Unit-I Part-I Fundamentals of Electric Drives
Basic block diagram of electric drive:
Systems employed for the motion control are called drives– e.g.
transportation system, fans, robots, pumps, machine tools, etc. Prime movers
are required in drive systems to provide the movement or motion and energy
that is used to provide the motion can come from various sources: diesel
engines, petrol engines, hydraulic motors, electric motors etc. Drives that use
electric motors as the prime movers are known as electrical drives
A typical conventional electric drive system for variable speed
application employing multi-machine system is shown in Figure 1. The
system is obviously bulky, expensive and inflexible and requires regular
maintenance. In the past, induction and synchronous machines were used
for constant speed applications – this was mainly because of the unavailability
of variable frequency supply.
Fig (1): A typical conventional drive system
With the advancement of power electronics, microprocessors and digital
electronics, typical electric drive systems nowadays are becoming more
compact, efficient, cheaper and versatile – this is shown in Figure 2. The
voltage and current applied to the motor can be changed at will by employing
power electronic converters. AC motor is no longer limited to application
where only AC source is available, however, it can also be used when the
power source available is DC or vice versa.
Fig (2) : Modern electric drive systems employing power electronic converters
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
Components of Electrical Drives
The main components of a modern electrical drive are the Electrical
sources, Power processor, Motors, Loads, Sensing Unit, Control unit and
electrical source. These are briefly discussed below.
a) Sources:
Electrical sources or power supplies provide the energy to the electrical
motors. For high efficiency operation, the power obtained from the electrical
sources need to be regulated using power electronic converters. Power sources
can be of AC or DC in nature and normally are uncontrollable, i.e. their
magnitudes or frequencies are fixed or depend on the sources of energy such
as solar or wind.
For very low power applications: 1-phase, 230V, 50Hz AC supply is
used.
For low & medium power applications: 3-phase, 440V, 50Hz AC supply
is used.
For high power applications: 3- phase, 2.2 kV, 3.3kV, 6.6kV & 11 kV AC
supplies are used.
Also some drives are powered by a battery, which uses the source voltage
ranges as 12V, 24V, 48V & 110V dc.
b) Power processor (or) Power modulator:
The power processor in electric drive system is a power electronic
converter. The processor regulates the input voltage of the motor, there by
controls the load. There are several functions performed by the power
processor in drive systems. Those are:
(a) It modulates the flow of power from source to load, in such manner
that motor is imparted speed – torque characteristics required by the
load.
(b) During transient operations such as starting, braking & speed reversal
it restricts the source and motor currents to permissible limits.
(c) It converts the electrical energy of the source in the form suitable to
the motor.
(d) It selects the mode of operation of motor. i.e., motoring or braking.
The power modulators are classified into the following types:
(i)
AC to DC Converters (Rectifiers)
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
(ii)
DC to DC Converters (Choppers)
(iii)
AC to AC Converters
Cycloconverters)
(iv)
DC to AC Converters ( Inverters)
(AC
Voltage
controllers
or
c) Motors:
Motors obtain power from electrical sources. They convert energy from
electrical to mechanical - therefore can be regarded as energy converters. In
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
braking mode, the flow of power is reversed. Depending upon the type of power
converters used, it is also possible for the power to be fed back to the sources
rather than dissipated as heat. There are several types of motors used in
electric drives – choice of type used depends on applications, cost,
environmental factors and also the type of sources available.
Broadly, they can be classified as either DC or AC motors:
(i) DC motors: Series motors, shunt motors, separately excited motors &
compound motors.
(ii) AC motors:
Induction motors – squirrel cage, wound rotor and linear induction motors.
Synchronous motors – wound field and salient pole.
