Modeling and Analysis of a Flywheel Energy Storage
System for Voltage Sag Correction
A Thesis
Presented in Partial Fulfillment of the Requirements for the
Degree of Master of Science
With a
Major in Electrical Engineering
in the
College of Graduate Studies
University of Idaho
by
Satish Samineni
December 2003
Major Professor: Brian K. Johnson, Ph.D.
iii
ABSTRACT
A shipboard power system is a stiff, isolated power system. Power is
generated locally, and distributed over short distances making the system vulnerable
to system transients. Power quality problems such as voltage sags, which arise due
to a fault or a pulsed load, can cause interruptions of critical loads. This can be of a
serious concern for the survivability of a combat ship. A series voltage injection type
flywheel energy storage system is used to mitigate voltage sags. The basic circuit
consists of an energy storage system, power electronic interface and a series
connected transformer. In this case the energy storage system consists is a flywheel
coupled to an induction machine. The power electronic interface consists of two
voltage sourced converters (VSC) connected through a common DC link. The
flywheel stores energy in the form of kinetic energy and the induction machine is
used for energy conversion. Bidirectional power flow is maintained by regulating the
DC bus voltage. Indirect field orientated control with space vector PWM is used to
control the induction machine. Sinusoidal PWM is used for controlling the power
system side VSC. This paper presents the modeling, simulation and analysis of a
flywheel energy storage system and with a power converter interface using EMTDC.
iv
ACKNOWLEDGEMENTS
I would like to thank my advisor Dr. Brian K. Johnson for giving me the opportunity to
work on this thesis. I am greatly indebted for his encouragement, support and
guidance given during this project. It is an honor and pleasure to have him as my
advisor.
I am greatly thankful to Dr. Herbert L. Hess for his fruitful discussions and valuable
suggestions throughout this project. His approach of solving complicated problems
with simplified analysis helped greatly in this thesis.
I also wish to thank Dr. Dean B. Edwards for his interest in this topic and patience
during the preparation of this thesis.
I am thankful to Dr. Joseph D. Law for sharing his technical knowledge and spending
his valuable time during the crucial part of this thesis.
Financial supports from the Office of Naval Research and Department of Electrical
and Computer Engineering are greatly acknowledged.
v
DEDICATION
“Dedicated to my beloved parents, brother and sister who have provided me
encouragement and support throughout my studies”
vi
TABLE OF CONTENTS
Preliminary
Title page……………………………………………………….. i
Authorization to Submit……………………………………….. ii
Abstract ………………………………………………………… iii
Acknowledgements …………………………………………… iv
Dedication ……………………………………………………… v
Table of Contents ………………………………………….….. vi
List of Figures ………………………………………………….. ix
List of Tables …………………………………………………... xiii
Chapter 1 Introduction…………………………………………………. 1
1.1 Flywheel Basics………………………………………………… 1
1.2 Shipboard power system……………………………………… 8
1.3 Voltage sags …………………………………………………… 10
1.4 Energy storage and topologies………………………………. 19
1.5 Problem statement and Proposed Solution….……………… 24
Chapter 2 Basic circuit and operation………………………………… 26
vii
Chapter 3 Modeling strategy………………………………….…….…. 28
3.1 Software background..………………………………………… 28
3.2 Module breakup…………...…………………………………… 29
Chapter 4 Field oriented control AC drive…..………………………… 33
4.1 Machine modeling……………………………………………… 33
4.2 Field oriented controller..……………………………………… 43
4.3 Space vector PWM pulse generator model.………………… 45
Chapter 5 Static series compensator model……..…………………… 55
5.1 Shipboard power system model.……………………………... 56
5.2 Series transformer and filters…………………………………. 56
5.3 Sinusoidal PWM pulse generator model.……………………. 57
Chapter 6 Control system……….………………….………………….. 58
6.1 Sag detector and corrector…….……………………………... 59
6.2 Energy control system………………………………………… 61
Chapter 7 Results …………………………………………………….… 62
7.1 Test case.…………………………….…………………………. 62
7.2 Analysis of simulation results…………………………………. 63
viii
Chapter 8 Conclusions and future work……………………………… 68
8.1 Conclusions.…………………………….…………………………. 68
8.2 Future work………………………………………………………… 69
Bibliography ………………………………………………………………. 72
Appendix A ……………………………………………………………….. 73
Appendix B ………………………………………………………………... 83
ix
LIST OF FIGURES
1.1 Trip signal from circuit protection……….……………………. 12
1.2 Phase to ground voltages at the sensitive load………….…. 12
1.3 RMS voltages at the sensitive load and faulted load………. 12
1.4 Sequence currents from the feeder………………………….. 13
1.5 Phase to ground voltages at the sensitive load………….…. 13
1.6 RMS voltages at the sensitive load and faulted load………. 14
1.7 Sequence currents from the feeder………………………….. 14
1.8 Phase to ground voltages at the sensitive load………….…. 14
1.9 Phase to ground voltages at the sensitive load………….…. 15
1.10 RMS voltages at the sensitive load and faulted load………. 15
1.11 Sequence currents from the feeder………………………….. 16
1.12 Phase to ground voltages at the sensitive load……….……. 16
1.13 RMS voltages at the sensitive load and faulted load………. 17
1.14 Sequence currents from the feeder………………………….. 17
1.15 Phase to ground voltages at the sensitive load………….…. 18
1.16 RMS voltages at the sensitive load and faulted load………. 18
1.17 Sequence currents from the feeder………………………….. 18
2.1 Basic circuit of flywheel energy storage system……………. 26
2.2 Basic circuit showing series connection……….………….… 27
3.1 Single line diagram of a flywheel energy storage system…. 29
x
3.2 Field oriented control AC drive model breakup…………….. 30
3.3 Static series compensator model breakup………………….. 31
4.1 Two phase equivalent representation of induction machine. 34
4.2 Three phase to two phase stationary transformation………. 35
4.3 Stationary to synchronous frame transformation…………… 37
4.4 Stator currents in synchronous reference frame………….... 41
4.5 Stator currents in asbscs reference frame………………… 41
4.6 Electromagnetic torque, T
e
……………………………………. 42
4.7 Rotor angular velocity, ω
r
……………………………………… 42
4.8 Basic layout of Indirect field oriented controller model…….. 44
4.9 Bridge converter switching states …………………………… 45
4.10 Vector representation of switching states ……..……………. 46
4.11 Basic layout of space vector PWM pulse generator model . 47
4.12 Angle reference, θ
e
, Time computer input ………………….. 48
4.13 Sector, S, Time computer output ……………………………. 48
4.14 Sector reference, S1S6, Sector pulse generator output …. 49
4.15 Asynchronous timer output for 1.0kHz………………………. 51
4.16 Asynchronous timer output for 1.2kHz ……………………… 51
4.17 Space vector PWM output pulses in sector 1………………. 53
4.18 Software layout of a field oriented AC control drive …..…… 54
5.1 Basic layout of a static series compensator………………… 55
xi
5.2 Shipboard power system model ….…..………………………… 56
6.1 Control System Layout …………………………………………. 58
6.2 Sag detector and sag corrector layout …………………………. 60
6.3 Energy control system layout …………………………………… 61
7.1 Test case for analyzing FESS performance …………………… 62
7.2 Sag detector response …………………………………………. 63
7.3 DC bus voltage variation ……………………………………….. 64
7.4 Rotor angular velocity variation ………………………………… 64
7.5 Power flow into the machine and static series compensator…… 64
7.6 RMS voltages measured at the critical load side and SPS side.. 65
7.7 Phase to ground voltages on the SPS side ……………………. 65
7.8 Phase to ground voltages on the critical load side ……………… 66
7.9
Phase AGround voltage at the critical load and SPS, injected
voltage and Phase A line current…………………………………... 67
8.1 Analog model power system………………………. ……………… 69
8.2 Induction machine coupled flywheel.……………………………... 70
11.1 Flywheel energy storage system model ……………………. 83
11.2 Static series compensator model…………………………….. 84
11.3 Field oriented control AC drive model ……………………….... 84
11.4 Machine side inner control system ………………………….…. 85
11.5
Shipboard power system side inner control system and
outer control system …………………….…………………….. 85
xii
11.6 Space vector PWM pulse generator model part1………..…. 86
11.7 Space vector PWM pulse generator model part2……….…. 87
11.8 Space vector PWM pulse generator model part3………..…. 87
11.9 Sag detector and corrector model.………………….……….…. 88
11.10 Sinusoidal PWM pulse generator model part1………..…….. 89
11.11 Sinusoidal PWM pulse generator model part2……….……... 90
xiii
LIST OF TABLES
1.1 Flywheel shape factors……..………………………………… 6
1.2 Specific strength of flywheel materials……………………… 6
1.3 Comparison of typical flywheel energy storage capabilities. 7
4.1 Time distribution of eight vectors in the sectors……………. 52
4.2 Common sequence for time distribution……….……………. 52
4.3 Sequence for time distributions of in each sector………….. 53
11.1 Technical data………………………………………………….. 90
1
1.0 INTRODUCTION
1.1 Flywheel basics
Flywheels have been used for a long time as mechanical energy storage devices.
The earliest form of a flywheel is a potter’s wheel that uses stored energy to aid in
shaping earthen vessels [1]. The wheel is a disc made of wood, stone or clay. It
rests on a fixed pivot and can be rotated around its center. The energy stored in a
potter’s flywheel is about 500J, which is by no means negligible. The main
disadvantages are friction and material integrity. Most of energy is lost in overcoming
frictional losses.
The word ‘flywheel’ appeared first during the start of industrial revolution.
During this period, there were two important developments: one is the use of
flywheels in steam engines and the other is widespread use of iron. Iron flywheels
have greater material integrity than flywheels made up of wood, stone or clay. They
can be built in a single piece and can accommodate more mass and moment of
inertia in the same volume. These flywheels were used mostly for smoothing torque
pulses in steam engines.
In the years after industrial revolution, the trend was mostly towards
increasing mass for higher energy storage rather than increasing speed. Large
flywheels made of cast steel, with heavier rims, were built for the largest engines.
However, with the advent of the small internal combustion engine in the middle of
19
th
century, the trend shifted towards highspeed flywheels with low inertia for
automotive applications. More recently, the ability of a flywheel to deliver high power
in a short time has been used in applications such as mechanical presses,
lubrication or cooling pumps, mine locomotives, inertial friction welding and inertial
starters.
The constant stress profile for steam turbines, developed by De Laval and
later by Stodola, was very useful in the design of highspeed flywheels. During the
2
Stodola period it was demonstrated that a rotating mass supported by a shaft stores
energy mechanically.
The second part of 20
th
century saw advances in the field of highstrength
composite materials. Composite flywheels can operate at higher speeds and can
store more energy for a given mass than a conventional steel flywheel. These
flywheels have high material integrity, can be operated at high speeds and, as will
be shown below, store more energy. The concept of a flywheel energy storage
system for electric vehicles and stationary power backup was proposed during this
period. Also, a distinction has been made between the flywheels that are used for
smoothing torque pulses and the flywheels that store energy for backup power
applications.
Flywheels store energy in the form of kinetic energy. The amount of energy
‘E’ stored in a flywheel varies linearly with moment of inertia ‘I’ and with the square
of the angular velocity ‘ω’.
E
1
2
I ⋅ ω
2
⋅
(1.1)
The moment of inertia is a physical quantity, which depends on the mass and
shape of the flywheel. It is defined as the integral of the square of the distance ‘x’
from the axis of rotation to the differential mass ‘dm
x
’.
I m
x
x
2
⌠
(
⌡
d
(1.2)
The solution for a cylindrical flywheel of mass ‘m’ and radius ‘r’ will be:
I m r
2
⋅
(1.2a)
and
3
E
1
2
m ⋅ r
2
⋅ ω
2
⋅
(1.2b)
Since the energy stored is proportional to the square of angular velocity,
increasing the angular speed increases stored energy more effectively than
increasing mass. But increasing angular speeds results in increased frictional losses
and hence thermal problems. With the help of magnetic bearing technology, the
frictional losses due to bearings can be overcome, but at the expense of reliability.
Also the energy stored can be expressed in terms of peripheral velocity ‘v’,
which is defined as the product of perpendicular distance from the axis of rotation
and angular speed as:
E
1
2
m ⋅ v
2
⋅ since v r ω ⋅
(1.3)
The tensile strength, σ, of the material limits the peripheral velocity, and
hence the amount of energy stored. For a mass density ‘ρ’, the tensile strength is
defined as:
σ ρ v
2
⋅
(1.4)
Energy density is a term generally used to characterize an energy storage
system. Usually high energy density is preferred, but this can pose thermal
problems. Energy density, E
m
, is loosely defined for a flywheel as the ratio of energy
stored to its mass:
E
m
1
2
r
2
⋅ ω
2
⋅
(1.5)
The volume energy density, E
v
, is obtained by substituting m in the stored
energy equation, as the product of volume and the mass density:
E
v
1
2
ρ ⋅ r
2
⋅ ω
2
⋅
(1.6)
4
Therefore, if the dimensions are fixed, the maximum energy stored per
volume ‘E
vmax
’ depends on the tensile strength of the material as:
E
vmax
1
2
σ
max
⋅
(1.7)
where ‘σ
max
’ is the maximum tensile strength of the flywheel material.
Similarly the maximum energy stored per mass ‘E
mmax
’ is
E
mmax
1
2
σ
max
ρ
⋅
(1.8)
Therefore, the maximum energy storage capacity can be achieved by using a
material with a low density and high tensile strength. Depending on the application,
either volume energy density or mass energy density takes precedence during the
design stage. For a transportation application, mass energy density is a major
consideration, since mass is a limiting factor.
The energy density expressions above apply for a simple rim type flywheel.
There are many designs for flywheels, and the general expression of maximum
energy stored per mass is:
E
mmax
K
σ
max
ρ
⋅
(1.9)
where K is defined as the flywheel shape factor, which depends on the geometry of
the flywheel. The flywheel shape factors for several different types of flywheels are
given in Table 1.1.
The value of K is obtained from the equation for the moment of inertia (1.2).
The stress distribution in a flywheel due to centrifugal loading becomes complex for
shape factors greater than 0.5, and a detailed analysis needs to be done to safely
achieve it.
5
For low speed flywheels, the best way to maximize stored energy is by
increasing moment of inertia. A massive rim or disc made of high density material
such as cast iron or steel is sufficient in these cases. The main advantages of low
speed flywheels are that they use a wellestablished technology and they are
cheaper to build.
For highspeed applications, small discs with a constant stress profile, built
with a low density and high strength materials, are better for maximizing energy
density. The most commonly used composite material is Kevlar, a plastic material
reinforced with glass, carbon or aramid fibers. The main disadvantage of this
material is its high cost. The cheapest composite material is Sglass, but this
material has a lower fatigue strength. The specific strengths of different flywheel
materials is listed in Table 1.2. A comparison of flywheel energy storage capabilities
is given in Table 1.3.
There is also a safety factor, which limits the amount of stored energy
available for discharge [2]. When this is considered, the useful energy stored per
mass is given by:
E
m
1 s
2
−
( )
K ⋅
σ
ρ
⋅
(1.10)
where ‘s’ is the ratio of minimum to maximum operating speed, usually set at 0.2.
So the maximum amount of energy stored doesn’t depend directly on inertia
or on the angular velocity, since either of these can be chosen independently to
obtain the required design stress. And within the design stress, the amount of
energy stored is linearly proportional to the moment of inertia and to the square of its
angular velocity.
