–9 pm). This case still
involves one wind plant and one storage in the power system. And the simulation is for one day.
TABLE 4.2
EES PARAMETERS FOR LIMITED-CAPACITY CASE [26]
CAES
(Best)
4.2.2
Life Cycles
Average Cycles
per Year
n
i
(%)
25,000
250
50
3.00
3.89
Capital Cost
($/kW)
Capital Cost
($/kWh)
ACR
($/MW)
ACR
($/MWh)
O&M
($/MWh)
Efficiency
(%)
500
3
19,433
117
3
70
CRF
(%)
Limited Capacity Results and Analysis
Figure 4.6 shows a comparison of operating costs under different situations in the limited
capacity case. The wind rating is increased from 40 MW to 200 MW, as shown on the x-axis.
The storage capacity is increased from 80 MWh to 150 MWh, as shown the curves with different
colors. The value of the operating cost is the vertical axis, y-axis. It is obvious that the operating
cost is decreasing. This figure shows that for a specific amount of capacity storage, the operating
cost drops with increasing wind energy in the power system. For capacity sizes of 140 MWh and
150 MWh, the curves stop at the 130 MW wind rating, since the congestion of the system means
that no convergence results can be provided. The congestion problem emerges with largecapacity storage. With increasing power from renewable wind energy, this free natural resource
reduced the operating cost. At the same time, with the help of storage, the renewable energy fully
functioned at peak hours.
36
Thousands
Operating Cost ($)
2100
2098
2096
2094
2092
2090
2088
2086
2084
2082
40
50 60
70
80
90 100 110 120 130 140 150 160 170 180 190 200
80 MWh
110 MWh
140 MWh
Wind Rating (MW)
90 MWh
120 MWh
150 MWh
100 MWh
130 MWh
Figure 4.6. Comparison of operating costs in limited capacity case
From Figure 4.6, the operation cost curves for different types of storage look similar to a
straight line, but actually they are not. A window occurs at every three points on the curve in
order to obtain the decreasing rate value for a piece of the curve. When the window moves to the
end of that line, group values for the decreasing rate can be obtained for different pieces of the
curve. Then the average value of this group can be seen as the decreasing rate of that cure. Figure
4.7 shows the decreasing rate for each curve in the limited capacity case. The horizontal axis, in
this figure is the storage capacity. As can be seen, the decreasing rates are almost at the same
level. This information shows that for a certain capacity of storage, the benefits from wind
energy are increasing almost linearly with the increased wind energy.
37
80
90
100
110
120
130
140
150
0
-10
Decreasing Rate
-20
-30
-40
-50
-60
-70
-80
-90
Storage Capacity (MWh)
Decreasing Rate
Figure 4.7. Decreasing rates in limited capacity case
Looking at Figure 4.6 from left to right by sections, the curves show information about
the changes in operating cost under the same wind rating condition with different storage
capacities. Figure 4.8 shows the operating cost variation with different storage capacities when
the wind rating is 40 MW. The blue curve is the variation in operating cost. The x-axis represents
the storage capacity increasing from 80 MWh to 150 MWh and indicates that the operating cost
is rising when the capacity value is increased. Figure 4.9 shows the same situation of the
operating cost increasing with increased capacity when the wind rating is 50 MW. Other sections
can be found in Appendix A, when the wind rating is from 60 MW to 200 MW, where the
operating costs have the same performance as these two examples, all of which are increasing. A
fixed wind rating means that the low-price renewable energy is constant for different cases. The
increased capacity of the EES unit does not have the ability to absorb more renewable energy.
And the working scheme and cost of storage forces the operating cost of the power system to
increase continuously. This information suggests the importance of a suitable capacity of storage
as well as storage working scheme to controlling the operating cost level.
38
Thousands
Operating Cost ($)
2097.8
2097.7
2097.6
2097.5
2097.4
2097.3
2097.2
2097.1
2097
2096.9
80
90
100
110
120
130
140
150
Storage Capacity (MWh)
Operating Cost
Thousands
Operating Cost ($)
Figure 4.8. Operating costs (wind rating of 40 MW) in limited capacity case
2097.6
2097.4
2097.2
2097
2096.8
2096.6
2096.4
2096.2
2096
2095.8
2095.6
80
90
100
110
120
130
140
150
Storage Capacity (MWh)
Operating Cost
Figure 4.9. Operating costs (wind rating of 50 MW) in limited capacity case
A comparison of CO2 emissions under different situations in the limited capacity case is
shown in Figure 4.10. The wind rating is increased from 40 MW to 200 MW, as shown on the xaxis. Storage capacity is increased from 80 MWh to 150 MWh, as shown the curves with
different colors. The value of CO2 emissions is the vertical y-axis. For a specific storage, the
amount of CO2 emissions decreases when the wind rating is increased, because wind energy
reduces the emissions from fossil-fuel-fired generation with the help of storage. For the same
39
wind rating, the amounts of CO2 emissions are fairly the same, with small variations, for the
Hundreds
same reason as mentioned previously.
174.55
174.5
CO2 Emission (ton)
174.45
174.4
174.35
174.3
174.25
174.2
40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
80 MWh
110 MWh
140 MWh
Wind Rating (MW)
90 MWh
120 MWh
150 MWh
100 MWh
130 MWh
Figure 4.10. Comparison of CO2 emissions in limited capacity case
The energy used for charging the EES unit is also analyzed in the limited capacity case
case. Figure 4.11 shows a comparison of energy for charging the storage under different wind
ratings and storage capacities. As shown, the x-axis indicates the wind rating, from 40 MW to
200 MW. The curves with different colors are the storage capacities, which increase from 80
MWh to 150 MWh. The vertical y-axis represents the amount of charging energy in MWh.
40
500
450
400
Energy (MWh)
350
300
250
200
150
100
50
0
40
50
60
70
80
90 100 110 120 130 140 150 160 170 180 190 200
80 MWh
110 MWh
140 MWh
Wind Rating (MW)
90 MWh
120 MWh
150 MWh
100 MWh
130 MWh
Figure 4.11. Charging energy in limited capacity case
Using the 80 MWh storage capacity as an example, Figure 4.12 reflects the charging
energy increasing rate of this storage. As shown, the charging energy increased quickly at first