(iii) Special Electric motors: Brush less Dc motors, Permanent magnet
synchronous motor, Stepper motors, Switched Reluctance motors etc.
d) Loads:
In electric drives the driving equipment is an electric motor. One of the
essential requirements in the selection of a particular type of motor for driving
a machine is the matching of speed- torque characteristic of the driven unit
and that of motor. Therefore, the knowledge of how the load torque varies with
speed of the driven machine is necessary. Different types of load exhibit
different speed-torque characteristics. However, most of the industrial loads
can be classified into the following four general categories:
1. Constant torque type loads such as lifts and cranes.
2. Variable torque type loads: Based on the speed variation with respect
to the torque, the variable torque loads are further classified as:
(i) Torque proportional to speed (generator type load;
T ∝ N)
(ii) Torque proportional to square of the speed (fan type load;
T ∝ N2
)
(iii) Torque inversely proportional to speed (constant power type load;
T ∝ 1⁄N)
e) Sensing Circuit:
Sensing units are of speed sensing and current sensing types.
Speed Sensing: It is required for implementation of closed loop speed control
schemes. Speed is usually sensed by using tachometer. When very high
accuracies are required, as in computer peripherals & paper mills, digital
tachometers are used.
Current Sensing: There are two common methods for sensing the current are:
(i)
Using current sensors employing Hall effect
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
(ii)
Using a non-inductive resistance shunt in conjunction with an
isolation amplifier, this has an arrangement for amplification and
isolation between the power & control circuits.
f) Control Unit:
The controls for the power modulator are provided in the control unit.
The nature of control unit for a particular drive depends on the power
modulator that is used. If the power modulator is power electronic converter,
the control unit consists of firing circuits which employ linear (analog), digital
integrated circuits and transistors & DSPs/ Microprocessors when
sophisticated control is required.
The types of the main controllers can be:
• Analog - This is noisy, inflexible. However analog circuit ideally
has infinite bandwidth.
• Digital – Immune to noise, configurable. The bandwidth is
obviously smaller than the analog controller’s – depends on
sampling frequency
• DSP/microprocessor – Flexible, lower bandwidth compared to
above. DSPs perform faster operation than
microprocessors (multiplication in single cycle).
With DSP/microprocessors, complex estimations
can be easily implemented.
Advantages of Electrical Drives:
There are several advantages of electrical drives:
(a) Flexible control characteristic – This is particularly true when power
electronic converters are employed where the dynamic and steady state
characteristics of the motor can be controlled by controlling the applied
voltage or current.
(b) Available in wide range of speed, torque and power.
(c) High efficiency, lower noise, low maintenance requirements and cleaner
operation.
Torque Equation of Motor Load System:
A motor generally drives a load (machine) through some transmission system.
While motor always rotates, the load may rotate or may undergo a
translational motion. Load speed may be different from that of motor, and if
the load has many parts, their speeds may be different and while some may
rotate, others may go through a translational motion. It is, however,
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
convenient to represent the Torque Equation of Motor Load System by an
equivalent rotational system shown in Fig. 2.1
Various notations used are:
J = Polar moment of inertia of motor-load system referred to the motor
shaft, kg-m2.
ωm = Instantaneous angular velocity of motor shaft, rad/sec.
T = Instantaneous value of developed motor torque, N-m.
T1 = Instantaneous value of load (resisting) torque, referred to motor
shaft, N-m.
Load torque includes friction and windage torque of motor.
Torque Equation of Motor Load System of Fig. 2.1 can be described by the
following fundamental torque equation:
Equation (2.1) is applicable to variable inertia drives such as mine winders,
reel drives, industrial robots. For drives with constant inertia, (dJ/dt) = 0.
Therefore
Equation (2.2) shows that torque developed by motor is counter balanced by
a load torque T1 and a dynamic torque J(dωm/dt). Torque component
J(dωm/dt) is called the dynamic torque because it is present only during the
transient operations.
Drive accelerates or decelerates depending on whether T is greater or less than
T1. During acceleration, motor should supply not only the load torque but an
additional torque component J(dωm/dt) in order to overcome the drive inertia.
In drives with large inertia, such as electric trains, motor torque must exceed
the load torque by a large amount in order to get adequate acceleration. In
drives requiring fast transient response, motor torque should be maintained
at the highest value and Torque Equation of Motor Load System should be
designed with a lowest possible inertia. Energy associated with dynamic
torque J(dωm/dt) is stored in the form of kinetic energy given by (Jω2m/2).
