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Grzegorz DZIECHCIARUK1,2, Lech GRZESIAK1, Andrea VEZZINI2, Hardi HÕIMOJA3
Warsaw University of Technology (1), Bern University of Applied Sciences (2), Tallinn University of Technology (3)
Parameters of flywheel storage system with high efficiency
surface permanent magnet machine
Abstract. This paper introduces an efficiency aspect of flywheel storage system with surface permanent magnet electrical machine. Calculations of
nominal efficiency of the machine, round-trip cycle and long term efficiency of flywheel system have been presented. Finite element analysis of
surface permanent magnet motor was carried out in order to obtain motor characteristics and estimate performance of entire system. The results
have shown approximate value of system efficiency and acceptable time for energy storage using this type of motor.
Streszczenie. W artykule przedstawiono zagadnienie sprawności magazynu energii kinetycznej z wykorzystaniem silnika z magnesami trwałymi
umieszczonymi na powieszchni wirnika. Pokazano relację pomiędzy sprawnością znamionową silnika, pojedyńczego cylku ładowania oraz
długookresowego gromadzenia energii. W celu określenia parametrów silnika posłużono się analizą elementów skończonych. Otrzymane wyniki
pokazują przewidywaną sprawność systemu, jego parametry, jak również czas dla jakiego gromadzenie energii jest uzasadnione. (Parametry
magazynu energii kinetycznej przy zastosowaniu maszyny z magnesami trwałymi o wysokiej sprawności).
Keywords: Efficiency of Flywheel Storage System, Flywheel Energy Storage Systems (FESS), Energy Storage Systems, Surface
Permanent Magnet machine (SPM)
Słowa kluczowe: Akumulatory energii kinetycznej, silnik z magnesami trwałymi, sprawność magazynu energii kinetycznej
Introduction
As the share of renewable energy sources and open
energy markets is growing, many companies put a lot of
effort to develop electricity storage systems of various
physical natures. The principle of flywheel storage is to
transform electrical energy into kinetic one, accumulated in
a rotating mass, where the stored energy is proportional to
the rotating speed squared. Since high strength carbon fibre
composites appeared, flywheel energy storage systems
(FESS) have become more competitive to batteries.
Lifetime and high power capabilities are their main
advantages. The main drawback is relatively low stored
energy per mass unit, i.e. the gravimetric energy density,
making them suitable rather for applications where weight is
not a matter of high importance. They have been used in
some commercial applications such as uninterruptible
power supplies [1] [2], grid frequency regulation [3] and
heavy electric vehicles [4] [5]. Also a few automotive
companies are making some effort to use FESS in hybrid
vehicles as an alternative to batteries [6].
In our case we have investigated feasibility of a flywheel
storage unit for ultrafast charging station of electric vehicles
(EV). The main purpose of this unit is to ensure high
charging power despite of power limitation of a standard
400 V low-voltage grid. The idea is to use the storage unit
as a buffer in order to deliver high peak charging power and
continuously draw small power from the grid. The energy
can be released rapidly during car charging cycles and
slowly restored between them.
Although several flywheel storage systems exist on the
market, their energy capacities and powers vary one from
another. From this reason new system studies has been
made. In this paper an attention has been paid to an electric
machine and it was shown which parameters are especially
important and how they affect the total system performance.
An approximate energy storage efficiency of such system
has been studied considering its duty ratio. The given
efficiency of flywheel systems often refers to single charge-
discharge (round-trip) cycle, which has not the same
relevance as an operational storage system with variable
idle times. Therefore an investigation of system efficiency
has been done more widely. The system with permanent
magnet machine has been chosen and justification of this
choice will be given in further part of the paper.
In the beginning fundamental information about flywheel
system is given and the influence of motor torque on stored
energy is explained. It is shown, how motor torque affects
utilization of energy stored in a flywheel and what torque
value is necessary to obtain required power. Then main
requirements for motor and basic assumptions are shown
as well. An illustrative design of surface permanent magnet
motor is presented, which is further used to estimate motor
losses and other system parameters. The parameters are
obtained from finite element analysis (FEA) and used to
assess the field weakening properties of the machine.
