POWER ELECTRONICS
Electric Drives
DC Drives
Dc motors can provide a high starting torque and it is Controlled rectifiers provide a variable dc output
also possible to obtain speed control over a wide range. voltage from a fixed ac voltage, whereas a dc–dc
converter can provide a variable dc voltage from
a fixed dc voltage.
The methods of speed control are normally simpler and
less expensive than those of ac drives.
Controlled rectifiers are generally used for the
speed control of dc motors.
Dc motors play a significant role in modern industrial
drives. The alternative form would be a diode rectifier
followed by dc–dc converter,
Both series and separately excited dc motors are normally
used in variable-speed drives, but series motors are Dc drives can be classified, in general, into three types:
traditionally employed for traction applications.
1. Single-phase drives
Due to commutators, dc motors are not suitable for very 2. Three-phase drives
high speed applications and require more maintenance
than do ac motors. 3. Dc–dc converter drives
Electric Drives
DC Drives
Controlled rectifier-fed drive
Single-phase drives are used in low-power
applications in the range up to 100 kW.
Three-phase drives are used for applications
in the range 100 kW to 500 kW.
Dc–dc converter-fed drives
Electric Drives
DC Drives
Separately Excited Dc Motor
When a separately excited motor is excited by a field
current of if and an armature current of ia flows in the
armature circuit, the motor develops a back emf and a
torque to balance the load torque at a particular speed.
The field current if of a separately excited motor is Equivalent circuit of separately
independent of the armature current ia and any change in excited dc motors.
the armature current has no effect on the field current.
The instantaneous armature current can be
The equations describing the characteristics of a found from
separately excited motor
2
The instantaneous field current if obtained from,
The motor back emf, which is also known
as speed voltage, is expressed as
1
3
Electric Drives
DC Drives
Separately Excited Dc Motor
The torque developed by the motor is
4 Under steady-state conditions, the time
derivatives in these equations are zero and
The developed torque must be equal The steady-state average quantities are,
to the load torque
The developed power is
Electric Drives
DC Drives
Separately Excited Dc Motor
The relationship between the field current
If and the back emf Eg is nonlinear due to
magnetic saturation.
The speed of a separately excited motor
can be found from (2) Controlling the field current If, known as
field control
6
(3) Torque demand, which corresponds to an armature
current Ia, for a fixed field current If.
Eqn. (6) shows the motor speed can be varied by,
The speed, which corresponds to the rated
armature voltage, rated field current, and
(1) Controlling the armature voltage Va, known as rated armature current, is known as the rated
voltage control (or base) speed.
Electric Drives
DC Drives
Separately Excited Dc Motor
Figure below shows the characteristics of torque, power,
In practice, for a speed less than the base speed, the armature current, and field current against the speed
armature current and field currents are maintained
constant to meet the torque demand, and the armature
voltage Va is varied to control the speed.
For speed higher than the base speed, the armature
voltage is maintained at the rated value and the field current
is varied to control the speed.
However, the power developed by the motor
(= torque * speed) remains constant.
Electric Drives
TRANSFER FUNCTIONS OF SEPARATELY
EXCITED DC MOTOR The motor load system equation
Taking the Laplace transform (assuming zero initial conditions)
Dynamic equivalent circuit of
separately excited dc motor
Armature Control
The voltage equation of the armature circuit
where the armature circuit time constant is
'
Electric Drives
Armature Control Field Control
Armature current is constant.
; ;
where the mechanical time constant of the
motor load system is Taking the Laplace transform of
Block diagram of separately excited dc motor
with armature control.
Block diagram of separately excited motor with field control
Electric Drives
State space model of dc motor
Dynamic equation of separately excited dc motor
In state-space form:
where p is the differential operator with respect
to time and Kb = KvIf
Electric Drives
DC Drives
1 A 230 V, 500 rpm, 100 A separately excited dc motor has an armature resistance of 0.1Ω. The motor is driving, under
rated conditions, a load whose torque is constant and independent of speed. The speeds below the rated speed are
obtained with armature voltage control (with full field) and the speeds above the rated speed are obtained by field
control (with rated armature voltage).
1. Calculate the motor terminal voltage when the speed is 400 rpm.
2. By what amount should flux be reduced to get a motor speed of 800 rpm?
Neglect the motor's rotational losses.
Solution: Back emf at 500 rpm,
Electric Drives
DC Drives
Problem Cont..
The feasib1e value of k = 0.61.
Thus the flux must be reduced to 0.61 of
its rated value.
Electric Drives
2 A variable-speed drive system uses a dc motor that is supplied from a variable-voltage source.
The torque and power profiles are shown in Fig. The drive speed is varied from 0 to
1500 rpm (base speed) by varying the terminal voltage from 0 to 500 V with the field current
maintained constant.
