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UPTEC ES11 031
Examensarbete 30 hp
December 2011
Flywheel energy storage
a conceptual study
Rickard Östergård
Abstract
Flywheel energy storage - a conceptual study
Rickard Östergård
Teknisk- naturvetenskaplig fakultet
UTH-enheten
Besöksadress:
Ångströmlaboratoriet
Lägerhyddsvägen 1
Hus 4, Plan 0
Postadress:
Box 536
751 21 Uppsala
Telefon:
018 – 471 30 03
Telefax:
018 – 471 30 00
Hemsida:
http://www.teknat.uu.se/student
This master thesis was provided by ABB Cooperate Research in Västerås. This study
has two major purposes: (1) to identify the characteristics of a flywheel energy
storage system (FESS), (2) take the first steps in the development of a simulation
model of a FESS.
For the first part of this master thesis a literature review was conducted with focus
on energy storage technologies in general and FESS in particular. The model was
developed in the simulation environment PSCAD/EMTDC; with the main purpose to
provide a working model for future studies of the electrical dynamics of a FESS.
The main conclusion of the literature review was that FESS is a promising energy
storage solution; up to multiple megawatt scale. However, few large-scale installations
have so far been built and FESS is not a mature technology. Therefore further
research and development is needed in multiple areas, including high strength
composite materials, magnetic bearings and electrical machines. The model was
implemented with the necessary control system and tested in a simulation case
showing the operational characteristics.
Handledare: Frans Dijkhuzien
Ämnesgranskare: Hans Bernhoff
Examinator: Kjell Pernestål
ISSN: 1650-8300, UPTEC ES11 031
Sponsor: ABB
SAMMANFATTNING
Detta examensabete har två huvudsyften: (1) att identifiera och beskriva de ingående
komponenterna hos ett energilagringssystem med svänghjul (Flywheel Energy Storage
System, FESS), (2) ta första stegen i utvecklingen av en simuleringsmodell.
Första delen av examenarbetet genomfördes genom en litteraturstudie med fokus på
energilagringsteknik i allmänhet och FESS i synnerhet. Modellen är utvecklad med hjälp
av simuleringsprogrammvaran PSCAD/EMTDC med huvudsyftet att uveckla en
fungerande modell för framtida studier av den elektriska dynamiken hos ett FESS.
Den viktigaste slutsatsen av litteraturstudien är att FESS är en lovande
energilagringsteknik med kapacitet upp till flera megawatt. Hittills har endast ett fåtal
storskaliga installationer byggts, vilket betyder att FESS inte är en mogen teknik. Det
behövs därför vidare forskning och utveckling inom flertal områden; bland annat inom
materialvetenskap, magnetiska lager och generatorer.
Simuleringsmodellen har implementerats med nödvändiga styrsystem och testats i ett
simuleringscase som visar de viktigaste egenskaperna hos ett FESS.
TABLE OF CONTENTS
1
INTRODUCTION ........................................................................................................................ 3
1.1
1.2
1.3
2
BACKGROUND ........................................................................................................................ 3
SMART GRID .......................................................................................................................... 3
AIM ........................................................................................................................................ 4
ELECTRICAL ENERGY STORAGE SYSTEMS (ESS) ............................................................ 5
2.1 APPLICATION IN ELECTRICAL GRIDS ...................................................................................... 5
2.2 ENERGY STORAGE TECHNOLOGIES ........................................................................................ 6
2.2.1 Pumped hydro (PHS)................................................................................................... 7
2.2.2 Compressed air energy storage (CAES) ................................................................... 7
2.2.3 Battery energy storage (BESS) .................................................................................. 8
2.2.3.1 Sodium Sulphurs Batteries ................................................................................... 8
2.2.3.2 Lithium-Ion Batteries .............................................................................................. 8
2.2.3.3 Lead-acid batteries ................................................................................................. 8
2.2.3.4 Flow batteries ........................................................................................................... 9
2.2.4 Super conducting magnetic energy storage (SMES) .............................................. 9
2.2.5 Supercapacitors......................................................................................................... 10
2.3 TECHNOLOGY SUMMARY ...................................................................................................... 10
3
FLYWHEEL ENERGY STORAGE ........................................................................................... 11
3.1 GENERAL ............................................................................................................................. 11
3.2 HISTORY .............................................................................................................................. 11
3.3 FLYWHEEL BASICS................................................................................................................ 11
3.3.1 Geometries and material ............................................................................................. 12
3.4 FLYWHEEL SYSTEMS COMPONENTS ...................................................................................... 14
3.4.1 Electrical machine........................................................................................................ 14
3.4.2 Bearings ....................................................................................................................... 14
3.4.3 Housing ........................................................................................................................ 15
3.4.4 Power electronic interface ........................................................................................... 16
3.5 RANGE OF CAPACITIES ......................................................................................................... 16
3.6 ENVIRONMENTAL ISSUES ...................................................................................................... 16
3.7 COMMERCIALLY AVAILABLE FLYWHEEL SYSTEMS .................................................................. 16
3.7.1 Beacon Power ............................................................................................................. 17
3.7.2 Vycon Energy .............................................................................................................. 18
3.7.3 Piller ............................................................................................................................. 18
3.7.4 Active Power ................................................................................................................ 19
3.7.5 Market summary .......................................................................................................... 19
3.8 SUMMARY ............................................................................................................................ 20
4
MODEL DESIGN ...................................................................................................................... 21
4.1 SCOPE ............................................................................................................................... 21
4.2 MODEL DESCRIPTION ........................................................................................................... 21
4.3 SINUSOIDAL PULSE WIDTH MODULATION ............................................................................... 21
4.4 D-Q-0 TRANSFORMATION .................................................................................................... 22
4.5 MOTOR/GENERATOR ............................................................................................................ 23
4.5.1 Machine-side VSC control strategy ............................................................................. 24
4.5.2 Grid connected VSC Model ......................................................................................... 26
4.5.3 Grid-side VSC control strategy .................................................................................... 27
4.6 FLYWHEEL ........................................................................................................................... 28
SIMULATION ............................................................................................................................ 29
5
5.1
5.2
CASE STUDY ........................................................................................................................ 29
SIMULATION RESULTS .......................................................................................................... 31
6
CONCLUSIONS AND DISCUSSION ....................................................................................... 32
7
RECOMMENDATIONS FOR FUTURE WORK ....................................................................... 33
8
ACKNOWLEDAGEMETS ........................................................................................................ 34
9
REFERENCES.......................................................................................................................... 35
10
APPENDICES ....................................................................................................................... 37
2
1
1.1
INTRODUCTION
Background
Renewable energy technologies are an effective answer in the effort to reduce CO 2 emissions. In an
electrical system the supply and demand must be in balance to keep the electrical grid stable. Since most
renewable energy, for example wind and solar power, are of intermittent nature the production cannot be
controlled. The supply varies with season, time and weather conditions. The ever-increasing demand and
need for renewable energy sources, dictates new requirements for the electrical grid. Important aspects as
power system stability, reliability and power quality must be ensured when more intermittent energy
sources are being installed. These requirements can be met by upgrading the grid to be more dynamic and
intelligent, a so called smart grid, where energy storage devices are an important part of the solution.
Unlike other forms of energy, electric energy is difficult to store in any useful quantity. Under somewhat
rare circumstances, electricity can be transformed into potential energy in reversed hydro power plants.
Some attempts (less than 1% of the total available storage worldwide) have been done with chemical,
kinetic and thermal energy. While transmission lines and distribution grids transport electricity over land to
end users, energy storage systems can move electricity through time. This ensures constant electricity
supply when and where it is most needed. Energy storage systems, at the right place and properly designed
can help improve electric grid reliability and efficiency.
1.2
Smart Grid
The existing electric grid systems are not designed to meet requirements of the modern society, including
small scale independent generation units, increasing use of digital equipment, installations of renewable
energy and introduction of a fleet of electrical vehicles. The traditional electric grid consists of large
generation units far form end users and power is transferred in a main high voltage transmission grid to
local low voltage distribution grids. In today’s grid topology the electricity flows mainly in one direction,
as illustrated in Figure 1.1.
Figure 1.1 Today's grid topology. The power flow is mainly one-way [39].
In order to meet the demands described above todays grid topology must change into a two-way flow of
both electricity and information to form a automated, widely distributed transmission grid, as illustrated in
Figure 1.2. This vision for the future grid is called Smart Grid [1].
3
Figure 1.2 The future Smart Grid. The power flow is two-way [39].
The vision of the smart grid still depends on support of large-scale generation units, but it includes a
considerable quantity of electric energy storage and renewable energy, both at large scale power system
level and in local distribution grids. The main benefits of a future Smart Grid will include: large scale use
of renewable energy source, reduction of peaks in electricity demand, more active consumers and increased
efficiency in use of electrical energy. The EU’s Technology Platform for Smart grid summarizes the central
objectives as follows [2]:
-
Better facilitate the connection and operation of generators of all sizes and technologies.
Allow consumers to play a part in optimizing the operation of the system.
Provide consumers with greater information and choice of supply.
Significantly reduce the environmental impact of the whole electricity supply system.
Deliver enhanced levels of reliability and security of supply.
Energy storage systems (ESS) will play a central role in in the research and development of smart grids.
1.3
Aim
ABB is a global leader in power and automation technologies. Energy storage system for gird integration is
a growing market of interest for ABB. Today they have a battery system ready for commercial deployment,
but other energy storage technologies are also of interest. This master thesis is done with collaboration with
ABB Cooperate Research in Västerås. The main goal of this thesis is to provide a market overview and a
technical description of a flywheel energy storage system (FESS), in order to provide a basis for future
research and development. The aim is to describe and identify the essential system components and
highlight important aspects when designing FESS. Furthermore, this thesis aims to give a comparative
overview of flywheels vs. other technologies for energy storage systems.