Furthermore charge-discharge efficiency of flywheel unit is
calculated. At the end, the efficiency in function of idle time
is presented. This illustrative system approach shows how
singular properties of the machine are related with whole
system and when a use of flywheel storage system is
justified taking into consideration idle time and performance
of electric machine.
Fundamental parameters of a flywheel storage system
In a basic construction the flywheel and electric machine
are mounted on a common shaft, suspended on contactless
magnetic bearings (Fig. 1). All rotating components are
placed in vacuum, so the mechanical friction and air drag
are minimized. The flywheel system has an advantage of
long lifetime, above 20…25 years, during which it may
perform up to 300’000 cycles. Moreover, its performances
do not degrade in time and do not dependent on ambient
temperature. On the other hand the main drawback of
flywheel system is high idle losses. All these features make
flywheel systems very suitable for application where high
power and short storage time are expected.
The power of the system is determined by electric
machine and the stored energy is strongly related with
mechanical construction of flywheel. The key issues for
energy capacity per mass unit are the flywheel’s material
and its geometry [7]. It is important to point out that limit of
stored energy does not depend on maximal rotational
speed until flywheel dimensions are not determined. In
other word a flywheel can be designed for different
operating speeds and stored energy may be kept
unchanged. A change of maximal speed requires change of
flywheel diameter in order to keep the mechanical stress on
the same level. The moment of inertia is changed but the
amount of kinetic energy remains the same [8].
Fig. 1. Construction of a flywheel energy storage unit
The comparison of different flywheel materials is shown
in [8] [9], according to which the best of them are
composites of epoxy matrix and carbon fibres, which give
the highest energy/mass ratio. Approximate energy density
of this material is about 350 Wh/kg, but this is only
theoretical limit obtained from maximal material strength
referring only to flywheel itself. The effective energy density
of the system is lower due to mass of additional
components, safety margins in mechanical construction and
only partial energy utilization. In fact, not all accumulated
kinetic energy can be transformed back into electrical form
and this is strongly related to electric machine. The first
obvious reason is efficiency of conversion process. The
second reason is a fact that only part of mechanical energy
can be discharged if a limit of minimal discharge power is
assumed. In order to determine how much kinetic energy
can be extracted from a flywheel, a discharge process will
be introduced and illustrated by a simple numeric example.
While energy is being discharged from flywheel, the
rotational speed decreases. In order to keep the constant
power, braking torque must increase proportionally to
decreasing speed (Fig. 2). Since maximal torque of the
motor is limited, not all energy can be discharged with a
given power restriction. That moment is visible on the graph
as a minimal speed below which a discharging power is no
longer constant. Discharge characteristics of two motors
with different values of maximal torque were plotted in Fig.
2. As a result, the two flywheel systems operate in different
speed range. The figure shows that the motor with double
value of torque (Fig. 2b) is able to operate at half of minimal
speed than the other one. This has consequence in
utilization of accumulated energy. The discharged energy is
described by following equation:
(1)
22
max min
()
2
dis
J
E
where: Edis – discharge energy, ωmax, ωmin – maximal and
minimal rotational speed of the flywheel.
It can be noticed that for the first case (Fig. 2a) minimal
rotational speed ωmin = 0.5·ωmax and we can use 75% of
stored energy. For the second case (Fig. 2b)
ωmin = 0.25·ωmax and the discharged energy is 94%. In
conclusion higher torque of motor means the lower minimal
operating speed and more energy which can be
recuperated. On the other hand higher torque requires
bigger motor and increase total weight of the system. A
reasonable minimal speed point lays somewhere in a range
(0.5…0.75)· ωmax, however, a final choice is a complex
issue. A decision criterion may be defined as a minimal
weight, cost and the best efficiency of the system or a
different combination of them.
