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MATLABSimulation of Deceleration Characteristics of Advanced Flywheel
Rahul A. Lekurwale
Project Fellow,MTech.(IPS)
G.H.
Raisoni College of Engineering Nagpur
Dr. S. G. Tarnekar
Professor ,Department of Electrical Engg.
G.H. raisoni
College of Engineering Nagpur
Abstract-
Advanced flywheels are very effective and advantageous
energy storage systems. For exchanging the energy a Permanent magnet
synchronous machine (to work as motor/generator) is coupled to it. The motor/generator draws power provided by
the grid to accelerate it up to the required speed. The frictionless system
keeps the rotor of the flywheel spinning for a long period.. The flywheel get
decelerate for the different load condition is obtained in the MATLAB Software.
Flywheel operates in charging mode as positive torque is applied and in
discharging mode as negative torque is applied.
Keyword-
Flywheel, PMSM.
I. INTRODUCTION
Traditional flywheel rotors are usually
constructed of steel and are limited to a spin rate of a few thousand
revolutions per minute (RPM). Advanced flywheels constructed from carbon fiber materials and magnetic bearings can
spin in vacuum at speeds up to 40,000 to 60,000 RPM. The stored energy is
proportional to the moment of inertia and to the square of the rotational speed
by eq.(1). High speed flywheels can store much more energy than the
conventional flywheels.
Where the Ek is
the energy store in the flywheel ,J is
moment of inertia , ω is the angular
velocity of the flywheel. High speed
flywheel systems are designed to minimize losses in the system so that power is
able to be pulled from the system for the longest possible time .
There are a number of advantages that make flywheels useful for applications
where other storing units are now used.
-
High
power density.
- High energy density.
- The lifetime
of the flywheel is almost independent of
the depth of the discharge and discharge cycle. It can operate equally well on shallow and on deep discharges.
- Short recharge
time.
- Scalable technology and universal
localization.
-Environmental
friendly materials, low environmental impact.
Literature present that advanced
flywheel has many application like uninterruptible power supplies (UPS), dynamic
voltage compensators, overload compensators, and start-up of standby diesels.
This paper explain flywheel, PMSM, deceleration characteristic of the flywheel at
different load condition[1],[3].
II.
FLYWHEEL
A flywheel stores energy in a rotating
mass. Depending on the inertia and speed of the rotating mass, a given amount
of kinetic energy is stored as rotational energy. The flywheel is placed inside
a vacuum containment to eliminate friction-loss from the air and suspended by
bearings for a stabile operation. Kinetic energy is transferred in and out of
the flywheel with an electrical machine that can function either as a motor or
generator depending on the load angle (phase angle). When acting as motor,
electric energy supplied to the stator winding is converted to torque and
applied to the rotor, causing it to spin faster and gain kinetic energy. In
generator mode kinetic energy stored in the rotor applies a torque, which is
converted to electric energy. The differential equation describing the behavior
of the flywheel system is given by eq. (2) to understand how to arrange the
elements.
Te = J p wm + fm wm (2)
Here the motor torque tends to accelerate the
flywheel and the frictions tend to slow it down. The eq.(3) show the electrical representation of a torque
(voltage), source moving the series combination of an inertia (inductor), and a
friction (resistor)[2],[6].
v = Lpi + ri (3)
according to the
electrical analogy theory the mechanical side can be represented by an
equivalent electric circuit as shown in Fig. 2.
Fig. 1: Electrical
analogy representation of the flywheel.
The voltage
across the terminals of each element represents the torque actually applied to
it and the current through each element represents the speed of the shaft. This
circuit clearly illustrates the power dissipated due to the frictional losses
and the energy stored in the inertia and the mechanical power delivered by the
motor. The voltage across the inertia represents J times the
acceleration of the motor shaft.
III. PERMANENT MAGNET SYNCHRONOUS MACHINE
The permanent
magnet synchronous machine (M/G) is a key component of the flywheel system because
the energy conversion from the electrical form to the mechanical during the
charge (motor) mode and from the mechanical form to the electrical during the
discharge (generator) mode happens inside the M/G. The effectiveness of the
energy conversion process mainly depends on the efficiency of the M/G It exhibit lower
rotor losses and lower winding inductances, which make it more suitable for a
vacuum operating environment and the rapid energy transfer of flywheel
applications. cross-section
of the simplified three-phase surface mounted PMSM is shown in fig 3 [4],[7].
