Electncal Drives: An introduction

1.1 ELECTRICAL DRIVES

Motion control is required in large number of industrial and domestic applications like transportation
systems, rolling mills, paper machines, textile mills, machine tools, fans, pumps, robots, washing
machines etc. Systems employed for motion control are called drives and may employ any of the
prime movors such as, diesel or petrol engines, gas or steam turbines, steam engines, hydraulic
motors and electric motors, for supplying mechanical energy for motion control. Drives employing
electric motors are known as electrical drives.
Block diagram of an electrical drive is shown in Fig 1.1. Load is usually a macllinery designed
to accomplish a given task, e.g. fans, pumps, robots, washing machines, machine tools, trains
and drills. Usually load requirements can be specified in terms of speed ahd torque demands. A
motor having speed-torque characteristics and capabilities compatible tb the load requirements
is chosen. Power modulator performs one or more of the following four functions:

Fig. 1.1 Block diagram of an electrical drive

(i) Modulates flow of power from the soqrce to the motor in such a manner that motor is
imparted speed-torque characteristics required by the load.
(ii) During transient operations, such as starting, braking and speed reversal, it restricts source
and motor currents within permissible values; excessive current drawn from source may overload
it or may cause a voltage dip.
(iii) Converts electrical energy of the source in the form suitable to the motor, e.g. if the
 2 F'undamentals of Electrical Drives

source is dc and an induction motor is to be employed,

then the pou,er modulatbr is required to
convert dc into a variable frequency ac.
(iv) Selects the mode of operation of the motor,
i.e. motoring or braking.
when power modulator is employed mainly to perform
function (iii), ir is more appropriately
called converterwhile (iii) is the main function,
depending on its circuit, u.onu".i.. may also
perform other functions of power modulator.
controls for power modulator are built in control unit
which usually operates at much lower
voltage and power levels. In addition to operating
the power modulator as desired, it may also
generate commands for the protection of power
modulator and motor. Input command signal,
which adjusts the operating point of the drive, forms
an inpui to the control unit. sensing of
certain drive parameters, such'as rnotor current and
speed, may be required either for protection
or for closed loop operation.

I.2 ADVANTAGES OF ELECTRICAL

DRIVES
Electrical drives are widery used because of the folrowing
advanrages:
l' They have flexible control characteristics. The steady-state and dynamic
characteristics of
electrical drives can be shaped to satisfy load- requirements.
required' can be controlled in wide limrts-. Electiic
ip""a can be controlled and, if
braking .an ue employed. control gear
required for speed control, starting and braking
is usually siirple and easy to operate.
Availability of semiconductor converters employing
thyristors, power transistors, IGBTs and
GTos' linear and digital ICs, and microcomputers have
made the control characteristics even
more flexible' It is possible to reshape characteristics
of drives almost at will to meet load
requlrements in an optimum manner' Speed
and torque, and transitio"r'rr"- o'""'ioo. ro
another can be controlled smoothly and steplessly.
optimal control strategies can be implemented
to achieve high dynamic performance, high efficiency
or to minimime a suitable performance
index' Drives can be provided with automatic fault
detection systems. programmable 1ogic
controllers and cbmputers can be employed to automatically
controt the drive operations in a
desired sequence.
2. They are available in wide range of torque,
speed and power.
3' Electric motors have high efficiency, low no load losses
and considerable short time
o'erloading capability. can be made in uuii"ty
of designs to make them compatible with load.
compared to other prime movers they have longer life, lower noise, lower
marntenance requirements
and cleaner operation.
4' They are adaptable to almost any operating conditions
such as explosive and radioactive
envlronment, submerged in liquids, vertical
mountings, and so on.
5. Do not pollute the environment.
6' can operate in all the four quadrants of speed-torque
plane. Electric braking gives smooth
diceleration and increases of the equipment compared to other forms of
l1r9
regeneratn'e braking is possible' braking. when
considerable saving of energy is achieved.
not available in other prime movers. These features are
7' Ltnlike other prime movers' there is no need
to refuel or warm-up the motor. They can be
started instanth.and can immediately be fully
loaded.
 Electrical Drives-An introduction 3

