Steady-State Analysis of DC Motors
Steady-State Analysis of DC Motors
Steady-State Analysis of DC Motors
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Objectives
• Discuss the shunt DC motor steady state response.
• Derive the Power flow in shunt DC motor
• Discuss the speed control of shunt DC motor different
techniques.
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Shunt/SE DC Motor Characteristics
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Adding resistance to armature winding
• An armature circuit rheostat Rae is added to
armature winding to control the motor speed.
V I (R R ext )
a a a
K am
• This method is simple and attractive for short
term applications.
• The main disadvantage of this method is that
armature losses are increased substantially.
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Terminal voltage speed control
• In this method of speed control, the field
current If is kept constant and the armature
terminal voltage (Vt) is varied to change the
speed
• For a constant load torque, such as that applied
by an elevator or hoist crane load, the speed
will change linearly with Vt.
• In an actual application, when speed is changed
by changing the terminal voltage, the armature
current is kept constant (needs a closed-loop
operation) in order to keep Ea ∝ Vt ∝ ωm
Advantages:
• Provides a smooth variation of speed control
from zero to the base speed.
• Easily controlled by solid-state drives
• Const. current and torque are easily achieved
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Field control
• In this method the speed is controlled by
varying If. This is normally achieved by
using a field circuit rheostat (Rfc).
• If magnetic linearity is assumed, the flux
in the machine (Φ) will be proportional to
the If. Therefore,
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Const. Torque and Const. Power modes
• Speed control from zero to a base speed
is usually obtained by armature voltage
control Vt.
• Speed control beyond the base speed is
obtained by decreasing the field current,
called field weakening.
• At the base speed, the armature terminal
voltage is at its rated value. If armature
current is not to exceed its rated value
(heating limit), speed control beyond the
base speed is restricted to constant power,
known as constant-power operation
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Ex-4
E a1 E a 2
K a I f 11 K a I f 22
If 1 2
2 ( )1 ( )115.192 143.99 rad / sec
If 2 1.6
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Note:
All of times, the motor constant Kaϕ
can be calculated from base speed
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Solid state converters used in speed control of DC motors
1. Controlled Rectifier
If the supply is ac, controlled
rectifiers can be used to convert a
fixed ac supply voltage into a
variable-voltage dc supply
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Single-phase input
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Three-phase input, full converter
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Current control using full wave rectifier
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Ex-6
The speed of a 10 hp, 220 V, 1200 rpm separately excited dc motor is controlled by a single-
phase full converter. The rated armature current is 40 A. The armature resistance is R a =0.25
Ω and armature inductance is La =10 mH. The AC supply voltage is 265 V. The motor
constant is KaΦ=0.18 V/rpm. Assume that motor current is continuous and ripple-free. For a
firing angle α=30 and rated motor current, determine the
(a) Speed of the motor.
(b) Motor torque.
(c) Power to the motor
Solution
For a single-phase supply, full converter,
ab out the
re
Take ca stant units
on
motor c
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Ex-7
The speed of a 125 hp, 600 V, 1800 rpm, separately excited dc motor is controlled by a 3φ
(three-phase) full converter. The converter is operated from a 3φ, 480 V, 60 Hz supply. The
rated armature current of the motor is 165 A. The motor parameters are R a=0.0874 Ω,
La=6.5 mH, and KaΦ=0.33 V/rpm. The converter and AC supply are considered to be ideal.
(a) Find no-load speeds at firing angles α=0 and α=30. Assume that at no load, the
armature current is 10% of the rated current and is continuous.
(b) Find the firing angle to obtain the rated speed of 1800 rpm at rated motor current.
(c) Compute the speed regulation for the firing angle obtained in part (b).
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2. DC chopper
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Ex-8
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Summary
In this lecture, you have learnt:
• Construction of DC motor.
• Different types of DC motors.
• The SE/Shunt DC Motor dynamic characteristics.
• Speed control of SE/Shunt DC motor.
• Solid-state DC motor drives
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