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
During deceleration, dynamic torque J(dωm/dt) has a negative sign. Therefore,
it assists the motor developed torque T and maintains drive motion by
extracting energy from stored kinetic energy.
Speed torque conventions and multiquadrant operation
For consideration of multi-quadrant Operation of Motor Drive, it is useful to
establish suitable conventions about the signs of torque and speed. Motor
speed is considered positive when rotating in the forward direction. For drives
which operate only in one direction, forward speed will be their normal speed.
In loads involving up-and-down motions, the speed of motor which causes
upward motion is considered forward motion. For reversible drives, forward
speed is chosen arbitrarily. Then the rotation in opposite direction gives
reverse speed which is assigned the negative sign. Positive motor torque is
defined as the torque which produces acceleration or the positive rate of
change of speed in forward direction. According to Eq. (2.2), positive load
torque is opposite in direction to the Positive motor torque. Motor torque is
considered negative if it produces deceleration.
A motor operates in two modes motoring and braking. In motoring, it converts
electrical energy to mechanical energy, which supports its motion. In braking,
it works as a generator converting mechanical energy to electrical energy, and
thus, opposes the motion. Motor can provide motoring and braking operations
for both forward and reverse directions.
Figure 2.2 shows the torque and speed coordinates for both forward (positive)
and reverse (negative) motions of Four Quadrant Operation of Motor Drive.
Power developed by a motor is given by the product of speed and torque. In
quadrant I, developed power is positive. Hence, machine works as a motor
supplying mechanical energy. Operation in quadrant I is, therefore,
called forward motoring. In quadrant II, power is negative. Hence, machine
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
works under braking opposing the motion. Therefore, operation in quadrant
II is known as forward braking. Similarly, operations in quadrant III and IV
can be identified as reverse motoring and braking respectively.
For better understanding of the above notations, let us consider operation of
a hoist in Four Quadrant Operation of Motor Drive as shown in Fig. 2.3.
Directions of motor and load torques, and direction of speed are marked by
arrows.
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
from 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 to Eq. (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 independent of speed. This
is nearly true with a low speed hoist where forces due to friction and windage
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 Tl1 in quadrants I and IV
represents speed-torque characteristic for the loaded hoist. This torque is the
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
difference of torques due to loaded hoist and counter weight. The load torque
line Tl2 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 the
empty hoist. Its sign is negative because the weight of a counter weight is
always higher than that of an empty cage.
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 obtained if the motor produces positive
torque in anticlockwise direction equal to the magnitude of load torque Tl1.
Since developed motor power is positive, this is forward motoring operation.
Quadrant IV operation is obtained when a loaded cage is lowered. Since 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 Tl2 in
anticlockwise direction. As both power and speed are negative, drive 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 up. In order
to limit the speed within a safe value, motor must produce a braking torque
equal to Tl2 in clockwise (negative) direction. Since speed is positive and
developed power negative, it is forward braking operation.
Operation in quadrant III is obtained when an empty cage is lowered. Since
an empty cage has a lesser weight than a counter weight, the motor should
produce a torque in clockwise direction. Since speed is negative and developed
power positive, this is reverse motoring operation.
Components of Load Torques:
Components of Load Torques Tl can be further divided into following
components:
(i) Friction torque TF :
Friction will be present at the motor shaft and also in various parts of the
load. TF is equivalent value of various friction torques referred to the motor
shaft.
(ii) Windage torque, Tw :
When a motor runs, wind generates a torque opposing the motion. This is
known as windage torque.
(iii) Torque required to do the useful mechanical work, TL:
Nature of this Components of Load Torques depends on particular
application. It may be constant and independent of speed; it may be some
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
function of speed; it may depend on the position or path followed by load; it
may be time invariant or time-variant; it may vary cyclically and its nature
may also change with the load’s mode of operation.
Variation of friction torque with speed is shown in Fig. 2.6(a). Its value at
standstill is much higher than its value slightly above zero speed. Friction at
zero speed is called stiction or static friction. In order for drive to start, the
motor torque should at least exceed stiction. Friction torque can be resolved
into three components (see Fig. 2.6(b)). Component Tv which varies linearly
with speed is called viscous friction and is given by:
where B is the viscous friction coefficient.