8. They are powered by electrical energy which has a number of advantages over other forms
of energy. It can be generated and transported to the desired point economically and efficiently.
Conversion of electrical to mechanical energy and vice versa, and electrical energy from one
from to another can also be done efficiently and economically.
Because of the above advantages, the mechanical energy already available from a, non-
electrical prime mover is sometimes first converted into electrical energy by a generator and
back to mechanical energy by an electric motor. Electrical link thus provided between the,non:
electrical prime mover and the load imparts to the drive flexible control characteristics. Consequently,
the load requirements are fully met. For example, in diesel-electric locomotive and ship, the
mechanical energy produced by diesel engine is converted into electrical energy by an electrical
generator and is utilised to drive electric motors which drive locomotive and ship. The operations
of generator and motors can be controlled to shape speed-torque curves and other parameters to
meet traction or propulsion requirements in the best possible manner.

1.3 PARTS OF ELECTRICAL DRIVES

Electrical drive h:is the following major parts: load, motor, power modulator, control unit and
source. There are large number of loads and each load has its own specific requirements. Some
common aspects to loads are discussed in Sec. 2.5 and specific requirements of some common
Ioads in later chapters. Here we examine four parts of electrical drives; viz. motors, power
modulators, souries and control unit.

1.3.1 ' Electrical Motors

Motors commonly used in electrical drives are: dc motors-shunt, series, compound and permanent
magnet; Induction motors-squirrel-cage, wound rotor and linear; Synchronous motori-wound
field and permanent magnet; Brushless dc motors; Stepper motors; and Switched reluctance
motors.
In the past, induction and synchronous motors were employed mainly in constant speed
drives.'Variable speed drives consisting these macbines were either too expensive or had very
po.or efficiency. Consequently, variable speed drive applications were dominated
by dc motors.
ac motors are now employed in variable speed drives also due to development of semiconductor
converters employing thyristors, power transistors, IGBTs and GTos.
Due to presence of commutator and brushes dc motors have a number of dis4dvantages as
compared to ac motors (induction and synchrcinous motbrs): higher cost, weight, volume
and
inertia for the same rating, need for frequent maintenance, unsuitable for explosive and contaminated
environments and restrictions on maximum voltage, speed and power ratings. Squirrel-cage
induction motor, which costs nearly one-third of a dc motor of the same rating, is extremely
rugged, requires practically no maintenance and can be built for higher rp""dr, torques and
power ratings' Wound-rotor motors are more expensive than squirrel-cage motors. Their
maintenance
needs, although more than squirrel-cage motors, are much less compared to dc motors.
They are
also available in high power ratings. Wound field and permanent magnet synchronous motors
have a higher full load efficiency and. power factor than induction motors. Wound field
motors
can be designed for a higher power rating than induction motors. However, compared to squirrel-
cage induction motors tfey have higher cosf and size for the same rating and require more
4 Fundamentals of Electrical Drives

maintenance. The permanent magnet synchronous motors have all the advantages of squirrel-
cage induction motors except that they are available in lower power rhtings.
Because of numerous advantages of ac motors described above, ac drives have succeeded in
replacing dc drives in a number of variable speed applications.
Brushless dc motor is somewhat similar to a permanent magnet slmchronous motor, but has
lower cost and requires simpler and cheaper converter. It is being considered for low power high
speed drives and for servo applications, as an alternative to dc servo motor which has been very
popular so far. The dc servo motor motor has all the disadvantages of commutator and brushes
listed above. At low power levels, *1s gsrrlomb friction between the brushes and commutator is
objectionalle, as it a,flversely affects the steady state accuracy of the drive.
Recently, stepper motor has become popular for position control and switched reluctance
motor drive for speed control. -

1.3.2 Power Modulators

It is difficult to classify power modulaton. A somewhat satisfactory classification is: (a) Converters;
(b) Variable impedances and (c) Switching circuits.
Some drives may employ more than one of these modulators. Those power mo{ulators which
are employed in industrial drives will be discussed.

