1. business and industrial
2. business operations
3. management
4. project management

ANALYSIS AND SIMULATION OF A STATE-SPACE BASED
BATTERY ENERGY STORAGE SYSTEM
A Project
Presented to the faculty of the Department of Electrical and Electronic Engineering
California State University, Sacramento
Submitted in partial satisfaction of
the requirements for the degree of
MASTER OF SCIENCE
in
Electrical and Electronic Engineering
by
Xiaojun Feng
SPRING
2015
© 2015
Xiaojun Feng
ALL RIGHTS RESERVED
ii
ANALYSIS AND SIMULATION OF A STATE-SPACE BASED
BATTERY ENERGY STORAGE SYSTEM
A Project
by
Xiaojun Feng
Approved by:
__________________________________, Committee Chair
Mahyar Zarghami, Ph.D.
__________________________________, Second Reader
Preetham Kumar, Ph.D.
____________________________
Date
iii
Student: Xiaojun Feng
I certify that this student has met the requirements for format contained in the University
format manual, and that this project is suitable for shelving in the Library and credit is to
be awarded for the project.
__________________________, Graduate Coordinator
Preetham Kumar, Ph.D.
Department of Electrical and Electronic Engineering
iv
___________________
Date
Abstract
of
ANALYSIS AND SIMULATION OF A STATE-SPACE BASED
BATTERY ENERGY STORAGE SYSTEM
by
Xiaojun Feng
Statement of Problem
Power systems are transitioning into a new era by replacing fossil sources of energy with
renewable resources. Due to factors such as intermittent nature of renewable, application
of energy storage systems such as Battery Energy Storage Systems (BESS) will be
expanded in the coming years in order to smooth the variability of generation associated
with renewable. The BESS can be applied in modern power grids, and it can
economically shave the peak-load to prevent energy loss. As a result, it is essential to
understand the operational behavior and control requirements of BESS. This project is a
continuation of a previous work based on a state-space model for a bidirectional AC/DC
converter and a bidirectional DC/DC converter for charging and discharging of batteries.
It is desired that the system containing converters and batteries will be able to control the
active power, reactive power, and the DC link voltage independently. This project will
v
focus on integration of the state-space model(s) of batteries with bidirectional AC/DC and
DC/DC converters in order to form a unified state-space model with charging/discharging
modes.
Sources of Data
The simulation are done using Simulink toolbox under Matlab, and the models of
batteries are from several published research papers.
Conclusions Reached
Simulated a BESS using state-space based model with a Thevenin battery model by using
AC/DC converter and DC/DC bidirectional converter, and controlled the system
parameters with two control methods.
_______________________, Committee Chair
Mahyar Zarghami, Ph.D.
_______________________
Date
vi
ACKNOWLEDGEMENTS
I have taken efforts in this project; However, it would not have been possible without the
kind support and help of the following people: my advisors, family and friends. I would
like to extend my sincere thanks to all of them.
I am highly indebted to Dr. Mahyar Zarghami, for his guidance and encouragement. He
provided necessary information regarding the project and offered me constant supervision
on the completion of the project.
I would like to express my thanks to Dr. Vaziri and Dr. Kumar for spending time on
reading my report and providing me with guidance.
Finally, I would like to thank my family and friends, who provided me support at any
time. The accomplishment of the project would not have been possible without them.
vii
TABLE OF CONTENTS
Page
Acknowledgements .................................................................................................... vii
List of Tables ................................................................................................................. x
List of Figures ............................................................................................................. xi
Chapter
1. INTRODUCTION .................................................................................................. 1
1.1. Background of the Project ......................................................................... 1
1.2. Advantages of Battery Energy Storage System ......................................... 2
1.3. Goal of the Project ..................................................................................... 2
1.4. Layout of Paper ...........................................................................................3
2. BATTERIES IN ENERGY STORAGE SYSTEMS ................................................ 4
2.1. Different types of Batteries ........................................................................ 4
2.2. Different Electrical Models of Batteries .................................................... 5
2.3. Battery Type and Model of the Project ...................................................... 7
3. STATE-SPACE MODELING OF BATTERY ENERGY STORAGE SYSTEM .... 8
3.1. Overview of BESS Model ......................................................................... 8
3.2. DC/DC Converter ...................................................................................... 9
3.3. AC/DC Rectifier....................................................................................... 13
3.4. State Space Modeling Function ............................................................... 14
viii
4. CONTROL METHODS OF THE BESS…………………………………………... 16
4.1. Control of Active Power…………………………………………… ……...16
4.2. Control of Reactive Power and DC-Link Voltage ……………… ………...17
5. SIMULATION RESULTS ……………………...…………………..………………20
5.1. Auto Switching of Battery Charging/Discharging Mode………… ……….20
5.2. Results of Active Power, Reactive Power and DC-link Voltage………….. 21
5.3. Analysis on Control of DC-link Voltage …………………………………...23
6. CONCLUSIONS AND FUTURE WORK ………………..………………………...27
References……………………………………………………………………….………28
ix
LIST OF TABLES
Tables
Page
1.