Additionally, an overview of commercially available flywheel energy storage system is given, together
with the purpose of evaluate where the market stands and how far the technology development has come.
The last part of the thesis is dedicated to developing a simulation model of flywheel energy storage A
primary model design is performed with the goal to be a starting point for future studies of electrical
dynamics of a FESS. A case study is carried out to show the operational principles of flywheel energy
storage systems. An example of a future case study that can be performed is how a FESS can handle power
quality problems associated with a wind farm.
4
2
ELECTRICAL ENERGY STORAGE SYSTEMS (ESS)
The following section gives an overview of energy storage systems for storing of electrical energy. It will
describe the technical characteristics and give the reader an overview of the general properties, advantages
and disadvantages for each system. The aim is to give the reader background information about the
alternatives to electrical energy storage with flywheels. This section gives also an overview for the
applications for energy storage systems in electrical grids.
2.1 Application in Electrical Grids
Energy storage systems (ESS) can be applied to a wide range of applications in the electrical system. It can
be the solution for problems in the whole electrical energy value chain, from generation support,
transmission and distribution to the end-consumer users. The following list summarizes applications in
electrical power systems where energy storage system can be used [3].
1. Electric energy time shift - Energy is purchased during off-peak hours when prices are low and
sold at a later time when the price is high. The stored energy can also be used by the storage-owner
to avoid expensive energy purchase during hours of high demand. Also known as energy arbitrage.
2. Load following – A requirement to keep the stability of the electricity grid, the storage power
respond to the demand of the end-user. The storage system either produce power or consume
(charge) to meet the supply and demand requirements.
3. Transmission and distribution upgrade deferral - By adding storage resources to a nearly
overloaded transmission and distribution system, investments can be delayed or entirely avoided.
4. Time of use energy cost management – Refers to the same mechanism as 1 but here end-users
reduce their total costs for electricity by utilizing storage systems.
5. Electric Service Reliability - Involves energy storage to provide better reliability of electric
service. In the case of a long-term power outage (more than a few seconds) the energy storage
provides enough energy to either preform a safe shutdown of vulnerable equipment or ride though
the entire outage.
6. Electric Service Power Quality – The energy storage is used to provide power quality services.
This can improve the quality of the power to loads during short duration faults in the electrical
system. Examples of poor power quality include: voltage sags, variation in frequency and
harmonics.
7. Renewables energy time shift – Energy is stored to increase the value of the produced energy. If
the price of energy is low when the renewable energy sources (RES) is producing the energy
storage unit can provide a time-shift so the energy can be sold when the price is higher.
8. Renewable capacity firming – This application applies to intermittent RES. The energy storage
provides a way to smooth the output form this type of energy source. The combined output from
the energy storage and the RES is close to constant. The application is especially valuable during
peak-demand periods.
5
Table 2.1 summaries these applications and gives an estimate of the different applications power and
discharge specifications.
Table 2.1 Estimate of need for storage power and discharge duration for different application for ESS [3]
1
2
3
4
5
6
7
8
2.2
Application type
Electric energy time shift
Load following
Transmission and distribution upgrade deferral
Time of use energy cost management
Electric Service Reliability
Electric Service Power Quality
Renewables energy time shift
Renewable capacity firming
Storage Power
1-500 MW
1-500 MW
250 kW - 5MW
1kW - 1MW
0.2kW - 10MW
0.2kW - 10MW
1kW - 500MW
1kW - 500MW
Discharge Duration
2-8 h
2-4 h
3-6 h
4-6 h
5 min - 1 h
10 s - 1 min
3-5h
2-4h
Energy storage technologies
Electric energy has for long been a commodity where storage has been achieve efficiently in only some
rare cases. However there are existing and emerging technologies that allow electric energy to be stored.
Implementing a well-functioning energy storage system, which is seamlessly integrated to the grid, is not
an easy task. The design of such a system must take many factors in consideration. As described in section
2.1 the applications for ESS have a variety of demands and different storage technologies are suitable for
different applications. There is a vast diversity of possible energy storage technology alternatives for the
electric sector, each with unique functioning, performance, cycling and durability characteristics.
To date about 100GW of electric energy storage systems is installed worldwide, where pumped hydro is
the most represented technology (~127,000 MW). The next largest is compressed air energy storage with
about 440 MW installed.
Figure 1.3 ESS installed capacity worldwide [4].
6
2.2.2 Pumped hydro (PHS)
Pumped hydroelectric energy storage is the most widespread electrical energy storage technology in the
world. The first pumped hydro station was built in Italy and Switzerland in the 1890s, thus it can be
considered as a mature technology. Further it was the only commercially available large-scale energy
storage until the 1970 when compressed air energy storage was introduced [4,5].
A typical pumped hydro power plant consists of two water reservoirs located on different altitudes. During
off peak hours when cheap electricity is available water is pumped from the lower reservoir and stored in
the higher. During times of high demand of electricity water flows, through a hydroelectric turbine, to the
lower reservoir to generate electricity [3]. The quantity of stored energy is a function of the total volume of
water in the upper reservoir and the differential height of between the two reservoirs. The reservoir can for
example be artificially built, natural bodies of water or the open sea. The latter is only used for the lower
reservoir.
The losses considered in a pump hydroelectric plant include turbulence, turbine/pump and motor/generator
efficiency. The overall efficiency is about 70-85% depending on design [5].
PHS technology is mature technology but is characterized by high capital investment and strong geological
barrier. This type of system is suited for applications with high power capability demand, a typical plant
has the power rating of 1000-2000 MW and the discharge time is somewhere around 6-12 h [5].
Advantages include:
- Very high energy capacity
- Large-scale
- Mature and commercial technology
Disadvantages include:
- Strong geological barrier.
- High capital investment
- Comparatively slow response time.
- Comparatively low efficiency
2.2.3 Compressed air energy storage (CAES)
A CAES plant has similar design as a gas turbine power plant. The basic difference to a conventional gas
turbine power plant is that the air is already compressed and the fuel consumptions can be significantly
lowered. The air is compressed during off peak hours and typically stored in an underground cavern,
vessel, or pipes. When the energy is needed the compressed air is mixed with natural gas and combusted in
a gas turbine to generate electricity. In a conventional gas turbine power plant about 2/3 of the energy
produced is consumed when pressurizing the air before combustion in the gas turbine. [5] In comparison
with a conventional gas turbine plant CAES consumes 40 % less fuel producing the same electricity output.
CAES usually is located near a suitable geological formation such as mines, depleted gas wells or salt
caverns.
Typical compressed air power plant has a power rating in the 110-290 MW range and can deliver power for
up to 10 hours [30]. There is about 440 MW installed worldwide [6]. The technology has been around since
the 1970’s but only two plants have been built. The first commercial CAES plant was built in 1978 in
Germany, with a capacity of 290 MW. The second commercial CAES was a 110 MW plant built 1991 in
Alabama, USA. These plants are used to supply peak load power.
Current research on CAES technology focus on development of adiabatic CAES systems where the heat
produced during compression is stored and reused to heat the compressed air before passing though the
turbine. This would eliminate the need for fuel in the system.
7
Advantages include:
- Very high energy capacity
Disadvantages include:
- Strong geological barrier. Despite many years of effort, no new suitable caverns have been
found.
- Comparatively slow response time
- Comparatively low efficiency
2.2.4 Battery energy storage (BESS)
Energy is stored chemically and electric energy is released during discharge through a redox reaction. A
basic battery cell consists of:
-
Negative electrode or anode, gives electrons and oxidized during the redox reaction.
Positive electrode or cathode, accepts electrons and is reduced during the redox reaction.
Electrolyte, supplies medium for transfer of electrons.
The two electrodes are interconnected with an external circuit, which allows charge and discharge of the
cell. Depending of the desired output voltage and current multiple cells can be connected in serial or
parallel. There are several technologies to store electrical energy in batteries. The oldest, classical and
mature technology is Lead-acid. New technologies under development include Sodium Sulphurs and
Lithium-ion [7].
2.2.4.1 Sodium Sulphurs Batteries
The sodium sulphur battery consists of positive liquid sulphur electrode and a negative sodium electrode
separate by an alumina ceramic electrolyte. When the battery is discharged positive sodium ions flow
though to electrolyte and electrons flows in the external circuit producing around 2 V. This process is
reversed during charging; the positive sodium ions pass back though the electrolyte and reform elemental
sodium. The operational temperature of a sodium sulphur battery is high, about 300 ˚C. The high
temperature is required to maintain the molten states of the electrodes. The efficiency is about 80%. A
typical system has a rated power of 30 MW and able to provide power during 6 hours. There is about 316
MW installed worldwide [6].
2.2.4.2 Lithium-Ion Batteries
Lithium-ion batteries consists of a lithiated metal oxide cathode and a graphite carbon anode. The
electrolyte is made up of lithium salts. During charging lithium-ions from the cathode flows through the
electrolyte, to the anode where the ions combine with external electrons and is deposited as lithium atoms
between the carbon layers. When the battery is discharged this process is reversed. The efficiency of
lithium-ion battery system is high, about 90-95%. A typical system is has a rated power at 1-10 MW [6].