(q) Converters
Wlpn a power modulator peforms function (iii) (see Sec. 1.1), it can be classified as converrer.
Usually, a converter also performs fungtion (i) in adtlition to (ii). Depending on the circuit, it
may also be able to perform function (iv) of'the power modulator. Need for a converter arises
when nature of the available electrical power is different than what is required for the motor.
Power sorrces are usually of the following types:
(i) Fixed voltage and fixed frequency ac
(ii) Fixed voltage dc.
For the control of dc motors one requires variable dc voltage whereas for ac motors one
requires either fixed frequency variable voltage ac or variable frequency variable voltage ac.
These motor requirements are met by the followiirg converters and their combinations:

l- ac to dc Corwerters: ac-dc converters are shown in Fig. I.2.The converter of Fig. 1.2(a) is
used to get dc supply of fixed voltage from the ac supply of fixed voltage. Such a converter is
kndwn as uncontrolled rectifier. Converters, of Fig. 1.2(b) to () allow a variable voltage dc
supply to be obtained from the fixed voltage ac supply. In converters of Figs. 1.2@) and (c), a
stelss variatiron of output voltage can be achieved by controlling firing angle of converter
fryristus by low Power signals flom a control unit. Converter of F-ig. 1.2(b) is a iwo quadrant
convrE in the sense that it is capable of providing variable dc voltage of either polarity with
positircwrentHowever, converter of Fig. 1.2(c) is a single-quadrant converter (positive voltage
andcurreinlC-rnverters of Fig. 1.2(b) and (c) produce harmonics both on dc and ac side andhave
low powerfactrfalow dc voltages. The converters ofFig. 72(d), (e) and (f) operate at unity
fundamental pwufur- The output voltage in converter 1.2(d) is changed by applying mecha-
nicalforce. Fewdiscr@*ps of dc voltage can only be obtained. In cohverter of Fig. 1.2(e)
 Electrical Drives-An introduction 5

Fixed Fixed
voltage Variable
lor voltage dc
3-phase ac
o)
Fixed Variable voltage ac

l.
J
(d)
Fixed voltage dc Fixed
Fixed
voltage Variable v Variable
lor voltaee dc
I voltage dc
J
3-phase ac
(e) Fixed voltage ac (0
Fixed voltage ac

ac motor

Fixed
voltage Variable
lor voltage dc
3-phase ac
(D (j)
Fig. 1.2 ac-dc converters or rectlllers

devices of
output voltage can be varied steplessly by controlling the duty ratio of semiconductor
of Fig' 1'2(0 is
the chopper by low power electrical signals from a control unit. The converter
power transistors, IGBTs and
a controlled rectifier employing self-commutaied device such as
When connected in
GTOs. It can be a single or two quadrant converter depending on the circuit'
(fl canprovide four quadrant operation (variable voltage
antiparallel, converters ofFigs. ziu) ana
Fig. I'2(g), output voltage can be
and current of either polaritly;. In ac to dc converter of thg"
unit (amplifier) of higher
controlled by controlling tieid current of the generator from a control
power level than the control units of converters of Figs. 1.2(b), (c),
(e) and (fl' This can operate
of disadvantages:
in all four quadrants. Because of the two rotating machines, it has a number
expensive and requires special foundation'
bulky, heavy, noisy, less efficient, slow response,
of the dc generator (Fig' 1'2(g)) are
Disadvantages associated with commutator and brushes
operate in a single quadrant only'
removed in converter of Fig. 1.2(h). However, this converter can
Some very old equipments may also employ ac to dc converter of
Figs' 1'2(i) and () employing
amplidyne retp"tilu"ty. Magnetic amplifiers and amplidynes are controlled
magnetic amplifier and
from low power dc signals.
6 Fuidamentals of Electrical Drives

voltagey'cr
interposin
fed from r

current ha
frequency
conmlled
harmonicl
power tra
obtainedl
from a fn
due to nu

Fixed voltage
Lower (fixed)
I or 3-phase ac
ac voltage

Frxed voltage
+ Magnetic I Variable 5. Cyclot
I or 3-phase ac I amplifier [iG. u" voltage t
(d) signals d
Fig. fJ ac voltage controllers frequenq
limits.
get variab
such as p
be varied
ntrol unit.