6
Table 1.1 Flywheel shape factors [1]
Flywheel Shape K
Constant stress disk 0.931
Constant thickness disc 0.606
Thin rim 0.500
Constant stress bar 0.500
Rod or circular brush 0.333
Flat pierced disc 0.305
Table 1.2 Specific strengths of flywheel materials [1]
Flywheel material
Specific strength
(kJ/kg)
Cast iron 19
Carbon steel 44
Alloy steel 100
Wood (beech) 130
Kevlar 1700
Sglass 1900
Graphite 8900
7
Table 1.3 Comparison of typical flywheel energy storage capabilities [2]
Material
Density
10
3
kg/m
3
Useful
Energy
10
3
J/kg
Mass of the
flywheel
10
3
kg
Wood birch 0.55 21.0 1720
Mild steel 7.80 29.5 1220
SGlass 1.90 70.5 509
Maraging steel 8.00 86.4 417
Carbon 60% fibre 1.55 185.4 194
Kevlar 60% fibre 1.4 274.3 131
8
1.2 Shipboard Power System
The U.S. Navy is looking at methods to maximize the survivability of its combat ships
during battle situations [3]. A typical shipboard power system is radial with bus
tiebreakers to reconfigure it. There are usually three to four generators. Steam
turbines, gas turbines, or diesel engines are used as prime movers for these
generators. The generated 450V, 60Hz threephase AC generator output is
distributed throughout the ship over distances up to a few hundred meters. A
number of threephase step down transformers are used at the load centers to
provide different voltage levels.
For survivability reasons, the primary and secondary windings of these
transformers are connected in delta giving the system a floating neutral. This is done
so that a single line to ground fault due to battle damage doesn’t result in large
currents flowing in the system since there is no path for the zero sequence current to
flow (zero sequence impedance is very high). This blocks the protection devices
from acting and hence prevents interruptions to critical loads. Another advantage of
using this delta configuration is that an open circuit in the distribution line, or a loss
of one leg of transformer, will still allow balanced power to be supplied at reduced
levels. The main disadvantage of using this configuration is that a single line to
ground fault will increase the phase to ground voltages on the unfaulted phases to
1.732 times. This can result in insulation failure and possibly cause interruptions to
more loads. As a result, research being done on different grounding options for
shipboard power system and how they impact the critical loads [3]. One option is to
implement a solidly grounded system with fast reconfiguration during faults.
Since shipboard power systems are isolated and stiff (short electrical
distances to loads), system transients can penetrate deep into the system. Critical
loads such as computers, emergency lighting and communications, fire pumps,
search radars, pumps and weapon systems are sensitive to these system transients.
Keeping these loads operational plays a vital role in maximizing survivability of a
combat ship during battle situations. These loads require continuous quality power
for proper operation. System transients such as voltage sags, which arise due to
9
faults, can cause interruptions to critical loads. So isolating these critical loads from
these transients is key to maximizing survivability.
In this thesis investigation, the shipboard power system is assumed to be a
solidly grounded. The primary effort is on sag correction using a flywheel energy
storage system. Whether grounded or ungrounded, three phase voltage sags seen
by the critical loads are the same, so the correction of a balanced voltage sag was
considered as a common test case. A similar argument can be made for phase to
phase faults. SLG faults in an ungrounded system don’t cause sags.
10
1.3. Voltage Sags
A voltage sag is a short duration phenomenon at power system frequency resulting
in a decrease in the RMS voltage magnitude from 10% to 90% [4]. It typically lasts
about half a cycle to a minute. Loads such as adjustable speed drives, process
control equipment and computers are sensitive to these voltage sags. These loads
may trip or misoperate even for voltage sag of 10% and lasting two cycles. Process
industry applications such as paper mills and semiconductor fabrication plants take a
lot of time to restart when tripped. Since they are production oriented, the impact of
the voltage sag is enormous.
Voltage sags are quite common in modern power systems and generally
caused by motor starting, transformer energizing, pulsed load switching and
electrical faults. They are power quality problems. And the depth of the sag depends
on the electrical distance to the point of cause.
The starting current of a large induction machine is typically 612 (starter
compensators reduce it to 36) times the rated current when line started. The voltage
drop caused by this starting current is the same in the three phases causing a
balanced voltage sag. The voltage drops suddenly and recovers gradually as the
machine reaches its rated speed. The same behavior occurs for large synchronous
motors since most of them are started as induction machines before
synchronization.
The inrush current due to the energization of a large transformer is typically 5
times the rated current. The voltage drops are different in each phase, resulting in an
unbalanced sag. The voltage recovers gradually as the transformer reaches its rated
flux.
However, the majority of voltage sags are due to electrical faults. Unlike the
starting of large machines, voltage sags due to electrical faults are unpredictable.
When a fault occurs in a power system, loads connected to the feeders that
contribute current to the fault experience a voltage sag. In addition, loads down
stream from the fault, or from junctions to the faulted feeder, also experience a
11
voltage sag. This makes voltage sag a global phenomenon, compared to interruption
where the isolation of faulted feeder causes a local disruption. The severity of the
sag depends on the amount of fault current available at that feeder. In other words,
the number of loads affected by voltage sags depends on the source impedance.
A voltage sag is generally characterized by depth and duration. The depth of
the sag depends on the system impedance, fault distance, system characteristics
(grounded or ungrounded) and fault resistance. The duration of the sag depends on
the time taken by the circuit protection to clear the fault. High speed tripping is
desired to limit the duration of sags.
Consider an example system with a source, a bus and two loads. One is a
sensitive load, which is connected directly to the bus. The other is a distant load
connected to the same bus through a distribution line. The characteristics of voltage
sags were studied using this test setup for a number of different system
configurations, different faults at the distance load.
The following test cases use a solidly grounded system with a threephase
fault at a distant load. The source is stiff as seen by the sensitive load. A three
phase fault occurs at the distant load terminals, which is cleared by the protection in
five cycles.
Fig. 1.1 shows the trip signal for clearing the fault. Fig. 1.2 shows balanced
voltage sag of 82% seen at the sensitive load due to this fault. Fig. 1.3 shows the
RMS voltage measured at the sensitive load and at the distant load. Since it is a
balanced fault, the negative and zero sequence (a little seen at t = 0.6 sec) currents
from the feeder are zero (except during the transient state as seen in Fig. 1.4).
12
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
T
r
i
p
(
H
i
g
h
/
L
o
w
)
Time (s)
Fig. 1.1. Trip signal from circuit protection
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Phase A Phase B Phase C
Fig. 1.2. Phase to ground voltages at the sensitive load
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
R
M
S
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Sensitive Load Faulted Load
Fig. 1.3. RMS voltages at the sensitive load and faulted load
13
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
F
e
e
d
e
r
C
u
r
r
e
n
t
(
p
.
u
)
Time (s)
Negative Sequence Positive Sequence Zero Sequence
Fig. 1.4. Sequence currents from the feeder
The following waveforms use a weak source with the same threephase fault
applied at the distant load terminals. Fig. 1.5 shows a balanced voltage sag of 65%
at the sensitive load due to this fault. With a weak source, the sensitive load is more
affected than with a strong source due to increased voltage drop across the source
impedance. Fig. 1.6 shows the RMS voltage measured at the sensitive load and at
the distant load. Fig. 1.7 shows that the positive sequence current is reduced with
the weaker source due to the increased source impedance.
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Phase A Phase B Phase C
Fig. 1.5. Phase to ground voltages at the sensitive load
14
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
R
M
S
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Sensitive Load Faulted Load
Fig. 1.6. RMS voltages at the sensitive load and faulted load
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
F
e
e
d
e
r
C
u
r
r
e
n
t
(
p
.
u
)
Time (s)
Negative sequence Positive sequence Zero sequence
Fig. 1.7. Sequence currents from the feeder
The following cases again use with a weak source, but now a threephase
fault is applied at the middle of the transmission line. Fig. 1.8 shows a balanced
voltage sag of 50% at the sensitive load due to this fault. The electrical distance from
the sensitive load to the fault point determines the severity of the sag.
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
R
M
S
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Sensitive Load Faulted Load
Fig. 1.8. Phase to ground voltages at the sensitive load
15
The following cases are with the same threephase fault applied to an
ungrounded system at the distant load. The source is weak as seen from the
sensitive load. Fig. 1.9 shows the same balanced voltage sag of 65% as was seen
with the grounded system, since a three phase fault doesn’t involve ground. An
overvoltage is seen at the end of transient due to the fault current interruption at the
current zero crossing and redistribution of fault currents. Fig. 1.10 shows the RMS
voltage measured at the sensitive load and at the distant load. Since it is a balanced
fault, the negative sequence currents from the feeder are zero (except during the
transient state as seen in Fig. 1.11). Since the system is ungrounded the zero
sequence current is zero.
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Phase A Phase B Phase C
Fig. 1.9. Phase to ground voltages at the sensitive load
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
R
M
S
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Sensitive Load Faulted Load
Fig. 1.10. RMS Voltages at the sensitive load and faulted load
16
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
F
e
e
d
e
r
C
u
r
r
e
n
t
(
p
.
u
)
Time (s)
Negative Sequence Positive Sequence Zero Sequence
Fig. 1.11. Sequence currents from the feeder
The following cases use a solidly grounded system with a singlephase A to
ground fault at the distant load. The source is weak as seen from the sensitive load.
Fig. 1.12 shows an unbalanced voltage sag on phase A. The other two phases are
unaffected since the system is solidly grounded. Fig. 1.13 shows a ripple in the RMS
voltage measured at the sensitive load and at the distant load. The RMS voltage
measurements used here involve averaging all the three phase voltages and
assumes them to be balanced. The ripple depends on the smoothing constant of the
filter used for RMS measurement. The negative and zero sequence currents
distribution from the feeder during this fault is shown in Fig. 1.14.
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Phase A Phase B Phase C
Fig. 1.12. Phase to ground voltages at the sensitive load
17
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
R
M
S
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Sensitive Load Faulted Load
Fig. 1.13. RMS Voltages at the sensitive load and faulted load
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
F
e
e
d
e
r
C
u
r
r
e
n
t
(
p
.
u
)
Time (s)
Negative Sequence Positive Sequence Zero Sequence
Fig. 1.14. Sequence currents from the feeder
The following waveforms apply the same singlephase fault to an ungrounded
system at the distant load. The source is weak as seen from the sensitive load. Fig.
1.15 shows unbalanced voltages seen by the sensitive load. The phase A voltage
goes to zero but the voltages on the other two phases swell by 1.732 times the
rated. For a single phase to ground fault there is no path in the circuit for the zero
sequence current to flow, resulting in a shift of the neutral point to faulted potential.
In some cases the transients can increase this further. Fig 1.16 shows the RMS
voltage measured at the sensitive load and at the distant load. No sag is seen, as it
is a phasetophase voltage measurement. As a result, the loads in an ungrounded
system are connected phase to phase to maintain continuity of service during single
line to ground faults. Fig. 1.17 shows the zero sequence current magnitude to be
zero. In real systems, very small zero sequence currents flow through the parasitic
capacitances, limiting the swell somewhat less than 1.732 per unit.
18
2.0
1.6
1.2
0.8
0.4
0.0
0.4
0.8
1.2
1.6
2.0
0.40 0.45 0.50 0.55 0.60 0.65 0.70
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Phase A Phase B Phase C
Fig. 1.15. Phase to ground voltages at the sensitive load
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
R
M
S
V
o
l
t
a
g
e
(
p
.
u
)
Time (s)
Sensitive Load Faulted Load
Fig. 1.16. RMS voltages at the sensitive load and faulted load
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.40 0.45 0.50 0.55 0.60 0.65 0.70
F
e
e
d
e
r
C
u
r
r
e
n
t
(
p
.
u
)
Time (s)
Negative sequence Positive sequence Zero sequence
Fig. 1.17. Sequence currents from the feeder
19
1.4. Energy Storage and Topologies
This section discusses different energy storage technologies available for this
project and the reason for using flywheel energy storage.
1.4.1 Available energy storage technologies
Energy can neither be created nor destroyed. But it can be transformed from one
form to another. Electrical energy is the form of energy that can be transmitted
efficiently and easily transformed to other forms of energy. The main disadvantages
with electrical energy involve storing it economically and efficiently. Electrical energy
can be converted and stored in different forms:
• Electrochemical Energy
• Electrostatic Energy
• Electromagnetic Energy
• Electromechanical Energy
1.4.1.1 Electrochemical energy storage
In this type of storage, electrical energy is converted and stored in the form of
chemical energy. There are two main categories: batteries and fuel cells [2].
Batteries use internal chemical components for energy conversion and storage
whereas fuel cells use synthetic fuel (for example Hydrogen, methanol or hydrazine)
supplied and stored externally. Both use two electrodes, an anode and a cathode,
that exchange ions through an electrolyte internally and exchange electrons through
an electric circuit externally. The Leadacid battery, discovered by Plante in 1859, is
the most widely used battery. The battery consists of pairs of lead electrode plates
immersed in a dilute sulphuric acid that acts as an electrolyte. Every alternate lead
plate is coated with lead dioxide. Discharging results in the conversion of both of the
electrodes to lead sulphate. Charging restores the plates to lead and lead dioxide.
The physical changes in electrodes during charging and discharging deteriorates the
20
electrodes and hence reducing their life. The main advantages are they have a well
established technology. The main drawbacks with batteries are:
• Slow response during energy release
• Limited number of charge discharge cycles
• Relatively short life time
• High internal resistance
• Low energy density
• Maintenance requirements for some types
• Environmental hazards
W. R. Grove demonstrated the first hydrogenoxygen fuel cell in 1839. The
byproduct of a Hydrogen fuel cell is water. By electrochemical decomposition of
water into hydrogen and oxygen and holding them apart, hydrogen fuel cells store