but this amount almost stays the same at the end. This is due to the limited capacity storage.
Even when the wind energy is increasing, for a specific storage, the ability of storage is limited,
which will not exceed its capacity. The same situation occurs with other capacities, as shown in
Figure 4.13.
41
0.4
0.35
Charging Rate
0.3
0.25
0.2
0.15
0.1
0.05
0
-0.05
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
80 MWh
Figure 4.12. Charging rates (80 MWh of storage) in limited capacity case
2.5
Charging Rate
2
1.5
1
0.5
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
-0.5
80 MWh
110 MWh
140 MWh
90 MWh
120 MWh
150 MWh
100 MWh
130 MWh
Figure 4.13. Charging rates for different capacities in limited capacity case
Taking a look at Figure 4.11 from left to right by sections, these curves show information
about charging energy under certain wind energy. Figure 4.14 shows the charging energy under a
wind rating of 40 MW. The curve, which is increasing, shows that the larger capacity of storage
can store more energy and later can be used for discharging. Other sections of this curve can be
found in Appendix B, and all of them show a similar situation.
42
Charging Energy (MWh)
400
350
300
250
200
150
100
50
0
80
90
100
110
120
130
140
150
Storage Capacity (MWh)
Energy
Figure 4.14. Charging energy (wind rating of 40 MW) in limited capacity case
The locations of storage under different situations are showing in Table 4.3. As can be
seen, horizontal numbers at the top of this table show the capacity of storage from 80 MWh to
150 MWh. Vertical numbers on the left show the wind rating from 40 MW to 200 MW.
Numbers in the table are bus numbers, which are the desired locations. Since there are two levels
of voltage in the test system, bus numbers located in the high-voltage level have a red
background color. From this EES record, most of the preferred storage is located in the highvoltage section. Especially, when there is a large wind plant, storage units are all located in the
high voltage part. The high-voltage part of a transmission line has a larger capacity and could
relieve the congestion, which is an important factor.
43
TABLE 4.3
EES LOCATION RECORD FOR LIMITED CAPACITY CASE
MWh
MW
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
80
90
100
110
120
130
140
150
20
3
7
22
20
1
24
15
3
4
2
21
18
23
22
15
10
7
3
10
19
11
6
16
12
17
6
7
16
15
11
19
11
15
2
9
18
2
8
5
24
21
19
22
7
14
19
23
10
12
13
10
18
15
6
19
6
19
19
6
12
21
18
12
16
15
14
16
2
11
1
20
17
4
7
7
3
19
19
12
19
22
22
17
12
16
5
12
22
21
10
21
24
17
24
18
14
16
17
13
22
20
10
7
15
24
15
1
17
1
8
23
9
11
16
10
12
19
7
3
16
6
Case 3: Multiple Wind Plant
4.3
4.3.1 Multiple Wind Plant Case Information
The multiple wind plant case considers two wind plants in the power system, which
means that more input variables are introduced. When the point estimation method deals with
more input variables, as shown previously in Figure 3.4, the function F is evaluated K times for
each input variable
(
,
,
,… ,
. For each input variable, the function F is evaluated as
,
,… ,
composed of the location value
), which means that for each input variable
,
and the mean value
other words, for one specified input variable
, the
, the evaluation is
of the rest of the input variables. In
value is given as
,
for a total of K times,
and the rest of the variable values are fixed and assigned their mean values. From the above
44
explanation, the implementation of the PE method with more input variables needs additional
steps to consider the influence of other variables, as shown in Figure 4.15.
Initialize and input
l=1
Select input variable Pl
Computation:
standard central moments
standard locations
weights
l=l+1
Select point location
K times
Solve deterministic system
Update variables
Determine all
variables considered l
= m?
Outputs
Figure 4.15. Implementation steps of 2m+1 PE scheme with multiple variables
45
4.3.2
Multiple Wind Plant Results and Analysis
Figure 4.16 shows information about operating cost under different situations in the
multiple wind plant case. The wind ratings are increased from 40 MW to 120 MW, as shown on
the x-axis. The storage capacity is increased from 80 MWh to 150 MWh, as shown the curves
with different colors. The value of the operating cost is the vertical y-axis. It is obvious that the
operating cost is decreasing, showing that for a specific amount of capacity storage, the operating
cost decreases with increasing wind energy in the power system. For the storage capacity of 140
MWh and 150 MWh, the curves stop from the 80 MW wind rating, since the congestion of the
system cannot provide convergence results. With increasing power from the renewable wind
energy, this free natural resource has reduced the operating cost. Compared with the first basic
Operating Cost ($)
Thousands
case, the operating cost is much lower, since there is more renewable energy.
2090
2088
2086
2084
2082
2080
2078
2076
2074
2072
2070
40
50
60
70
80
90
Wind Rating (MW)
80 MWh
90 MWh
110 MWh
120 MWh
140 MWh
150 MWh
100
110
100 MWh
130 MWh
Figure 4.16. Operating costs in multiple wind plant case
46
120
The same method as mentioned in the second case is used to analyze the decreasing rate,
as shown in Figure 4.17. In this figure, the horizontal axis is the storage capacity. The decreasing
rates are almost the same levels. This information shows that for a certain capacity of storage, the
benefits from wind energy are increasing almost linearly with increased wind energy.
0
-20
80
90
100
110
120
130
140
150
Decreasing Rate
-40
-60
-80
-100
-120
-140
-160
-180
Storage Capacity (MWh)
Decreasing Rate
Figure 4.17. Decreasing rates in multiple wind plant case
Taking a look at Figure 4.16 from left to right by sections, the curves show information
about the changes in operating cost under the same wind rating condition with different storage
capacities. For example, the first section shows the operating cost variation with different storage
capacities when the wind rating is 40 MW, as shown in Figure 4.18. The blue curve is the
variation in operating cost. The x-axis represents the storage capacity increasing from 80 MWh
to 150 MWh, which indicates that the operating cost is rising when the capacity value is
increased. Other sections can be found in Appendix C, when the wind rating is from 50 MW to
120 MW, and indicate that the operating costs show the same performance as this example—all