Fixed (b) Varit

Variable
voltage dc
voltage dc Variable
- needed I
Fig. 1.4 dc to dc converter steps'an
varratrot
ble frequency as supply from a dc
supply. reslstan(
ned to behave as voltage source
o. reslstant
or current source inverters. For "uri"n,
the control to get sl
along with frequency- Variation in
output Indur
 Electrical Drives-An introduction 7

voltage/current can be achieved by varying the input dc voltage. This is achieved either by
interposing a chopper in between fixed voltage dc source and the inverter or the inverter may be
fed from an ac-dc converter from amoug those of Figs. 1.2(b), (c) or (0. Output voltage and
currenthave stepped waveform, consequently they have substantial amount of harmonics. Variable
frequency andvariable voltage ac is directly obtained from fixed voltage dc when the inverteris
controlled by pulse-width modulation (PWM) (Fig. 1.5(b)). The PWM conrrol also reduces
harmonics in the output voltage. Inverters are built using semiconductor devices such as thyristors,
power transistors, IGBTs, GTOs and power MOSFETs. They are controlled by firing pulses
obtained from a low power control unit. In the past variable frequency supply used to be obtained
from a frequency changer employing a rotating machine. Such schemes havb become outdated
due to numerous disadvantages.

Variable frequency
Fixed
fixed voltage/
voltage dc
cuTent ac

(a) Stepped wave inverters

Variable frequency
Fixed
variable voltage/
voltage dc
current ac

G) Pulse width modulated ihverters

Fig. 1.5 Inverters

5 ' Cycloconverter: Cycloconverter (Fig. 1.6) converts fixed voltage and frequency
ac to varidble
voltage and variable frequency ac. They are built using thyristors and are controlled by firing
signals derived from a low power control unit. Output frequency is restricted to 40Vo of supply
frequency in order to keep harmonics in the output voltage and.source curent within u"""ptabl"
limits.
Fixed

fixed
Fig. 1.6 Cycloconverter

(b) Variable Impedanc es

Variable resistors are commonly used for the control of low cost dc and ac drives and are also
needed for dynamic braking of drives. Variable resistors may have two (full and zero) or more
steps and can be controlled manually or automatically with the help of contactors. Stepless
variation of resistance can be obtained using a semiconductor switch in parallel with a fixed
resistance; variation ofduty ratio ofthe switch gives a stepless variation in effective value ofthe
resistance. In high power applications liquid rheostates, known as slip regulators, are employed
to get stepless variation of resistarice.
Inductors, usually in two steps (full and zero), are employed for limiting the starting current
8 Fundamentals of Electrical Drives

of ac motors. Old drives may also employ saturable reactors for the control of induction motors. frtors which I
In saturable reactors, reactance is controlled steplessly by controlling dc current of the control when drc r sq
winding. is &.
(c) Switching Circuits r3J C-d
Switching operations are required to achieve any one of the following: (i) for changing motor Cootrols fu l1
connections to change its quadrant of operation. (ii) for changing motor circuit parameters in a parti!:dr &i
discrete steps for automatic starting and braking control, (iii) for operating motors and drives only tro c-:s
according to a predetermined sequence, (iv) to provi.de interlocking to prevent maloperation and Wb str
(v) to disconnect motor when abnormal operating conditions occur. which emdry
Switching operations in motor's.power circuit are carried out by high power electromagnetic sopbisir:ted c
relays known as contactors. Recently attempts have been made to use thyristor switches. Thyristor
Frrpc Gcd
switches have disadvantages that they cannot provide perfect isolation between the source and inulatiry-A
motor circuit. Consequently, contactors continue to be widely used. Switching operation based logic cmolh
on load's particular position is implemented using limit switches.
In the past sequencing and interlocking operations used to be implemented using low power
electromagnetic relays. Solid state relays have replaced them almost in all applications. For the
l.{ cH(x(
implementation of complicated sequencing and interlocking operations, programmable logic Choice of ro e