electrical energy. During discharge, the hydrogen is combined with oxygen,
converting the chemical energy to electrical energy. The main advantages are
environment friendly. The main drawbacks with fuel cells as energy storage
elements are:
• Slow response during energy release
• Temperature dependence
• Corrosion problems
• Hydrogen storage
• Ineficient transfer of electrical energy to chemical energy
21
1.4.1.2 Electrostatic energy storage
Electric energy can be converted and stored in the form of electrostatic field between
the parallel plates of a charged capacitor. The amount of energy stored is
proportional to square of the voltage across the parallel plates and to its
capacitance. For a fixed voltage, the volume energy density for a parallel plate
capacitor is proportional to capacitance, which is proportional to the permittivity of
the insulator between the parallel plates. Most of the insulators have relative
permittivity in the range of 1 to 10. Due to the small capacitance, ordinary capacitors
can store very limited amount of energy. Ultracapacitors use electrochemical
material for improving permittivity and hence energy density. They require less
maintenance and have much longer lifetimes compared to batteries. They have high
energy density and does not having moving parts. The main drawbacks with
capacitors are:
• Cost
• Temperature dependence
• Not rugged
1.4.1.3 Electromagnetic energy storage
Electric energy can be converted and stored in the form of an electromagnetic field.
A Superconducting magnetic energy storage (SMES) coil consists of a
superconducting coil carrying large DC currents. The amount of energy stored is
proportional to the square of the DC current flowing through the coil and to its
inductance. The volume energy density is proportional to the permeability of the
material used for the coil. In order to keep the temperature of the superconductor
below its critical temperature, a cryogenic cooling system is required. Increasing the
DC current increases the amount of energy stored. Once the current in the coil
reaches its maximum value, the voltage across it is zero and the SMES is fully
charged. This storage scheme has very low losses due to negligible resistance in
22
the coil. Also SMES coils can be built for larger energy and power. The main
drawbacks with SMES are:
• Cost
• Reliability in maintaining cryogenic cooling
• Compensation of external stray fields
• Electromagnetic forces on the conductors
• Bulk/volume
1.4.1.4 Electromechanical energy storage
Electrical energy can be converted and stored in the form of kinetic energy in a
flywheel. Motor/generator sets, DC machines and induction machines are used for
energy conversion. The amount of energy stored in a flywheel is proportional to the
square of angular velocity and to its inertia for a given design stress.
The energy storage technologies discussed above have their own
advantages and disadvantages but the following advantages make flywheels a
viable alternative to other energy storage systems:
• Low cost
• High power density
• Ruggedness
• Greater number of charge discharge cycles
• Longer life
• Less maintenance
• Environmental friendly
• Fast response during energy release
23
Flywheels can be designed for low speed or highspeed operation. A low
speed flywheel has advantages of lower cost and the use of proven technologies
when compared to a highspeed flywheel system.
The main disadvantages are:
• less energy stored per volume
• higher losses
• increased volume and mass
24
1.5 Problem Statement and Proposed Solution
A shipboard power system is a stiff, isolated power system. Power is
generated locally and distributed over short distances. As a result, any system
transients impact the entire system. Critical loads such as computers, radar
systems, water pumps and weapon systems play an important role in the survival of
a combat ship during battle conditions. Power quality problems, such as voltage
sags [4], which arise due to a fault or a pulsed load, can cause interruptions of
critical loads. These interruptions can be a serious concern for the survivability of a
combat ship. The US Navy is looking for methods to maximize the survivability of its
combat ship [5]. An effective way to mitigate voltage sags is by the use of series
voltage compensation with energy storage [6]. Series voltage compensation
provides the flexibility to inject voltage at any angle with energy storage.
A low speed flywheel coupled to an induction machine is the option explored
in this thesis. The induction machine is used for bidirectional transfer of energy to
the flywheel. A voltagesourced converter is used to interface the induction machine
with the energy storage system. Indirect field oriented control with space vector
PWM is used to control the induction machine.
A voltage source converterbased static series compensator is interfaced with
the SPS for voltage sag correction. Sinusoidal PWM is used for controlling the static
series compensator. The two voltage sourced converters share a common DC link.
The power electronic interface is used for the bidirectional flow of energy for
charging and discharging the flywheel through the induction machine with DC link as
medium. An outer control system detects voltage sag and controls the energy flow
during sag correction. An inner control system is used to generate gate pulses for
each converter.
This thesis presents the modeling, simulation and analysis of a flywheel
energy storage system (FESS) based static series compensator for voltage sag
correction. The basic circuit and operation is explained in Chapter 2. Modeling was
done using PSCAD/EMTDC [7] and MATLAB as is explained in Chapters 3, 4 and 5.
The control system for sag detection, sag correction and energy flow is presented in
25
Chapter 6. The simulated performance of the flywheel energy storage system in
mitigating balanced voltage sag is analyzed in Chapter 7.
The future work will include a detailed analysis of a flywheel energy storage
system for unbalanced voltage sags and validating the simulation model with a
laboratory flywheel interfaced to an analog model power system.
26
2.0 BASIC CIRCUIT AND OPERATION
The basic circuit consists of an energy storage system, power electronic interface
and a series transformer as shown in Fig. 2.1. The energy storage system in this
case is a flywheel coupled to an induction machine. The induction machine is used
for energy conversion. The power electronic interface consists of two voltage
sourced converters connected through a common DC link. One voltage source
converter interfaces with the energy conversion and storage system and the other
with the shipboard power system.
The flywheel energy storage system has three modes of operation:
• Charge mode
• Standby mode
• Discharge mode
During charge mode, the VSC interfacing the shipboard power system runs
as a rectifier and the other as an inverter, with the transferred energy accelerating
the flywheel to its rated speed. In this mode, energy is stored in the flywheel in the
form of kinetic energy. The energy flow is from shipboard power system to flywheel
with induction machine as energy converter.
FW
SPS
M
CRITICAL
LOAD
VSC
VSC
Fig. 2.1. Basic circuit of flywheel energy storage system
27
Once the flywheel reaches its charge speed, the storage system is in stand
by mode and is ready to discharge when the critical load sees a voltage sag. In this
mode a little energy from the shipboard power system is used for meeting the
converter and machine losses.
During discharge mode, the VSC interfacing the shipboard power system
runs as an inverter injecting the required voltage in series with the line to correct the
voltage sag. The flywheel VSC runs as a rectifier. The flywheel slows as it
discharges. In this mode, the stored energy is used for sag correction and energy
flow is from the flywheel to shipboard power system.
Fig. 2.2 shows a simplified diagram that shows the series connection of
flywheel energy storage system.
SHIPBOARD
POWER
SYSTEM
CRITICAL
LOAD
FESS
Fig. 2.2. Basic diagram showing series connection
28
3.0 MODELING STRATEGY
The flywheel energy storage system was modeled using PSCAD/EMTDC [7] with an
interface to MATLAB. This section gives an introduction to the software and
modeling strategy adopted to simplify the complexity involved in modeling the
flywheel energy storage system.
3.1 Software background
Power system simulation involves solving a set of complex time dependent
equations. PSCAD/EMTDC was developed by Manitoba HVDC Research center in
the early 90’s. EMTDC is a transient simulator that can model power system
components, complex power electronic devices and controls whereas PSCAD is a
graphical user interface for visualizing the complex behavior of power system.
PSCAD/EMTDC is a powerful tool for simulating electromagnetic transients of
electrical systems. The PSCAD graphical user interface enhances the power of
EMTDC. A user can draw the circuit, run the simulation, and capture the results in a
completely graphical environment. A master library is available consisting all the
basic power system components such as resistors, capacitors, inductors, power
electronic devices, transformers, transmission lines and machines.
EMTDC uses interpolation with an instantaneous switch algorithm to give
accurate simulation results for power electronic simulations with larger time steps.
New components can be designed using a graphical component design tool. With
the proper FORTRAN compiler, EMTDC can interface with MATLAB. This is very
useful in simulations which involve complicated control algorithms.
29
3.2 Module breakup
A Flywheel energy storage system consists of the following components that need to
be modeled in PSCAD/EMTDC:
• Shipboard power system
• Two voltage sourced converters
• Induction machine
• Flywheel
• Firing schemes for the converters
• Control system
Fig. 3.1 shows a single line diagram of a flywheel energy storage system. To simplify
modeling and testing, it is broken into two sub models. Each sub model is separately
modeled, tested and integrated to make it a complete model. The sub models are:
• Field oriented control AC drive model
• Static series compensator model
M
Flywheel Energy Storage System
Fig. 3.1. Single line diagram of a flywheel energy storage system
30
3.2.1 Field oriented control AC drive model
Fig. 3.2 shows the outline of the field oriented control AC drive that was modeled in
EMTDC. It has the following sub models:
• Full transient induction machine model
• Indirect field oriented controller model
• Space vector PWM pulse generator model
• Self commutated voltage sourced converter
The induction machine model available in PSCAD/EMTDC library is a steady state
model. In order to study the behavior of energy storage system, a full transient
induction machine model (a new component built in EMTDC as part of the thesis)
was used. An indirect field oriented controller was modeled for controlling the
induction machine. A space vector PWM pulse generator was modeled for
controlling the gate pulses of machine side voltage sourced converter. The modeling
procedure is explained in more detail in Chapter 4. The space vector PWM
generator model uses the MATLAB interface for computing the switching times for
the converter.
M
Flywheel Energy Storage System
FIELD ORIENTED CONTROL AC DRIVE
Fig. 3.2. Field oriented control AC drive model breakup
31
3.2.2 Static series compensator model
Fig. 3.3 shows the outline of a static series compensator as it was modeled in
EMTDC. It has the following sub models:
• Shipboard power system model
• Series transformer and filters
• Sinusoidal PWM pulse generator model
• Self commutated voltage sourced converter
A sinusoidal PWM pulse generator was modeled for controlling the gate pulses to
the shipboard power system side voltage sourced converter. The Shipboard power
system was modeled as a simple radial system. The modeling procedure is
explained in Chapter 5.
M
Flywheel Energy Storage System
STATIC SERIES COMPENSATOR
Fig. 3.3. Static series compensator model breakup
32
3.2.3 Control system
The control system was modeled in EMTDC. It has the following sub models:
• Sag detector
• Sag corrector
• Energy control system
The modeling procedure is explained in Chapter 6.
The field oriented control AC drive model and static series compensator share a
common DC link. Initially static series compensator was modeled separately by
replacing the field oriented control AC drive with an equivalent current source.
Similarly field oriented control AC drive was initially modeled by replacing static
series compensator with an equivalent voltage source. Then they were integrated to
make a complete FESS model with control system.
33
4.0 FIELD ORIENTED CONTROL AC DRIVE MODEL
The field oriented control AC drive consists of the following custom models built in
the DQ domain:
• Full transient induction machine model
• Indirect field oriented controller model
• Space vector PWM pulse generator
• Self commutated voltage sourced converter
The following sections describe how these custom models were built and how
they are integrated to make a field oriented control AC drive model.
4.1 Machine modeling
An induction machine can be seen as a transformer with a moving secondary where
the mutual inductances change continuously with the rotor position [8]. An induction
machine modeled in abc reference frame is complex, consisting of six differential
equations with time varying mutual inductances (see Appendix A Section 10.1). The
inherent complexity in dealing with the induction machine voltage equations resulting
from the time varying mutual inductances between stator and rotor circuits led to the
concept of using alternative reference frames.
A complex space vector is defined as S
s
=(2/3)(S
A
+aS
B
+a
2
S
C
) where S
A
, S
B
and S
C
are three phase instantaneous machine variables such as voltage, current or
flux and a is a 120
0
phase shift operator [9]. The space vector can be projected onto
a set of direct and quadrature axes, with quadrature axis fixed along the axis of the
A phase stator winding. For motor convention, the direct axis lags the quadrature
axis by 90
0
. As a result, an ungrounded three phase induction machine can be
represented as a two phase induction machine as shown in Fig 4.1, where d
s
 q
s
correspond to stator direct and quadrature axes, and d
r
– q
r
correspond to rotor
34
direct and quadrature axes. This projection reduces the number of voltage equations
to four but time varying inductances still remain.
as
bs
cs
ar
br
cr
θ
r
Ref
q
s
q
r
d
s
d
r
Ref
Fig. 4.1. Two phase equivalent representation of induction machine
G. Kron proposed a transformation that eliminates time variant inductances
by projecting the stator and rotor variables onto a synchronously rotating reference
frame (with the quadrature axis fixed in synchronism with the rotating magnetic
field). Later Krause and Thomas generalized Kron transformation to show that the
time varying inductances can always be removed by projecting the stator and rotor
variables onto a common rotating reference frame which is not necessarily at
synchronous speed. The common reference frame can also be nonrotating in which
case it is fixed in the stator and is called stationary reference frame. This change of
variables decreases the complexity in modeling and control of a three phase
symmetrical induction machine.
35
4.1.1 dq axes transformation
Fig. 4.2 shows a symmetrical induction machine with stationary asbscs axes, 120
0
apart where s implies a stator quantity. The three phase stationary reference
variables (asbscs) are transformed to a two phase synchronously rotating
reference frame (d
e
– q
e
) variables in two steps. The first step is to transform the
three phase variables to a two phase stationary reference variables (d
s
– q
s
) and the
second step is to transform the two phase stationary variables to a two phase
synchronously rotating reference frame variables.
q
s
 axis
ref axis
d
s
 axis
as
bs
cs
S
qs
s
S
ds
s
S
as
S
bs
S
cs
θ
Fig. 4.2. Three phase to two phase stationary transformation
A matrix representation for converting three phase variables to two phase
stationary variables is given by:
S
qs
s
S
ds
s
S
0s
s