Fig. 2. Operating speed range of motors with different nominal
torque and minimum speed - motor works without field weakening;
a) 409 Nm and 7’000 rpm; b) 818 Nm and 3’500 rpm
Requirements on the electric machine
The flywheel storage system is quite special application
for an electric machine. Besides typical requirements such
as high efficiency and low weight possibly, the choice of
machine should be made taking in consideration some
special following requirements:
Relatively big air gap: The contactless suspension of the
flywheel causes higher shaft displacements than classic
mechanical bearings, so this imposes a special
requirement on the air gap. The gap must be big enough
to prevent mechanical contact between rotor and stator
in case of shaft displacement during rotation.
Tough rotor structure: The rotational speed of flywheel is
very high, and so are the centrifugal forces acting on the
rotor, necessitating a tough construction.
Brushless construction: In practise the high speed
eliminates all brushed constructions, which cause
additional friction losses and wear away very fast at high
speeds.
Low standby (idle) losses: When energy is stored in
flywheel the motor rotates at maximal speed without any
load. The losses caused by residual air drag and friction
deteriorate system efficiency. Therefore these losses
should be as low as possible when long stand-by time is
required.
Field weakening: This feature has two positive effects
on the system. Firstly it can reduce required power of
converter by improving its utilization in entire operating
speed range (considering the case when constant
power on the output is required e.g. charging station for
the EV). The second advantage is significant reduction
of eddy current losses in stator if magnetic flux
excitation can be switched off or reduced at idle state.
Choice of the machine type
The choice of electric machine is not self-evident since
any of present machine technology cannot fulfil all
presented requirements. In this FESS investigation a
surface permanent magnet machine (SPM) has been
chosen. In first approach, the choice of this machine type
has been done because the high air gap is easy to
flywheel
electrical machine
magnetic
suspension bearings
magnetic suspension
bearings
airproof
housing
a) b)
overcome by using strong permanent magnets (PM) and it
does not cause significant parameter deterioration. The
disadvantage is high idle power loss due to the presence of
PM, which is a point of investigation in this paper. The
reason of big air gap was due to a fact that mechanical
details of flywheel and bearings system were not known
beforehand, so conservative restriction of 5 mm air gap
length was assumed. Because small air gap is necessary
for good performance of induction and reluctance
machines, both types were abandoned during the initial
choice.
Overview of PM machine topologies concerning different
magnet placements inside the rotor was presented by Chau
[10]. The magnets’s position in rotor influences strength of
rotor construction and the difference in d- and q-
inductances. The ratio between those inductances (saliency
ratio) determines operating speed region above rated
speed.
Internal permanent magnet machines (IPM) have better
field weakening properties than machines with magnets on
surface [11]. Despite of that, in this approach the variant
with the magnets mounted on the surface has been chosen.
The reason was simple rotor construction. Although the
rotor with magnets glued to rotor surface using epoxy
adhesives is weak by itself, an additional strengthening
sleeve on magnets may be used to ensure high strength
against centrifugal forces. The sleeve is usually made of
high strength fibres and ensures withstanding high
rotational speeds. Despite of poor field weakening
properties of SPM machine, the assumption about the air
gap size determines the choice of this machine type. It
could be very difficult or even impossible to ensure required
saliency ratio for IPM machine with such a big air gap. From
this reason IPM type was abandoned in investigation and
studies of surface permanent magnet machine have been
done instead.
It should be pointed out that plenty of other PM machine
modifications exist in FESS, such as ironless construction,
slot-less stator, Halbach array of magnets [12], external
rotor construction integrated with flywheel [13] [14] or
construction with axial flux [15]. Although these machines
show slightly different parameters, general conclusions from
SPM machine studies are transferable to other types.
Therefore the research on SPM machine shows which
modifications of PM machine technology might be suitable
to achieve desired system features. The examples of PM
machine technology used in flywheel systems are
presented by companies/institutions such as BeaconPower,
Vycon, Boeing [16], ATZ [17], Williams F1 [14].