Another component Tc, which is independent of speed, is known as Coulomb
friction. Third component Ts accounts for additional torque present at
standstill. Since Ts is present only at standstill it is not taken into account in
the dynamic analysis.
Windage torque Tw, which is proportional to speed squared, is given by
2
𝑇𝑊 = 𝐶𝜔𝑚
where C is a constant.
From the above discussion, for finite speeds,
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
In many applications (Tc + Cω2m) is very small compared to Bωm and negligible
compared to TL. In order to simplify the analysis, term (Tc + Cω2m) is
approximately accounted by updating the value of viscous friction coefficient,
B. With this approximation, from Eq. (2.2)
If there is a torsional elasticity in shaft coupling the load to the motor, an
additional Components of Load Torques, known as Coupling Torque, will be
present. Coupling torque (Te) is given by
where θe is the torsion angle of coupling (radians) and Ke the rotational
stiffness of the shaft (Nm/rad).
In most applications, shaft can be assumed to be perfectly stiff and coupling
torque Te can be neglected. Its presence in appreciable magnitude has adverse
effects on motor. There is potential energy associated with coupling torque
and kinetic energy with the dynamic torque. Exchange of energy between
these two energy storage’s tends to produce oscillations which are damped by
viscous friction torque Bωm. When B is small, oscillations occur producing
noise. Further, shaft may also break when the drive is started.
Classification of Load Torques:
In electric drives the driving equipment is an electric motor. One of the
essential requirements in the selection of a particular type of motor for driving
a machine is the matching of speed- torque characteristic of the driven unit
and that of motor. Therefore, the knowledge of how the load torque varies with
speed of the driven machine is necessary. Different types of load exhibit
different speed-torque characteristics. However, most of the industrial loads
can be classified into the following four general categories:
1. Constant torque type loads such as lifts and cranes.
2. Variable torque type loads: Based on the speed variation with respect
to the torque, the variable torque loads are further classified as:
i)
Torque proportional to speed (generator type load;
T ∝ N)
ii)
Torque proportional to square of the speed (fan type load;
T ∝ N2
)
iii)
Torque inversely proportional to speed (constant power type load;
T ∝ 1⁄N)
As we know already, the nature of Classification of Load Torques depends on
particular application. A low speed hoist is an example of a load where the
torque is constant and independent of the speed (Fig. 2.3).
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
At low speeds, windage torque is negligible. Therefore, net torque is mainly
due to gravity which is constant and independent of speed. There are drives
where coulomb friction dominates over other torque components.
Consequently, torque is independent of speed, e.g. paper mill drive.
Fans, compressors, aeroplanes, centrifugal pumps, ship-propellors, coilers,
high speed hoists, traction etc. are example of the case where load torque is
a function of speed. In fans, compressors and aeroplanes, the windage
dominates, consequently, load torque is proportional to speed squared (Fig.
2.7(a)).
Windage is the opposition offered by air to the motion. Similar nature of
Classification of Load Torques can be expected when the motion is opposed
by any other fluid, e.g. by water in centrifugal pumps and ship-propellors,
giving the same characteristic as shown in Fig. 2.7(a). In a high speed hoist,
viscous friction and windage also have appreciable magnitude, in addition to
gravity, thus giving the speed-torque curve of Fig. 2.7(b). Nature of speed12
Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
torque characteristic of a traction load when moving on a levelled ground is
shown in Fig. 2.7(c). Because of its heavy mass, the stiction is large. Near zero
speed, net torque is mainly due to stiction.
The stiction however disappears at a finite speed and then windage and
viscous friction dominate. Because of large stiction and need for accelerating
a heavy mass, the motor torque required for starting a train is much larger
than what is required to run it at full speed. Torque in a coiler drive is also a
function of speed. It is approximately hyperbolic in nature as shown in Fig.
2.7(d). The developed power is nearly constant at all speeds.
Figure 2.7(c) shows the traction load torque to be function of only speed,
because we have assumed a levelled ground. In actual practice the train has
to negotiate upward and downward slopes. Consequently, a torque due to
gravity, which varies with position is also present. Furthermore, when a train
takes a turn the frictional force on wheels changes substantially. Thus,
traction is an example where the load torque also depends on position or path
followed.