2.2.4.3 Lead-acid batteries
There are many types of lead-acid batteries but all can be described by the same basic chemistry. The
anode is made of lead dioxide and the cathode is made of metallic lead. The electrolyte consists of
sulphuric acid, which is consumed during the discharge. The efficiency of a lead-acid battery system is
about 70-80% [4]. Lead-acid battery system is the oldest and most recognized electrical energy storage
today in small and medium scaled systems [5]. It has been the default choice for many small and medium
scale energy storage applications despite many disadvantages like low life expectancy, low energy density,
high maintenance and environmental hazards related to the handling of lead and sulphuric acid. Lead-acid
battery system can be used in numerous applications; however the technology has rarely been used in largescale energy management applications [4]. The largest installation was a 10 MW, 40 MWh energy storage
plant in Californa, USA, operational during 1988-1997.
8
2.2.4.4 Flow batteries
Flow battery energy storage system consists of two sets electrolytes that flow through two independent
loops. The loops are joined in the cell but separated by a membrane that prevent the electrolytes from
mixing but allow ion-exchange. Flow batteries have the advantage of being easy scalable, compared to
conventional battery cells. The fact that the electrolytes are stored outside the cell makes it possible to
increase the energy storage capacity simply by increasing the volume of the reservoirs of electrolyte. This
makes the technology suitable for large-scale systems [8]. The amount of energy stored is determined by
the size of the tanks [9].
There are various types of flow batteries technologies, e.g. ZnBr, Vanadium Redox and Polysulphide
Bromide. An example flow battery system is 15 MW, 120 MWh and efficiency of about 75 % from
Regenesys Technologies in England [9].
Advantages include:
- High power capacity
- Long life
- Scalable
Disadvantages include:
- Low power density
- High cost
- Moving mechanical parts, for example pumps.
2.2.5 Super conducting magnetic energy storage (SMES)
SMES store energy in a magnetic field; a DC current flowing through a superconducting coil creates the
field. Electric energy can be released from the system when needed. A power electronics interface is
required to connect the SMES to the grid. In order to sustain low losses the coil must be kept below a
critical temperature, somewhere around 4 K. The low temperature makes the resistive losses negligible
[11].
The response time for a charge- discharge cycle for SMES system is in the order of milliseconds. This
makes this technology suitable for power quality applications. The efficiency is high, over 90 %, however
the energy used to cool the system must be considered. SEMS systems has been proposed in a wide range
of energy storage capacities from 0.3 to 1000 MWh and power rating from 1 MW to 1000 MW [4,10].
Disadvantages of the SMES system are the massive electromagnetic fields that effect possible placement of
the systems.
Advantages include:
- High efficiency
- Comparatively quick response time
Disadvantages include:
- Massive electromagnetic fields
- Complex system due to cryogenically cooling
- High costs
9
2.2.6 Supercapacitors
Supercapacitors or double layer capacitor store energy much in the same way as a conventional capacitor,
hence the amount of stored energy can be described by:
A double layer capacitor consists of two electrodes, a separator, electrolyte, two current collectors and
housing. A very high capacitance is obtained in this way. Super capacitors are suitable for high power
applications and offer very quick response times and high efficiency. Disadvantages are comparatively low
energy density, high self-discharge and high cost [7, 4,8]. Small units exists, lager is under development.
Typical power ratings are 1kW-250 kW and efficiencies in the ranges of 85-98% [8].
Advantages include:
- Comparatively quick response time
Disadvantages include:
- High self-discharge
- High cost
- Low energy density
2.3
Technology summary
Table 2.2. Summary of storage technologies [3,5,6,8,9,10].
Technology
Battery
Pumped Hydroelectric Energy
Storage
Compressed air energy storage
Typical
Nominal Power
100-4000 MW
Discharge
time
6-24 h
Respones
Time
10s -3 min
Efficiency
Lifetime
65-85%
30-75
years
20-40
years
25-30000 MW
4- 24 h
3-15 min
50-85%
Flow Batteries
25 kW-10 MW
1-8 h
30 - 100 ms
65-85%
Lithium Ion
Lead Acid
10 kW - 10 MW
50 kW - 30 MW
Sodium Sulphur
50 kW - 30 MW
10 min - 1 h
15 min – 4
h
1-8 h
85-90%
70-80%
2-10
years
75-90%
10 kW - 1 MW
1s - 1min
5-10 ms
85-95%
40 years
Superconduction Magnetic
energy storage
1 MW - 100 MW
1s - 1min
5-10 ms
85-95%
30-40
years
Flywheels
10 kW - 20 MW
1s - 1 h
5-10 ms
85-95%
20 years
Supercapacitors
PHS- and CEAS-plants exists, however few places remain where it is feasible to build. Great
environmental impact is associated with these two technologies. Flywheels, batteries, SMES:s and
supercapacitors are the energy storage systems that compete in the same area, where SMES is still a
research area and few commercial applications exists. Supercapacitors have lower rated power than both
flywheel and battery system.
Frequency regulation is a market expected to grow with the expansion of wind and solar power. The
frequency regulation market was 2010 worth US $495 million in the United States; a number expected to
increase [12]. The dominant method today for frequency regulation is throttling power generation up and
down, which is not efficient due to the fact that generators operate at an optimum when held steady at high
10
output. Many power plants take a minute or longer to respond to dispatch signals. Therefore, grid operators
favour faster-acting regulators, such as flywheels and batteries.
Battery-based frequency regulators are cheaper per megawatt to install than flywheel and are a competitive
technology. But the flywheel energy storage manufacturer, Beacon Power, believes that the apparent cost
advantage of batteries will literally erode with time, as constant cycling degrades their capacity. David
Hawkins, a senior principal consultant for the Netherlands-based energy consulting firm KEMA, who until
2010 was chief engineer for integrating renewable energy at California's grid operator agrees that [13]:
”…batteries will lose their edge over flywheels under that level of use. A battery really doesn't like
to be totally charged and discharged, whereas flywheels can handle a pretty severe duty cycle."
A report for the U.S. Department of Energy also states that [12]:
“Flywheels and supercapacitors, with their high cycle life and ramping capabilities, are good
candidates for regulation. Batteries may be better for supplying load following, where cycle life
requirements and the ratio of peak power to stored energy are lower.”
3
3.1
FLYWHEEL ENERGY STORAGE
General
A literature review was conducted to find out the state of the art in flywheel systems. System design,
storage capacity and materials used were investigated.
To secure the reliability of the literature review information was gathered from multiple sources. These
include articles retrieved from international recognized databases, such as IEEExplore, Science Direct and
cited books relevant to the subject.
3.2
History
The use of flywheel to store energy is not a new technology. Basic flywheels such as stone wheels were
used to craft pottery thousands years ago. The stone wheel smoothens the pulsed power from the foot and
enabled a smooth rotation of the pottery turntable.
Under the industrial revolution the use of the flywheel increased significantly when the steam engine was
introduced. During this period technological development of flywheels started. The first milestone was
when Dr. A Stodola showed that certain shapes yield uniform stress distribution for isotropic materials. The
next milestone in flywheel development took place during 1970’s when applications for backup-power and
electric vehicles were proposed. During this period flywheels made of composite material was proposed
and built. The development continued during the 1980’s when magnetic bearings were introduced. Recent
developments in materials, magnetic bearings, microcomputers and power electronics have made it
possible to consider flywheels as competitive option for electric energy storage [14, 21].
3.3
Flywheel basics
Flywheels store energy in kinetic form. The energy is stored in a rotating mass and the amount of energy
stored is a function of the moment of inertia and angular velocity, as shown in equation (3.1).
(3.1)
is the moment of inertia and is the angular velocity. The moment of inertia is determined by the shape,
principal rotational axis and mass of the flywheel and is defined by the following equation.
(3.2)
Where
is the distance from the rotational axis of the differential mass
.
11
Equation (3.1) state that greater gain in stored energy come from increasing the angular velocity, rather
than increasing the moment of inertia. This is because the stored energy scales with the square of angular
velocity and only linearly with the moment of inertia. As an example a flywheel with the shape of a thin
rim (
where
is the outer radius and
is the inner radius) is considered. All the mass is
concentrated at the infinitely thin outer rim. Thus from equation (3.2) the moment of inertia is given by
(3.3)
where
is the mass and is the radius of the flywheel. The stored energy is given by
(3.4)
The amount of stored energy is limited by the tensile strength of the material. If the stresses in the flywheel
exceed the tensile strength of the material the flywheel will break apart. The limiting stress in a thin rim is
the tangential stress, which is given by equation (3.5) [15], where
(3.5)
is the maximum tensile strength and is the material density. From equation (3.4) and (3.5) the
maximum energy density and specific energy for a certain material can be obtained. Thus the specific
energy and energy density for the thin rim flywheel can be expressed as
(3.6)
(3.7)
From equation (3.7) it is clear that a material with high tensile strength is a requirement to obtain high
energy density. However for most applications the total mass of the system must be taken into
consideration which is considered with the specific energy of the flywheel, as described by equation (3.6).
This analysis of a thin rim flywheel shows that the specific energy is proportional to the maximum tensile
stress of the material divided by the mass density of the flywheel material. Equation (3.6) shows that a high
strength material with low density would be optimal for flywheels rotors. The factor in equation (3.6) and
(3.7) is only valid for a flywheel with the shape of a thin rim.
A flywheel made of high-density materials, such as steel, would indeed store more energy than an
equivalent size flywheel of low-density material at equal angular velocity. However low density materials
develop lower internal stresses, which allow higher angular velocities. This enables designs that store same
amount of energy at a lower weight, enabling compact system design.