Parameters of surface permanent magnet machine
In order to create a FEA model, the machine power was
assumed as 300 kW and discharged energy on the system
output as 25 kWh. The studies of flywheel mechanical
construction were being made in parallel with machine
investigation, so mechanical limitations of machine
construction have not been defined precisely on the
beginning. From this reason an approximate working speed
was assumed from 7’000 rpm to 14‘000 rpm in first
approach. The power and speed assumptions gave
approximately 409 Nm of required torque (Fig. 2a). In
further part of the paper also other speed ranges have been
investigated. A choice of operating speed has been made
after some simple mechanical calculations in order to keep
flywheel dimensions in reasonable limits. However this
investigation is out of the scope of this paper.
The FEA was performed in order to obtain SPM
machine parameters; the model is shown in Fig. 3 with the
motor parameters summarized in table 1. The main task of
the model is to estimate machine parameters in order to
investigate flywheel system’s parameters in the next step.
There was no objective to find optimal design, because
machine requirements were not precisely predefined. One
pole pair design was chosen in order to minimize flux
frequency and iron losses. Soft magnetic laminated steel
with very low magnetic losses was used as stator material.
The hysteresis and eddy current losses in iron parts were
calculated in FEA, based on loss characteristic of a steel
sheet. In table 1 we see that efficiency of machine is very
high at rated speed, due to good properties of magnetic
materials and relatively low flux density in iron. The losses
in magnets are also low, due to big air gap and quite
uniform field distribution on the magnet surface. All this
parameters are at the cost of machine weight which was not
so important for a stationary application.
Fig. 3. 3D model of SPM machine
Table 1. Surface permanent magnet machine parameters
Parameter:
Value:
Unit:
Rated speed
14’000
rpm
Torque (avg.)
409.3
Nm
Estimated machine mass
229
Kg
Mechanical Power
600
kW
Phase EMF voltage (RMS)
723
V
Phase current (RMS)
287
A
PM flux (RMS)
0.475
Wb
Phase resistance
10.6
mΩ
Phase Inductance
0.41
mH
Copper losses
2.620
kW
Losses in magnets
0.240
kW
Iron losses
0.973
kW
Apparent power
622.5
kVA
cos(φ)
0.97
-
Efficiency
99.37
%
N° of pole pairs
1
-
Air gap
5
mm
Flux density in air gap (avg.)
0.63
T
Flux density in tooth
1.32
T
Flux density in back iron
1.28
T
Current density in windings
10.8
A/mm²
Slot filling factor
50
%
Turns per phase
12
-
N° of slots
36
-
Operation in extended speed range
The extended speed region refers to operation above
rated speed. This region also is called constant power
speed range, but for PM machine it is rather difficult to say
that power is constant in that range. The rated speed is
defined as the speed at which the terminal voltage equals
rated voltage with rated torque and rated current [10].
Operation above rated speed is important because it can
reduce nominal power of converter and improve its
utilization. The importance of this fact will be illustrated
using a simple example. The machine torque is 409 Nm,
imposed to the requirement of minimal power 300 kW at
minimal speed of 7’000 rpm (Fig. 2a). It follows that rated
mechanical power of machine is 600 kW at rated speed but
only 300 kW of continuous power is required in entire speed
range (table 1). This also causes that converter must be
designed for higher power because of both nominal current
and voltage. In conclusion power converter must have twice
the power rating of the required discharge power and never
operates at rated point; neither does the electric machine.
The speed range where machine operates at constant
power (Fig. 2), should not be confused with constant power
speed region above nominal speed as previously defined.
In the Fig. 2 the machine works without field weakening in
the range below rated speed, which simply is constant
torque speed range according to the definition [11].
Moreover, the torque is not fully utilized at whole speed
range in this special case and that is why the torque is not
constant. Study of operation mode for this particular
machine design will be investigated below based on
Soong’s work [11].
The idea of field weakening in a PM machine is to
control current in such a manner that a part of stator current
produces a magnetic flux in opposition to flux produced by
PMs. This can be made by controlling the current vector in
dq reference frame, rotating together with the rotor. For an
assessment of extended speed range it is convenient to use
circle diagrams, which show possible current vector location
in dq-frame, subjected to certain limits. The first limitation is
rated current of machine and the second one is nominal
voltage of the converter or the machine. They can be
expressed as follows:
(2)
2 2 2
d q n
I I I
(3)
2 2 2
d q n
U U U
where: Id, Iq – currents in dq frame, In – nominal current, Ud,
Uq – voltages in dq frame, Un – nominal voltage.