of them increasing.
47
Thousands
Operating Cost ($)
2089.2
2089
2088.8
2088.6
2088.4
2088.2
2088
2087.8
2087.6
80
90
100
110
120
130
140
150
Storage Capacity (MWh)
Operating Cost
Figure 4.18. Operating costs (wind rating is 40 MW) for multiple wind plant case
The comparison of CO2 emissions under different situations for the multiple wind plant
case is shown in Figure 4.19. The wind rating is increased from 40 MW to 120 MW, as shown
on the x-axis. The storage capacity is increased from 80 MWh to 150 MWh, as shown the curves
with different colors. The value of CO2 emissions is shown on the vertical y-axis. For a specific
storage, the amount of CO2 emissions is decreasing when the wind rating is increased, because
the wind energy reduces the emission from fossil-fuel-fired generation with the help of storage.
For the same wind rating, the amounts of CO2 emissions are fairly the same, with only small
variations, for the same reason as mentioned previously.
48
17460
17455
CO2 Emission (ton)
17450
17445
17440
17435
17430
17425
17420
40
50
60
70
80 MWh
110 MWh
140 MWh
80
90
Wind Rating (MW)
90 MWh
120 MWh
150 MWh
100
110
120
100 MWh
130 MWh
Figure 4.19. Comparison of CO2 emissions in multiple wind plant case
The energy used for charging the EES unit is also analyzed in this case. Figure 4.20
shows the comparison of energy for charging the storage under different wind ratings and storage
capacities. In this figure, the x-axis is the wind rating, which is increased from 40 MW to 120
MW. The curves with different colors are the storage capacities, which are increased from 80
MWh to 150 MWh. The vertical y-axis represents the amount of charging energy in MWh.
49
450
400
Charging Energy (MWh)
350
300
250
200
150
100
50
0
40
50
60
70
80
90
100
110
120
Wind Rating (MW)
80 MWh
110 MWh
140 MWh
90 MWh
120 MWh
150 MWh
100 MWh
130 MWh
Figure 4.20. Charging energy in multiple wind plant case
Compared with Figure 4.11 for the limited capacity case, the curves in the multiple wind
plant case are much flatter. For example, with the 120 MWh storage capacity, in the limited
capacity case, the charging energy curve is obviously increasing with the wind rating from 40
MW to 80 MW. But this is not the case for the multiple wind plant situation. And the same
situation occurs with other storage because, in this case, there are two wind plants and they
provide much more wind energy than in the limited capacity case.
Looking at the sections of Figure 4.20 from left to right shows information about the
charging energy under certain wind energy. Figure 4.21 shows that the charging energy under the
wind rating is 40 MW. The curve, which is rising, represents the larger capacity of storage,
which can store more energy and later be used for discharging. Information on the other sections
can be found in Appendix D, all of them indicating a similar situation.
50
Charging Energy (MWh)
450
400
350
300
250
200
150
100
50
0
80
90
100
110
120
130
140
150
Storage Capacity (MWh)
Charging Energy
Figure 4.21. Charging energy (wind rating is 40 MW) in multiple wind plant case
51
CHAPTER 5
SIMULATION AND RESULTS II
In this chapter, three more case studies are discussed. Sections 5.1 and 5.2 present a
typical week and a typical year simulation time periods and results, respectively. In Section 5.3,
the day-ahead market concept will be introduced because market factors can also influence the
storage working scheme and results.
5.1
Case 4: Typical Week
5.1.1
Typical Week Case Information
In this case, a typical week totaling 168 hours is the simulation period, with one wind
plant and one storage device in the test system. Figure 5.1 shows the variation of settlement point
price (SPP) in the day-ahead market for one typical week, data of which was retrieved from the
ERCOT website [66]. From this figure, it can be seen that the SPP varies widely between the
first four days and the last three days in a week. In other words, there is a large difference in the
SPP between the weekdays and the weekend days. Base on this information, the storage working
scheme is to discharge at the peak hours in a week. This means that the storage discharge hours
are different between the first four days and last three days in a week.
Figure 5.2 shows the load data from the ERCOT website [64] for one week. In this
typical week case, the load data is derived by scaling down to the test system scale.
52
240
199
180
147.41
SPP ($)
120
110.55
104.69
98.48
133.24
96.6
60
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
0
Monday,
May 05,
2014
Tuesday, Wednesday, Thursday, Friday, May Saturday,
May 06,
May 07,
May 08,
09, 2014
May 10,
2014
2014
2014
2014
Time Line
Sunday,
May 11,
2014
Figure 5.1. SPP for one week in typical week case
2500
Load (MW)
2000
1500
1000
500
1
8
15
22
29
36
43
50
57
64
71
78
85
92
99
106
113
120
127
134
141
148
155
162
169
0
Time (h)
Load
Figure 5.2. Load data for typical week case
5.1.2
Typical Week Results and Analysis
Figure 5.3 shows a comparison of operating costs under different situations. The wind
rating is increased from 90 MW to 120 MW, as shown along the x-axis. The storage capacity is
increased from 80 MWh to 120 MWh, as shown the curves with different colors. The value of
53
the operating cost is along the vertical y-axis. It is obvious that the operating cost is decreasing,
showing that for a specific amount of capacity storage, the operating cost drops with increasing
wind energy in the power system. The increasing wind energy and the storage device both
x 100000
contribute to the reduction in operating cost.
148.5
148.4
Operating Cost ($)
148.3
148.2
148.1
148
147.9
147.8
147.7
90
100
110
120
Wind Rating (MW)
80 MWh
90 MWh
100 MWh
110 MWh
120 MWh
Figure 5.3. Comparison of operating costs in typical week case
Taking a look at Figure 5.3 from left to right by sections, the curves show information
about the changes in operating cost under the same wind rating condition with different storage
capacities. For example, the first section shows the operating cost variation with different storage
capacities when the wind rating is 90 MW, as depicted in Figure 5.4. The blue curve is the
variation of operating cost. The x-axis represented that the storage capacity increased from 80
MWh to 120 MWh. As can be seen, the operating cost is rising when the capacity value is