\




.
2
3
cos θ
( )
sin θ
( )
0.5
cos θ 120
o
−
( )
sin θ 120
o
−
( )
0.5
cos θ 120
o
+
( )
sin θ 120
o
+
( )
0.5

\


.
⋅
S
as
S
bs
S
cs

\


.
⋅ 4.1 ( )
36
where θ is the orientation angle of d
s
– q
s
axes relative to reference axis
(Phase A’s).
S
0s
s
is a zero sequence component, which is always zero in the case of a
balanced induction machine with no neutral connection. For convenience, the q
s
axis
is fixed along the as axis to make θ equal zero. So the transformation relations
simplify to:
S
qs
s
2
3
S
as
⋅
1
3
S
bs
⋅ −
1
3
S
cs
⋅ − S
as
4.2 ( )
S
ds
s
1
3
− S
bs
⋅
1
3
S
cs
⋅ + 4.3 ( )
Inversely, the relation for converting two phase stationary variables to three
phase variables is given by:
S
as
S
qs
s
4.4 ( )
S
bs
1
2
− S
qs
s
⋅
3
2
S
ds
s
⋅ − 4.5 ( )
S
cs
1
2
− S
qs
s
⋅
3
2
S
ds
s
⋅ + 4.6 ( )
Fig. 4.3 shows a synchronously rotating d
e
– q
e
axes at synchronous speed
ω
e
with respect to the d
s
– q
s
axes at an angle θ
e
(angular reference for rotating
magnetic field) where θ
e
=ω
e
t. The d
s
 q
s
variables can be converted to d
e
– q
e
variables as follows:
37
S
qs
S
qs
s
cos θ
e
( )
⋅ S
ds
s
sin θ
e
( )
⋅ − 4.7 ( )
S
ds
S
qs
s
sin θ
e
( )
⋅ S
ds
s
cos θ
e
( )
⋅ + 4.8 ( )
q
s
 axis
ref axis
d
s
 axis
as
S
qs
s
S
ds
s
θ
e
S
qs
S
ds
q
e
 axis
d
e
 axis
Fig. 4.3. Stationary to synchronous frame transformation
The prefix ‘e’ for representing as synchronous rotating reference variables
has been omitted for simplified representation. Similarly a reverse transformation
from the synchronous frame to stationary frame is given by:
S
qs
s
S
qs
cos θ
e
( )
⋅ S
ds
sin θ
e
( )
⋅ + 4.9 ( )
S
ds
s
S
qs
− sin θ
e
( )
⋅ S
ds
cos θ
e
( )
⋅ + 4.10 ( )
Consider the following example to demonstrate the main advantage of
choosing the synchronous reference frame. Let us start with a three phase stator
voltages given by:
38
v
as
t ( ) V
pk
cos ω
e
t ⋅ φ +
( )
⋅
4.11 ( )
v
bs
t ( ) V
pk
cos ω
e
t ⋅
2 π ⋅
3
− φ +

\

.
⋅
4.12 ( )
v
cs
t ( ) V
pk
cos ω
e
t ⋅
2 π ⋅
3
+ φ +

\

.
⋅
4.13 ( )
Substituting equations (4.11)(4.13) in (4.2)(4.3) and simplifying gives the
stationary reference frame values:
v
qs
s
V
pk
cos ω
e
t ⋅ φ +
( )
⋅ 4.14 ( )
v
ds
s
V
pk
− sin ω
e
t ⋅ φ +
( )
⋅ 4.15 ( )
Substituting equations (4.14)(4.15) in (4.7)(4.8) and simplifying gives the
synchronous reference frame values:
v
qs
V
pk
cos φ
( )
⋅ 4.16 ( )
v
ds
V
pk
− sin φ
( )
⋅ 4.17 ( )
Equations (4.16)(4.17) are important results. The time varying quantities in
stationary reference frame appear as DC quantities in synchronous reference frame.
This makes the control system less difficult.
The stationary and synchronous reference stator voltage variables can be
represented as complex space vectors as follows:
39
v
qds
s
v
qs
s
j v
ds
s
⋅ − 4.18 ( )
v
qds
v
qs
s
j v
ds
s
⋅ −

\

.
e
j − θ
e
⋅
⋅ 4.19 ( )
Equation 4.19 is direct result obtained using eulers rule (e
jθ
=cosθ+jsinθ,
where j=√1 and θ=θ
e
=ω
e
t).
40
4.1.2 Full transient induction machine model
The induction machine can be mathematically modeled in a synchronously rotating
dq reference frame using the state space flux equations (4.20) – (4.24), where p is a
derivative operator with respect to time (see Appendix A Sections 10.4 and 10.5 for
the derivation of these equations).
p λ
qds
⋅ V
qds
λ
qds
L
r
⋅ λ
qdr
L
m
⋅ −
( )
R
s
L
s
L
r
⋅ σ ⋅
⋅ + j λ
qds
⋅ ω
e
⋅ −
4.20 ( )
p λ
qdr
⋅ λ
qdr
L
s
⋅ λ
qds
L
m
⋅ −
( )
R
r
L
s
L
r
⋅ σ ⋅
⋅
¸
(
(
(
¸
− j λ
qdr
⋅ ω
e
ω
r
−
( )
⋅ −
4.21 ( )
i
qds
λ
qds
L
m
L
r
λ
qdr
⋅ −

\

.
1
L
s
σ ⋅
⋅ 4.22 ( )
T
e
3
2
P
2

\

.
⋅ λ
ds
i
qs
⋅ λ
qs
i
ds
⋅ −
( )
⋅
4.23 ( )
p ω
r
⋅
P
2 J ⋅
T
e
T
L
−
( )
⋅
4.24 ( )
The mathematical model, with V
qds
, ω
e
and T
L
as inputs, calculates the currents (i
qds
),
rotor speed (ω
r
) and electromagnetic torque (T
e
) in the synchronous dq reference
frame. The outputs are stator currents in synchronous reference frame, the rotor
angular velocity and the electromagnetic torque. A built in dq to abc transformation
component in EMTDC is used for converting the output stator currents to abc
reference frame.
The induction machine appears as current source to the voltage sourced converter
so the electrical model is represented as three dependent current sources driven by
41
the currents computed by the mathematical model. The voltages at the converter
terminals are transformed to synchronous dq reference frame and are inputs to the
mathematical model.
Figs. 4.44.7 shows the start up performance of the full transient induction machine
model for a negative load torque (for simplicity the converter is initially replaced with
a three phase voltage source). A negative torque of –11.74 Nm was applied to the
induction machine model. Fig. 4.4 shows the full transient output synchronous dq
reference frame stator currents. Fig. 4.5 shows the actual currents seen in the
electrical model. Fig. 4.6 shows the electromagnetic torque output which settles to 
11.74 Nm after 0.5 sec. Fig. 4.7 shows the rotor angular velocity variation in the
transient and steady state period.
20
0
20
40
60
80
100
120
0 140 280 420 560 700
M
a
g
n
i
t
u
d
e
(
A
)
Time (ms)
Ids Iqs
Fig. 4.4. Stator currents in synchronous reference frame
120
90
60
30
0
30
60
90
120
0 140 280 420 560 700
M
a
g
n
i
t
u
d
e
(
A
)
Time (ms)
Ia Ib Ic
Fig. 4.5. Stator currents in asbscs reference frame
42
30
0
30
60
90
120
150
0 140 280 420 560 700
M
a
g
n
i
t
u
d
e
(
N

m
)
Time (ms)
Fig. 4.6. Electromagnetic torque, T
e
10
32
74
116
158
200
242
284
326
368
410
0 140 280 420 560 700
M
a
g
n
i
t
u
d
e
(
r
a
d
/
s
)
Time (ms)
Fig. 4.7. Rotor angular velocity, ω
r
43
4.2 Field oriented controller
The control of the magnitude and phase of the AC excitation to the induction
machine resulting in a controlled spatial orientation of the electromagnetic fields is
termed as vector control or field oriented control [10]. The basic concept of field
orientation is to align the rotor flux space vector along the daxis so that the qaxis
component of the flux is zero at all times. With this alignment, torque and flux of the
machine can be controlled instantaneously and independently as in a separately
excited DC machine. The rotor flux angle can be obtained either by directly
computing it from the flux measurement using Hall effect sensors (called direct field
oriented control) and the other by indirectly computing it from the measured rotor
position and slip relation (called indirect field oriented control).
Indirect field orientation using voltage as control variable is modeled in
EMTDC for this investigation (see Appendix A 10.4 for the EMTDC implementation).
Fig. 4.8 shows the basic layout of the controller. The controller uses flux and torque
commands as inputs with a compensated flux response for correctly handling flux
variations. The torque command comes from the energy control system (see chapter
6). The flux is kept constant. The outputs, synchronous reference stator voltages
and rotating magnetic field angular velocity, are input commands to space vector
PWM pulse generator model.
The main disadvantage of the indirect field oriented controller is that it is
sensitive to parameter variations, especially rotor resistance. This can be rectified by
the use of flux observers [11]. In the future a flux observer will be added to make the
field oriented controller more robust.
The flywheel is modeled as an added inertia on the rotor of the induction
machine.
44
ω
sl
VOLTAGE DECOUPLER
Σ
1
p
Σ
FLUX
COMMAND
T
C
MEASURED
SPEED
1
p
1 τ
r
p ⋅ +
L
m
L
s
1 σ τ
r
⋅ p ⋅ +
1 τ
r
p ⋅ +
⋅
V
qs
I
qs
R
s
⋅ pλ
qs
⋅ + ω
e
λ
ds
⋅ +
V
ds
I
ds
R
s
⋅ pλ
ds
⋅ + ω
e
λ
qs
⋅ −
σ L
s
⋅
ω
r
I
qs
I
qs
I
ds
I
ds
λ
dr
λ
dr
λ
ds
λ
qs
τ
r
1 τ
r
p ⋅ +
θ
r
θ
sl
4
3
L
r
L
m
P ⋅
⋅
ω
e
ω
e
θ
e
V
qs
V
ds
Fig. 4.8. Basic layout of Indirect field oriented controller model
45
4.3 Space vector PWM pulse generator model
The space vector PWM technique is used for controlling the switching of the
machine side converter. Advantages of this method include higher modulation index,
simpler control system, lower switching losses and less harmonic distortion
compared to sinusoidal PWM [12].
A threephase bridge converter has eight possible switching states with the
constraint that no two switches in the same phase leg are both ON (or OFF) at the
same time as shown in Fig. 4.9. Each state impresses a voltage across the wye
connected machine windings, which can be represented by a voltage space vector.
3
A B C
Vdc
+

1
2
5
4 6
State Switch Vector
I 612 V1
II 123 V2
III 234 V3
IV 345 V4
V 456 V5
VI 561 V6
VII 135 V7
VIII 462 V8
Fig. 4.9. Bridge converter switching states
This results in six active vectors and two zero vectors as shown in Fig.4.10.
The six active vectors divide the plane into six sectors each 60° apart with the other
two zero vectors remain at the origin [12].
46
I
II
III
IV
V
VI
θ
e
V
1
V
2
V
3
V
4
V
5
V
6
V
7
V
8
V
qds
*
ω
e
Fig. 4.10. Vector representation of switching states
The commanded voltage space vector (V
qds
*
) can be constructed by the time
distribution of the eight vectors over the switching interval (T
Z
). To minimize the
number of switching actions and thereby switching losses, only the two adjacent
active vectors and the two zero vectors are used in a sector [12]. The time
distribution of the two active vectors (T
a
and T
b
) and the zero vectors (T
0
/2 and T
0
/2)
in each sector are computed using equations (4.25)(4.27) where α is the active
vector angle with reference to stationary reference frame qaxis.
T
a
3
V
s
V
dc

\

.
⋅ T
Z
⋅ sin
π
3
α + θ
e
−

\

.
⋅ 4.25 ( )
T
b
3
V
s
V
dc

\

.
⋅ T
Z
⋅ sin θ
e
α −
( )
⋅
4.26 ( )
T
0
T
Z
T
a
T
b
+
( )
− 4.27 ( )
47
A space vector pulse width modulator has been modeled in EMTDC. Fig. 4.11
shows the basic layout of the modulator model. The modulator fabricates the space
vector PWM pulses with the commanded V
ds
and V
qs
voltages from IDFOC model,
output frequency (ω
e
), switching frequency and DC bus voltage (V
DC
). It has the
following submodels:
• Time computer
• Asynchronous timer
• Sector pulse generator
• Variable Sample and hold circuit
• Pulse fabricator
T
I
M
E
C
O
M
P
U
T
E
R
F
O
R
Z
E
R
O
A
N
D
A
C
T
I
V
E
V
E
C
T
O
R
S
W
I
T
C
H
I
N
G
EDGE
TRIGGER
S
A
M
P
L
E
&
H
O
L
D
6
SPG
PULSE FABRICATOR
S
P
A
C
E
V
E
C
T
O
R
P
W
M
P
U
L
S
E
S
COMMANDED
FREQUENCY
COMMANDED
DQVOLTAGE
DC BUS
VOLTAGE
SWITCHING
INSTANT
SWITCHING
FRQUENCY
ASYNCHRONOUS
TIMER
MATLAB
INTERFACE
Ta
Tb
To
Tas
Tbs
Tos
S1,S2,S3,S4,S5,S6
t
S
V
qds
V
DC
T
Z
θ
e
Fig. 4.11. Basic layout of space vector PWM pulse generator model
The distribution of the time the two active vectors and the zero vectors spend
in each sector is computationally intensive. A time computer is modeled using a
MATLAB script interfaced to EMTDC (see Appendix B 11.9 and 11.10). The script
outputs the active and zero switching times (T
a
, T
b
and T
0
) and sector reference (S).
The inputs to the time computer are the commanded V
ds
and V
qs
voltages from
48
IDFOC model, angle reference (θ
e
), the switching frequency and the DC bus voltage
(V
DC
). The angle reference, θ
e
, is obtained using a Voltage Controlled Oscillator
(VCO) component in EMTDC. The output is shown in Fig. 4.12.
0
1
2
3
4
5
6
7
450.0000000 456.6666698 463.3333397 470.0000095 476.6666794 483.33334
T
h
e
t
a
r
e
f
(
r
a
d
)
Time (ms)
Fig. 4.12. Angle reference, θ
e
, Time computer input
A sector pulse generator (SPG) generates pulses for the sector reference. It
has one input (S) and six outputs (S1S6). Fig. 4.13 shows the output ‘S’. Depending
on the sector the commanded space vector is in, only one of the six outputs are
going to stay high as shown in Fig. 4.14.
0
1
2
3
4
5
6
7
450.0000000 456.6666698 463.3333397 470.0000095 476.6666794 483.33334
S
e
c
t
o
r
Time (ms)
Fig. 4.13. Sector, S, Time computer output
49
0.5
0.0
0.5
1.0
1.5
450.0000000 456.6666698 463.3333397 470.0000095 476.6666794 483.33334
S
e
c
t
o
r

