SEPARATELY ECXITED DC MOTOR

1
SEPARATELY ECXITED DC MOTOR

• Applied Newtonian mechanics to find the
  differential equations for mechanical systems.
• Using Newtons second law
• Electromagnetic torque developed by separately
  excited DC motor
• Viscous torque
• Load torque TL

equivalent moment of inertia
2
SEPARATELY EXCITED DC MOTORS
Equivalent circuit for separately excited DC
motors
3
SEPARATELY ECXITED DC MOTOR

• From Newtons Second Law, Torsional-Mechanical
  equation is given as

• The nonlinear differential equation for
  separately excited DC motor which is
• found using Kirchhoffs Voltage Law

4
SEPARATELY ECXITED DC MOTOR

• Using Newtons second law
• Dynamics of rotor angular displacement
• The derived three first order differential
  equations are rewritten in the s-domain

5
SEPARATELY ECXITED DC MOTOR
6
SEPARATELY ECXITED DC GENERATOR

• From Newtons Second Law, Torsional-Mechanical
  equation is given as

• The nonlinear differential equation for
  separately excited DC generator which is
• found using Kirchhoffs Voltage Law

• The expression for the voltage at the load
  terminal must be used.
• For the resistive load

7

• Analysis of eqn(3) indicates that the angular
  velocity of the separately excited motor can be
  regulated by changing the applied voltages to the
  armature and field windings.
• The flux is a function of the field current in
  the stator winding, and higher angular velocity
  can be achieved by field weakening by reducing
  the stator current eqn(3)
• However, there exists a mechanical limit imposed
  on the maximum angular velocity. The maximum
  allowed (rated) armature current is specified as
  well, one concludes that the electromagnetic
  torque is bounded.

8
(No Transcript)
9
(No Transcript)
10
(No Transcript)
11
SEPARATELY ECXITED DC MOTOR
Example

• A separately excited, 2 kW DC motor with rated
  armature current 20 A and angular velocity 200
  rad/s operates at the constant voltages
  and . The motor
  parameters are ,
  , , and
  .
• Calculate
• The steady state angular velocity at the minimum
  and maximum load conditions, Nm
  and Nm.
• The armature current at the minimum and maximum
  load conditions, Nm and
  Nm.

12

• Steady state condition

13

• Steady state condition

14
Example

• Plot the torque-speed characteristic curves for a
  
• separately excited, 2-kW DC motor if the
• rated (maximum) armature voltage is
• and the field voltage is . The
• motor parameters are ,
  ,
• , and
  
• The load characteristic if

15

• parameters of separately-exited motor
• ra0.18 Laf0.1 Bm0.007 If5.7 Tl05
• Te0110
• for ua1110100
• wrua/(LafIf)-(ra/((LafIf)2))Te
• wrl01200 TlTl0Bmwrl
• plot(Te,wr,'-',Tl,wrl,'-')hold on
• axis(0, 10, 0, 160)
• end disp('End')

16
SEPARATELY ECXITED DC MOTOR (cont)

• transient dynamics of a separately excited dc
  motor
• function yprimedifer(t,y)
• ra0.18 rf3.5 La0.0062 Lf0.0095 Laf0.1
  J0.04 Bm0.007
• T10
• T110
• ua100 uf20
• yprime(-ray(1,)-Lafy(2,)y(3,)ua)/La...
• (-rfy(2,)uf)/Lf...
• (Lafy(1,)y(2,)-Bmy(3,)-T1)/J

17
SEPARATELY ECXITED DC MOTOR (cont)

• transient dynamics of a separately excited dc
  motor
• clc
• t00 tfinal0.4 tol1e-7 trace1e-7 y00 0
  0'
• t,yode45('CHP5_1mdno',t0,tfinal,y0,tol,trace)
• subplot(2,2,1) plot(t,y(,1),'r-')
• xlabel('Time (seconds)') title('Armature Current
  ia, A')
• subplot(2,2,2) plot(t,y(,2),'g-.')
• xlabel('Time (seconds)') title('Field Current
  if, A')
• subplot(2,2,3) plot(t,y(,3),'b-')
• xlabel('Time (seconds)') title('Angular Velocity
  wr, rad/s')
• subplot(2,2,4)plot(t,y(,1),'r-',t,y(,2),'g-.',t
  ,y(,3),'b-')
• xlabel('Time (seconds)') title('LAB 1')

18
SEPARATELY ECXITED DC MOTOR (cont)
19
SEPARATELY ECXITED DC MOTOR (cont)
20
SHUNT CONNECTED DC MOTOR

• The armature and field windings are connected in
  parallel

21
SHUNT CONNECTED DC MOTOR

• From Newtons Second Law, Torsional-Mechanical
  equation is given as

• The nonlinear differential equation for
  separately excited DC motor which is
• found using Kirchhoffs Voltage Law

22

• Steady state condition

• Substituting the currents equation into torque
  equation, gives

• It shows that
• The electromagnetic torque is a linear function
  of the angular velocity
• The electromagnetic torque varies as the square
  of the armature voltage applied

23
SHUNT CONNECTED DC MOTOR (Example)

• A shunt connected motor, drives a fan.
• Given
• When one applies the angular
  velocity is 150rad/s. For steady state operating
  condition and assuming the viscous friction is
  negligibly small, find the developed
  electromagnetic torque and the currents in the
  armature and field windings

24
SHUNT CONNECTED DC MOTOR (cont)
25
SERIES CONNECTED DC MOTOR

• The armature and field windings are connected in
  series

26

• The nonlinear differential equation for series
  connected DC motor which is
• found using Kirchhoffs Voltage Law

• Steady state condition

• Then, currents equation

• Substituting the currents equation into torque
  equation, gives

• It shows that
• The developed electromagnetic torque is
  proportional to the square of the current
• Saturation effect should be taken into account

27
SERIES CONNECTED DC MOTOR

• From Newtons Second Law, Torsional-Mechanical
  equation is given as

• The nonlinear differential equation for series
  connected DC motor which is
• found using Kirchhoffs Voltage Law

28
(No Transcript)
29
(No Transcript)
30
(No Transcript)