increased; hence, a suitable size of capacity is very important.
54
x 100000
Operating Cost ($)
148.45
148.4
148.35
148.3
148.25
148.2
148.15
148.1
148.05
148
80 MW
90 MW
100 MW
110 MW
120 MW
Storage Capacity (MWh)
Operating Cost
Figure 5.4. Operating costs (wind rating is 90 MW) in typical week case
Other sections of Figure 5.3, when the wind rating is from 100 MW to 120 MW, can be
found in Appendix E and indicate that operating costs show the same performance—all of them
increasing. A fixed wind rating means that the low-price renewable energy is a constant value.
The working scheme and cost of increased storage capacity make the operating cost of the power
system rise continuously. This information suggests the importance of both a suitable storage
capacity and the storage working scheme to control the operating cost level.
A comparison of CO2 emissions in the typical week case is shown in Figure 5.5. Here the
wind rating is increased from 90 MW to 120 MW, as shown on the x-axis. The storage capacity
is increased from 80 MWh to 120 MWh, as shown the curves with different colors. The value of
CO2 emissions is shown on the vertical axis, Y axis. For a specific storage, the amount of CO2
emissions decreases when the wind rating increases, because the wind energy reduces the usage
of traditional generation with the help of storage. For the same wind rating, the amount of CO2
emissions is fairly the same with only small variations, for the same reason as discussed
previously.
55
x 10000
CO2 Emission (ton)
12.265
12.26
12.255
12.25
12.245
12.24
12.235
90
100
110
120
Wind Rating (MW)
80 MWh
90 MWh
100 MWh
110 MWh
120 MWh
Figure 5.5. Comparison of CO2 emissions in typical week case
Figure 5.6 shows CO2 emissions during charging periods for storage capacities of 80
MWh and 100 MWh. During this time, the storage with capacity of 100 MWh has more
emissions than that with capacity of 80 MWh. Figure 5.7 shows emissions during discharging
periods for storage capacities of 80 MWh and 100 MWh. During this time the storage with
capacity of 100 MWh has fewer emissions than that with capacity of 80 MWh. A comparison of
these figures illustrates that the emissions from coal during the discharging time is replaced by
the emissions from gas.
56
x 10000
9
8
CO2 Emission (ton)
7
6
5
oil
4
gas
3
coal
2
1
0
80 MWh
100 MWh
CO2 Emission (ton)
x 10000
Figure 5.6. CO2 emissions in charging periods in typical week case
2.5
2
1.5
oil
gas
1
coal
0.5
0
80 MWh
100 MWh
Figure 5.7. CO2 emissions in discharging periods in typical week case
Figure 5.8 shows the sum of emissions in Figures 5.6 and 5.7, illustrating that the
emission savings from the discharging periods cannot offset the charging periods. Therefore,
storage with capacity of 100 MWh has more emissions. The emissions during storage does not
work, no action, is not including in the chart. Since the periods of storage with no action status
are the same, the amount of emissions is almost the same. For example, when the storage with no
57
action status occurs, the storage needs to be charged, but the wind speed is so small that it cannot
CO2 Emission (ton)
x 10000
provide the required energy to do so.
12
10
oil discharging
8
gas discharging
coal discharging
6
oil charging
4
gas charging
coal charging
2
0
80 MWh
100 MWh
Figure 5.8. Comparison of charging and discharging CO2 emissions in typical week case
Figure 5.9 shows the comparison of energy for charging the storage under different wind
ratings and storage capacities. In this figure, the x-axis is the wind rating and is increased from
90 MW to 120 MW. The curves with different colors are the storage capacities, which are
increased from 80 MWh to 120 MWh. The vertical axis, Y axis, represents the amount of
charging energy in MWh. From Figure 5.9, the curve for the smaller-sized storage is much flatter
than the curve for the larger-sized storage. This is because the smaller storage capacity has less
ability to charge more energy, so the amount of energy used for charging is increased with the
storage capacity.
58
Hundreds
Charging Energy (MWh)
100
90
80
70
60
50
40
30
20
10
0
90
100
110
120
Wind Rating (MW)
80 MWh
90 MWh
100 MWh
110 MWh
120 MWh
Figure 5.9. Comparison of charging energy in typical week case
5.2
Case 5: Typical Year
5.2.1
Typical Year Case Information
In this case, a typical year is the simulation period. There is one wind plant and one
storage device in the test system. For simplicity, one typical year is composed of four typical
weeks. Each week stands for one season, and 672 hours represent a typical year. Figure 5.10
shows the load data for a typical year from the ERCOT website [64]. There are two curves: the
blue line is the total load for the entire ERCOT area, and the red line is the load for the west area.
Both curves show that the loads have a definite distinction by seasons. The summer week has the
largest load, which is mostly over 60,000 MW for the entire area. Loads during the spring week
are the smallest group, which are not over 40,000 MW. Based on this information, in order to set
the working scheme of storage, the influence of seasons must be considered. Although it not easy
to obtain the SPP value for an entire year, these values should be affected by the seasons. Then
59
the discharging time of the peak hours are different by seasons. In this case, the discharging
times are at 7 pm and 8 pm in the spring, 8 pm and 9 pm in the summer, 7 pm and 8 pm in the
fall, and 5 pm and 6 pm in the winter.
70000
2000
1800
60000
1600
1400
1200
Load (MW)
50000
40000
1000
800
600
400
30000
20000
10000
200
0
spring
spring
spring
spring
spring
spring
spring
summer
summer
summer
summer
summer
summer
summer
fall
fall
fall
fall
fall
fall
fall
winter
winter
winter
winter
winter
winter
0
Time (h)
Load_total
Load_west
Figure 5.10. Load data for typical year case
5.2.2
Typical Year Results and Analysis
Figure 5.11 shows a comparison of operating cost under different situations. The wind
rating is increased from 90 MW to 120 MW, as shown on the x-axis. The storage capacity is
increased from 80 MWh to 100 MWh, as shown the curves with different colors. The operating
cost value is the vertical z-axis. It is obvious that the operating cost is decreasing for a specific
amount of capacity storage, dropping down with the increasing wind energy in the power system.