The voltage limitation should be expressed as a function
of d and q component of current vector, therefore the
simplified PM machine equations in steady state with
neglected resistance are used, which are:
(4)
3
2
dq
q d m
mq
U LI
U LI
T p I
where: L – machine’s inductance, Ψm – permanent magnet
flux, p – N° of pole pairs, ω – electrical rotation frequency.
By substituting Ud and Uq into Eq. (3), the mathematical
equation of circle can be obtained:
(5)
22
2mn
dq
U
IILL
The radius of voltage circle decreases with increasing
speed (Eq. 5). The current space vector can be placed only
inside the common area of both voltage and current circles
(Fig. 4). When the speed is higher than rated, the current
vector cannot be set to obtain nominal torque because of
limited position inside voltage and current circle on dq
plane. Physically it means that d-axis component of current
vector must be used to compensate PM flux as well as
induced back-EMF [12]. In consequence the q-axis
component is reduced as well as produced torque. The
torque of SPM machine only depends on q-component;
therefore it is represented by a straight line in Fig. 4.
In Fig. 4 and Fig. 5 the characteristics of chosen
machine design are presented according to the previous
simplification. The current space vector is shown when
machine is operating with 300 kW power at 18’400 rpm.
The machine is capable of exceeding rated speed by 30 %
with required power, but it cannot work at this speed
because we had previously assumed that maximal
mechanically limited speed is 14’000 rpm. On the other
hand the extended speed region can be shifted down by the
reduction of rated speed and suitable control method. The
change of machine construction is not necessary, because
the rated speed is a preliminary assumption and is below
the machine design limit. Obviously rated voltage and rated
power will be lower too, but this fact does not matter if
machine can still produce required power above the rated
speed, which was artificially shifted. The characteristics at
new rated speed are shown in Fig. 6. The rated speed was
reduced to 11‘900 rpm and nominal voltage to 560 V, so the
power at new rated operation point is 483 kW instead of
600 kW. Furthermore the machine is still capable of
delivering required 300 kW at the maximum speed of
14’000 rpm. The downscaling of power converter is clearly
visible. Nevertheless an operation above rated speed
requires that the current in d-axis must be supplied
instantaneously to keep the voltage on allowable level.
Therefore, the idle losses will be higher by amount of
copper losses produced in the windings by this current. In
this case the current in d-axis must be 255 A what adds
689 W of losses at idle state.
Fig. 4. Field weakening performance of SPM: a) circle diagram; b)
a zoomed fragment
Fig. 5. Field weakening performance of SPM, voltage torque and
power in function of speed
a) b)
Iq / A
Id / A
I
Iq / A
Id / A
Fig. 6. Use of extended speed region: voltage, torque and power in
function of speed (reduced rated voltage and speed)
Efficiency of a flywheel storage system
As it was mentioned before, the efficiency of the
machine does not directly translate into efficiency of energy
storage. To obtain storage efficiency of the system, we
have to calculate energy coming in and out, as well as take
in consideration all losses in function of time. The
calculation of efficiency for charge, discharge and round-trip
cycle of flywheel storage unit was made as follows:
(6)
__
100%
stored stored
ch
in ch stored losses ch
EE
E E E
(7)
__
100%
out dis stored losses dis
dis
stored stored
E E E
EE
(8)
__
__
100%
out dis stored losses dis
in out
in ch stored losses ch
E E E
E E E
where: Estored energy accumulated in flywheel as kinetic
energy, Elosss_ch, Elosss_dis charging and discharging energy
losses, Ein_ch, Eout_dis input and output energy of each
process.
To calculate energy losses we have to integrate the
power losses with respect to time according to equation:
(9)
t
losseslosses dttPE
0
)(
where: Plosses - power losses of the machine.