Values of System Parameters………………………………….………………20
2.
Different Values of Cdc …………………………………………..……………23
x
LIST OF FIGURES
Figures
Page
1.
Simple Battery Model…………………………………………………………… 5
2.
Thevenin Battery Model………………………………………………………… 6
3.
Fourth Order Dynamic Model ………………………………………………….. 6
4.
Schematic diagram of Battery Energy Storage System ….…….……………...... 9
5.
Schematic diagram of the DC/DC converter in Discharge mode………………..10
6.
Schematic diagram of the DC/DC converter in charge mode……………………11
7.
Schematic diagram of Voltage Oriented Control[2] ……..……………………….18
8.
Curves of SOC …………………………………………………….……………..21
9.
Curves of Active Power.…………………………………………………………22
10.
Curves of Reactive Power ………………………………………………………22
11.
Curves of DC-link Voltage ……………………………………………………...23
12.
Curve of DC-link Voltage with Cdc(
) = 0.05..………………….……………..24
13.
Curve of DC-link Voltage with Cdc(
) = 0.5………………….………………..24
14.
Curve of DC-link Voltage with Cdc(
) = 5……………………………………..25
15.
Curve of DC-link Voltage with Cdc(
) = 50……..……………………………..25
xi
1
CHAPTER 1
INTRODUCTION
1.1. Background of the Project
Traditionally, fossil Fuels, such as coal, oil and natural gas, have been the main energy
source for human beings’ social and economic development. With characteristics of
convenience, low cost, safety and controllability, fossil fuels have been the major source
of global energy for a long time. In the power industry, generation by burning coal
thermal power plants occupy the first place of world electricity generation. However,
fossil fuels are non-renewable energy sources, which can take millions of years to
regenerate, and their speed of consumption is much faster than their rate of formation.
Moreover, it costs billions of dollars every year for the whole world to prevent the
pollution caused by fossil fuels. Based on the shortage of fossil fuel sources, and the
ecological pollution caused by fossil fuels, they need to be gradually replaced by clean
sources, such as solar, wind and hydro energy. Compared to traditional energy sources
(fossil fuels), new energy sources are renewable, non-exhaustible and bring less pollution
to our environment. With these advantages, renewable resources are becoming more
popular all over the world. However, renewable energies are intermittent in nature, and
are difficult to predict and control. For example, the total amount of wind power
generation in 2011 was 70.6 billion kWh, in which more than 10 billion kWh was wasted
[1]
because the generation could not be stored. Therefore, energy storage systems, such as
2
batteries will be an important topic for improving energy efficiency, stability and
reliability in modern power systems.
1.2. Advantages of Battery Energy Storage System
Due to the rapid depletion of traditional fossil fuels and their environmental constraints,
energy generated by renewable resources has become more popular. However, renewable
energy is hard to control, predict and store. Therefore, applications of battery energy
storage systems are increasingly applied in smart grids. On the power generation side,
battery energy storage systems can help with improvement and stability of the generation
of renewable, and hence enhancement of the grid operations. On the load side, battery
energy storage systems can effectively smooth the fluctuations of the load profile, and
can support the system during loss of energy. With the application of BESS, utilization of
energy can be improved effectively. Based on these aspects, BESS will have a very
important and indispensable role in the power grid of the near future.