The increasing wind energy and the storage device both contribute to the reduction of operating
cost. Taking a look at Figure 5.11 from left to right by sections, the curves provide information
about the change in operating cost under the same wind rating condition with different storage
capacities. The operating cost rises when the capacity value is increased.
60
x 100000
Operating Cost ($)
609
608.5
608
607.5
607
606.5
606
90
100
110
120
Wind Rating (MW)
80 MWh
100 MWh
Figure 5.11. Comparison of operating costs in typical year case
A comparison of CO2 emissions in a typical year is shown in Figure 5.12. The wind
rating is increased from 90 MW to 120 MW, as shown on the x-axis. The storage capacity is
increased from 80 MWh to 100 MWh, as shown the curves with different colors. The value of
CO2 emissions is the vertical y-axis. For a specific storage, the amount of CO2 emissions is
decreasing when the wind rating is increased because the wind energy reduces the usage of
traditional generation with the help of storage.
61
514000
CO2 Emission (ton)
513800
513600
513400
513200
513000
512800
512600
512400
90
100
110
120
Wind Rating (MW)
80 MWh
100 MWh
Figure 5.12. Comparison of CO2 emissions in typical year case
Figure 5.13 shows the comparison of energy for storage charging under different wind
ratings and storage capacities. In this figure, the x-axis represents the wind rating and is
increased from 90 MW to 120 MW. The curves represent the storage capacities, which are
increased from 80 MWh to 100 MWh. The vertical y-axis, represents the amount of charging
energy in MWh. The amount of charging energy increases when the wind rating is increased for
x 10000
Energy (MWh)
both of these storages.
4
3.5
3
2.5
2
1.5
1
0.5
0
90
110
100
120
Wind Rating (MW)
80 MWh
100 MWh
Figure 5.13. Comparison of charging energy in typical year case
62
The locations of storage under different situations for the typical year base are shown in
Table 5.2. Here the horizontal numbers on top show the capacity of storage, 80 MWh and 100
MWh. The vertical numbers on the left show the wind rating, from 90 MW to 120 MW. The
numbers within the table are bus numbers, indicating the desired locations. As can be seen, all
storage locations are found in the high-voltage level.
TABLE 5.1
EES LOCATION RECORD FOR TYPICAL YEAR CASE
80 MWh 100 MWh
5.3
90 MW
15
16
100 MW
17
17
110 MW
19
18
120 MW
18
18
Case 6: Market Factor
5.3.1 Market Factor Case Information
In this case, the market factor is considered. By analyzing the day-ahead market, such as
in the typical week case, the day-ahead SPP values provide a reference for setting the working
scheme of storage. For example, a certain price value is selected based on the day-ahead market.
The storage is charging when the price is below this value and discharging when the price is
above this value; hence, a benefit will be produced. This benefit can be seen as a reduction of the
operating cost. In this case, as shown in Figure 5.14, $65 is selected as the bounded line, as
indicated in red in this figure. During the periods below this red line, the storage is charging, and
during the periods above this red line, the storage is discharging, as shown in Table 5.1. The rest
of time is for charging. The benefit from considering the market factor is that it reduces the
63
operating cost and influences the storage. All other data are the same as the typical week case. A
comparison is presented in Section 5.4.2.
250
150
100
50
0
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
1:00
7:00
13:00
19:00
SPP ($)
200
Mon, May Tue, May 06 Wed, May Thu, May 08 Fri, May 09 Sat, May 10 Sun, May 11
05
07
Time (h)
SPP
bounded line
Figure 5.14. Settlement point prices and bounded line in market factor case
TABLE 5.2
DISCHARGING TIMES FOR MARKET FACTOR CASE
Date
Discharging Time
Monday
13:00–20:00
Tuesday
14:00–19:00
Wednesday
13:00–18:00
Thursday
15:00–19:00
Friday
11:00–21:00
Saturday
14:00–20:00
Sunday
16:00–20:00
64
5.3.2
Market Factor Results and Analysis
For this case, the optimal location of EES unit and the operating cost under different
situations are known. Utilizing this information, the market factors are introduced. Figure 5.15
shows the comparison of operating cost when the wind rating is 90 MW and the storage capacity
is 100 MWh. The before data is the operating cost data from the typical week case, while the
after data is the operating cost considering the market factor. As can be seen, there is a great
reduction between these two cases. A similar situation occurred when the wind rating is 100 MW
and the storage capacity is 110 MWh, as shown in Figure 5.16. In both of these cases, the
operating cost after considering the market factor is much lower, even smaller than for all storage
location selections.
The information from this case shows that utilization of the market factor with the storage
system will greatly reduce the operating cost. There may be other potential ways to fully utilize
Operating Cost ($)
x 10000
market factors in order to improve the economics of the power system.
1490
1480
1470
1460
Operating Cost
1450
1440
1430
1420
Before
After
Figure 5.15. Operating costs (wind 90 MW and storage 100 MWh) in market factor case
65
x 10000
Operating Cost ($)
1490
1485
1480
1475
1470
1465
Operating Cost
1460
1455
1450
1445
1440
1435
Before
After
Figure 5.16. Operating costs (wind 100 MW and storage 110 MWh) in market factor case
66
CHAPTER 6
CONCLUSIONS AND FUTURE WORK
6.1
Conclusions
This research developed a general procedure to optimize the location of electrical energy
storage units in a power system with renewable energy. In order to have more credible results, a
stochastic method—point estimation method—was applied in this model. Also, the improved 2m
PE method and genetic algorithm method were investigated to make the calculation more
efficient. At the same time, optimal power flow incorporated with the price of CO2 were
considered in order to meet environmental policies. The core optimization problems in this
dissertation were solved by using the MATPOWER simulation tool, which permits users to have
full authority for modifying or adding variables, constraints, costs, objective functions, etc.
Several cases were presented to show the performances of EES units under different conditions.
The observations and conclusions are summarized as follows:

Both wind rating and storage capacity impact the performance of EES units and their
location.

Congestion in the power system is the main constraint to storage capacity.

The optimal locations of EES units are dependent on several factors and specific
conditions of the power system. These factors are the working pattern of storage devices,
the desired objective of the optimization, and limitations of transmission line.

Generally speaking, large-capacity storage is preferably located in the high-voltage part
of a transmission system, where has a larger capacity.

To schedule the storage working patterns appropriately, it is critical to make EES units
that better impact the power system.
67

The cost of EES units also produces an impact on its performance in the power system
with renewable energy.

Considering market factors and utilizing them to schedule the storage working pattern
can also benefit the entire power system.

Considering market factors can eventually impact the location of the EES and reduce the
operating cost.

With the help of EES units, CO2 emissions and operating costs are greatly reduced. These
factors are also impacted by the working scheme of the EES units.
6.2
Future Work
According to the conclusions in this research, several issues are recommended as future
work:

Apply this method to a real power system with more renewable energy and practical
parameters, such as a power system from CAISO, WECC, or ERCOT, in order to analyze
the performance of EES units under different situations.

Investigate the performance of EES units with more detailed parameters, such as the
ramp rate cost.

Investigate how effective the EES units will be in meeting the latest requirements from
the Clean Power Plan proposed rule, which was released in June, 2014.

Add more renewable variables and load variables as inputs, in order to analyze the
influences to a power system.

Add more practical parameters, such as capacity factors, to other types of generators.

Apply other stochastic models to simulate the renewable energy and compare the
different models’ performances on simulating the uncertainty of natural resources.
68

Compare the performances of other types of EES units in a power system with renewable
energy.

Consider the EES model with more and practical market models in order to verify the
real value of EES units in power markets.