(a) Determine the motor armature current if the torque is held constant at 300 N m up to the
base speed.
(b) The speed beyond the base speed is obtained by field weakening while the armature
voltage is held constant at 500 V. Determine the torque available at a speed of 3000 rpm if
the armature current is held constant at the value obtained in part (a).
Electric Drives
The field of a dc motor connected in series with the armature
circuit, as shown in Figure is called a series motor
The speed of a series motor can be determined as,
Equivalent circuit of dc series motors
The speed can be varied by controlling the (1) armature voltage
The steady-state average quantities are Va; or (2) armature current, which is a measure of the torque
demand.
A series motor can provide a high torque, especially at starting
For a speed up to the base speed, the armature voltage is varied
and the torque is maintained constant.
Electric Drives
Operating Modes
In variable-speed applications, a dc motor may
be operating in one or more modes:
Motoring.
The arrangements for motoring are shown in
Figure.a. Back emf Eg is less than supply voltage Va. The kinetic energy of the motor is returned to the supply.
Both armature and field currents are positive. The A series motor is usually connected as a self-excited generator.
motor develops torque to meet the load demand.
Regenerative braking. For self-excitation, it is necessary that the field current aids the
The arrangements for regenerative braking are shown in residual flux. This is normally accomplished by
Figure.b. Reversing the armature terminals or the field terminals.
The motor acts as a generator and develops
an induced voltage Eg.
Eg must be greater than supply voltage Va.
The armature current is negative, but the field current is
positive.
Electric Drives
Operating Modes
Dynamic braking.
The arrangements shown in Figure.c. are similar to those
of regenerative braking, except the supply voltage Va is
replaced by a braking resistance Rb.
The kinetic energy of the motor is dissipated in Rb.
For a series motor, either the armature terminals
Plugging. or field terminals should be reversed, but not both.
Plugging is a type of braking. The connections
for plugging are shown in Figure.d.
The armature terminals are reversed while running.
The supply voltage Va and the induced voltage Eg act
in the same direction.
The armature current is reversed, thereby producing a
braking torque. The field current is positive..
Electric Drives
Four quadrants.
The armature current must be positive. The induced
Figure shows the polarities of the supply voltage Va, back
Emf Eg must satisfy the condition |Va |< |Eg |.
emf Eg, and armature current Ia for a separately excited motor.
In forward motoring (quadrant I), Va, Eg, and Ia are all positive.
During forward braking (quadrant II), the motor runs in
the forward direction and the induced emf Eg continues
to be positive.
The armature current must be negative .So the supply
voltage Va should be kept less than Eg.
In reverse motoring (quadrant III), Va, Eg, and Ia are
all negative. |Va| > |Eg| .
During reverse braking (quadrant IV), the motor runs in the
reverse direction. Va and Eg continue to be negative.
Electric Drives
Single-Phase Drives
Basic circuit arrangement of a single-phase dc drive
Electric Drives
Single-Phase Semiconverter Drives
The average armature voltage can be given by The average field voltage is
Electric Drives
Single-Phase Full-Converter Drives
The average field voltage
The average armature voltage
Electric Drives
Single-Phase Dual-Converter Drives
If converter 1 operates with a delay angle of αa1,
the armature voltage is
If converter 2 operates with a delay angle of αa2
the armature voltage as
It is a four-quadrant drive and permits four modes
of operation:
1) forward powering,
2) forward braking (regeneration),
3) reverse powering, and The field voltage
4) reverse braking (regeneration).
Electric Drives
Three-Phase Drives
1. Three-phase half-wave-converter drives
2. Three-phase semiconverter drives
3. Three-phase full-converter drives
4. Three-phase dual-converter drives Three-Phase Dual-Converter Drives
The average armature voltage
Three-Phase Semiconverter Drives
The armature and field voltages voltage are
The average field voltage as
Three-Phase Full-Converter Drives
Electric Drives
Dc–Dc Converter Drives
The possible control modes of a
dc–dc converter drive are:
1. Power (or acceleration) control
2. Regenerative brake control
3. Rheostatic brake control
4. Combined regenerative and rheostatic
brake control
Principle of Power Control
The circuit arrangement of a converter-fed
dc separately excited motor is shown in Figure. The average value of the input current is Is = kIa
The average armature voltage is Va = kVs
The equivalent input resistance of the dc–dc converter
where k is the duty cycle of the dc–dc converter. drive seen by the source is
The power supplied to the motor is Po = Va Ia = kVs Ia
Pi = P0 = kVs Is By varying the duty cycle k, the power flow to the motor
(and speed) can be controlled.
Electric Drives
Principle of Regenerative Brake Control
If Ia is the average armature current, the regenerated
In regenerative braking, the motor acts as a power can be found from
generator and the kinetic energy of the motor
and load is returned back to the supply.