3.3.1 Geometries and material
A more general expression for the maximum specific energy and energy density given by
(3.8)
(3.9)
Where is the so-called shape factor and can be described as a measure of how efficient the material of the
flywheel is used. For a detailed derivation of the shape factor see [17]. Figure 3.1 shows the most common
types of flywheel geometries.
12
Figure 3.1 Shape factor of common flywheel shapes [16]
The Laval disk (named after the Swedish engineer Gustav de Laval) has a shape factor of K = 1. This disk
has the properties such that the radial and tangential stress components remain equal throughout the entire
disk. Depending on the material used the optimal flywheel shape will differ. Isotropic materials, such as
steel, have equal strength in both the tangential and radial direction [16]. Anisotropic materials, like fibrereinforced composites, have unidirectional tensile strength, i.e. are stronger in the longitudinal fibre
direction. As shown in Figure 3.1 there are shapes better suited for these types of materials. A thin rim
(hollow circular cylinder) flywheel is a very good candidate for composite material as this geometry exploit
the high unidirectional strength of the fibres [16, 17]. Multiple sources [18, 16,15] state that a hollow
circular cylinder is the optimal shape for a composite flywheel rotor.
Table 3.1 Rotor material comparison [15,16]
Material
Steel
4320 Steel
AISI 4340
Alloy
AlMnMg
Titanium
TiAl6Zr
Composites
E-glass
S-Glass
Carbon T-1000
Projected
composites
Density
[kg/m^3]
Tensile strength
[GPa]
Specific energy
[Wh/kg]
7700
7800
1.52
1.80
50
64
2700
0.60
62
4500
1.20
74
200
1920
1520
1780
0.10
1.4
1.95
10
14
210
350
780
Table 3.1 show the properties of different rotor material. Maximum specific energy is calculated with
equation (2.9) with
. The data in the table shows, as already described above, that the best material
for a flywheel rotor is a high strength material with low density. Composite materials have both high
strength and low density and are ideal for flywheel rotors used for energy storage. A composite material
allows a higher rotational speed and this result in flywheel rotors with high specific energy. Composite
materials are therefore a better choice than metals when designing flywheel rotors. The theoretical specific
energy of composite rotors is around five times higher than metallic ones [20]. The high-speed flywheel
concept originated in the early 1970s. A researcher at Lawrence Livermore National Laboratory presented
an article in Scientific American proposing a new approach to rotor design, recommending the use of
composite materials instead of metal [21].
13
Composite materials also have safety advantage over metallic material. If a potential failure at high angular
velocity and the radial stresses exceed the material strength composite flywheel is less likely to break apart
in free flying projectiles. Instead circumferential cracks develop and the flywheel breaks apart gradually.[4]
3.4
Flywheel systems components
Basically, a modern flywheel energy storage system (FESS), consists of five key components; 1) flywheel
rotor, 2) bearings, 3) electrical machine, 4) power electronic interface, and 5) housing.
3.4.1 Electrical machine
The energy is stored in the flywheel, as presented in section 3.3, and in order to charge and discharge the
flywheel must be coupled to an electrical machine. When the flywheel is charging the machine accelerates
the flywheel and when energy is extracted the machine slows the flywheel down. Thus the electrical
machine must be able to operate as both a motor and a generator. In [18] a design is described with separate
motor and generator, however the typical design of a FESS is to use only one machine.
The key design criteria that the machine must meet include high efficiency, high power density, low idle
losses and low rotor losses. High efficiency is an important requirement for FESS to be an effective energy
storage system. Low rotor losses are critical since most FESS operates in vacuum and the heat removal is
limited. Low idle or stand-by losses are desirable for energy storage over longer times.
Common types of electrical machines used in FESS include: the induction machine (IM), the switched
reluctance machine (SR) and the permanent magnet synchronous machine (PMSM) [22]. A summary of
the main properties of these machines is summarized in Table 3.2
Table 3.2 Advantages and disadvantages of common electrical machines in FESS [15, 16,22].
PMSM
IM
SR
Advantages
+ No need for excitation
+ Rotor design complexity reduced, no need
for
electric wiring
+ High overall efficiency possible
+ Highest power density
Disadvantages
- Risk of demagnetization
- Electromagnetic spinning losses at zero
torque
- Low-strength of PM material require
structural support against centrifugal forces
- Sensitive to heating
+ Demagnetization impossible
- Poor overload capability
+ Possibility to control excitation field, no
electromagnetic spinning losses
+ Can be built with low-cost high-strength
materials
- High maintenance
+ Very robust
- Low power factor and low power density
- Adds complexity to the rotor design, due to
the need of wiring
- High losses due to the need of excitation
- Need of excitation
+ No idle losses
- High rotor eddy current losses
In most high-speed flywheel energy storage systems PMSM is chosen due to superior properties when it
comes to power density and efficiency.
3.4.2 Bearings
The rotor must be supported by bearings. The bearings minimize the friction and keep the rotor in place. In
most modern flywheel designs high speed is desirable, implying extensive requirements on the bearings.
The bearings must have low losses in order to run the flywheel system efficient.
14
Mechanical bearings are the best choice for FESS with speed under 20000 rpm and with speeds over 40000
rpm magnetic bearings are the only option [19]. Mechanical bearings offer straightforward implementation
and low initial cost but relative high friction. The need of lubrication makes these types of bearings
unsuitable for high-speed flywheel systems. As later will be discussed, high speed flywheel are operated in
low-pressure environment, therefore lubrication of mechanical bearings is hard to implement [23].
Magnetic bearings are not in contact with the rotor or shaft and offer low losses, long lifetime and require
no lubrication. These properties make magnetic bearing suited for use in high-speed flywheel systems.
Basically, a magnetic bearing consists of permanent magnets that levitate the mass of the flywheel and
controlled electromagnets that stabilize the flywheel rotor radially. The stabilization requires a complex
control system, with expensive sensors. A combination of both mechanical and magnetic bearings is used
in some systems [15].
High temperature super-conducting magnetic bearing (HTS) is a recently developed type of bearing which
significantly lowers the losses [16]. With this type of bearing a control system is not needed but the bearing
system requires cryogenic cooling [15]. These types of bearings are still under research and development
by Boeing in 2011.
Table 3.3 Comparison of different types of bearings [27].
Bearing type
Approximate
power loss
Advantages
Disadvantages
Ball
(mechanical)
5–200 W
+ Simple, low cost,
compact
- Needs lubrication, seals,
hubs and axle.
Magnetic
10–100 W
+ Acts directly on rotor,
allows high speeds.
- High cost, requires
‘‘touchdown bearings’’ and
reliability uncertainty.
HTS
10–50 W
+ Low loss, high forces
- Long-term development
requirement, housekeeping
losses (cryogenic cooling)
3.4.3 Housing
One of the more important parameters of FESS is efficiency. The aerodynamical drag loss contributes
largely to the total system losses [24], as these losses increase with the cube of the rotational speed.
Therefore, the losses will be significant if a high-speed flywheel is operated in atmosphere pressure.
Therefore reduction of these losses is an effective way to reduce total losses of the overall system
efficiency. One solution to reduce the aerodynamically drag loss is to mount the flywheel in a vacuum
housing. This eliminates air drag and thereby reduces the losses. However, this adds complexity to the
overall system and requires auxiliary system such as vacuum pump and a cooling system. A vacuum
environment may require a more efficient cooling system that can handle heat removal from the electrical
machine and other part of the flywheel system that produces heat, since the heat transfer is less effective in
vacuum.
Another approach is proposed in [24]. Instead of operating the flywheel in low pressure it is shown that by
using a gas-mixture of helium and air can be another effective way to reduce aerodynamically drag loss.
One advantage is that the requirement on the cooling system is reduced.
The task for the housing is not only to reduce losses; it must also withstand a potential failure. If the rotor
breaks apart the housing chamber must be able to stop free flying projectiles. The housing is typically thick
steel or other high strength material. The safety can be enhanced by multiple-barriers. The flywheel system
15
can be installed underground where a thick steel housing can provide a first protection and a second barrier
is provide by the underground installation [26].
3.4.4 Power electronic interface
In modern FESS, power electronics are a vital part of the system. It provides a control interface for the
electrical machine and interface for the power transfer. The power electronic interface usually consists of a
bi-directional inverter/converter and a variable speed drive. The power from/to the flywheel is available at
a DC-link. To interface the FESS to an ac-grid, another bi-directional converter is needed, i.e. the converter
may be single-stage (AC-DC) or double-stage (AC-DC-AC).
The generator will produce AC current with decreasing frequencies as the flywheel slows down. It is
therefore needed to convert the AC current to a constant frequency; this is done by the power electronic
interface. Depending on requirements of the FESS application the controller operation of the converters
may vary. For a FESS interconnected with an ac-grid, control of both active and reactive power may be
needed.
Desired attributes for the power electronic interface are high power capability, high switching frequency
and high efficiency. With the recent development of semiconductors, rectifiers and power converters can
meet high power ratings and efficient demands. The converter is usually based on insulated-gate bipolar
transistors (IGBTs). The power electronic components are compact which make it possible to house them
in a unit that is comparable to the flywheel unit itself [15].
3.5
Range of Capacities
When it comes to the power and energy capacity of a FESS it is important to point out that these are
completely decoupled. This fact can be shown by equation (3.9), the specific energy of the flywheel is set
by four mechanical parameters: Shape, strength of material, mass density, and angular velocity. The
electrical machine and the power electronics is not part of this equation and therefore do not affect the
energy stored in the flywheel. However, the rotor of the electrical machine does indeed add to the total
amount of stored energy but generally it contributes significantly less than the actual flywheel.