1.3. Goal of the Project
With increased application of battery energy storage systems, more research and
development projects are necessary for understanding the control requirements of the
BESS in the future grid. As a continuation of the previous work which presented a model
of battery energy storage system with bidirectional AC/DC and DC/DC converters, this
project intends to extend the previous work[2] by including the model of a battery in an
integrated state-space based model for the whole BESS. With the provided state-space
3
model, charging and discharging of BESS can be simulated using Matlab/Simulink.
Control schemes, based on voltage oriented control (VOC)[4] and sliding mode control[6]
are used in the project in order to control the DC link voltage between AC/DC converter
and DC/DC converter, and the active and reactive powers injected/absorbed to/from the
system.
1.4. Layout of the Paper
In this project, first a proper electrical model for the battery is selected in order to
represent the battery as close as possible to its actual conditions. Then the selected battery
model is integrated with the proposed battery energy storage system model[2] which is
based on state-space equations. In the following, charging and discharging conditions of
the system are simulated and analyzed, and control methods are utilized for regulating the
DC link voltage as well as active power and reactive powers. The project description is
organized as follows: The behavior of different types of batteries and their models are
introduced in chapter 2; Detailed model of the battery energy storage system based on
state-space modeling method is presented in chapter 3; Then in chapter 4, the control
methods for DC link voltage, and active and reactive powers are presented; The
simulation results of the system are presented in chapter 5; and lastly, concluding remarks
are brought in chapter 6.
4
CHAPTER 2
BATTERIES IN ENERGY STORAGE SYSTEMS
2.1. Different Types of Batteries
Different types of batteries have different characteristics, some of them might be
designed for small applications, and their energy cannot last for a long time; while some
of them may be used for higher energy levels and bigger size. In this part of the paper,
we list three types of batteries (Nickel Cadmium, Lead Acid and Lithium Ion) that are
commonly used in battery energy storage systems.
Nickel Cadmium(NiCd) battery: NiCd battery is a mature battery that has been used for
a long time in some applications, such as biomedical equipment and video cameras. The
NiCd battery contains toxic metals and is environmentally unfriendly with lower energy
density compared to some newer types of batteries[8].
Lead Acid battery: As the most economical battery type, the lead acid battery is widely
used for hospital equipment and emergency lighting system. The poor weight-to-energy
density is among the biggest problem for lead acid battery[8].
Lithium Ion(Li-ion) battery: Li-ion battery is the fastest growing battery type with high
energy density. Compared to NiCd and lead acid batteries, the Li-ion battery does not
5
discharge when not utilized, and does not have memory, but the price of Li-ion battery is
higher than other types of batteries[8].
2.2. Different Electrical Models of Batteries
In this section, we will introduce several different types of electrical battery models[3] in
order to find out the proper battery model to be used for this project.
Simple Battery Model, as Figure 1 shows, is the most commonly used battery model, and
consists of an ideal voltage source with open circuit voltage
, and an internal resistance
connected in series with the voltage source. This model is only suitable in some
simple circuit simulations, and its state of charge cannot be clearly expressed.
R0
Vbat
E0
Figure 1. Simple Battery Model
Another commonly used battery model is the Thevenin battery model, which is shown in
Figure 2. This model has a voltage source
another resistance
and internal battery resistance
in parallel with a capacitance
.
, and
6
Ct
R0
Rt
Vbat
E0
Figure 2. Thevenin Battery Model
Figure 3 shows a Fourth Order Dynamic Battery, which provides a complicated but
accurate model for simulations. However, its simulation requires more computational
time due to its high order and its modeling requires proper knowledge of numerous
empirical data.
Cd
Cw
Rw
Rd
Rp
Rs
Ep
Vbat
Es
Figure 3. Fourth Order Dynamic Model
7
2.3. Battery Type and Model of the Project
For electrical modeling in this project, we select Thevenin battery model, since it can
successfully fulfill our purpose of simulation for this project.
8
CHAPTER 3
STATE-SPACE MODELING OF BATTERY ENERGY STORAGE SYSTEM
3.1. Overview of the BESS Model
In this project, the battery energy storage system (BESS) includes four major parts:
AC grid side, AC/DC rectifier, DC/DC converter and battery as shown in Figure 4.