The stator windings, as-as’, bs-bs’, and cs-cs’ are shown as lumped windings
for simplicity, but are actually distributed about the stator. Electrical rotor
speed and position, ωr θr and are defined as P/2 times the corresponding
mechanical quantities, where P is the number of poles. Based on the above motor
definition, the voltage equation in the abc stationary reference frame is given
by (4)
Fig. 2:
Cross section of the PMSM
The
flux linkages equation can be expressed by
Where,
Rs is stator resistance of motor, Ls is stator self inductance, λ is PM flux
linkages and its magnitude is given by
denotes
the amplitude of the flux linkages established by the PM as viewed from the stator
phase windings. The electromagnetic torque may be written as
The
above expression for torque is positive for motoring operation. The torque and
speed are related by the
electromechanical motion equation given by
(7).
Where J in kg.m2 is the inertia of the rotor and the coupled
flywheel. p is the derivative operator and the constant, fm is a
damping coefficient associated with the rotational system of the machine and
the coupled flywheel .In the high-speed flywheel applications, the flywheel
shaft is suspended on magnetic bearings and operated in a vacuum. Thus the
typical machine losses, friction and windage amount to almost zero, in other
words, f m effect can be ignored in this application.
The voltage and torque equations can be expressed in the rotor reference frame[5],[7]
in order to transform the time-varying variables into steady state constants.
The transformation of the three-phase variables in the stationary reference frame to the rotor reference frame
is defined as
Where, Ks is
Multiplying (4)
by Ks and carrying out the differentiation of the last term results in
Where
=
=
r X
X=
so that eq.(8) reduce to
(9)
Similarly,
if the flux linkages equation (5) is multiplied by K s , it results
in (10).
The electromagnetic
torque can be written as
(11)
It can be seen that
torque is related only to the d and
q axes current. So that Te is represented as
Where,
(13)
Fig.
3 MATLAB Simulink Model for Deceleration
Characteristic and Speed of Flywheel
When the flywheel act as PM motor as positive torque is applied during
this process converter act as the
inverter . In generating mode the converter is act as the rectifier and supply the
power to dc bus ; here resistive load
are connected on dc bus.
In
the initial condition when the flywheel
speedup to 22138 rpm in Fig.4, for 6 sec
so it will bring the flywheel to the
charging mode. The power output from the PM motor is shown in Fig. 5.
Fig. 4 Speed of
PM Synchronous Machine.
When
flywheel start discharging after
6 sec, PMSM operates as the
generator and speed start falling from 22138 rpm to 5000 rpm in Fig.4. At the time
of discharging of flywheel output
power which shown in Fig. 5 from the PM
generator is 46.5 KW, it means that
power is being supply from the generator to the load on DC bus side.
Fig. 5 Power Output of PM Synchronous Machine
And Deceleration Characteristic of Flywheel
Power at time of discharging is drop according to the load, shown in Fig.
5, here deceleration characteristic is obtained for three different load
condition. Deceleration curve ‘A’ in
Fig. 5 is obtained at resistive load
of 18Ω
and power is drop to 20 KW and
curve ‘B’ show that power is drop to
6.4KW As the load is increased
from the 18Ω to 40Ω ,it show the
decrease in the power at high load. Curve
‘C’ indicated that load is reduced to 6Ω
and power is drop to 33KW
Deceleration characteristics show that
power decreased very rapidly with the increasing load .
V.
CONCLUSIONS
Flywheel is the high speed rotating
device which stored the rotational energy ; it get charged when positive torque
is applied from the Fig. 4 it show the flywheel is fully charged at 22138 rpm. It acts as a generator during
discharge and speed drop to 5000
rpm. From this , output power is changes
from 46.5 KW to 6.4 KW, 20KW and 33 KW
according to different load are 40Ω, 18Ω, 6Ω . It show s that deceleration
characteristics of flywheel for
different load condition and it also show that power is decreased with the increasing load .
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