Furthermore, the power level of the system depends mainly on the properties of the electrical machine and
the power electronic interface. Thus the systems energy storage capacity is limited by the mechanical
properties (mainly rotational speed limit of the flywheel) and the limit for the power capacity is set by the
electrical machine and power electronics.
Individual flywheels with the storage capacity up to 138 kWh have been stated in literature [15]. However,
to the author’s knowledge, the range of stored energy for commercially available FESS is 0.2 – 25 kWh. It
should be pointed out that several flywheel units can be connected in parallel/series to increase the storage
and/or power capabilities.
The data for the specific energy in presented in Table 3.1 is only considering theoretical limit of the
flywheel rotor. Specific energy for a complete system must take the all the system components into
consideration, which will imply a decreased specific energy for the entire system. Commercially available
FESS today has specific energy significantly lower than the values presented in Table 3.1[26]. With the
development of new high strength materials, which enables higher speeds the specific energy for the
complete system will increase. According to [27] FESS with specific energy up to 200 Wh/kg and specific
power up to 30 kW/kg is expected in the next few decades.
3.6
Environmental issues
The materials used in FESS are generally non-hazardous. The materials used are mainly; composite-fibres
(carbon-, glass- and epoxy-fibers), steel, copper, aluminium, silicon and rare earth magnates. Under
normal operation there are close to-zero emissions. If properly handled all materials used can be re-cycled
at end-of-life [4]. The main hazardous concern is the potential failure of the flywheel rotor.
3.7
Commercially available flywheel systems
There are a number of companies around the world that manufacture flywheel energy storage systems. This
section provides an overview over some of the systems that are commercially available today.
16
Flywheel energy storage systems are usually categorized as either low-speed or high-speed. The border
between these two types is found around 10 000 rpm [7]. Low-speed flywheels have long been
commercially available, these systems typically utilize metal rotor and are characterized by low energy
density. The most common application for low speed flywheels is to act as a power quality device to
provide ride-through of interruptions up to 15 s long or to bridge the shift from one power source to
another. Examples of leading commercial manufactures of low speed flywheels are Piller and Active Power
[24].
The current R&D on flywheel energy storage systems has focused towards high-speed composite
machines, running at rotational speed over 10,000 rpm. As shown above the high directional strength
properties of composites materials, combined with their comparatively low density, allows optimal design
of the overall system with respect to specific energy [29]. Examples of leading commercial manufactures of
high speed flywheel systems are Beacon Power and Vycon Energy [28,29].
3.7.1 Beacon Power
Beacon Power Corporation, based in Massachusetts, USA, aims to develop advanced flywheel-based
energy storage systems. Their first systems was backup power solutions for telecommunication application
but the focus have now changed towards development of grid-scale flywheel energy storage system for
applications such as grid-scale frequency regulation service.
Beacon Power's main product is the “Smart Energy Matrix”, based on a concept of a multi-flywheel energy
storage system. This system consists of multiple 100kW/25kWh flywheel units. The main components of
each flywheel unit are the following [29]:
- Rotor assembly – Composite flywheel, metal hub and shaft, interface for active lift and magnetic
bearing system, motor rotor
- Motor/generator – Permanent magnet machine
- Magnetic bearings and active lift system
- Vacuum system
- Vacuum housing – Structural support for the rotor assembly and low-pressure vessel.
Figure 3.2. Conceptual overview of Beacon Power Flywheel System [44].
Each flywheel unit is coupled to a bi-directional power converter, which acts as an inverter and variable
speed motor drive. The power converter provides a DC interface which makes it possible to connect
multiple units in parallel to a common DC bus bar in order to meet higher power demands, as shown in
Figure 3.3.
17
Figure 3.3 Multiple flywheel units parallel connected to a common DC bus bar.
Beacon Power has a 20 MW test “Smart energy matrix”-plant in operation, located in Stephentown, USA.
The purpose of this plant is to provide frequency regulations services. This plant is comprised of 200
parallel-connected 100kW/25kWh flywheel units. The speed range of the rotor is 8000 – 16000 rpm. The
plant can provide a maximum output power of 20 MW for 15 minutes. The response time is <4 seconds,
input/output voltage is 480 V three phase AC, 50 / 60 Hz [25].
Figure 3.4 Left: Beacon Power 20 MW Smart energy matrix test facility. Right: Close up of flywheel unit. [26]
3.7.2 Vycon Energy
Vycon market a system with product name VDC-XE which consists of a high speed steel flywheel with a
speed range of 14,500 -36750 rpm. The flywheel is coupled to a high-speed motor/generator that interfaces
via power electronics to a 400-600 V DC-link. The maximum output power for one unit is 300 kW.
Discharge time at rated output is around 14 s. It is possible to parallel several units to increase power output
and/or discharge time.
Vycon targets the UPS market segment and the flywheel system can be an alternative to lead acid batteries.
Another application is in the railway industry (traction applications). The flywheel system absorbs breaking
energy from the train, which can be used when the train accelerates. This can give subway operator a way
to lower their energy consumption. Vycon also market their flywheel system for usage in large cranes. The
use is similar to traction system, breaking energy is stored in the flywheel and released when the crane
needs power to lift [29].
3.7.3 Piller
Piller is another company that provides flywheel based UPS solution and load levelling in local grids, such
as traction applications. Piller flywheel technology is based on a low speed steel flywheel with a speed
range of 3,600 to 1,500 rpm. The electrical machine is a high power synchronous machine with a maximum
power rating of 1.65 MW. The maximum discharge time is around 10 seconds [31].
18
3.7.4 Active Power
Active Power provides flywheel based UPS solutions. The core technology is a vacuum operated low speed
flywheel with a power rating of 250 kW. The flywheel is made from forged steel and has an operational
rotational speed range of 2500-7700 rpm. The system utilizes a combination of ceramic ball bearings and
magnetic lift to increase bearing lifetime. The power is available either at a DC-link or AC-terminal. One
single flywheel unit can provide the nominal output power if 250 kW for 14 seconds. The standby
efficiency is 99,8%. Modular system design, were multiple flywheel units is parallel connected can provide
power up to 2 MW [32].
Figure 3.5 Active Power flywheel unit.
3.7.5 Market summary
As seen on the examples above the flywheel market is focusing on UPS and traction system. With
exception for Beacon Power all companies mentioned above are competitors in the UPS solution market.
These systems are mainly for power quality application where long discharge times not are needed. At
present and to the author’s knowledge, Beacon Power the only company focusing on grid-scale solution.
Table 3.4 Manufactures of flywheel systems [29,30,31,32].
Manufacturer
Low Speed
Rated power [kW] Discharge time [s] Rot. Speed [rpm]
Active Power
250
14
2500-7700
Piller
1650
10
1800-3600
215
14
14500-36700
900
8000-16000
High Speed
Vycon Energy
Beacon Power 100
19
3.8
Summary
Features that flywheel energy storage systems include:
-
High power density
Relative high specific energy density
Low or no capacity degradation during discharge/charge. – Flywheel have very high cycling
capacity, up to 90 000 charge-discharge cycles have been reported.
Easy to measure the state of charge - Function of the rotational velocity.
Very low maintenance – Manufactures claim that flywheel have close to zero maintenance.
Quick response time
Scalable and no geological barrier
Low environmental impact
-
Long lifetime > 20 years
20
4
4.1
MODEL DESIGN
SCOPE
In this thesis the first steps in the development of simulation FESS model were taken. The essential
components have been identified which are needed for simulating a FESS system. The model is built using
the electromagnetic time domain transient simulation environment PSCAD/EMTDC. The model can later
be used for evaluating a grid connected FESS capability to handle various power quality problems or other
applications in electrical grids. The model is later verified with usage in a peak shaving application. The
model developed is further described in appendix A1.
The model and control system is built using standard components from the PSCAD/EMTDC master
library. The focus will be on the power electronic interface. In a real system multiple parallel-connected
power converters are needed to meet the power requirements, however to simplify the developed model
one power converter module is considered.
4.2
Model description
The developed model of a the flywheel energy storage system (FESS) include the following components
- Two voltage source converters (VSC)
- Permanent magnet synchronous machine (PMSM)
- Step-up transformer
- Grid
The VSC connected to the PMSM (machine-side VSC) provides a variable speed control for the PMSM
while the grid connected VSC (grid-side VSC) control the DC-voltage of the DC-link. The VSCs are
formed by six Insulated Gate Bipolar Transistors (IGBTs). The VSCs are back-to-back connected to enable
bidirectional power flow. The grid is modelled as a voltage source.
PMSM
FW
M/G
VSCs
~
=
Step-up transformer
=
~
Grid
~
Flywheel
Figure 4.1 Model topology
4.3
Sinusoidal pulse width modulation
In order to produce the desired AC output from both VSC, sinusoidal pulse width modulation (SPWM) is
performed. The output from the VSC is a square wave with two possible voltage values: +Vdc/2 or
–Vdc/2. The three phase converter bridge consists of six switches, each formed by an IGBT with an antiparallel diode. The anti-parallel diodes provide protection for peak load inductive current when the switch
is off.
Figure 4.2 Schematic figure of a VSC
21
A schematic view of the VSC is shown in Figure 4.2. The gate signals for controlling the switches (G1-G6
in figure 4.2) are generated by comparing a triangular wave (carrier) with a sinusoidal wave (desired phase
voltage reference), as shown in Figure 4.3.
Figure 4.3 Voltage reference for phase A, B or C and triangular wave
When the instantaneous value of reference voltage is greater than the triangular wave the gate signal is 1
and 0 when the voltage reference is less than the triangular wave. This signal controls switch G1 and the
inverse signal controls switch G4. The configuration of the switches is shown in Figure 4.2.