AC/DC rectifier is connected through
which represents the combined inductance
of the transformer and line on the grid side, and it is assumed that the grid side
resistance is negligible. The DC/DC converter is directly connected to the battery
model. The AC/DC rectifier is connected to the DC/DC converter through a DC-link,
with capacitor
in parallel with a resistance
which represents DC link losses.
The DC-link capacitor also works as part of the bidirectional DC/DC converter which
can charge and discharge the battery. Detailed explanation will be presented in the
coming sections.
9
DC/DC
iabc
Pac
Lac
idc
+
+
Q
ir
D1
ic
S1
ibat
+
Rdc
eabc
Grid
Vabc
Vdc
R0
Cdc
AC/DC
Ldc
D2
-
Rt
S2
Pdc
Ct
E0
-
Figure 4. Schematic diagram of the Battery Energy Storage System
3.2. DC/DC Converter
In order to achieve the discharging and charging modes of the battery, the DC/DC
converter must be bidirectional. The bidirectional DC/DC converter consists of an
inductance
, a capacitance
, two diodes D1 and D2 with two switches S1 and S2, as
shown in the DC/DC converter part in Figure 4.
10
D1
S1
D1
S1
Vdc
Vbat
D2
Vdc
Vbat
S2
0 < t < d.T
D2
S2
d.T < t < T
Vbat = (1-d)Vdc
Figure 5. Schematic diagram of the DC/DC converter in discharge mode[2]
As show in Figure 5, S1 is kept open in the discharging mode of the battery, and S2 switch
opens and closes by the duty ratio d (0<d<1). T is the time period that S2 switches. When
0 < t < d.T, S2 is closed, and we have:
(1)
When dT < t < T, S2 is opened, and we have:
(2)
We notice that after the system reaches steady state, the average of current through
inductance
should be constant. Therefore, we have:
(3)
Integrating both sides of (3), and rewriting the equation in terms of
, we get:
11
(4)
D1
D1
S1
S1
Vdc
Vdc
Vbat
D2
Vbat
S2
0 < t < d’.T
D2
S2
d’.T < t < T
Vbat = d’.Vdc
Figure 6. Schematic diagram of the DC/DC converter in charge mode[2]
As shown in Figure 6, in battery charging mode, S2 keeps open and S1 switches.
Assuming the duty ratio in charging mode is d’, when 0 < t < d’.T, S1 is closed, then we
have:
(5)
When d’T < t < T, S1 is open, and we have:
(6)
Same as discharging mode, we can have:
(7)
12
Integrating both sides of (7), and writing the equation in terms of
, we can get:
(8)
Comparing equations (4) and (8), for having the same duty ratio in the charging and
discharging modes of the DC/DC converter, we set:
(9)
Then we can write both equations (4) and (8) as:
(10)
Assuming the DC/DC converter to be lossless, we can express the relation between
and
in steady-state as:
(11)
13
3.3. AC/DC Rectifier
On the grid and AC/DC converter side, through KVL we get:
(12)
Assuming the AC/DC converter to be lossless, and equalizing the power on the two
sides, we can get:
(13)
Assuming the DC/DC converter to be lossless, power will be the same on its both sides.
As a result:
(14)
Transforming the abc stationary reference frame in the above equations to the dq
reference frame rotating at synchronous speed we get[4]:
(15)
Where
.
Equation (12) can be written in the dq reference frame as:
(16)
(17)
14
Neglecting the harmonics and assuming a sinusoidal pulse width modulation of the
AC/DC converter,
and
can be written as:
(18)
(19)
where k and
are modulation amplitude and angle, respectively.
By substituting (18) and (19) into (16) and (17), we get:
(20)
(21)
We can also rewrite equation (13) by transforming the stationary abc reference frame to
the rotating dq frame, and as a result:
(22)
3.4. State Space Modeling Function
In this project, by using the Thevenin battery model, we find five state variables for the
battery energy storage system, including
inside the Thevenin battery model
,
,
,
and the voltage of the capacitor
, which is related to the battery’s current through
the following differential equation:
(23)
where
is the voltage of the voltage source inside the Thevenin battery model. The
differential equation for
is written as:
15
(24)
In summary, we can express equations (20) to (24) in state-space form as follows:
(25)
where:
(26)
(27)
(28)
(29)
(30)
(31)
16
CHAPTER 4
CONTROL METHODS OF THE BESS
In this project, we use two control methods to control the DC link voltage, active power
and reactive power in the system. Based on the state-space modeling introduced in
chapter 3, our system is an affine system which can be controlled by unified nonlinear
methods to control all desired outputs simultaneously[5]. In this project, however, we
separate the control of active power from the control of DC link voltage and reactive
power. Active power of the system is controlled through the duty ratio of the DC/DC
converter by using a sliding mode control method
[6]
, and DC link voltage and reactive
power are controlled through modulation of the AC/DC rectifier using voltage oriented
control[4] (based on linear PI controllers).