Classification of Load Torques can be broadly classified into two categories1. Active and
2. Passive.
Load torques which have the potential to drive the motor under equilibrium
condition are called Active Load Torques. Such load torques usually retain
their sign when the direction of the drive rotation is changed. Torque(s) due
to gravitational force, tension, compression and torsion, undergone by an
elastic body, come under this category.
Load torques which always oppose the motion and change their sign on the
reversal of motion are called Passive Load Torques. Such torques are due to
friction, windage, cutting etc.
Types of Electrical drives:
There are three types of industrial drives, indicating the trends in the
form of advancement. These are the group drive, the individual drive and the
multi-motor drive.
1. The group electric drive:
The group electric drive was used in the earlier days. It had a single
motor of sufficient capacity to drive an entire group of machines used in a
shop. The motor was connected to a line shaft and through the use of belts
and pulleys all the machines were driven. This form of drive was very
inefficient, difficult to control, unsafe, and had many other objectionable
features. This type of drive is not used now and is of historical interest only.
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
Fig: Group electric drive
2. The individual drive:
In the individual drive there is one motor for each working machine.
The electric motor is an integral part of the machine and can be specially
designed to the needs of that machine.
Fig: Individual drive
3. Multi-motor drive:
The third type of drive is the multi-motor drive. This type of drive has
more than one motor for each working machine. Examples are metal cutting
machine tools, paper making machines and rolling mills, etc. The multi motor
drive systems are mostly employed for aerospace applications.
Speed Control and Drive Classification are the Drivers where the driving
motor runs at a nearly fixed speed are known as Constant Speed or Single
Speed Drives. Multi-speed drives are those which operate at discrete speed
settings. Drives needing stepless change in speed and multispeed drives are
called Variable Speed Drives.
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
Speed range of a variable speed drive depends on the application. In some
applications it can be from rated speed to 10% of rated speed. In some other
applications, speed control above rated speed is also desired, and the ratio of
maximum to minimum speed can be as high as 200. There are also
applications where the speed range is as low as from rated speed to 80% of
rated speed.
A variable speed drive is called constant torque drive if the drive’s maximum
torque capability does not change with a change in speed setting. The
corresponding mode (or region) of operation is called Constant Torque Mode.
It must be noted that the term ‘Constant Torque’ refers to maximum torque
capability of the drive and not to the actual output torque, which may vary
from no load to full load torque. The Constant Power Drive and Constant
Power Mode (or region) are defined in the same way.
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
Types of DC Motor:
The commonly used Types of DC Motor are shown in Fig. 5.1. In a separately
excited motor, the field and armature voltages can be controlled independent
of each other. In a shunt motor, field and armature are connected to a
common source. In case of a series motor, field current is same as armature
current, and therefore, field flux is a function of armature current. In a
cumulatively compound motor, the magneto-motive force of the series field is
a function of armature current and is in the same direction as mmf of the
shunt field.
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
Basic Speed – Torque relations of d.c. motors:
We know that the back emf in a d.c. motor is
∅ZN P
Eb = 60 (A) volts
---------- (1)
Where,
∅ = Flux per pole
Z = Number of armature conductors
N = Speed of the motor
P = Number of poles
A = Number of parallel paths in armature
Here, the parameters Z, P & A are the machine dependent. Therefore
for a given d.c. motor these are constant. Then the equation (1) can be rewritten as,
ZP
Eb = (60 A) ∅ N----------- (2)
But, the mechanical speed of the motor in radians per second is given
by
ωm =
N=
2πN
60
60 ωm
2π
rad/sec.----------- (3)
----------- (4)
Substituting equation (4) in equation (2), we have
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
ZP
Eb = (60 A) ∅
60 ωm
2π
ZP
Eb = (2 π A) ∅ ωm
ZP
Letting K a = motor constant = (2 π A)
Eb = K a ∅ ωm ---------- (5)
Also, the power developed in the d.c. motor is given by
P = Eb Ia ---------- (6)
Substituting equation (5) in equation (6), we have
P = K a ∅ ωm Ia ---------- (7)
Also, we know the developed power is equal to the product of developed
torque and the mechanical speed of the motor.