controllers (PLCs) are employed. li) Stod\'-r

s@ rage- t
1.3.3 Sources OjlTresb
In India l-phase and 3-phase 50Hz ac supplies are readily available in most locations. Very low andrerusi4
power drives are generally fed from l-phase source. Rest ofthe drives are powered from 3-phase (llil Rcq..n
source; except in the case of traction drives where even at very high power levels, I -phase supply voltage- rclu
is used because of economy. Most drives are powered from ac source either directly or through acc-ept regff
a converter link. When fed directly from 50 Hz ac supply, maximum speeds of induction and (iv) Ca$u
synchronous motors are limited to 3000 rpm. For higher speeds, conversion to higher frequency (v) SPre
supply becomes mandatory. Low and medium power motors (tens of kilowatts) are generally fed (vi) Envin
from 400 V supply; for high ratings, motors may be rated at 3.3 kV 6.6 kV, 11 kV and higher. (vii) Relia
In case of aircraft and space applications , 400 Hz ac supply is generally used to achieve high
power to weight ratio for motors.
In main line traction a high voltage supply is pieferred because of economy. In India 25 kV,
15 STAI
50 Hz supply is employed. In underground traction major expenditure is cost of the tunnel which In the Past in
should be minimised by keeping its cross-section just enough for the train. Consequently, clearance Variable sPer
between live conductor and the earth has also to be minimum. In view of this, underground lead to Se I
traction systems employ a low voltage (500 to 750 V) dc supply. In Western India (Bombay to efficient and
Igatpuri) 1500 V dc is used for main line and the suburban traction which is uneconomical, and of squirrel-c
therefore, future installations will not use it. motor drive:
Some drives are powered from a battery, e.g. fork lift trucks and milk vans. Depending on forbided for
size- battery voltage may have typical values of 6 V 12V,24 V 48 V and 110 V dc. Another (i) Althot
example of drives fed from a low voltage dc supply is solar powered drives used in space and control circt
water pumpin-e applications. These drives, though presently very expensive have a great future
Therefore. t
for rural \r'ater pumping and low power transport applications. (ii) Whilr
Although choice of a motor does depend on the type of sUpply but there are many other (iii) ac dr
 Electrical Drives-An introduction 9

factors which are even more important. Therefore, a dc motor may be prefened over ac even
when the ac supply is available and ac motors may be preferred over dc even when the supply
is dc.

1.3.4 Control Unit

Controls for a power modulator are provided in the control unit. Nature of the control unit for
a particular drive depends on the power modulator that is used. Because of their large number,
gnly two cases are discussed here.
When semiconductor converters are used, the control unit will consists of firing circuits,
which employ linear and digital integrated circuits and transistors, and a microprocessor when
sophisticated control is required. When control of switching circuits is required for any of the
purpose described in Sec. 1.3.2(c), function of control unit will be to provide sequencing and
interlocking. As already stated, solid state relays are used and when control is complex programmable
logic controllers (PLCs) can be used.

I.4 CHOICE OF ELECTRICAL DRIVES

Choice of an electrical drive depends on a number of factors. Some of the important factors are:
(i) Steady state oper.qtion requiremenfs.' Nature of speed torque characteristics, speed regulation,
speed range, efficiency, duty cycle, quadrants of operation, speed fluctuations if any, ratings.
(it) Transient operation requirements.' Values of acceleration and deceleration, starting, braking
and reversing performance.
(iti) Requirements related to the source: Type of source, and'its capacity, magnitude of
voltage, voltage fluctuations, power factor, harmonics and their effect on other loads, ability to
accept regenerated power.
(iv) Capital and running cost, maintenance needs, life.
(v) Space and weight restrictions i-f qny.
(vi) Environment and location.
(vii) Reliability:

1.5 STATUS OF dc AND ac DRMS

In the past induction and synchronous motor drives were mainly used in fixed speed applications.
Variable speed applications were dominated by dc motor drives. Emergence of thyristors in 1957
Iead to the development of variable speed induction motor drives in late sixties which were
efficient and could match the performance of dc drives. Consequently, because of the advantages
of squirrel-cage induction motors over dc motors (Sec. 1.3.1), it was,predicted that induction
motor drives will replace dc drives in variable speed applications. However, following hurdles
forbided for the prediction to come true:
(i) Although squirrel-cage induction motor was cheaper than dc motor, the converter and
control circuit of an induction motor drive was very expensive compared to those for a dc drive.
Therefore, total cost of an induction motor drive was significantly higher than that of a dc drive.
(ii) While the technology of dc drives was well established, that of ac was new.
(iii) ac drives were not as reliable as dc.
 Dynamics grylectrical Drives

to all types of electrical drives'

This chapter presents the dynamic relations applicable

2.r FUNDAMENTAL TORQUE EQUATIONS

A motor generally drives a load (machine)
always rotates, the load may rotate or may u
diffeient from that of motor, and if the load
while some may rotate, others may go through
rotational system shown in Fig' 2'1
to represent the motor load system by an e{uivalent
Motot Load