4.1. Control of Active Power
We use sliding mode control method to control the duty ratio d of the DC/DC converter
in the system. Assuming the DC/DC converter to be lossless, the desired active power to
be injected into BESS can be written as:
(32)
where
is the desired current of the battery,
is the desired voltage of the battery, and
is the desired DC-link voltage,
is the desired active power on the AC side.
17
In the sliding mode control method [6], the convergence factor
value of a variable
to be close to its desired value
is used to control the
, as the equation shows below:
(33)
By the following equation, we have the ability to control the value of battery current as:
(34)
By applying equation (4) in chapter 3 to the above equation, the duty ratio can be found
as:
(35)
4.2. Control of Reactive Power and DC-Link Voltage
In this project, we use Voltage Oriented Control (VOC) method based on
the reactive power
and the DC-link voltage
diagram of the VOC method.
[4]
to control
, and Figure 7 shows the schematic
18
va vZac
vb Zac
AC/DC
vc
idc
DC/DC
&
Battery
vdc
ia
ea
ib
eb
ic
ec Grid
θ = wt+θ0
k
α
abc/dq
function
vd*
vq*
PI
PI
id iq vd
vq
id*
iq*
PI

vdc
v*dc
-1.5
Q*
Figure 7. Schematic diagram of Voltage Oriented Control[2]
~
19
By assuming
in the dq reference frame (taking the angle of grid voltage as the
reference), we get
. Then using the following equations we can find the active and
reactive powers on the AC side as:
(36)
(37)
Assuming
(the max value of grid voltage) to be constant, from equations (36) and
(37), we can see that the active and reactive powers can be related with the changes of
and
, respectively. As seen in Figure 7, PI controllers are applied for controlling
(through control of
) and .
20
CHAPTER 5
SIMULATION RESULTS
The battery energy storage system is simulated in Matlab/Simulink, and the results of
simulation are presented in the following. Parameters of the systems are shown in Table 1.
Parameter
Value
Parameter
Value
R(
Lac (mH)
0
0.1098
ed(V)
eq(V)
163.2993
0
Rdc(
Cdc(
)
0.05
Rb (
0.0207
f(Hz)
Ldc(mH)
Ct( )
60
0.755
50
Vdc(V)
800
E0(V)
1800
400
Rt(
0.007
Table 1. Values of System Parameters
Initial values of k, , id, iq, d and Vt, are found based on an initial state of charge of 50%
for the battery and by using KCL, KVL. As a result, these values are calculated as: k0 =
0.5353,
0
= -0.0351, id0 = -163.5606, iq0 = 81.6497, d0 = 0.75, vt0 = -204.14.
5.1. Auto Switching of Battery’s Charging/Discharging Mode
In order to control the charging and discharging modes of the battery, we add a function
to calculate the state of charge (SOC) of the battery. When the SOC is below 20%, an
active power of 40 kW is injected into the battery, and when the SOC is above 80%, the
direction of the injected active power will be reversed with the same magnitude. By
setting the initial state of charge of the battery to 50%, Figure 8 shows the state of charge
during the simulation time from 0 to 0.2 seconds.
21
Figure 8 Curves of SOC
5.2. Results of Active Power, Reactive Power and DC-link Voltage
As the SOC changes, results of the active power are shown in Figure 9. As can be seen,
the active power stays positive when battery is in charging mode, and becomes negative
in discharging mode.
Figure 9 Curves of Active Power
22
Meanwhile, the reactive power is fixed at 20 kVar as shown in Figure 10. It was noticed
that controlling reactive power to different settings was accomplished very well.
Moreover, reactive power changes would not impact active power or DC-link voltage in
the simulations.