1
(
H
i
g
h
/
L
o
w
)
Time (ms)
0.5
0.0
0.5
1.0
1.5
450.0000000 456.6666698 463.3333397 470.0000095 476.6666794 483.33334
S
e
c
t
o
r

2
(
H
i
g
h
/
L
o
w
)
Time (ms)
0.5
0.0
0.5
1.0
1.5
450.0000000 456.6666698 463.3333397 470.0000095 476.6666794 483.33334
S
e
c
t
o
r

3
(
H
i
g
h
/
L
o
w
)
Time (ms)
0.5
0.0
0.5
1.0
1.5
450.0000000 456.6666698 463.3333397 470.0000095 476.6666794 483.33334
S
e
c
t
o
r

4
(
H
i
g
h
/
L
o
w
)
Time (ms)
50
0.5
0.0
0.5
1.0
1.5
450.0000000 456.6666698 463.3333397 470.0000095 476.6666794 483.33334
S
e
c
t
o
r

5
(
H
i
g
h
/
L
o
w
)
Time (ms)
0.5
0.0
0.5
1.0
1.5
450.0000000 456.6666698 463.3333397 470.0000095 476.6666794 483.33334
S
e
c
t
o
r

6
(
H
i
g
h
/
L
o
w
)
Time (ms)
Fig. 4.14. Sector reference, S1S6, Sector pulse generator output
An asynchronous timer acts as a time reference for sampling and pulse
fabrication. The inputs to this timer are the commanded frequency and the switching
frequency. The output is a switching time in seconds that resets every time a
switching occurs. Since the time computer calculates the zero and active switching
times in a particular sector, the timer needs to be forcefully reset whenever there is a
sector transition.
For a switching frequency of 1kHz (the switching time is 1ms) and
commanded frequency of 60Hz, (the sector time is 2.778ms ≈ 3ms), the
asynchronous timer output resets three times (3ms/1ms) as shown in Fig. 4.15. A
forced reset is not necessary in this case. Now consider for the same case but
different switching frequency of 1.2kHz (the switching time is 0.83ms). The
asynchronous timer output now resets 3.33 times (2.778ms/0.83ms=3.33). Now a
forceful reset is necessary as shown in Fig. 4.16. A similar case results if the
switching frequency stays the same and the commanded frequency changes. The
51
reset feature was added to make the space vector PWM pulse generator more
flexible and reliable. A reset feature was added to the VCO component in EMTDC,
the output of which is shown as Forced reset in Fig. 4.15 and Fig. 4.16.
0.0000
0.0005
0.0010
450 452 454 456 458 460
T
i
m
e
(
s
)
Time (ms)
Forced reset Timer output
Fig. 4.15. Asynchronous timer output for 1.0kHz
0.0000
0.0005
0.0010
450 452 454 456 458 460
T
i
m
e
(
s
)
Time (ms)
Forced reset Timer output
Fig. 4.16. Asynchronous timer output for 1.2kHz
The active and zero switching times calculated by the time computer are
continuously varying with reference angle θ
e
. They need to be constant during
switching interval, so a sampler component in EMTDC is used. The sampling rate is
dependent on the pulse train obtained from the edge triggered asynchronous timer.
52
Using the time reference, the sampled active and zero switching times, and
sector reference, the pulse fabricator generates space vector PWM pulses. Table
4.1 shows the time distribution of the eight vectors in the sectors. The 135
indicates switches on the upper leg of the converter. The corresponding rows
indicate the logic state of the switches HHigh and LLow. Note that only a single
switch changes its state in a sector (to minimize switching losses). Also note that at
the end of every sector the switches are back to their starting state.
Table 4.1 Time distributions of eight vectors in the sectors.
Sector Tos/2 Tas Tbs Tos Tbs Tas Tos/2
I 8 1 2 7 2 1 8
135 LLL HLL HHL HHH HHL HLL LLL
II 8 3 2 7 2 3 8
135 LLL LHL HHL HHH HHL LHL LLL
III 8 3 4 7 4 3 8
135 LLL LHL LHH HHH LHH LHL LLL
IV 8 5 4 7 4 5 8
135 LLL LLH LHH HHH LHH LLH LLL
V 8 5 6 7 6 5 8
135 LLL LLH HLH HHH HLH LLH LLL
VI 8 1 6 7 6 1 8
135 LLL HLL HLH HHH HLH HLL LLL
A common sequence for time distribution is hidden in Table 4.1 which is
shown in Table 4.2. They are named X, Y and Z.
Table 4.2 Common sequence for time distributions.
Sequence Tos/2 Tas Tbs Tos Tbs Tas Tos/2
X L H H H H H L
Y L L H H H L L
Z L L L H L L L
The pulse fabricator generates pulses that are high for the Tas, Tbs and Tos
times using comparators. These pulses need to be distributed according to the
sequence shown in Table 4.3. This was done by using an array of AND gates (see
AppendixA). The outputs are OR’ed output of each sequence column in Table 4.3,
which are the gate pulses to 135 of the converter. Fig. 4.17 shows the space vector
53
PWM pulse generator output pulses for the top three IGBT’s (135) of the converter.
The gate pulses to 246 are the inverted 135 gate pulses.
Table 4.3 Sequence for time distributions in each sector.
Sector Sequence
I XYZ
II YXZ
III ZXY
IV ZYX
V YZX
VI XZY
0.5
0.0
0.5
1.0
1.5
0.5
0.0
0.5
1.0
1.5
0.5
0.0
0.5
1.0
1.5
163.15 163.26 163.37 163.48 163.59 163.70 163.81 163.92 164.03 164.14 164.25
P
P
1