i.e. P = Td ωm ---------- (8)
Substituting equation (8) in equation (7), we have
Td ωm = K a ∅ ωm Ia
Td = K a ∅ Ia --------- (9)
The back emf of the d.c. motor is,
Eb = Va − Ia R a --------- (10)
From equation (5),
K a ∅ ωm = Va − Ia R a
ωm =
Va − Ia Ra
Ka ∅
=
Va
Ka ∅
−
I a Ra
Ka ∅
---------- (11)
The armature current from equation (9) can be written as,
Ia =
Td
--------- (12)
Ka ∅
On substituting equation (12) in equation (11), we have
V
ωm =K a∅ −
a
Td Ra
--------(Ka ∅)2
(13)
Case (i): For shunt and separately excited d.c motors, with constant field
current, the flux can be assumed to be constant.
Hence, K a ∅ = K m (motor constant)--------- (14)
On substituting equation (14) in equation (9) & (5), we have
Therefore,
Td = K m Ia &Eb = K m ωm
Eb = K m ωm
⇒ωm =
Also, Ia =
Eb
Km
Td
Km
=
Va
Km
−
I a Ra
Km
--------- (15)
, substituting this in equation (15), we have
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
V
ωm =K a −
Td Ra
K2m
m
--------- (16)
Case (ii): In series motors the flux is a function of armature current. In
unsaturated region of magnetization characteristic, ∅ can be assumed to be
proportional to Ia .
Therefore,
∅ ∝ Ia
⇒∅ = K f Ia --------- (17)
Substituting equation (17) in equations (9) and (5),
Td = K a K f Ia . Ia = K a K f Ia2
Td
⇒Ia = √
K
a Kf
--------- (18)
Eb = K a K f Ia ωm
⇒ωm =
⇒ωm =
Eb
Ka Kf Ia
Va
Ka Kf Ia
−
Ia (Ra +𝑅𝑓 )
Ka Kf Ia
--------- (19)
Substituting equation (18) in equation (19)
ωm =
ωm =
Va
T
K a Kf √ d
Ka Kf
Va
√Ka Kf √Td
−
−
Ra +𝑅𝑓
Ka Kf
Ra +𝑅𝑓
Ka Kf
---------- (20)
Speed Control of DC Motor Drives:
The Speed Control of DC Motor Drives can be any of the following methods:



Armature voltage control
Field flux control
Armature resistance control
Speed-torque curves of dc motors for these methods of speed control are
shown in Figs. 5.16 to 5.18.
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
Armature voltage control is preferred because of high efficiency, good
transient response and good speed regulation. But it can provide Speed
Control of DC Motor Drives only below base (rated) speed because the
armature voltage cannot be allowed to exceed rated value. For speed control
above base speed, field flux control is employed.
In a normally designed motor, the maximum speed can be allowed up to twice
rated speed and in specially designed machines it can be six times rated
speed.
The maximum torque and power limitations of dc drives operating with
armature voltage control and full field below rated speed and flux control at
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Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT
Unit-I Part-I Fundamentals of Electric Drives
rated armature voltage above rated speed are shown in Fig. 5.19. In armature
voltage control at full field, T ∞ Ia consequently, the maximum torque that the
machine can deliver has a constant value. In the field control at rated
armature voltage, Pm ∞ Ia (because E ≈ V = constant). Therefore, maximum
power developed by the motor has a constant value.
In a separately excited motor, flux is controlled by varying voltage across field
winding and in a series motor it is controlled either by varying number of
turns in the field winding or connecting a diverter resistance across the field
winding.
In armature resistance control, speed is varied by wasting power in external
resistors that are connected in series with the armature. Since it is an
inefficient method of Speed Control of DC Motor Drives, it was used in
intermittent load applications where the duration of low speed operation
forms only a small proportion of total running time, for example in traction.
It has, however, been replaced by armature voltage control in all these
applications.
21
Dr. C. Subba Rami Reddy, Professor in EEE, BVRIT