Figure 10 Curves of Reactive Power
As part of our design, we need to control the DC-link voltage to stay close to 800 V (the
initial value of
). Figure 11 shows the simulation result of the DC-link voltage, and as
can be seen the voltage stays around 800 V, with small variations around the desired
value.
23
Figure 11 Curves of DC-link Voltage
5.3. Analysis on Control of DC-link Voltage
Different curves of the DC-link voltage with respect to different values of the DC-link
capacitor (Table 2) are shown in Figure 12 through Figure 15.
Cdc(
) = 0.05
Figure 12
Cdc(
) = 0.5
Figure 13
Cdc(
)=5
Figure 14
Table 2. Different Values of Cdc
Cdc(
) = 50
Figure 15
24
Figure 12 Curve of DC-link Voltage with Cdc(
Figure 13 Curve of DC-link Voltage for Cdc(
) = 0.05
) = 0.5
25
Figure 14 Curve of DC-link Voltage for Cdc(
)=5
Figure 15 Curve of DC-link Voltage for Cdc(
) = 50
As we can see from Figure 12 to Figure 15, with the value of Cdc(
) increasing from
0.05 to 50 in steps of 10 times, the curves of DC-link voltage become more stable and
very close to 800 volts. When Cdc = 0.05
, the value of DC-link voltage is changing
26
between 793 volts and 816 volts as the state of charge changes, and when Cdc = 50
the value of DC-link voltage almost stays at 800 volts. This is an indication that the
state-space based battery energy storage system can regulated the DC-link voltage
correctly based on the characteristics of the circuit.
,
27
CHAPTER 6
CONCLUSIONS AND FUTURE WORK
As the continuation of the previous work [2], this project presents a detailed battery energy
storage system which contains an AC/DC voltage source converter and a DC/DC
bidirectional converter. By applying state-space modeling, the project successfully
simulated the battery energy storage system considering the control of the DC link
voltage, active power and reactive powers by using sliding mode control and voltage
oriented control methods. The previous work [2] used only four state variables to develop
the simulation of the battery energy storage system. In this project, however, a dynamic
model for battery was presented, which resulted in five state variables by adding the
voltage of the capacitor in the Thevenin battery model as an extra state. With these five
states, the function of the BESS model behaves correctly in both charging and
discharging modes. Moreover, with the application of Thevenin battery model in BESS,
the behavior of this system is closer to real conditions in the field.
Nowadays, as the utilization of renewable resources, such as wind and solar power is
increasing, battery energy storage systems can provide proper functionalities to alleviate
variations of power generation associated with them. Therefore, future projects could
focus on combined application of BESS alongside with renewable-energy generation, in
order to reduce the impacts of generation intermittency and uncertainty.
28
REFERENCES
[1] X. Xiu, B. Li, “Study on Energy Storage System Investment Decision Based on
Real Option Theory”, IEEE international conference on sustainable power
generation and supply (SUPERGEN), Sep. 8-9, 2012
[2] Dongyi Zhang, Mahyar Zarghami, Tao Liang, Mohammad Vaziri, “A State-Space
Based Model for Integration of Battery Energy Storage System”, IEEE, 2014
[3] H.L. Chan, D. Sutanto, “A New Battery Model for use with Battery Energy
Storage Systems and Electric Vehicles Power Systems”, IEEE, 2000
[4] P. C. Krause, O. Wasynczuk, S. D. Sudhoff, ”Analysis of Electric Machinery and
Drive Systems”, 2nd Edition, 2002, ch 3.
[5] Q. Lu, Y. Sun, S. Mei, ”Nonlinear Control Systems and Power System
Dynamics”, Kluwer Academic Publishers, 2001, ch 2.
[6] J. Mahdavi, A. Emadi, “Application of State Space Averaging Method to Sliding
Mode Control of PWM DC/DC Converters”, IEEE Industry Applications Society
Annual Meeting, Oct. 5-9, 1997.
[7] B. Wu, Y. Lang, N. Zargari, S. Kouro, “Power Conversion and Control of Wind
Energy Systems”, IEEE Press Series on Power Engineering, 2011, ch 4.
[8] http://batteryuniversity.com/learn/article/whats_the_best_battery