The voltage generated by the motor acting as a generator is
where Kv is machine constant and ω is the machine
speed in rads per second
The equivalent load resistance of the motor acting
as a generator is
The average voltage across the dc–dc converter is
By varying the duty cycle k, the equivalent load resistance
seen by the motor can be varied from Rm to (Vs/Ia + Rm) and the
regenerative power can be controlled.
Electric Drives
Principle of Regenerative Brake Control
The conditions for permissible potentials and polarity
of the two voltages Va and Eg are
The regenerative braking would be effective only
if the motor speed is between these two speed limits
which gives the minimum braking speed of the
motor as
At any speed less than ωmin, an alternative
braking arrangement would be required.
The maximum braking speed of the motor can be Note: The motor speed would decrease with time.
found from To maintain the armature current at the same level,
the effective load resistance of the series generator
should be adjusted by varying the duty cycle of the
dc–dc converter
Electric Drives
Principle of Rheostatic (dynamic) Brake Control
The average voltage across the braking resistor,
The equivalent load resistance of the generator,
The power dissipated in the resistor Rb is
In a rheostatic braking, the energy is dissipated in a
rheostat
By controlling the duty cycle k, the effective load
The rheostatic braking is also known as dynamic braking resistance can be varied from Rm to Rm + Rb, and the
braking power can be controlled.
The average current of the braking resistor
Electric Drives
Principle of Combined Regenerative and
Rheostatic Brake Control
A combined regenerative and rheostatic brake
control would be the most energy efficient.
During regenerative braking, the line voltage is sensed
continuously.
If it exceeds a certain preset value, normally 20% above
the line voltage, the regenerative braking is removed and
a rheostatic braking is applied.
In every cycle, the logic circuit determines the receptivity
of the supply. If it is nonreceptive, thyristor TR is turned on to
divert the motor current to the resistor Rb. Thyristor TR is self-
commutated when transistor Q1 is turned on in the next cycle.
Electric Drives
Closed-Loop Control of dc Drives
The speed of dc motors changes with the load torque.
To maintain a constant speed, the armature (and or field) voltage should be varied continuously by varying
the delay angle of ac–dc converters or duty cycle of dc–dc converters.
In practical drive systems it is required to operate the drive at a constant torque or constant power in
addition, controlled acceleration and deceleration are required.
Most industrial drives operate as closed-loop feedback systems.
A closed-loop control system has the advantages of improved accuracy, fast dynamic response, and reduced
effects of load disturbances and system nonlinearities
Closed-Loop Control of dc Drives
In practice, the motor is required to operate at a desired
speed, but it has to meet the load torque, which
depends on the armature current.
While the motor is operating at a particular speed, if a
load is applied suddenly, the speed falls and the motor
takes time to come up to the desired speed.
A speed feedback with an inner current loop, as shown
in Figure, provides faster response to any disturbances
in speed command, load torque, and supply voltage.
The current loop is used to cope with a sudden
torque demand under transient condition.
The output of the speed controller ec is applied to
the current limiter, which sets the current reference
Ia(ref) for the current loop.
Closed-loop speed control with inner
current loop and field weakening
Closed-Loop Control of dc Drives
The armature current Ia is sensed by a current sensor, For any large positive speed error, the current
filtered normally by an active filter to remove ripple, limiter saturates and limits the reference current
and compared with the current reference Ia(ref). Ia(ref) to a maximum value Ia(max).
The error current is processed through a current controller whose
output vc adjusts the firing angle of the converter and brings the The speed error is then corrected at the maximum
motor speed to the desired value. Permissible armature current Ia(max) until the speed
error becomes small and the current limiter comes
out of saturation.
Any positive speed error caused by an increase in either
speed command or load torque demand can produce a high Normally, the speed error is corrected with Ia less
reference current Ia(ref). than the permissible value Ia(max).
The motor accelerates to correct the speed error, and finally
The speed control from zero to base speed is normally
settles at a new Ia(ref), which makes the motor torque equal to
done at the maximum field by armature voltage control
the load torque, resulting in a speed error close to zero.
Closed-Loop Control of dc Drives
Control above the base speed should be done by
For a speed command above the base speed,
field weakening at the rated armature voltage
the speed error causes a higher value of Va.
In the field control loop, the back emf Eg(= Va - Ra Ia) The motor accelerates, the back emf Eg increases,
is compared with a reference voltage Eg(ref), which is and the field error ef decreases.
generally between 0.85 to 0.95 of the rated armature
voltage.
The field current then decreases and the motor
speed continues to increase until the motor speed
For speeds below the base speed, the field error reaches the desired speed.
ef is large and the field controller saturates, thereby
applying the maximum field voltage and current
When the speed is close to the base speed, Va is
almost near to the rated value and the field
controller comes out of saturation.