Combine the proposed method used in this research with other generation or transmission
planning work in order to analyze the influences from EES units to a planning work.
69
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76
APPENDIXES
77
APPENDIX A
209.7
x 10000
x 10000
OPERATING COST FIGURES FOR LIMITED-CAPACITY CASE
209.68
209.66
209.7
209.65
209.64
209.6
209.62
209.55
209.6
209.5
209.58
209.56
209.45
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Operating Cost
Operating Cost
Figure A.2. Wind rating of 70 MW
209.65
x 10000
x 10000
Figure A.1. Wind rating of 60 MW
209.6
209.56
209.54
209.52
209.55
209.5
209.5
209.48
209.46
209.45
209.44
209.4
209.42
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Operating Cost
Operating Cost
Figure A.3. Wind rating of 80 MW
Figure A.4. Wind rating of 90 MW
78
209.55
x 10000
x 10000
APPENDIX A (continued)
209.5
209.45
209.5
209.45
209.4
209.4
209.35
209.35
209.3
209.3
209.25
209.25
209.2
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Operating Cost
Operating Cost
Figure A.6. Wind rating of 110 MW
209.45
209.4
209.35
209.3
209.25
209.2
209.15
209.1
209.05
x 10000
x 10000
Figure A.5. Wind rating of 100 MW
209.4
209.35
209.3
209.25
209.2
209.15
209.1
209.05
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Operating Cost
Operating Cost
Figure A.7.Wind rating of 120 MW
Figure A.8. Wind rating of 130 MW
79
209.22
x 10000
x 10000
APPENDIX A (continued)
209.2
209.18
209.2
209.15
209.16
209.1
209.14
209.05
209.12
209
209.1
209.08
208.95
80
90
80
100 110 120 130
Storage Capacity (MWh)
Operating Cost
x 10000
x 10000
Figure A.10. Wind rating of 150 MW
209.15
209.1
209.05
209.1
209.05
209
209
208.95
208.95
208.9
208.9
208.85
208.85
90
100 110 120 130
Operating Cost
Figure A.9. Wind rating of 140 MW
80
90
Storage Capacity (MWh)
208.8
100 110 120 130
80
Storage Capacity (MWh)
90
100 110 120 130
Storage Capacity (MWh)
Operating Cost
Operating Cost
Figure A.11. Wind rating of 160 MW
Figure A.12. Wind rating of 170 MW
80
209
x 10000
x 10000
APPENDIX A (continued)
208.95
208.9
208.9
208.85
208.85
208.8
208.8
208.75
208.75
208.7
80
90
100 110 120 130
80
Storage Capacity (MWh)
Figure A.14. Wind rating of 190 MW
208.9
208.85
208.8
208.75
208.7
208.65
90
100 110 120 130
Operating Cost
Figure A.13. Wind rating of 180 MW
80
90
Storage Capacity (MWh)
Operating Cost
x 10000
208.95
100 110 120 130
Storage Capacity (MWh)
Operating Cost
Figure A.15. Wind rating of 200 MW
81
APPENDIX B
500
500
400
400
Energy (MWh)
Energy (MWh)
CHARGING ENERGY FIGURES FOR LIMITED-CAPACITY CASE
300
200
100
0
300
200
100
0
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Energy
Energy
Figure B.2. Wind rating of 60 MW
500
500
400
400
Energy (MWh)
Energy (MWh)
Figure B.1.Wind rating of 50 MW
300
200
100
0
300
200
100
0
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Energy
Energy
Figure B.3. Wind rating of 70 MW
Figure B.4. Wind rating of 80 MW
82
500
500
400
400
Energy (MWh)
Energy (MWh)
APPENDIX B (continued)
300
200
100
0
300
200
100
0
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Energy
Energy
Figure B.6. Wind rating of 100 MW
500
500
400
400
Energy (MWh)
Energy (MWh)
Figure B.5. Wind rating of 90 MW
300
200
100
0
300
200
100
0
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Energy
Energy
Figure B.7. Wind rating of 110 MW
Figure B.8. Wind rating of 120 MW
83
500
500
400
400
Energy (MWh)
Energy (MWh)
APPENDIX B (continued)
300
200
100
0
300
200
100
0
80 90 100 110 120 130 140 150
80
Storage Capacity (MWh)
90
110
120
130
Storage Capacity (MWh)
Energy
Energy
Figure B.9. Wind rating of 130 MW
Figure B.10. Wind rating of 140 MW
500
500
400
400
Energy (MWh)
Energy (MWh)
100
300
200
100
0
300
200
100
0
80
90