M
a
in
.S
V
P
W
M
_
1
(
M
a
g
)
P
P
3

M
a
in
.S
V
P
W
M
_
1
(
M
a
g
)
P
P
5

M
a
in
.S
V
P
W
M
_
1
(
M
a
g
)
Time (ms)
IGBT 1 IGBT3 IGBT5
Fig. 4.17. Space vector PWM output pulses in sector 1
54
The software layout of a field oriented control AC drive is shown in Fig. 4.18.
It consists of all of the custom models that were discussed in this chapter integrated
into a field oriented controlled AC drive.
SPACE
VECTOR
PWM
Firing
Pulses
FLUX
COMMAND
TORQUE
COMMAND
MEASURED
SPEED
6
I
N
D
U
C
T
I
O
N
M
A
C
H
I
N
E
M
O
D
E
L
3
3 2
DQ
ABC
DQ
ABC
Te
Va,Vb,Vc
Ia,Ib,Ic
2
Vqs,Vds
Iqs,Ids
IDFOC
Vqs
Vds
We
θe
Vdc
We
Wr
θe
SERIES VOLTAGE
COMPENSATOR
Fig. 4.18. Software layout of a field oriented AC control drive
55
5.0 STATIC SERIES COMPENSATOR MODEL
A static series compensator injects three AC voltages of variable amplitude and
phase angle into the line for voltage sag correction. Without energy storage, the
compensator can only inject voltages in quadrature with the load current and hence
larger voltage injection is required to mitigate the voltage sag. In addition, purely
reactive static series sag compensator is only effective for small voltage sags. With
energy storage, the static series compensator has flexibility to inject voltage at any
phase angle and can compensate for deeper and longer voltage sags.
Fig. 5.1 shows the basic layout of the static series compensator, modeled in
EMTDC (see Appendix B). It consists of a shipboard power system model, series
transformer, LC filters, VSC and a sinusoidal PWM pulse generator for controlling
the SPS side VSC.
SHIPBOARD
POWER
SYSTEM
CRITICAL
LOAD
Firing
Pulses
6
SINUSOIDAL
PWM
SERIES
TRANSFORMER
FILTER VSC DC
LINK
Modulation Index
Phase Angle
DC bus
voltage
FIELD
ORIENTED
CONTROL
AC DRIVE
Fig. 5.1. Basic layout of a static series compensator
56
5.1 Shipboard power system model
The shipboard power system is modeled as a simple radial system with a
source, a bus and two loads as shown in Fig. 5.2. One is a sensitive load to which
the flywheel energy storage system is connected in series. The other load is
connected to the same bus through a distribution line. When a fault occurs at this
load, the sensitive load experiences voltage sag. Faults are created using a three
phase fault component. The duration of the fault is controlled by a timed fault logic
component. The depth of the sag can be changed by varying the length of the
distribution line or source impedance.
FESS
CRITICAL
LOAD
OTHER
LOADS
S
Fig. 5.2. Shipboard power system model
5.2 Series transformer and filters
The series injection transformer can be connected in two ways, either
wye/open winding or delta/open winding. Delta/open winding is used since it
prevents the third harmonic and zero sequence currents from entering the system
and also maximizes the use of the DC link compared to wye/open winding. A delta
connected LC filter bank is used to smooth the injected voltage. Filters delay the
response of the energy storage system to voltage sags.
57
5.3 Sinusoidal PWM pulse generator model
A sinusoidal pulse width modulator is modeled in EMTDC to control the
switching of the VSC on the SPS side. For a given amplitude modulation index,
phase angle reference, AC system frequency and DC bus voltage, it generates firing
pulses for the converter. The switching frequency is 10.8kHz. The amplitude is fixed
at 1.0 and phase angle is controlled such that during standby mode the injected
voltage and line current are in quadrature. During the discharge mode a proportional
integral feedback error between the per unit magnitude of the measured critical load
voltage space vector and the reference value (0.95) is computed such that the
phase angle reference remains the same as the pre sag value. During the charge
mode the speed and DC bus controllers allow the energy to flow into the flywheel
and when the flywheel reaches its rated speed it is again in standby mode with the
line current in quadrature to the injected voltage.
The models were integrated and tested by replacing the machine side with an
equivalent current source before integrating it with the field oriented control AC drive
model (see Appendix B).
58
6.0 CONTROL SYSTEM
The control system consists of two main parts, an inner control system and an outer
control system. The inner control system consists of the two firing schemes for
controlling the two voltage sourced converters. A sinusoidal PWM scheme is used
for static series compensator, and a space vector PWM scheme is used for the field
oriented controlled AC drive. The control system can be viewed as having two
levels. The outer control system responds to the external system. The inner control
system generates the gate pulses for the devices in the converters based on inputs
from the outer control system. The inputs to the sinusoidal PWM are controlled
directly by the outer control system. The inputs to the space vector PWM are
indirectly controlled by the outer control system with a field oriented controller. The
outer control system consists of a sag detector, sag corrector and an energy control
system. The basic layout is shown in Fig. 6.1.
SAG
DETECTOR
ENERGY
CONTROL SYSTEM
OUTER CONTROL SYSTEM
SPACE VECTOR
PWM PULSE
GENERATOR
SINUSOIDAL
PWM PULSE
GENERATOR
INDIRECT
FOC
SAG
CORRECTOR
M
Fig. 6.1. Control System Layout
59
The outer control system determines the energy to flow in to and out of the
system according to the sag correction and flywheel recharging needs. The outputs
of this control system are a torque command, modulation index and phase angle,
which are inputs to the inner control system.
6.1 Sag Detector and Corrector
6.1.1 Sag Detector
The sag detector detects the presence of voltage sag and activates the
control system for sag correction. The layout of the sag detector is shown in Fig. 6.2.
The output, SD, is a pulse that is active as long as the voltage is out of tolerance
during the sag. The inputs are the voltages measured on the SPS side of the series
transformer. The measured voltages are converted to DQ space vectors in a
synchronously rotating reference frame. The per unit magnitude of this space vector
is compared to a reference value of 0.98. Theoretically, the reference value could be
set to 1.0, but that makes the energy storage system overly sensitive resulting in
incorrect compensation of transients at the end of sag. A transient of 1% reduction is
seen at the end of the voltage sag, so the reference value is set to 0.98 to prevent
sag detector detecting it. It can be set to any value from 0.91 to 1.0 depending on
the maximum transient that may occur after a voltage sag.
The sag detector provides an accurate result for balanced voltage sags. The
energy storage response is based on how fast the sag is detected and how reliably it
is detected.
The advantage of using synchronous reference frame is that the inputs are
DC and hence control system is simpler. Also, compared to RMS based sag
detectors, the DQ based sag detectors have faster response time as they are based
on instantaneous quantities. RMS based sag detectors have slow response time
since they are based on half cycle or full cycle of instantaneous data [4].
60
6.1.2 Sag Corrector
A proportional feedback controller for voltage sag correction is shown in Fig.
6.2. The output, T
SAG
, is a negative torque command to the energy control system.
T
SAG
, is a scaled error of the difference between the per unit magnitude of the SPS
voltage space vector measured and the reference value (1.0 p.u). T
SAG
value is
limited by the amount of energy available for discharge and stability conditions of the
energy storage system. A detailed analysis of this will be a future topic. A simple
hard limiter was used for limiting the maximum and minimum value of the negative
torque output.
3
DQ
ABC
2
V
SPS
V
QDS
M
1
0.36
θ
e
V
QDS
0.98
COMPARATOR
perunitizing
Σ
1.0
K
P
T
SAG
SD
SAG CORRECTOR
TORQUE
LIMITER
SAG DETECTOR
REF
K
P
100 −
FROM
PLL
Fig. 6.2. Sag detector and sag corrector layout
61
6.2 Energy Control System
Fig. 6.3 shows the basic layout of the energy control system. The output is a net
torque command to the Indirect FOC, which is the sum of outputs from three main
control blocks: DC voltage control, speed control and sag correction control. The
torque command, T
C
, is an input to the Indirect FOC in Fig. 4.8.
A proportional integral feedback controller is used for controlling rotor speed
and DC bus voltage. Speed control, the slowest controller, is used for charging the
flywheel to its rated speed when the sag is cleared. If the sag detector detects a sag,
SD goes high. This results in bypassing the speed and DC bus voltage controllers
(as shown with the inverters), such that T
C
equals T
SAG
, and improves the response
time. Once the sag is cleared, SD goes low, reactivating the speed and DC bus
voltage controllers. The speed controller is intentionally made slower to prevent sag
due to charging the flywheel and thereby improving stability of the energy storage
system.
SPEED
CONTROLLER
Σ
DC BUS
VOLTAGE
CONTROLLER
Σ
SD
SD
Σ
T
SAG
SD
X
COMMANDED
SPEED
ω
r
MEASURED
MEASURED
V
DC
COMMANDED
DC VOLTAGE
T
SAG
T
DC
T
SP
TORQUE
COMMAND
TO IDFOC
T
C
K
P
1 −
K
I
1000 −
K
P
0.5 −
K
I
0.013 −
Fig. 6.3. Energy control system layout
62
7.0 RESULTS
The models discussed in Chapters 4 through 6 are integrated with a flywheel energy
storage system model and a test case was created to analyze its performance.
Appendix B provides more detail on how these models were integrated.
7.1 Test case
The flywheel energy storage system performance is analyzed by creating a three
phase fault at the location shown in Fig. 7.1, resulting in a balanced voltage sag of
63% on the SPS side of the series transformer. The depth of the voltage sag
depends on this distance of the fault from the bus. The fault occurs at 1.5sec in to
the simulation time frame, and has duration of 20 cycles (60Hz). The simulation
time step is 10 microseconds.
CRITICAL
LOAD
OTHER
LOAD
S
FESS
+
=
Fig. 7.1. Test case for analyzing FESS performance
63
7.2 Analysis of simulation results
Fig. 7.2 shows the detection of the voltage sag by the sag detector. SD is zero until
the fault is detected and then goes high (logic value 1.0) when the SPS voltage is
out of tolerance. The output VdqSPS is the per unit magnitude of SPS side voltage
space vector and VabcSPS is the per unit RMS voltage. Note that the space vector
voltage magnitude changes much more quickly, since it is based on instantaneous
quantities, and not averaged over a cycle as the RMS voltages are. Therefore, a
RMS voltage reference based sag detector will react more slowly, and hurt the
response of the system. The space vector based DQ voltage is used to provide
faster, more accurate detection of the voltage sag.
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.46 1.50 1.54 1.58 1.62 1.66 1.70 1.74 1.78 1.82 1.86 1.90 1.94
M
a
g
n
i
t
u
d
e
(
H
i
g
h
/
L
o
w
,
p
.
u
,
p
.
u
)
Time (s)
SD VdqSPS VabcSPS
Fig. 7.2. Sag detector response
When SD goes high, as shown in Fig. 7.2, the sag corrector is activated and
the speed and DC bus controllers are bypassed. The sag corrector commands a
negative torque, T
SAG
, to the IDFOC, for energy conversion. The flywheel was in
standby mode, running at 346 rad/s, until t=1.5sec when SD goes high.
Fig. 7.3 shows the flywheel slowing down due to the negative torque
command from 346 rad/s to 318 rad/s. Fig. 7.4 shows the DC bus voltage variation
from rated (340V) during energy reversal.
64
300
310
320
330
340
350
360
1.46 1.50 1.54 1.58 1.62 1.66 1.70 1.74 1.78 1.82 1.86 1.90 1.94
R
o
t
o
r
V
e
l
o
c
i
t
y
(
r
a
d
/
s
)
Time (s)
Fig. 7.3. Rotor angular velocity variation
0
340
1.46 1.50 1.54 1.58 1.62 1.66 1.70 1.74 1.78 1.82 1.86 1.90 1.94
D
C
B
u
s
V
o
l
t
a
g
e
(
V
)
Time (s)
Fig. 7.4. DC bus voltage variation
Fig. 7.5 shows the power flow measured into the machine terminals and into
the secondary of the series transformer. It shows the response of the power
electronic interface during energy reversal.
P
o
w
e
r
(
k
W
)
Time (s)
7
6
5
4
3
2
1
0
1
1.46 1.50 1.54 1.58 1.62 1.66 1.70 1.74 1.78 1.82 1.86 1.90 1.94
MACHINE INJECTED
Fig. 7.5. Power flow into the machine and static series compensator
Fig. 7.6 shows the perunit RMS voltage on the critical load side and the SPS
side. The RMS voltage on the SPS side was initially at 1.0p.u. A voltage sag of 63%
is seen lasting for 20 cycles (60Hz). The RMS voltage on the critical load side was
65
corrected to 0.95p.u (5% less from presag voltage). An over voltage of 1.1p.u is
seen at the end of the sag.
0.4
0.6
0.8
1.0
1.2
1.46 1.50 1.54 1.58 1.62 1.66 1.70 1.74 1.78 1.82 1.86 1.90 1.94
R
M
S
V
o
l
t
g
a
e
(
p
.
u
)
Time (s)
CRITICAL LOAD SPS
Fig. 7.6. RMS voltages measured at the critical load side and SPS side
Fig. 7.7 and Fig. 7.8 show the phasetoground voltages on the SPS side and
critical load side of the FESS. The FESS responded within 2 cycles to keep the
critical load voltage within the 5% tolerance (i.e. the sag is corrected to 0.95 per unit,
not to 1.0 per unit).
425
340
255
170
85
0
85
170
255
340
425
1.46 1.50 1.54 1.58 1.62 1.66 1.70 1.74 1.78 1.82 1.86 1.90 1.94
V
o
l
t
a
g
e
(
V
)
Time (s)
AG BG CG
Fig. 7.7. Phase to ground voltages on the SPS side
66
425
340
255
170
85
0
85
170
255
340
425
1.46 1.50 1.54 1.58 1.62 1.66 1.70 1.74 1.78 1.82 1.86 1.90 1.94
V
o
l
t
a
g
e
(
V
)
Time (s)
AG BG CG
Fig. 7.8. Phase to ground voltages on the critical load side
The sag correction can be done for 0% tolerance, but it will result in larger
overvoltages at the end of the sag, with the potential to cause insulation damage. In
this case, the critical load voltage was regulated below 5% of the nominal.
Fig. 7.9 shows the phase relationship between series injected voltage by the
VSC on the SPS side and the load current to the critical load. There is no power
injection initially since the injected voltage is in quadrature with line current. During
voltage sag correction the phase angle is almost in phase thereby allowing energy to
flow into the shipboard power system.
67
175
105
35
35
105
175
1.46 1.50 1.54 1.58 1.62 1.66 1.70 1.74
P
h
a
s
e
A
V
o
l
t
a
g
e
,
C
u
r
r
e
n
t
(
V
,
A
)
Time (s)
Series injected voltage Critical load current
Fig. 7.9. Phase AGround voltage at the critical load and SPS, injected voltage and
Phase A line current
68
8.0 CONCLUSIONS AND FUTUREWORK
8.1 Conclusions
The modeling and analysis of a flywheel energy storage system for voltage sag
correction on a shipboard power system has been presented. A control scheme has
been proposed for voltage sag correction and energy control. The sag correction is
based on negative torque command, which is a scaled error of the difference
between shipboard power system side of the synchronously rotating reference dq
voltage and its reference. An energy control system that regulates the DC bus
voltage and charges the flywheel has been described. A dq space vector based sag
detector has been modeled for sag detection. A feed forward control by the sag
detector output which disables the speed and DC bus voltage controller improves
the energy storage system performance in mitigating voltage sags.
The shipboard power system and the power converters were modeled using
EMTDC, along with the full transient synchronous reference based dq induction
machine and flywheel model. An indirect field oriented controller for the control of
flywheel induction machine was also modeled in EMTDC. The space vector PWM
pulse generator model to generate firing pulses for the flywheel converter was
modeled in MATLAB and interfaced to the switching device models in EMTDC. The
overall energy management scheme, the sag detector, and the sag corrector were
all modeled in EMTDC, along with the control scheme for the shipboard power
system side VSC.
The response of the energy storage system to a balanced voltage sag was
presented. The advantage of a dq space vector based sag detector over RMS based
sag detector has been shown. The instantaneous voltages are compensated within
2 cycles to keep the voltage tolerance within 5% of rated voltage. The main
advantage of this FESS is high power density. It can mitigate long duration voltage
sags efficiently.
69
8.2 Future work
The future work should include more detailed analysis of the control scheme for
energy storage system for unbalanced sags and comparison of its performance with
a laboratory flywheel interfaced to an analog model power system (AMPS). The
same approach done for modeling the energy storage system in EMTDC can be
applied to build a laboratory model.
The following figures shows the lab setup that is going to be used in future.
Fig. 8.1 shows the analog model power system on the right and flywheel coupled
induction machines on the left.
Fig. 8.1. Analog model power system
(From left to right Amit Somani, Ganesh Balasubramanian, Mangapathi Mynam, Dr.Johnson and
Satish Samineni)
Fig. 8.2 shows an induction machine, flywheel and DC machine connected to
the same shaft. The DC machine is used for supplying energy storage system
losses.
70
Fig. 8.2. Flywheel coupled induction machine
The practical approach is to build and test two separate models: a static
series compensator and a field oriented control AC drive, the same strategy that was
followed in EMTDC modeling. A static series compensator can be built and tested by
replacing the field oriented control AC drive with a DC source. Similarly a field
oriented control AC drive can be built by replacing the static series compensator with
a DC source. Upon successful completion of this testing, they can be integrated and
tested with the proposed outer control system. The laboratory results will be
compared with the simulation results and the flywheel energy storage system
performance can be analyzed.
There are several challenges that might arise during practical implementation,
especially software coding for controlling the power converters, parameter
dependancy of indirect field oriented controller and designing tests for obtaining
induction machine parameters, filter design and series transformer design.
71
The EMTDC models developed in this thesis could be used as a starting point
to investigate the following:
• Flywheel energy storage system performance with a flux observer in the indirect
field oriented controller. A flux observer eliminates the parameter dependancy of
indirect field oriented controller thus improving the performance of the control
system.
• Performance analysis of a flywheel energy storage system for voltage swell
correction on ungrounded systems. The energy storage system can be used for
mitigating swells in a fashion similar to that for mitigating voltage sags by simply
adding a swell detector.
• An adaptive flywheel energy storage system that can switch from static series
compensator during sag/swell corrections to static shunt compensator for
mitigating interruptions. The static shunt compensator with energy storage
system then acts as a UPS. This adaptive energy storage system is an efficient
way for mitigating sags, swells and interruptions as it uses the combined
advantages of static series compensator and static shunt compensator.
• The static series compensator can act as an active filter for mitigating voltage
harmonics. An analysis should be performed on the tradeoffs between sag
correction and harmonic correction.
• Modeling and analysis of a Static Synchronous Series Compensator (SSSC) for
power flow applications. SSSC is used for controlling the transmission line
loading, thereby improving the transmission capacity. In other words it can make
a line look shorter or longer thereby increasing or decreasing the real power
transfer capability. With energy storage, a SSSC can be used for improving
transient stability and damping power oscillations.
• Implementation of a dynamically varying torque limiter in the proposed sag
corrector that limits the T
SAG
value depending on the amount of energy available
for discharge and stability of the storage system.
72
BIBILIOGRAPHY
[1] G. Genta, Kinetic Energy Storage, University Press, Cambridge, 1985.
[2] A. TerGazarian, Energy Storage Systems For Power Systems, IEE Power
and Energy Series, 1994.
[3] J. G. Ciezki, R. W. Ashton, “Selection and stability issues associated with a
Navy shipboard DC Zonal electric distribution system,” IEEE Transactions on
Power Delivery, Vol. 15, No. 2, pp. 665669, April 2000.
[4] Math. H. J. Bollen, Understanding Power Quality Problems, IEEE Press,
2000.
[5] A. T. Adediran, H. Xiao and K.L. Butler, “Fault Studies of an U.S. Naval
Shipboard Power System,” NAPS, Univerity of Waterloo, Canada, pp 118 to
125, October 2000.
[6] R. S. Weissbach, G. G. Karady and R. G. Farmer, “Dynamic Voltage
Compensation on Distribution Feeders using Flywheel Energy Storage,” IEEE
Transactions on Power Delivery, Vol.14, No.2, pp. 465471, April 1999.
[7] PSCAD/EMTDC User’s Manual, Manitoba HVDC Research Center,
Manitoba, Canada.
[8] B. K. Bose, Modern Power Electronics and AC Drives, Prentice Hall PTR,
2002.
[9] Field Oriented Control of 3 phase AC Motors, BPRA073, Texas Instruments
Europe, 1998.
[10] D. W. Novotny and T. A. Lipo, Vector Control and Dynamics of AC Drives,
Oxford Science Publications, 1997.
[11] P. L. Jansen and R. D. Lorenz, “A Physically Insightful Approach to the
Design and Accuracy Assessment of Flux Observers for Field Oriented
Induction Machine Drives,” IEEE Transactions on Industry Applications, Vol
30, No. 1, pp. 101110, Jan/ Feb., 1994.
[12] H. W. Van Der Broeck, H. C. Skudelny and G. V. Stanke, “Analysis and
Realization of a Pulsewidth Modulator Based on Voltage Space Vectors,”
IEEE Transactions on Industry Applications, Vol.24, No.1, pp. 142150,
January/February 1988.
73
APPENDIX A
10.1 Three phase variable representation of induction machine voltage
equations
The stator and rotor circuit voltage equations of an induction machine can be
conveniently written in matrix form:
v
abcs
r
s
i
abcs
⋅ p λ
abcs
⋅ + 10.1 ( )
0 r
r
i
abcr
⋅ p λ
abcr
⋅ + 10.2 ( )
where p is d/dt and v
abcs
, i
abcs
and λ
abcs
(stator voltage, stator current and
stator flux in abc reference) are 3X1 vectors defined by:
v
abcs
v
as
v
bs
v
cs

\


.
i
abcs
i
as
i
bs
i
cs

\


.
λ
abcs
λ
as
λ
bs
λ
cs

\



.
10.3 ( )
The rotor variables i
abcr
and λ
abcr
are similar.
The stator and rotor circuits have inductive coupling, so the flux linkages can be
written in terms of machine currents as follows:
λ
abcs
λ
ss
λ
sr
+ 10.4 ( )
λ
abcr
λ
rs
λ
rr
+ 10.5 ( )
where:
74
λ
ss
L
as
L
abs
L
acs
L
abs
L
bs
L
bcs
L
acs
L
bcs
L
cs