Firstly losses characteristic in function of speed should
be found, then a change of speed in function of time.
It was assumed that there are no mechanical losses and
the speed change is described by dynamic equation as
follows:
(10)
1
m
dT
dt J
where: Tm - machine torque applied to the shaft of flywheel,
J – flywheel’s moment of inertia.
Using integration by substitution method, a formula for
energy losses with respect to speed can be obtained:
(11)
d
T
J
PE
m
losseslosses
max
min
The discharge losses in function of speed are shown in
Fig. 7. They were obtained based on internal resistance of
machine’s windings and losses characteristics of soft
magnetic steel sheets, which were used to build the stator.
The eddy current losses on magnet’s surface were not
taken in consideration, as well as additional ones like losses
in converter, magnetic bearing system, air friction and
evacuation. In order to calculate cycle efficiency, the stored
energy in flywheel was assumed as Estored = 25 kWh. The
discharging time was 5 min and charging time 2.5 h. This
corresponds to mechanical power of 300 kW on shaft
during discharge and 10 kW during recharge. Speed range
is 7’000 rpm…14’000 rpm. For the assumed power and
speed range, the charging and discharging torque were
calculated in function of speed. The charging and
discharging torques are substituted to Eq. (11). Then Eq.
(6) … Eq. (8) were applied. Calculated efficiencies are
presented in Table 2. It should be emphasized that power of
the machine during charging and generated power during
discharging are not equal. Figure 6 shows only discharge
losses; however other similar characteristic was used in
charging cycle calculation.
Table 2. Efficiency of a single cycle:
Discharge, ηdis
Charge, ηch
Round-trip, ηin-out
99.3 %
93.2 %;
92.6 %
We can notice that in-out efficiency of singular flywheel
cycle is lower than machine’s nominal efficiency because
losses are not constant at entire speed range. Also the long
duration of energy accumulation decreases efficiency of a
charging cycle. The round-trip efficiency is quite high
because it refers to singular charge-discharge cycle and
additional losses were not included. The calculation
assumptions cause, that electrical power will not be
constant. Average value of charging power on machine
terminals will be higher than 10 kW and the discharge one
will be lower than 300 kW.
Fig. 7. Losses in machine during discharging, torque was controlled
in order to obtain constant mechanical power 300 kW at entire
speed range
Study of different operating speed range was introduced
in Fig. 8 and Fig. 9. In Fig. 8 an efficiency map is shown
with efficiency variation for different maximal speeds and
relative minimal speeds. Fig. 9 shows weight variation of
flywheel system in function of the same parameters. The
additional assumptions in this case were made as follows:
the energy density of the flywheel is 60 Wh/kg, charge and
discharge intervals are constant, the required rated torque
of machine for different speeds was obtained by changing
the machine’s length, the machine’s diameter was kept
constant and the centrifugal force was not considered as a
limiting factor. Also the amount of energy in use was kept
constant. Only iron losses in stator and copper losses in
windings were taken into account for each case.
The results show that the operation in narrow speed
range and low maximal speed give better round-trip
efficiencies. On the other hand, the Fig. 9 shows that in
these points the weight of system increases very rapidly.
The reason is pure utilization of energy which had been
discussed earlier. This leads to oversize of flywheel in order
to keep the required amount of stored energy. We see that
the choice of minimal speed is a trade-off between
efficiency and weight. It should be mentioned that the
maximum speed is not determined by the machine’s design,
but by mechanical design of flywheel for given capacity.
Fig. 8. Round-trip cycle efficiency map for different operation
ranges of flywheel
Fig. 9. Cumulated mass map of flywheel and machine for various
speed operation ranges.
Storage time versus efficiency
Despite of good round-trip efficiency, the drawback of
flywheel is relatively high loss during idle state. In order to
show how the efficiency deteriorates, we must take these
losses into account. The most significant additional losses
at idle state apart from machine losses are caused by air
drag on the surface of the flywheel and the losses in
magnetic bearings. The magnetic bearing losses were
roughly estimated as 500 W by the provider and air drag
losses as 400 W by preliminary calculations. Finally 1 kW of
total idle losses was assumed in conservative approach.