100
110
120
130
80
Storage Capacity (MWh)
90
100
110
120
130
Storage Capacity (MWh)
Energy
Energy
Figure B.11. Wind rating of 150 MW
Figure B.12. Wind rating of 160 MW
84
500
500
400
400
Energy (MWh)
Energy (MWh)
APPENDIX B (continued)
300
200
100
0
300
200
100
0
80
90
100
110
120
130
80
Storage Capacity (MWh)
90
110
120
130
Storage Capacity (MWh)
Energy
Energy
Figure B.13. Wind rating of 170 MW
Figure B.14. Wind rating of 180 MW
500
500
400
400
Energy (MWh)
Energy (MWh)
100
300
200
100
0
300
200
100
0
80
90
100
110
120
130
80
Storage Capacity (MWh)
90
100
110
120
130
Storage Capacity (MWh)
Energy
Energy
Figure B.15. Wind rating of 190 MW
Figure B.16. Wind rating of 200 MW
85
APPENDIX C
20.88
x 100000
x 100000
OPERATING COST FIGURES FOR MULTIPLE WIND PLANT CASE
20.875
20.87
20.865
20.86
80 90 100 110 120 130 140 150
20.864
20.862
20.86
20.858
20.856
20.854
20.852
20.85
20.848
20.846
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Operating Cost
Figure C.1. Wind rating of 50 MW
Figure C.2. Wind rating of 60 MW
20.85
20.84
x 100000
x 100000
Operating Cost
20.845
20.835
20.84
20.83
20.835
20.825
20.83
20.82
20.825
20.815
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Operating Cost
Operating Cost
Figure C.3. Wind rating of 70 MW
Figure C.4. Wind rating of 80 MW
86
20.83
x 100000
x 100000
APPENDIX C (continued)
20.825
20.82
20.815
20.81
20.805
20.812
20.81
20.808
20.806
20.804
20.802
20.8
20.798
20.796
80 90 100 110 120 130 140 150
80
Storage Capacity (MWh)
100 110 120 130
Storage Capacity (MWh)
Operating Cost
Operating Cost
Figure C.5. Wind rating of 90 MW
Figure C.6. Wind rating of 100 MW
20.81
x 100000
x 100000
90
20.805
20.8
20.79
20.785
20.795
20.78
20.79
20.775
20.785
20.77
20.78
20.775
20.765
80
90
80
100 110 120 130
Storage Capacity (MWh)
90
100 110 120 130
Storage Capacity (MWh)
Operating Cost
Operating Cost
Figure C.7. Wind rating of 110 MW
Figure C.8. Wind rating of 120 MW
87
APPENDIX D
500
500
400
400
Energy (MWh)
Energy (MWh)
CHARGING ENERGY FIGURES FOR MULTIPLE WIND PLANT CASE
300
200
100
0
300
200
100
0
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Charging Energy
Charging Energy
Figure D.2. Wind rating of 60 MW
500
500
400
400
Energy (MWh)
Energy (MWh)
Figure D.1. Wind rating of 50 MW
300
200
100
0
300
200
100
0
80 90 100 110 120 130 140 150
80 90 100 110 120 130 140 150
Storage Capacity (MWh)
Storage Capacity (MWh)
Charging Energy
Charging Energy
Figure D.3. Wind rating of 70 MW
Figure D.4. Wind rating of 80 MW
88
APPENDIX D (continued)
400
Energy (MWh)
Energy (MWh)
500
300
200
100
0
400
350
300
250
200
150
100
50
0
80 90 100 110 120 130 140 150
80
Storage Capacity (MWh)
Energy (MWh)
Energy (MWh)
110
120
130
Figure D.6. Wind rating of 100 MW
400
350
300
250
200
150
100
50
0
100
110
Charging Energy
Figure D.5. Wind rating of 90 MW
90
100
Storage Capacity (MWh)
Charging Energy
80
90
120
400
350
300
250
200
150
100
50
0
80
130
90
100
110
120
130
Storage Capacity (MWh)
Storage Capacity (MWh)
Charging Energy
Charging Energy
Figure D.8. Wind rating of 120 MW
Figure D.7. Wind rating of 110 MW
89
APPENDIX E
148.5
x 100000
x 100000
OPERATING COST FIGURES FOR TYPICAL WEEK CASE
148.4
148.3
148.2
148.1
148
80
90
100
110
148.35
148.3
148.25
148.2
148.15
148.1
148.05
148
147.95
120
80
Storage Capacity (MWh)
Operating Cost
100
110
120
Operating Cost
Figure E.1. Wind rating of 90 MW
Figure E.2. Wind rating of 100 MW
148.4
x 100000
x 100000
90
Storage Capacity (MWh)
148.3
148.2
148.4
148.3
148.2
148.1
148.1
148
148
147.9
147.9
147.8
147.8
147.7
80
90
100
110
120
80
Storage Capacity (MWh)
90
100
110
120
Storage Capacity (MWh)
Operating Cost
Operating Cost
Figure E.3. Wind rating of 110 MW
Figure E.4. Wind rating of 120 MW
90