\


.
i
abcs
⋅
10.6 ( )
λ
sr
L
asar
L
bsar
L
csar
L
asbr
L
bsbr
L
csbr
L
ascr
L
bscr
L
cscr

\


.
i
abcr
⋅
10.7 ( )
λ
rs
L
as
L
abs
L
acs
L
abs
L
bs
L
bcs
L
acs
L
bcs
L
cs

\


.
i
abcs
⋅
10.8 ( )
λ
rr
L
ar
L
abr
L
acr
L
abr
L
br
L
bcr
L
acr
L
bcr
L
cr

\


.
i
abcr
⋅ 10.9 ( )
Note, the mutual inductances between stator and rotor windings are
dependent on the rotor position θ
r
, so λ
sr
and λ
rs
are functions of θ
r
.
75
10.2 Space vector representation of induction machine voltage equations
The stator and rotor circuit equations of an induction machine can be conveniently
written in space vector form as:
v
abcs
r
s
i
abcs
⋅ p λ
abcs
⋅ + 10.10 ( )
0 r
r
i
abcr
⋅ p λ
abcr
⋅ + 10.11 ( )
where
v
abcs
2
3
v
as
α v
bs
⋅ + α
2
v
cs
⋅ +

\

.
⋅ 10.12 ( )
and α is a 120
0
operator (1.0e
j120deg
) . Similarly for i
abcs
, v
abcr
and i
abcr.
This approach helps in representing the induction machine voltage equations
in a compact form. However the mutual inductances between stator and rotor
windings are still dependent on the rotor position θ
r
, so λ
sr
and λ
rs
are still functions
of θ
r
.
10.3 Stationary DQ reference frame representation of induction machine
voltage equations
The stator and rotor circuit equations of an induction machine can be conveniently
written as stationary DQ reference variables in the form:
v
qds
s
r
s
i
qds
s
⋅ p λ
qds
s
⋅ + 10.13 ( )
0 r
r
i
qdr
s
⋅ p λ
qdr
s
⋅ + j ω
r
⋅ λ
qdr
s
⋅ − 10.14 ( )
76
where
v
qds
s
v
qs
s
j v
ds
s
⋅ −
i
qds
s
i
qs
s
j i
ds
s
⋅ −
λ
qds
s
λ
qs
s
j λ
ds
s
⋅ −
10.15 ( )
i
qdr
s
i
qr
s
j i
dr
s
⋅ −
λ
qdr
s
λ
qr
s
j λ
dr
s
⋅ −
This assumes that v
qdr
s
is zero (secondary short circuited).
The electromagnetic torque can be calculated using:
T
e
3
2
P
2

\

.
⋅ Im i
qdr
s
λ
qdr
s
⋅

\

.
⋅ 10.16 ( )
where P is the number of stator poles.
The torque can be calculated from a combination of any of the variables discussed
above. Equation (10.16) is one possible form.
Then the rotor angular velocity, ω
r
can be calculated using:
T
e
T
L
2
P
J p ⋅ ω
r
⋅ + 10.17 ( )
where T
L
is the load torque, J is the inertia of the rotor.
77
10.4 Synchronous DQ reference frame representation of induction machine
voltage equations
The stator and rotor circuit equations of an induction machine can be conveniently
written in stationary DQ reference variables form:
v
qds
r
s
i
qds
⋅ p λ
qds
⋅ + j ω
e
⋅ λ
qds
⋅ + 10.18 ( )
0 r
r
i
qdr
⋅ p λ
qdr
⋅ + j ω
e
ω
r
−
( )
⋅ λ
qdr
⋅ + 10.19 ( )
and
λ
qds
L
s
i
qds
⋅ L
m
i
qdr
⋅ +
10.20 ( )
λ
qdr
L
r
i
qdr
⋅ L
m
i
qds
⋅ +
10.21 ( )
λ
qdm
L
m
i
qds
i
qdr
+
( )
⋅
10.22 ( )
L
s
and L
r
are given by:
L
s
L
ls
L
m
+ L
r
L
lr
L
m
+ 10.23 ( )
where L
ls
and L
lr
are leakage reactances of stator and rotor respectively and L
m
is
magnetizing inductance. Then the electromagnetic torque can be calculated using:
T
e
3
2
P
2

\

.
⋅ L
m
⋅ Im i
qds
i
qdr
⋅
( )
⋅
10.24 ( )
T
e
3
2
P
2

\

.
⋅
L
m
L
r
⋅ Im i
qds
λ
qdr
⋅
( )
⋅
78
10.5 State space flux equations for modeling induction machine
The following procedure gives an introduction for deriving state space flux equations
useful for modeling induction machines.
Consider a Qaxis based form of equation (10.18)
v
qs
r
s
i
qs
⋅ p λ
qs
⋅ + ω
e
λ
qs
⋅ + 10.25 ( )
Consider a Qaxis based form of equations (10.20) and (10.21)
λ
qs
L
s
i
qs
⋅ L
m
i
qr
⋅ +
10.26 ( )
λ
qr
L
r
i
qr
⋅ L
m
i
qs
⋅ +
10.27 ( )
Rearranging equations (10.26) and (10.27) for i
qs
, i
qr
results in:
i
qs
λ
qs
L
m
i
qr
⋅ −
L
s
10.28 ( )
10.29 ( )
i
qr
λ
qr
L
m
i
qs
⋅ −
L
r
Substituting equation (10.29) in (10.28) and rearranging:
79
i
qs
λ
qs
L
m
λ
qr
L
m
i
qs
⋅ −
L
r

\

.
⋅ −
L
s
λ
qs
L
m
λ
qr
L
r
⋅ −
L
m
2
L
r
i
qs
⋅ +
L
s
10.30 ( )
i
qs
σ ⋅
λ
qs
L
s
L
m
L
s
L
r
⋅
λ
qr
⋅ −
i
qs
λ
qs
σ L
s
⋅
L
m
L
s
L
r
⋅ σ ⋅
λ
qr
⋅ − L
r
λ
qs
⋅ L
m
λ
qr
⋅ −
( )
1
L
s
L
r
⋅ σ ⋅
⋅
where
σ 1
L
m
2
L
s
L
r
⋅
−
10.31 ( )
substituting the simplified form of (10.30) in (10.25), results in:
p λ
qs
⋅ v
qs
L
r
λ
qs
⋅ L
m
λ
qr
⋅ −
( )
r
s
L
s
L
r
⋅ σ ⋅
⋅ + ω
e
λ
ds
⋅ −
10.32 ( )
The same procedure can be applied for deriving state space flux equations
for λ
ds
, λ
qr
and λ
dr
.
80
10.6 Indirect field oriented controller equations
The objective for field oriented control is to zero out the flux linkage along the
qaxis, so:
λ
qr
0 10.33 ( )
Substituting equation (10.33) in equations (10.19) and separating it in q and d forms
results in:
0 r
r
i
qr
⋅ ω
e
ω
r
−
( )
λ
dr
⋅ + 10.34 ( )
0 r
r
i
dr
⋅ p λ
dr
⋅ + 10.35 ( )
Similarly substituting equation (10.33) in equation (10.21) and writing it in q form
separately:
λ
qr
L
m
i
qs
⋅ L
r
i
qr
⋅ + 0 10.36 ( )
Similarly substituting equation (10.33) in flux linkage form for torque in equation
(10.24):
T
e
3
2
P
2

\

.
⋅
L
m
L
r
⋅ i
qs
λ
dr
⋅
( )
⋅ 10.37 ( )
Using equations (10.34) and (10.36) for slip angular velocity expression:
81
i
qr
L
m
L
r
− i
qs
⋅ 10.38 ( )
ω
e
ω
r
− S ω
e
⋅ ω
sl
r
r
i
qr
⋅
λ
dr
− 10.39 ( )
ω
sl
r
r
L
m
⋅ i
qs
⋅
L
r
λ
dr
⋅
10.40 ( )
Using the d form of equation (10.21) and simplifying:
λ
dr
L
r
i
dr
⋅ L
m
i
ds
⋅ + 10.38 ( )
λ
dr
L
r
p λ
dr
⋅
r
r
−

\

.
⋅ L
m
i
ds
⋅ +
10.39 ( )
λ
dr
L
m
i
ds
⋅
1 τ
r
p ⋅ +
10.40 ( )
where
τ
r
L
r
r
r
10.41 ( )
Using the q form of equation (10.20) and simplifying:
λ
qs
L
s
i
qs
⋅ L
m
i
qr
⋅ + L
s
1
L
m
2
L
s
L
r
⋅
−

\

.
i
qs
⋅ σ L
s
⋅ i
qs
⋅ 10.42 ( )
82
Using the d form of equation (10.20) and simplifying:
λ
ds
L
s
i
ds
⋅ L
m
i
dr
⋅ +
λ
ds
L
s
i
ds
⋅ L
m
p λ
dr
⋅
r
r
−

\

.
⋅ +
λ
ds
L
s
i
ds
⋅ L
m
p
L
m
i
ds
⋅
1 τ
r
p ⋅ +

\

.
⋅
r
r
−
¸
(
(
(
(
¸
⋅ +
10.43 ( )
λ
ds
L
s
i
ds
⋅
τ
r
L
m
2
⋅ p ⋅ i
ds
⋅
1 τ
r
p ⋅ +
( )
L
r
⋅
−
λ
ds
L
s
1
1 σ −
( )
τ
r
⋅ p ⋅
1 τ
r
p ⋅ +
−
¸
(
(
(
¸
i
ds
⋅
λ
ds
L
s
1 σ τ
r
⋅ p ⋅ +
1 τ
r
p ⋅ +

\

.
i
ds
⋅
Using equation (10.37) and (10.40):
i
qs
4
3 P ⋅
L
r
L
m
⋅
T
e
λ
dr
⋅ 10.44 ( )
i
ds
1 τ
r
p ⋅ +
L
m
λ
dr
⋅
10.45 ( )
83
APPENDIX B
EMTDC/PSCAD diagrams
The following figures show the PSCAD/EMTDC diagrams of a flywheel energy
storage system model. The PSCAD/EMTDC implementation of models discussed in
Chapters 4, 5 and 6 are shown in this chapter.
11.1 Flywheel energy storage system electrical model
Fig. 11.1 shows the PSCAD/EMTDC layout of the flywheel energy storage system
electrical model. Fig. 11.1 was split at the common DC link, into Fig. 11.2 and Fig.
11.3 for clarity.
C
Ec
D D
D D D
D
fp4 fp6
I I I
fp2
fp5 fp3 fp1
Ea
Ia1
Ic1
Eb
M
M
B
1.0e+013
M
Ecm
Iai
Ibi
Ici
I
A
B
C
Pmac Qmac
A
B
C
Ebm
A
I
M
Eam
Pow
er
A B
P Q
D
D D
2
I
2
I
2
I
D
Eatr
ans
Eai
nv A
B
C
A
B
C
A
B
C
Vb
0.001
0.001
0.001
Eclo
ad
2
I
0.01
0.01
0.01
0.01
D
2
I
Pow
er
A B
P Q
3 Phase
RMS
0.2
0.2
0.2
480V,
50KVA
60Hz, 3Ph
Z1=0.4ohm
Easource
Ebsource
Ecsource
Eal
oad
Ebl
oad
Eaact
5.0
5.0
5.0
2
I
S
S
Eab
Ebs
Ias
Ibs
Ics
480/480,
50KVA
XL=10%
#1 #2
#1 #2
D
10.0 10.0 10.0
I
Idcmachine Idcsps
Aa
Bb
Cc
Iaa
P
N
Edcmachine
fpa1 fpa3 fpa5
fpa4 fpa6 fpa2
Icc
Ibb
CRITICAL LOAD
Eas
Pcon
Ib1
100
0.0
1.0e005
1.0e005
1.0e005
1.0e005
1.0e005
1.0e005
20.0
20.0
FAULTS
C
B
A
ABC>G
20.0
A B C
A
B
C
Vload
Vso
urce
3 Phase
RMS
3
Pha
se
RM
S
Easer
Ebser
Ecser
Qcon
0.4
A
B
C
#1 #2
0.01
0.01
Ti med
Fault
Logic
SOURCE
SERIES TRANSFORMER
POWER METER
RC FILTER
SHIPBOARD POWER SYSTEM SIDE
VOLTAGE SOURCED CONVERTER
COMMON DC LINK
MACHINE SIDE
VOLTAGE SOURCED CONVERTER
POWER METER INDUCTION MACHINE
ELECTRICAL MODEL
100
0.0
OTHER LOAD DISTRIBUTION LINE
FAULT CREATOR
GATE PULSES FROM
SINUSOIDAL PWM PULSE
GENERATOR
GATE PULSES FROM
SPACE VECTOR PWM
PULSE GENERATOR
DRIVEN BY THE
DATA MODEL
Fig. 11.1. Flywheel energy storage system model
84
11.2 Flywheel energy storage system electrical model
D
D D
2
I
2
I
2
I
D
E
a
tr
a
n
s
E
a
in
v
A
B
C
A
B
C
A
B
C
Vb
0.001
0.001
0.001
E
c
lo
a
d
2
I
0.01
0.01
0.01
0.01
D
2
I
P
o
w
e
r A B
P Q
3 Phase
RMS
0.2
0.2
0.2
480V,
50KVA
60Hz, 3Ph
Z1=0 4ohm
Easource
Ebsource
Ecsource
E
a
lo
a
d
E
b
lo
a
d
Eaact
5.0
5.0
5.0
2
I
S
S
Eab
Ebs
Ias
Ibs
Ics
480/480,
50KVA
XL 10%
#1 #2
#1 #2
D
1
0
.0
1
0
.0
1
0
.0
Idcsps
Aa
Bb
Cc
Iaa
P
N
fpa1 fpa3 fpa5
fpa4 fpa6 fpa2
Icc
Ibb
CRITICAL LOAD
Eas
Pcon
1
0
0
0
.0
1.0e005
1.0e005
1.0e005
2
0
.0
2
0
.0
FAULTS
C
B
A
ABC>G
2
0
.0
A B C
A
B
C
Vload
V
s
o
u
r
c
e
3 Phase
RMS
3
P
h
a
s
e
R
M
S
Easer
Ebser
Ecser
Qcon
0.4
A
B
C
#1 #2
0.01
0.01
Timed
Fault
Logic
SOURCE
SERIESTRANSFORMER
POWERMETER
RCFILTER
SHIPBOARDPOWERSYSTEMSIDE
VOLTAGESOURCEDCONVERTER
COMMONDCLINK
1
0
0
0
.0
OTHERLOAD DISTRIBUTIONLINE
FAULTCREATOR
GATEPULSESFROM
SINUSOIDAL PWMPULSE
GENERATOR
Fig. 11.2. Static series compensator model
C
Ec
D D
D D D
D
fp4 fp6
I I I
fp2
fp5 fp3 fp1
Ea
Ia1
Ic1
Eb
M
M
B
1.0e+013
M
Ecm
Iai
Ibi
Ici
I
A
B
C
Pmac Qmac
A
B
C
Ebm
A
I
M
Eam
P
o
w
e
r A B
P Q
I
Idcmachine
P
N
Edcmachine
Ib1
1
0
0
0
.
0
1.0e005
1.0e005
1.0e005
COMMON DC LINK
MACHINE SIDE
VOLTAGE SOURCED CONVERTER
POWER METER INDUCTION MACHINE
ELECTRICAL MODEL
1
0
0
0
.
0
GATE PULSES FROM
SPACE VECTOR PWM
PULSE GENERATOR
DRIVEN BYTHE
DATAMODEL
Fig. 11.3. Field oriented control AC drive model
85
11.3 Flywheel energy storage inner and outer control system and data models
fp1
fp2
fp3
fp4
fp5
fp6
TeC
LdrC
W
r
Wr
Te
Vqs
Vds
Vds
We
Ib Ia
Vqsinv
Vdsinv
Iqs
Ids
Ic
I
b
Ia
*
0.001
*
0.001
*
0.001
Vqs Ids
Iqs
Th
Th
We
id ia
iq ib
theta ic
dq to abc
Iai
I
b
i
Vdcbl
Vqsbl
Vdsbl
0.50748
We
Iqs
Ids
IM Vds
Vqs
We
Wr
Te
TeC
LdrC
Vqs
Vds
Ib Ia
ref
Wr
IDFOC
Vdsinv
Vqsinv
We
1
2
3
4
5
6
PWM
Vector
Space
Vdc
Vds
Vqs
Ici
SPACE VECTOR PWM
PULSE GENERATOR
INDUCTION MACHINE
DATAMODEL
INPUTS TO INDUCTION
MACHINE ELECTRICAL MODEL
INDIRECT FIELD
ORIENTED CONTROLLER
Note: Extra inputs to be used
later for direct field
i t ti
Fig. 11.4. Machine side inner control system
1 2 3
Ebsource Ecsource
Ecload
Ias Ibs Ics
1 2 3
Eaload Ebload
Easource
1 2 3
Edcsps
srf
*
500
srf
Va
Vb
Vc
PLL
Six
Pulse
6
thetaY
Easource
Ebsource
Ecsource
fpa1
fpa2
fpa3
fpa4
fpa5
fpa6
Enewfilt
Edcsps
Wr torq detec torq
0.34
350.0
*
detec
Vdc*
Wr*
TCFF
Tdc
B
+
D
+
F
+
detec
G
1 + sT
Tsp
Tsa
D
+
F