The gate signals are generated in the same manner for all three phase, the voltage reference for each phase
is compared with the triangular wave and the gate signals for the corresponding switch is generated. G1 and
G4 corresponds to phase A, G3 and G6 to phase B, G5 and 62 to phase C.
The output voltage for the VSC is not a perfect sine wave and will contain voltage components with higher
frequencies than the desired fundamental frequency. However the undesired harmonics can be reduced by
using an appropriate filter, for example a low-pass filter. The amplitude of the output voltage is governed
by
.
is the modulation index, with is always less or equal to 1.
4.4
D-Q-0 Transformation
The mathematical analysis of three phase system can be complicated; however there exists methods to
simplify the analysis of such systems. One of these methods is the dq0 transformation. This transformation
simplifies the analysis and derivation of control systems of three phase synchronous machines and power
converter and will be used in the following sections.
The dq0 transformation is a mathematical transformation used to transfer stationary three phase (abc)
quantizes to three rotating quantities (dq0). In balanced three phase systems the 0-componets can be
neglected, and the dq0 transformation can be reduced to d- and q- components. In this thesis only balanced
system are considered. The d- and q-components are time invariant (DC quantities). The abc-dqo and the
inverse dq0-abc transformation are performed according to the following matrix equations.
(4.1a)
(4.1b)
22
Where
, are the dqo components, , , are the three phase components and is the reference
angle to the stationary three phase component . The d,q components are rotating with the rate of change of
the angular position. In Figure 4.4 a graphical representation of the dq transform is shown.
xb
xq
dθ/dt
xd
θ
xa
xc
Figure 4.4 Graphical representation of the dq-transformation.
4.5
Motor/generator
The motor/generator is modelled with a permanent magnet synchronous machine (PMSM) model from the
standard PSCAD library. The model is a linear state model in the d-q rotating reference frame; the
equations of the PMSM are expressed in the d-q reference frame to transform the nonlinear equations three
phase equations to a linear state model [33]. The dq representation also simplifies the implementation of
the control system. The stator voltages is given by the following equations
(4.2)
Where
and
are the d- and q-axis stator inductances, respectively.
is the angular velocity of the
rotor,
are the stator currents and
is the rotor flux. The electromagnetic torque can be calculated
with the following equation [33]
(4.3)
Where is the torque and
is the number of magnetic poles in the rotor. The machine considered has
two magnetic poles, which implies that the electrical frequency is equal to the angular frequency of the
machine rotor. The maximum torque is achieved by keeping,
, hence the electromagnetic torque is
given by [33]
(4.4)
23
4.5.1 Machine-side VSC control strategy
The PMSM control is based on vector control, also called field oriented control. This control method
consists of controlling the stator currents. The goal of the vector control is to separately control the torque
producing and magnetizing flux components of the stator current. To achieve this decupled control, the daxis component of the stator current is aligned with the rotor flux. This leads to a control structure similar
to the control of a DC-machine. In Figure 4.5 the block diagram for the PMSM control implementation is
presented.
The control system consists of the following subsystems:
-
Current measurement
Rotor angle and speed measurement
Current control
isa
isb
PMSM
Gate
Signals
isc
isq
ωr
isd
Current
Control
vsd ref*
vsc ref*
Rotor angle
and speed
messurement
PWM
ABC to dq
vsa ref*
vsb ref*
θr
ABC to dq
θr
vsq ref*
Isq ref*
Isd ref*
Figure 4.5 Vector control of the PMSM.
The stator currents are measured ( , ,, ,) and transformed from abc to the rotating d-q reference frame
( ,
). To keep the d-axis aligned to the rotor flux, the rotor angle (θ) is used in this transformation. To
control the stator currents a current control is derived from equation (4.2) Laplace transform yields
(4.5)
The current controller can be formed by a feedback loop as shown in Figure 4.5. The error between the
reference stator currents
and
and the measured stator currents are processed by a PI
controller. As shown in equation (4.5) is the d- and q-axis stator currents components are coupled and
needs to be cancelled to achieve a functioning current control. In order to keep the d- and q-axis
components of the stator reference voltages synchronized to the rotor, the rotor angle (θ) is used in the d-q
to abc transformation. The coupled machine dynamics are added to the output signal from the controller
which results in the voltage reference signals (
). The voltage reference signals passed the
PWM modulator which outputs the gate signals to the IGBT bridge.
24
isd ref*
+
vsd ref*
+
PI
-
ωrLsqisq
isd
ωrΨm
Isq ref*
+
+
PI
-
+
vsq ref*
+
ωrLsdisd
isq
Figure 4.6 Current controller.
The reference currents passed to the current control is calculated either by a speed controller or power
controller. The speed controller is implemented as shown in the following block diagram
ω*
+
PI
Isq ref*
ω
Figure 4.7 Speed controller.
As shown in Figure 4.7 the speed controller calculates the q-axis current reference signal (
), which
is proportional to the torque according to equation (4.4), by finding the difference between the reference
speed (ω*) and the measured speed (ω). The PI controller process the error in order to achieve accurate
control.
The power controller also calculates a q-axis current reference signal. Since the power developed when the
flywheel deceleration is given by
(4.6)
Where is the angular velocity of the flywheel,
is the power reference and is the torque. The torque
required to keep a constant power output can be calculated as
(4.7)
Assuming a stiff shaft coupling between the flywheel and generator, the mechanical power is equal the
electrical power,
. The q-axis current reference,
, can by calculated by combing equation
(4.7) and (4.4).
(4.8)
25
P*
+
PI
1/ω
isq ref*
3/2
1/Ψ
P
Figure 4.8 Power controller
The power controller is implemented as shown Figure 4.8. The error between the reference power (P*) and
the measured power (P) is processed by a PI-controller in order to achieve accurate control.
4.5.2 Grid connected VSC Model
The objective of the gird-side converter is to keep the DC-link voltage constant regardless of the magnitude
and direction of the PMSM power output. The control system shown in Figure 4.9 consists of the following
subsystems:
RMS voltage measurement
Current measurement
DC voltage control
Current control
Phase-locked loop (PLL)
Lf
Transfomer
vsa
vtc
itb
vsb
vtc
itc
vsc
Grid
Gate
Signals
vdc
Rf
ita
vta
~
-
ABC to
d-q
θp
id
iq
vdc
vc ref*
va ref*
PLL
vb ref*
PWM
Vdcref*
d-q to
ABC
vtq ref*
Current
Control
id ref*
Vdc
Control
iq ref*= 0
vtd ref*
vsd
Figure 4.9 Complete control system of grid-side VSC
The AC-dynamics of the VSC model in the stationary three phase (abc) can be described with the
following equations.
(4.9)
26
Where
are the output voltages from the VSC,
,
are the grid side voltages ,
are the three phase currents.
is the interface resistance and is the interface inductance.
,
,
4.5.3 Grid-side VSC control strategy
Transforming equation (4.9) to the rotating dq reference frame synchronized with the grid voltage yields
[36].
(4.10)
Where
and
are the output voltages from the VSC,
and
are the grid side voltages,
and
are the output d-axis q-axis currents components and
is the system frequency in radians per second.
With the dq-reference frame synchronized to the grid voltage ( ) d- and q-components become:
(4.11)
The d- and q-axis currents in equation (4.9) are coupled with the terms
and
respectively. In
order to derive independent current control loop for the d-axis and q-axis currents these terms must be
cancelled. Equation (4.8) transformed to the laplace-domain gives
(4.12)
By denoting
(4.13)
and based on the decupled compensator model presented in [34] the VSC model can be described by two
decupled first order systems as shown in Figure 4.10.
utd
1
-------sLf+Rf
utq
1
-------sLf+Rf
Itd
Itq
Figure 4.10 Decoupled VSC model.
The VSC can now be controlled with the input signals
and
. These input signals,
and
are
computed by subtracting the reference currents value (
and
) by the measured current (
and
). The error is processed by a PI controller and outputs
and
.
From these signals the VSC terminal voltage references (
are computed be adding the
compensation terms according to equation (4.13). The terminal voltage references are then passed to the
PWM, which outputs the gating signals to the IGBT bridge. In order to synchronize the frequency of the
terminal voltage with the grid frequency, the phase angle of the grid voltage is obtained from the phaselocked loop is used in the dq-abc transformation of the voltage references passed to the PWM.
27
The derived control loops are capable of separately controlling the d- and q-axis currents, as shown in
Figure 4.11.
vsd
Itd ref*
+
Itq ref*
PI
utd
+
-
-
+
itd
ωLfitq
+
PI
utq
-
-
+
itq
ωLfitd
vtd ref*
vtq ref*
Figure 4.11 Grid-side VSC current controller.
The DC-link voltage is controlled by exchanging active power between the grid and the VSC by controlling
the DC-link voltage can be controlled [38], hence the DC-voltage controller generates a d-axis current
reference signal
. The error between the reference DC-voltage value and the measured DC-voltage
is processed by a PI controller, as shown in Figure 4.12. The output is limited to make sure the current
reference is kept in safe operation range of the VSC.
Vdc ref*
+
PI
Itd ref*
Vdc
Figure 4.12 DC voltage control
The reactive power can be calculated with the following equation, with
as stated in equation (4.11)
(4.14)
Hence the reactive power is controlled by the q-axis current. The q-axis current reference signal is set equal
to zero in order to maintain unity power factor [35].