Fig. 2.1 Equivalent motor-load system

Various notations used are:

refbrred to the motor shaft' kg-m2'
J = Polar moment of inertia of motor-load system
01, = Instantaneous angular velocity of motor
shaft' rad/sec'
N-m'
T = Instantaneous value of developed motor torque'
of load (resisting) torque, referred to motor shaft' N-m'
4 = Instantaneous value
Load torque includes friction and windage torque of
motor'
Fig. 2.I canbe described by the following fundamental torque equation:
Motor-load system of

r-11=ftUr)=J+*r^# (2.r)

Equation(2.1)isapplicabletovariableinertiadrivessuchasminewinders,reeldrives,
ro, driu"s with constant inertia, (dJldt) = 0. Therefore'
industrial robots.

r=rr*J+ (2.2)

is counter balanced by a load torque fi

Equation (2.2) shows that torque developed by motor
and a dynarnic rorque J(da,/dt). Torque component
J(dahldt) is called the dynamic torque
because it is present only during the transient operations'
 12 Fundamentals of Electrical
Drives

Drive accererates or decererates

depending on whether ?n is greater or less than z;. ,__
3i;:;:;i"i;#::".',ril:1"'""i:'il"ii*i:i*;*::{*"i,:i,.rlTliona1 ,orque componen,
rainslmotor,o.qo"".n"u,,:;:::iT:f
acceleration' In drives
ii.:i'i_"-tJrT'I;:I,liili?;ffi f "*ng;:*:
requiring fast transient response,
the highest value and. motor-lo;d ,,'oto. to.que should be maintained
system should'be a"rtg""i ,i,,n at
Energy associated with dynami lowest possibre inertia.
tt q;-iiirr/aDis storej rnit " of kinetic
by (JaA/2)' Duringdeclleration," a],*m'a energy given
rque J(daJdt)has"-ror,n
a negadve sign. Therefore,
torque ranomaintains drive ir
3,Hf *:,?:::r:;veloeed motion by extracting energy from

2.2 SPEED TORQUE CONVENTTONS

AND
1.s\ MULTIeUADRANT OpnnertON
For consideration of multiquadrant
operation of drives, it is usefur
about the signs of torque and to establish suitable conventions
speed' Motor speed is considered
forward direction' For drives positive when rotating in the
*itiJ"p"Lte only i" forward speed wilr be their
normal speed' In loads involving """ii.*.rron,
up-und-do*n motions, the speed of motor which causes
motion is considered forward r*tion. upward
For reversibre drives, forward
Then the rotation in opposite s
direction giv"s reverse speed
Positive motor torque is defined
u. ,t ,8rqo" which produces
which is as :ilJ
e sign.
" accelera, rate of
;*:f;il1"1",:r1"1,fil111ff:;::"itj::rding to i'r *a",."!'i'* road torque is opposite in
A motor operates in rwo
energy to mechanical
_o0"._*ffiii:"riliff.,1.ffi# iiTff:jffr::lHli
which supports rts motion. In
converting mechanical,energy'
energy to electri'cal energy, -oopo.". it works as a generator
braking,
provide motoring and-braking and thus, the motion. Motor can
ope.ations r". u"if;?r*"ro'""0"r!"".se
Figure 2'2 shows^the torque and directions.
,p"LJ for both forward (positive) and
(negative) motions' Power "oo.ainates reverse
aevelopediy a motor is given by th; iroduct of speed and torque.
quadrant I, developed power In
is posltive. ttence, machine
enersv. operation in quadranr works as
i ir, tr,"r"r-", calred forward;;r"r,il:fiTjliljlirffiH:Til
negative' Hence' machine works
under braking opporinf it,"-irorron.
Therefore, operation in

Fig. 2.2 Multiquadrant-operation of drives

 Dynamics of Electrical Drives 13

ng quadiant II is known as forward braking. Similarly, operations in quadrant III and IV can be
)nt identified as reverse motoring and braking respectively.
ric For better understanding of the above notations, let us consider operation of a hoist in four
[e quadrants as shown in Fig. 2.3. Directions of motor and load torques, and direction of speed are
at marked by arrows.
ta.
tn nT
-tT
t-.r.
it
m
Counter
6
weight
I uotion