*
D
+
F

*
detec
*
detec
I
P
I
P
SPWM
M
Vdc
1
2
3
4
5
6
F
P
Sag
Corrector
SAGDETECTOR
AND
CORRECTOR
SINUSOIDAL PWM
PULSE
GENERATOR
ENERGYCONTROL SYSTEM
Torque
comm...
to IDFOC
Fig. 11.5. Shipboard power system side inner control system and outer control
system
86
11.4 Space vector PWM pulse generator model
1
2
3
4
1 2 3
Ta Tb To
4
Switching
frequency
t SwiFreq
SwiFreq
Swiinst Swiper
Swiinst
N
D
N/D
Vi
Vds
Vqs
X
2
X
2
D
+
F
+
X
2 Pi
We
x
1.0
Freq
Freq
*
6
N
D
N/D
S
cos(th)
Vc th
sin(th)
VCO
sq
cos(th)
Vc th
sin(th)
VCO
Edge
Detector
Interface with a matlab program
*
0.5
*
0.000159154
Time computer
cos(th)
Vc th
sin(th)
VCO
Clear
Asynchronous timer
1000.0
SVPWMfuncnew
SVPWMfuncnew.m
Switching frequency =1k Hz
Time step = 10 micro sec
This part outputs the time distribution
of the active and zero switching states in a
switching instant.
Fig. 11.6. Space vector PWM pulse generator model part1
87
Ta Tas
Tb Tbs
To Tos
Tbs
Tbn
Tan
Tas
Tbs
S
S
S
S
Modulo
3.0
Modulo
5.0
S
kn2
kn2
kn3
kn3 kn4
kn6
kn5 kn4
kn6
kn6
kn6
S3
S4
S5
S6
S2
S3
S4
S5
kn4
kn5
S
S1
A
B
Ctrl
Ctrl = 0.0
A
B
Ctrl
Ctrl = 1.0
t Samp
Samp
Sampler
Pulse
Samp
Modulo
2.0
Samp
Tas
Modulo
2.0
Sampler
Pulse
Modulo
4.0
Variable Sample/Hold circuit
S6
S2
Modulo
6.0
Sector Pulse Generator
Sampler
Pulse
Edge
Detector
Fig. 11.7. Space vector PWM pulse generator model part2
Tos Tos
Tos Tos
*
0.5
D
+
E
+
F
+
Tbn Tan
*
0.5
t
t
D

F
+
t
t
*
0.5
D

F
+
*
0.5
t
S1 S2 S3 S4 S5 S6
S1 S2 S4 S5 S6 S3
S1 S2 S3 S5 S6 S4
h1
h3
h3
h1 h1
h3
h3
h1
h3
h1
h1
h3
aa1 bb1 cc1 dd1 ee1 ff1
aa2 bb2
aa3 bb3
cc2
cc3
dd2
dd3
ee2
ee3
ff2
ff3
aa1
bb1
aa2
bb2
aa3
bb3
cc1
cc2
cc3
dd1
dd2
dd3
ee3
ee2
ee1
ff1
ff2
ff3
Tbn Tan
Tos
Tos
t
h3
Testa
Tan
Tan
PP1
PP1
PP3
PP3
PP5
*
0.5
*
0.5 Testb
h5 h5
h5 h5
h5 h5
h5 h1
Swiper
D
+
E
+
F
+
Swiper
D
+
F
+
Swiper
PP5
M1
M5
M6
D
+
F
+
D

F
+
PP1
PP3
PP5
A
B
Compar
ator
A
B
Compar
ator
A
B
Compar
ator
A
B
Compar
ator
M3
A
B
Compar
ator
M4
Pulse
Fabricator
Space vector PWMoutput
pulses
M2
A
B
Compar
ator
Fig. 11.8. Space vector PWM pulse generator model part3
88
11.5 Sag detector and corrector
Ebsource Ecsource
Ecload Ebload
Ias
Easource
pll
pll
Ebsource
Ecsource
Easource
Eaload
1 2 3
1 3
Ibs
2
1 3 2
Eaload
Ebload
Ecload
Edload
Eqload
Ics
VL
Is
X
2
Eqsource
Edsource
Edsource
X
2
X
Eqsource
Eqds
N
D
N/D
Eqds
Ecsource
Ebsource
Easource
A
B
Compar
ator
TIME
trig
trig
X
2
X
2
X
N
D
N/D
B
+
D
+
Edload
Eqload
Eqdload
Eaload
Ecload
Ebload pllload
Vs
Ecsource
Ebsource
Easource
sourceref
torq
detect
detect
B
+
D
+
0.35
Va
Vb
Vc
PLL
theta
*
blok
ia id
ib iq
ic
theta
abc to dq
Va
Vb
Vc
PLL
theta
0.3613
1.0
E
q
d
s
detect
Tsag
Tsag
B

D
+
Sag Corrector
Va
Vb
Vc
PLL
theta
ia id
ib iq
ic
theta
abc to dq
pllload
*
100
0.98
Sag Detector
Fig. 11.9. Sag detector and corrector model
89
11.6 Sinusoidal PWM pulse generator model
1 2 3
M1 M1 M1
Ph1Ph1Ph1
M
1 2 3
Ph
detect
* 0.0
M1
Ph1
B
+
D
+
phasIa
*
sagang
sagang
1.0
Eqdload
G
1 + sT
B
+
D
+
F

B

D
+
*
0.2
0.001
180.0
0.95
I
P
detect
detect
Ias
Ibs
Ics
m
a
g
1
phasIa
X1
X2
X3
Ph1
Ph2
Ph3
Mag1 Mag2 Mag3
(7)
(7)
(7)
(7) (7) (7)
dc1 dc2 dc3
F F T
F = 60.0 [Hz]
Fig. 11.10. Sinusoidal PWM pulse generator model part1
90
Vinv
blok
M
M1r M2r
M1r M1
Vinv
M2 M2r
Vinv
Vinv
*
M3 M3r
M3r
P
1 2 3
Ph1 Ph2 Ph3
3 2
TIME
*
Vinv
F
180.0
*
Triangular signal
generators
R
e
f
I
o
f
f
F3
F5
F4
F6
60.0
4
5
6
1
2
1
2
3
4
5
6
R
e
f
I
o
n
R
e
f
I
o
n
tron
tron
troff
troff
Ph1
3
cos(th)
Vc th
sin(th)
VCO
1
2
3
4
5
6
*
Vinv
1
2
3
4
5
6
M1r
M1r
1
Dblck
6
6
6
6
L
H
H
ON
OFF
L
(1)
(4)
(5)
(6)
2
2
2
(2)
(3)
2
2
2
F2
B

D
+
F1
R
e
f
I
o
f
f
Multip
6 6
Shift:
(insh)
6 6
sh
in
Sin
Array
6 6
Sin
Array
6 6
Multip
6 6
Modulo
360
30.0
Fig. 11.11. Sinusoidal PWM pulse generator model part2
11.7 Technical data
Table 11.1 Technical data
Shipboard Power system 3Ph, 480V, 60Hz, 50kVA
Series Transformer 480/480V, 50kVA, 10%
LC Filters 10mH, 20µF
Critical Load Passive, 3PhResistive load, 10Ω
Other Loads Passive, 3PhRL load, 5Ω, 10mH
Line Impedance to other loads 0.2Ω, 1mH
DC Bus 340V, 2X1000µF center tapped
Flywheel Inertia 0.911 kgm
2
Induction Machine
240V, 60Hz, 23.8A, 10hp, 4pole and
1755RPM
SVPWM switching frequency 1kHz
SPWM switching frequency 10.8kHz
91
11.8 Induction machine parameters (Courtesy Dr. Joseph D. Law)
R
s
0.162Ω := R
r
0.317Ω :=
ω
e
376.99112
rad
s
:=
L
m
0.05367 H := L
ls
0.001299 H := L
lr
0.001949 H :=
L
s
L
ls
L
m
+ := L
r
L
lr
L
m
+ :=
L
s
0.05497 H := L
r
0.05562 H :=
λ
drrated
0.50748 Wb ⋅ :=
P 4 :=
J
ind
0.089kg m
2
⋅ := J
flywheel
0.911kg m
2
⋅ :=
J
tot
J
ind
J
flywheel
+ :=
J
tot
1.0kg m
2
⋅ :=
92
11.9 Fortran file for MATLAB interface component
#STORAGE REAL:8
#DEFINE INTEGER I_CNT
IF($Enabl.GT.0.9) THEN
DO I_CNT=1,4,1
STORF(NSTORF+I_CNT1) = $In(I_CNT)
END DO
CALL MLAB_INT("$Path", "$Name", "R(4)" , "R(4)" )
DO I_CNT=1,4,1
$Out(I_CNT) = STORF(NSTORF+4+I_CNT1)
END DO
ENDIF
NSTORF = NSTORF + 8
11.10 MATLAB program
function [T] = SVPWMfuncnew (in)
global x Tz Vs Vi
x=in(1);
Tz=in(2);
Vs=in(3);
Vi=in(4);
if (x >= 0) & (x <= pi/3)
k=0;
T= SVP(k,x,Tz,Vs,Vi);
T(4)=1.0;
elseif (x >= pi/3) & (x <= 2*pi/3)
k=pi/3;
T= SVP(k,x,Tz,Vs,Vi);
T(4)=2.0;
elseif (x >= 2*pi/3) & (x <= pi)
k=2*pi/3;
T= SVP(k,x,Tz,Vs,Vi);
T(4)=3.0;
elseif (x >= pi) & (x <= 4*pi/3)
k=pi;
93
T= SVP(k,x,Tz,Vs,Vi);
T(4)=4.0;
elseif (x >= 4*pi/3) & (x <= 5*pi/3)
k=4*pi/3;
T= SVP(k,x,Tz,Vs,Vi);
T(4)=5.0;
elseif (x >= 5*pi/3)
k=5*pi/3;
T= SVP(k,x,Tz,Vs,Vi);
T(4)=6.0;
end
function [T] = SVP(k,x,Tz,Vs,Vi)
if (x >= k) & (x <= (k+pi/6))
T(1)=(sqrt(3))*(Vs/Vi)*Tz*sin(k+(pi/3)x);
if T(1) > Tz
T(1)=Tz; T(2)=0; T(3)=0;
else
T(2)=(sqrt(3))*(Vs/Vi)*Tz*sin(xk);
if (T(1)+T(2)) > Tz
T(2)=TzT(1); T(3)=0;
else
T(3)=Tz(T(1)+T(2));
end
end
else
T(2)=(sqrt(3))*(Vs/Vi)*Tz*sin(xk);
if T(2) > Tz
T(2)=Tz; T(1)=0; T(3)=0;
else
T(1)=(sqrt(3))*(Vs/Vi)*Tz*sin(k+(pi/3)x);
if (T(1)+T(2)) > Tz
T(1)=TzT(2); T(3)=0;
else
T(3)=Tz(T(1)+T(2));
end
end
end