4.6
Flywheel
The flywheel is modelled as inertia added to the PMSM rotor. The flywheel is assumed to have a direct
connection between the motor/generators rotor shaft. The dynamics of the rotor/flywheel is modelled with
the following equation
(4.15)
Where
is the electromagnetic torque,
is the mechanical losses,
flywheel, is the damping coefficient and is the inertia of the flywheel.
is the angular velocity of the
28
5
5.1
SIMULATION
Case study
To verify the flywheel energy storage system (FESS) a peak shaving case is considered. The case will show
that the FESS can supply a sudden peak load and then recharge. This case is chosen to show the
operational characteristics of a flywheel energy storage system. The aim of this case study is to test the
FESS capability to transfer active power from the PMSM to the grid and vice versa. The load considered is
a star connected resistive load, as shown in Figure 5.1. This load is switched in at a certain time, and should
be supplied by the flywheel system instead of the grid. Therefore, a 3-phase breaker is interconnected
between the load and the grid transmission line.
FW
M/G
~
=
=
~
Grid
~
Transfomer
0.690k V / 30 kV
Figure 5.1 Case study topology.
The case study is carried out with the machine running at 50 Hz (3000 rpm). When the machine is running
at 3000 rpm the flywheel is fully charged. The resistances of the IGBT switches are chosen to a low level, 1
uΩ, which makes the system close to ideal. The mechanical losses of the flywheel is neglected, hence the
term in equation (4.15) is disregarded. The damping coefficient, , is chosen to 0.02 PU. The stator
inductance is measured in PSCAD/EMDTC and the d- and q axis components are assumed to be equal
(
). The measure value is 0.15 PU. The machine is rated at 3 MW and the three phase resistive
load is chosen to 0.5 pu (1.5 MW) of the rated power of the PMSM. The parameter for the case study is
presented in Table 5.1.
29
Table 5.1. Parameters of the case study.
PMSM
Rated power
3 MVA
Magnetic flux
1 PU
Rated frequency
50 Hz
Stator Inductance
0.15 PU
Rated Voltage
690 V
Flywheel/Rotor Inertia
152 kgm^2
Interface inductance
0.382 mH
DC-link capacitor
1000 mF
Interface resistance
9.6 mΩ
Machine-side VSC
Switching frequency
2000 Hz
Grid-side VSC
Switching frequency
1800 Hz
DC-link voltage
1.1 kV
Load
600 ohm per phase
Transformer
Low voltage side
690 V
High Voltage side
30 kV
The case study simulation was carried out as follows
1. The PMSM initially run at rated speed of 3000 rpm. The speed controller maintains the reference
value, as describe in section 4.5.1. The FESS is fully charged.
2. After 1 sec the load is switched in by closing the breaker. The PMSM control system change to
power control and a reference signal of 0.5 pu is fed to the power controller. The FESS should now
discharging and provide power to the load in order to shave the peak.
3. After 3 sec the load is disconnected and the PMSM control system change to speed control and a
speed reference of 1 PU (3000 rpm) is fed to the speed controller. The FESS system should
recharge until the speed increases to the reference value.
30
5.2
Simulation results
The FESS is preforming as expected. When the load is connected the FESS is supplying the power required
by the load, as shown in Figure 5.
2
FESS
Load
Grid
1.5
Active power [MW]
1
0.5
0
-0.5
-1
-1.5
-2
-2.5
0
1
2
3
4
5
Time [s]
6
7
8
9
10
Figure 5.1 Active power FESS (blue ), load (red) and grid (green).
Figure 5. shows that during the time the load is connected the FESS supplies the active power to the load
while the grid power is zero. When the load is disconnected and the grid starts to supply power to the
PMSM in order to recharge the FESS.
As the FESS is discharging the speed of the flywheel is decreasing. The speed decreases from 3000 rpm to
approximately 1600 rpm during the discharge, as shown in Figure 5.2. At 4.2 seconds the FESS starts to
recharge and the speed is increasing until the speed of the flywheel reaches 3000 rpm.
3200
3000
Rotational speed [rpm]
2800
2600
2400
2200
2000
1800
1600
1400
0
1
2
3
4
5
Time [s]
6
7
8
9
10
Figure 5.2 Rotational speed of the flywheel.
31
6
CONCLUSIONS AND DISCUSSION
A technical description of a flywheel energy storage system has been outlined. The main system
components, i.e. flywheel, electrical machine, power electronic interface, bearing system, and housing have
been described. It has been shown that composite materials are advantageous when building flywheel
rotors due to its higher tensile strength to density ratio. This allows high-speed rotation and therefore high
specific energy, which enables compact design. There are multiple options when choosing the electrical
machine. It has been concluded that a permanent magnet synchronous machine is the most advantageous
design, mainly due to advantages in efficiency and high power density.
As the grid is likely to develop into a more dynamic system with future development of smart grid
technology, the author concludes that the functional requirements on the power interface of the FESS are
expected to increase. It should be able to handle for example load following and power quality services.
FESS can be the solution for a multiple of applications in the electrical utility system, such as load
levelling, frequency regulation and renewable energy capacity firming. FESS is best suited for applications,
which are characterized by high cycling and fast dynamics. The drawbacks are the relative short discharge
time. BESS and FESS have common characteristics. Comparing these systems FESS has advantages such
as higher power density, no cycling degradation, environmentally friendly and fast response time. However
FESS system must become cheaper to really be an alternative to battery system (UPS). With further
development of flywheel rotors, power electronics and magnetic bearings flywheel energy storage system
will be a strong candidate for grid applications up to multiple megawatts.
Today fully commercial FESS exists primarily in the UPS market with both high-speed and low-speed
technology. The systems are marketed as an alternative to other UPS solutions, such as lead-acid batteries.
To the author’s knowledge there is only one company, Beacon Power, focusing on grid-scale FESS.
Beacon Power markets their FESS as a competitive alternative solution for frequency regulation. However,
they are in a development stage of the technology and have only one test facility operational.
In this thesis work a simulation model of a FESS has been developed by using the electromagnetic time
domain transient simulation environment PSCAD/EMTDC. The main model components include PMSM
coupled to a variable speed drive and grid connected converter. A rudimentary control system has also been
implemented. A case study showed the operational principles of the FESS. It can be concluded that the
model has the necessary functions to make further studies of a FESS.
A difficulty during the studies was the lack of system context, describing the smart grid environment,
which was aimed to be defined after a working FESS model in PSCAD. With hindsight, a system context
should have been clearly defined before starting to develop the FESS model. This is crucial when designing
the entire model, because depending on requirements of the FESS application and grid characteristics the
power controller operation of the converters may vary which also impacts the design. The model lacked the
system context and it was therefore difficult to draw any other conclusion other than the flywheel
operational characteristics; the FESS in the case study can supply the resistive load with 1.5 MW during
4.2 seconds.
I think FESS can be a good solution as to electrical energy storage, however there is still a need of
extensive development (R&D) and further cost reduction in order to make it competitive alternative. The
battery industry has up to now gained more attention in media, more R&D and financial support. This is
interesting due to the fact that batteries will literally erode with time, as constant cycling degrades their
capacity; an issue not present in the FESS concept. It is clear that energy storage is needed in the smart grid
environment. In the future, the most probable scenario is a market with various technologies of ESS, each
with its unique niche.
32
7
RECOMMENDATIONS FOR FUTURE WORK
Future work into the concept of mechanical energy storage system splits into three main areas:
 Mechanical design and development of the flywheel rotor
 Development of the bearing system
 Development of the electrical machine
As to the simulation model development of model the following steps should be further worked out



Connection to an advanced grid model (eg. describing dynamical load variations)
Further development of the grid side control, such as reactive power control
Detailed analysis of the dynamics of the control system for booth power converters.
It would be interesting to model the functionality of a FESS in a renewable capacity firming case. A wind
turbine with integrated flywheel energy store for example.
33
8
ACKNOWLEDAGEMETS
I would like thank my supervisor Frans Dijkhuizen for giving me the opportunity to do my master thesis at
ABB Corporate Research.
Also, I wish to thank Johan Abrahamsson and Magnus Hedlund at the division of electricity at Uppsala
University for their feedback and help during the work with this master thesis. Furthermore I wish to thank
the examiners of this thesis Kjell Pernestål and Hans Bernhoff.
Finally I wish to give my thanks to Linda Karlsson who has been a great support throughout the whole
project.
34
9
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LABORATORY, dec 2004
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Technische Universiteit Delft,2003
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[17] G. Genta, Kinetic Energy Storage: Theory and Practice of Advanced, Flywheel Systems, ButterworthHeinemann Ltd, 1985.
[18] Ribeiro, P., Johnson, B., Crow, M., Arsoy, A., & Liu, Y. (2001). “Energy storage systems for
advanced power applications”. Proceedings of the IEEE , 1744-1756.
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applications”, Journal of Electrical Systems 7-2 (2011), 225-23.
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Transmission Systems, 2004 IEEE Aerospace Conference Proceedings,
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[28] http://www.beaconpower.com/ 2011-05-20
[29] http://www.vyconenergy.com/ 2011-05-20
[30] http://www.power-thru.com/ 2011-05-20
[31] http://www.piller.com (2011-05-20)
[32] http://www.active-power.com (2011-05-20)
[33] Janaína Goncalves de Oliveira et al , “Battery Discharging Power Control in aDouble-Wound
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9-12 Aug. 2009
36
10 APPENDICES
A1 PSCAD Model
In this section, the PSCAD model developed in this thesis work, is described and illustrated in the
following figures. The complete system with the permanent magnet synchronous machine coupled to the
machine-side VSC, the grid side VSC, load and grid is presented. Further the control system for both VSC
is presented.