Empty
cage

Fig. 2.3 Four quadrant operation of a motor driving a hoist load

A hoist consists of a rope wound on a drum coupled to the motor shaft. One end of the rope
is tied to a cage which is used to transport man or material form one level to another level. Other
end of the rope has a counter weight. Weight of the counter weight is chosen to be higher than
the weight of an empty cage but lower than of a fully loaded cage'
Forward direction of motor speed will be one which gives upward motion of the cage' Speed-
torque characteristics of the hoist load are also shown in Fig. 2.3. Though the positive load
torque is opposite in sign to the positive motor torque, according toEq' (2'2), it is convenient to
plot it on the same axes. Load-torque curve drawn in this manner is, in fact, negative of the
actual.
Load torque has been shown to be constant and independqrt of speed. This is nearly true with
a low speed hoist where forces due to friction and winddge can be considered to be negligible
compared to those due to gravity. Gravitational torque does not change itS sign even when the
direction of driving motor is reversed. Load torque line 711 in quadrants I and IV represents
speed-torque characteristic for the loaded hoist. This torque is the diffei'ence of torques due to
loaded hoist and counter weight. The load torque line Tp in quadrants II and III is the speed-
torque characteristic for an empty hoist. This torque is the difference of torques due to counter
weight and qhe empty hoist. Its sign is negative because the weight of a counter weight is always
higher than that of an empty cage.
 14 Fundamentals of Electrical Drives

The quadrant I operation of a hoist requires the movement of the

cage upward, which corresponds
to the positive motor speed which is in anticlockwise direction
here. This motion will be
to the magnitude"ilinJ
if the motor produces positive torque in anticlockwise direction equal
of load
torque Since developed motor power is positive; this is forward motoring
211'
of,eration.
Quadrant IV operation is obtained when a loaded cage is lowered. sinci the weight
of a
loaded cage is higher than that of a counter weight, it is able to
come down due to the gravity
itself' In order to limit the speed of cage within a safe value, motor must produce
a positive
torque T equal to Tp in anticlockwise direction. As both power
and speed ari negative, irive is
operating in reverse braking.
operation in quadrant II is obtained when an empty cage is moved up.
Since a counter weight
is heavier than an empty cage, it is able to pull it ip. In order to limit
the speed within a safe
value, motor must produce a braking torque equal to Tpin
clockwise (negative) direction. Since
speed is positive and developed power negative,
operation.
Operation in quadrant III is obtained when an e
Since an empty cage has
a lesser weight than a counter weight, the motor S
s in clockwise direction.
Since speed is negative and developed power positive, this is reverse
motoring operation.

2.3 EQUMLENT VALUES OF DRM PARAMETERS

Different parts of a load may be coupled through different mechanisms,
such as gears, V-belts
and crankshaft. These parts may have djfferent speeds and
different types of rhotions such as
rotational and translational' This section presents methods of finding
the equivalent moment of
inertia' ("/) of motor-load systerp and equivalent torque
components, all referred to motor shaft.

2.3.1 Loads with Rotational Motion

I-et us consider a motor driving two loads, one coupled directly rtrere I1 i
to its shaft and other through a From I
L). Let the moment of inertia of motor and
load
que of the directly coupled load be al,n and
torque of the load coupled through a gear
If in ad
Amt n fimt(
d =
i=o, (2.3)
where c1 is the gear tooth ratio.
If the losses in transmission are neglected, then the kinetic energy due If n lmd
to equivalent inertia
must be the same as kinetic energy of various moving parts. a- and tr
Thus

Lzror?^*
Ltrl= |trr'^, (2.4)
From Eqs. (2.3) md (2.4) If loads a
irertia an
J = Jo+ alJl tobe the
(2.s)
the load r

Power at the loads and rnqtor must be the same. If tt'ansmission efficiency of the gears b" ,lr,
then 232 L
Let us cc
 Dynamics of Electrical Drives 15

(a) Lnads with rotational motion

/o ----{

(b) Loads with translational and rotational motion

Fig.2.4 Motor load system with loads with rotational and linear motions

Tto)^= Trco)^.+ (2.6)

wherefi is the total equivalent torque referred to motor shaft.