The idle losses of the machine equal 1 kW at maximum
speed (Fig. 7), which are mostly iron losses, almost the
same at idle and load states due to small armature reaction.
The assumption had been made that idle losses are
compensated from the grid at idle (stand-by) state, so they
can be added to charging losses. The new equation for
efficiency is as follows:
(12)
_
__
100%
losses dis
in out
losses ch losses idle
EE
E E E
Fig. 10 shows that efficiency decreases rapidly during
the first hours of stand-by time. The first point of
characteristic at zero time is input-output efficiency (round-
trip), same as presented in Table 2. This value of efficiency
has decreased from 92.6 % to about 85 % by additional
losses. The reason of such big deterioration is long time
(95 min) of round-trip cycle, resulting in ~3.2 kWh of losses.
If the cycle were 10 min, it would be only ~0.3 kWh. We can
see then, that short round-trip cycle (high charge and
discharge power) will ensure better efficiency. A more
detailed example of idle losses, considering different
system components, can be found in [17]. For the system
with 3 kW power and 5 kWh of stored energy, the losses at
idle state are predicted as 136 W. It gives 2.7 % loss of
initial energy in first hour; in comparison, our system has
8 % losses. According to Fig. 10, the reasonable time of
storage should not be longer than 1 hour in order to obtain
efficiency above 80 % for this simple assumption.
Fig. 10. Storage efficiency in function of idle time for different cases
Conclusions
In this paper the surface permanent magnet machine
was proposed as an illustrative example in order to assess
performance of a flywheel storage system. The choice of
this machine type was determined by big air gap, the size of
which was assumed due to unknown tolerances of bearing
systems and additional safety margin. Meanwhile the SPM
machine has being investigated; the parallel studies of
mechanical construction have shown that the air gap size
can be reduced to 1.0 mm …. 1.5 mm. This means that
actual size of the machine can be reduced keeping the
same machine parameters. Also other machine types might
be used and could demonstrate good performance. The
FEA showed that the big air gap size was not an obstacle to
obtain good machine performance. The size of air gap has
a positive effect on machine design by reduction of power
losses in magnets. The investigation of field weakening
revealed that machine is capable of working above rated
speed what may be used to reduce power converter ratings
at the cost of higher idle losses. The comparison of results
between round-trip cycle efficiency and long-term system
efficiency has showed that idle losses are very important,
especially when long stand-by time is required. The results
lead to conclusion that SPM machine is suitable for flywheel
systems where stand-by time is shorter than one hour. In
this case machine ensures acceptable efficiency and also
field weakening operation can be justified. However if
charging and discharging times are long and idle losses
high, even round-trip cycle may show low efficiency. From
this reason the high power operations with short stand-by
time are more preferable. The studies clearly show that for
long time storage more effort must be done in reduction of
stand-by losses. The ironless or slot-less construction of
stator have potential to improve that issue.
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Authors: mgr inż. (M.Sc) Grzegorz Dziechciaruk, prof. nzw. dr hab.
Lech M. Grzesiak, Warsaw University of Technology, Institute of
Control and Industrial Electronics, Electric Drive Division, ul.
Koszykowa 75, 00-662 Warszawa, E-mail: dziechcg@ee.pw.edu.pl,
E-mail: L.Grzesiak@isep.pw.edu.pl; prof. Andrea Vezzini, Bern
University of Applied Sciences, department of Engineering and
Information Technology, Quellgasse 21, 2501 Biel, Switzerland, E-
mail: andrea.vezzini@bfh.ch; dr. inż. Hardi Hõimoja, Tallinn
University of Technology, Department of Electrical Drives and
Power Electronics, Ehitajate tee 5, 19086 Tallinn, Estonia, E-mail:
hardi.hoimoja@ttu.ee.
The correspondence address is:
e-mail: grzegorz.dziechciaruk@gmail.com