A1.1 Complete system PMSM, Machine side VSC, Grid-side VSC, grid and load.
Figure A1.1 shows the complete system. Two back-to-back connected VSC, one coupled to the permanent
magnet machine and one the grid. Between the gird-side VSC and the grid (voltage source) is a step-up
transformer interconnected, with the voltage level 0.690kV/30kV and a star connected restive load (600
ohm/phase ).
VmRms
3 Phase
RMS
Idc
I
2
gt4
I
D
2
gt6
I
D
igt1b
0.000382 [H]
0.0096 [ohm]
0.000382 [H]
0.0096 [ohm]
0.000382 [H]
I
D
2
gt2
2
g4g1
I
D
2
g6g1
I
D
P
A
A
B
#1
B
#2
Iabc3
C
C
NA1
D
Power
Q
B
0.0096 [ohm]
Iabc2
igt1c
NB1
NC1
Vsan1 Vsbn1 Vscn1
2
g2g1
Va Vb Vc
A
Iabc4
Timed
Breaker
Logic
Open@t0
600 [ohm]
A
BRKLoad
P
Power
Q
B
C
Isc
B
Vbc
A
D
2
g5g1
1000[mF]
C
I
D
2
g3g1
igt1a
Isb
Iabc1
Te
I
D
2
g1g1
Isa
w
Vab
P
I
D
2
gt5
600 [ohm]
A
B
I
D
2
gt3
600 [ohm]
W
Te
I
D
Power
Q
B
V_dc
I
2
gt1
A
P
A
Power
Q
B
Pgen_MW
A
B
BRKLoad
C
1.0e6 [ohm]
Figure A1.1. The complete system
A1.1.1 Grid-side VSC- Model
Gird-side VSC which of six IGBT-switches and parallel-diodes. Measurements of all phase currents and
line-neutral voltages.
Idc
V_dc
I
I
D
2
g1g1
I
D
2
g3g1
D
2
g5g1
igt1a
1000[mF]
igt1b
igt1c
I
2
g4g1
I
D
2
g6g1
I
D
0.0096 [ohm]
0.000382 [H]
0.0096 [ohm]
0.000382 [H]
0.0096 [ohm]
0.000382 [H]
D
2
g2g1
A
B
C
NA1
NB1
NC1
Vsan1 Vsbn1 Vscn1
Figure A1.2. The grid- side VSC.
37
A1.1.2 Grid-side VSC control block.
Control block for the grid side VSC. The inputs are the measured currents and voltages shown in figure
A1.3. The outputs are the six gate signals which controls the IGBT switches of the gide-side VSC .
Vsan1 Vsbn1 Vscn1
Vsan Vsbn
igt1a
ita
igt1b
itb
V_dc
Vscn
V_dc
g1
g1g1
g2
g2g1
g3
g3g1
g4
g4g1
g5
g5g1
g6
g6g1
Controller VSC 1
igt1c
itc
Figure A1.3. Gird-side VSC control block.
A1.1.3 Complete control system
The inside of control block shown in figure A1.4. The voltage measurement and current measurements are
converted to the dq reference frame. The inside DC-link voltage control block is shown in the next figure
and the current control block is shown in figure A1.6. The voltage reference from the current control are
passed to the PWM generator outputs the gate signals which controls the IGBT switches of the gird side
VSC.
theta
Theta
Vsa
Vsan
Vsbn
Vscn
Vsb
Vsc
Vsan
Va
Vsbn
Vb
Vscn
Vc
PLL
theta
theta
theta
Vrms
ita
Measurement
itb
Vrms
G
1 + sT
Sqrt (2)
Current
itba
Measurement
itca
itd
itd
itq
itq
*
*
itc
Vacrms
itaa
theta
1/Sqrt(3)
vsd
g1
PWM
vsd
0.0
itqref
itqref
itdref
Current
Control
itd
g2
vtdUlim
vtdUlim
g3
vtqUlim
Generator
vtqUlim
g4
itq
g5
v_dc
itd
itq
g6
g1
g2
g3
g4
g5
g6
TrgOn TrgOff
V_dc
V_dc
V_dc
1.1
Vdcref
Vdcref
Vdc
Control
itdrefV
itdref
theta
theta TrgOn TrgOff
Sawtooth
Waveform
Generator
Figure A1.4. Complete grid-side control.
38
A1.1.4 DC-link voltage control
*
-
itdrefV
*
I
B
G
1 + sT
V_dc
P
D +
Vdcref
GainScale
TIME
Figure A1.5. DC-link voltage control as described in section 4.5.3.
A1.1.5 Current control
G
1 + sT
vsd
F
P
D +
itdref
itd
*
I
B
D - +
+
B
*
itq
vtdUlim
TIME
wL
itqref
itq
P
D +
B
*
D -
I
vtqUlim
B
*
itd
TIME
wL
Figure A1.6. Current control of the grid-side VSC as described in section 4.5.3.
39
A1.2 PMSM/Flywheel model
The PMSM have the rotational speed of the rotor as input and outputs the electromagnetic torque. The
PMSM is connected to the machine-side VSC that consists of six IGBT-switches and parallel-diodes.
3 Phase
RMS
VmRms
A
P
Power
Q
B
Pgen_MW
I
W
A
Te
B
I
D
2
gt1
D
2
gt3
I
D
I
D
2
gt5
Isa
Vab
1000[mF]
w
Isb
Iabc1
Te
C
Vbc
Isc
I
I
D
2
gt4
D
2
gt6
2
gt2
Va Vb Vc
Figure A1.7. PMSM model and machine-side VSC.
.
A1.1.6 Rotor/flywheel dynamics block
This block calculates the rotational speed of the rotor, input to the PMSM, from the electromagnetic torque
according to eq. 4.14 in section 4.5.1.
5.0
Rotor Interia [pu]
wm
Te
A
D + -
Ctrl = 1
D + F
1.0
Inital speed
B
w
Ctrl
1
sT
N
D
N/D
wm
F
S/H
in out
hold
*
0
A
TIME
0.0
Ctrl = 1
B
Ctrl
TIME
Figure A1.8. Machine/flywheel dynamics.
40
A1.1.7 PMSM control block
The inputs is the (left side of the block) reference speed, measured generator power, reference power,
measured speed, electromagnetic torque, rotor angle and (top of the block ) measured three-phase currents.
The outputs are the gate signals passed the IGBT switches of the machine-side VSC (shown in figure
A1.7).
Isa
isa
Isb
isb
w_ref
Isc
isc
g1
1.0
gt1
g2
gt2
g3
gt3
Pgen
Pgen_PU
PMSG_Block
Pref
0.5
g4
gt4
g5
gt5
w
g6
w
gt6
Te
Te
Theta
Theta
Figure A1.9. The control block of the PMSM.
41
A1.1.8 Current control
N
Isa
N/D
D N
Isb
N/D
D N
Isc
A
B
D
Q
C
0
Isd
Isq
N/D
D
3.54998513447
Figure A1.10. ABC-dq transformation of the current measurements. The dividing block converts the measured
currents to PU –values.
P
*
Block
Isdref D + -
D + - Usd_ref
I
F
Isd
F
*
Isq
*
L
Decoupling
w
*
1
psi_m
B
Isqref D
+
P
*
Block
-
+
D
I
F
Isq
+
+ Usq_ref
F
Isd
*
*
L
Decoupling
w
Figure A1.11. Current control as described in section 0. Implemented in PU.
A1.1.9 Speed control
w_ref
*
Block
D + -
P
Isqref_w
I
F
w
Figure A1.12. Speed control gives the q-axis current reference to the current control.
42
A1.1.10
Power control
w
D
+
*
Block
-
N
N/D
*
Isqref_Te
I
F
-1.0
Pgen
Pref
D
P
Figure A1.13. Power control gives the q-axis current reference to the current control.
43
A1.1.11
PWM signal generator
M
X
M
Y
Usd_ref
P
X
Y
X
P
P
PhaseInv
Y
Usaref
A
B
C
Usbref
Uscref
0.0
Usq_ref
D
Q
0
M
Y
MagInv
P
X
M
Figure A1.14. DQ-abc transformation of the voltage reference from the current control passed to the PWM
shown in figure A1.16.
CAR1
Block
Dblck
H
Dblck
H
Dblck
H
OFF
OFF
OFF
L
L
L
H
Usaref
ON
L
CAR1
H
ON
L
Uscref
H
ON
L
gt2
gt3
gt1
gt3
gt5
gt4
gt4
gt6
gt2
gt5
L
ON
H
L
ON
H
L
ON
H
L
L
L
OFF
OFF
OFF
H
Dblck
Usaref
Usbref
gt1
Usbref
H
Dblck
Uscref
gt6
g1
g2
g3
g4
g5
g6
H
Dblck
Block
Figure A1.15. Machine-side PWM signal generator. Outputs the gate signals to the IGBT switches of the
machine-side VSC.
44
A1.3 Transformer, grid and load.
A
P
Power
Q
B
A
P
Power
Q
B
Close up of step-up transformer, grid and load shown in figure A1.1. The transformer has 690 V lowvoltage side and 30kV high voltage-side. Power measurements are done at three points, before the
transformer, at the grid and load.
A
A
B
Iabc2
#1
B
#2
Iabc3
C
C
Timed
Breaker
Logic
Open@t0
A
P
600 [ohm]
B
C
Power
Q
B
600 [ohm]
600 [ohm]
A
Iabc4
BRKLoad
A
BRKLoad
B
C
1.0e6 [ohm]
Figure A1.16. Transformer, load and gird.
45