From Eqs. (2.3) and (2.6)

Tt=Tto.+ (2.7)

If in additio4to load directly coupled to the motor with inertia Js there are m other'loads with
moment of inertias Jv Jz,. . . , J. and gear teeth ratios of a1' a2,. . . a. then

J = Jo+ alJl+ alJ2+ ... + a2^J^ (2.8)

lfmloadswithtorquesT6T1,,,..,Tt^arecoupledthroughgearswithteethratiosaya2,.-.
am and transmission efficiencies 4y 42, . . . , 4^, in addition to one directly coupled, then

rt=rn.+.++...+ +
belt drive instead of gears, then, neglecting slippage, the equiyalent
(2.e)

If loads are driven through a

inertia and torque can be obtained from Eqs. (2.8) and (2.9) by considering d1, Q2,. ' . , a- each
to be the ratios of diameters of wheels driven by motor to the diameters of wheels mounted on
the load shaft.

2.3.2 Loads with Translational Motion

Let us consider a motor driving two loads, one coupled directly to its shaft and other through a
 16 Fundamentals of Electrical Drives

transmission system converting rotational motion to linear motion (Fig. 2.a(b)). Let moment of Substit
inertia of the motor and load directly coupled to it be Js, load torque directly coupled to motor
be Tn, and the mass, velocity and force of load with translational motion be M1 ftg), u1 (m/sec)
and F1 (Newtons), respectively.
If the transmission losses are neglected, then kinetic energy due to equivalent inertia must From I
"/
be the same as kinetic energy of various moving parts. Thus

itrr^= |4ar^* turrT Here r

ah =
J= lo_ rr(#), (2.10)
148
Substit

Similarly, power at the motor and load should be the same, thus if efficiency of transmission be
4r

233 U
T1a^= a^.
Tto-
+ Mornenr
motor an
In refr
r,=r,0.
* (#) (2.rr) supply tc
due to m
If, in addition to one load directly coupled to the motor shaft, there are m other loads with At anl
translational motion with velocities u1, u2, . . . um and masses M t, M2, . , . , M^, respectively, then

r = ro. r,(*)' .
",(h)'+ r^(h)' + (2.r2)

and r,=r^.#(#) . *2(?^). .. *& fu')

4^ \o^ )
(2.r3)
From
srpply a
This is a
Exeuple 2:1 refhod
A motor drives two loads. One has rotational motion. It is coupled to the motor through a and rota
reduction gear with a = 0J and efficiency of 90Vo. The load has a moment of inertia of 10 kg- separate
m2 and a torque of 10 N-m. Other load has translational motion and consists of 1000 kg weight
included
to be lifted up at an uniform speed of 1.5 m/s. Coupling between this load and the motor has an and arm
efficiency of 85Vo. Motor has an inertia of 0.2kg-m2 and runs at a constant speed of 1420 rpm. carried t
Determine equivalent inertia refered to the motor shaft and power developed by the motor. J can
as abovt
Solution rotatroni
From Eqs. (2.8) and (2.12), the total moment of inertia referred to the motor shaft plor Th
and plo
t/ ,, 12
J=Jo+alJy*u,l#l tti
(shaded
during t
\-m -/
Here,/6 = O.2kE-m2, ar = 0.1, Jr = 10 kg-.r, u.= 1.5 m/s and a^= (1420 x n)130 ; 14gJ
rad/sec.
 Dynamics of Electrical Drives 17
of Substiruting in Eq. (l) gives
or
c)
t = 0.2+ (0.1)2 x 10 + 1000[#)' = o.o ks--,
From Eqs. (2.9) and (2.13)

' atru
r, =
0r . *(+)
ni\a^1 Q)
Here 41 = 0.9, a1= O.l, Ts l0 N-m,
= 4i= 0.g5, Fr = 1000 x 9.g1 N, u1 = 1.5 m/s and
@E 148.7 rad,/sec.
=
Substiruting in Eq. (2) gives

4=%#+ff(##) =1r753N-m

Academic Calendar 51 53 55 B.Tech,

_ luly 20!7-Nov 2OL7
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eaChing learninJ^.^racc ar *r.^--'^-- zz AUg
^,