Simulation of DC and Induction Machines

 1
Simulation of DC and Induction Machines
Part 1A
Model created in Simulink
Part 2A
La
1
2
Lf
1
2
Rf Ra
To compute the speed of a DC machine from the load it carries during its steady state
operation, a total of two equations will be used. The first gives the relationship between the
magnitude of the back EMF at the armature, the speed of the machine, and the field current.
Ea = LafIfω (1)
It is also known that at steady state, torque is equal to the mechanical load. Therefore, the following equation:
T = LafIfIa (2)
can be used to obtain a value for Ia since at steady state, If is constant because the back EMF
at the field drops to zero, making If simply equal to (Vf/Rf). Laf as well is a constant figure.
Knowing the value of the armature current, the magnitude of the armature back EMF can be
solved through Kirchoff’s voltage law at the armature circuit. Knowing the value of the armature back EMF would then give the value of the motor speed according to (1). The values for
the theoretical and simulated speeds are given below.
V
f
I
f
I
a
Va
L
af
2
Torque
(Nm)
Speed from simulation
(Rad/s)
Theoretical
0 120.3 121.6931217
10 119.2 120.2933848
20 117.8 118.893648
30 116.4 117.4939111
40 115.1 116.0941743
50 113.7 114.6944374
60 112.3 113.2947006
The speed decreases in an almost linear fashion as the mechanical load torque increases. This
is evident in the plot below. Additionally, the simulated speeds are lower than the speeds
predicted by theoretical analysis. This may be explained by the fact that the simulation takes
much more factors into consideration than the simplified analysis performed.
Part 3A
To solve for the efficiency of the machine, the amount of power output and input should be
solved. Power input is simply a matter of multiplying the field and armature currents with the
DC source voltage, giving the power in watts through VI. To get the output power, the torque
generated by the machine should be multiplied with the machine’s speed of rotation.
Efficiency is then a simple matter of dividing the output power with the input power. The
data from the simulation is given below. 
3
Load
Torque
Speed Em
Torque
If Ia Input
Power
Output
Power
Efficienc
y
0 120.3 5.77 2.7 3.055 1323.65 693.6498 0.524043
10 119.2 15.54 2.7 8.335 2538.05 1852.368 0.729839
20 117.8 25.78 2.7 13.64 3758.2 3036.884 0.808069
30 116.4 35.68 2.7 18.91 4970.3 4153.152 0.835594
40 115.1 45.63 2.7 24.22 6191.6 5252.013 0.848248
50 113.7 54.77 2.7 29.41 7385.3 6227.349 0.843209
60 112.3 65.55 2.7 34.73 8608.9 7361.265 0.855076
From the plot, it can be seen that efficiency increases as the load torque increases up to a
certain limit. At which point, the efficiency of the DC machine reaches a plateau.
Part 4A
The reduction of the resistance of the field winding has had significant effects. First, the
speed of the motor has dropped significantly. The efficiency has also dropped by more than
one decade. The motor is also more unstable compared to the previous scenario as the speed
undergoes more oscillations before reaching a stable speed. The instability can be seen in the
plots of the speed before and after the field resistance change. The speed plot before the
change is in the left and the speed plot after the change is at the right. 
4
5
Part 1B
Model created in Simulink
Part 2B
From the results of the simulation, it can be seen that having a lower voltage and frequency
results in lower steady state motor speeds. For a particular voltage, the speed appears to
decline linearly as torque increases. This linear decline can be seen in the plot below.
Speed
Torque 400V, 50hz 200V 25Hz
0 156.9 78.47
10 155.9 77.42
20 154.9 76.38
30 153.8 75.19
40 152.7 73.91
50 151.5 72.51
60 150.2 70.95
6
Part 3B
In extending simulation to even lower voltage and frequency combinations, an interesting
scenario occurs. At combinations of low voltages and high load torques, the simulation tends
to become unstable, and the speed declines continuously without reaching steady state. For all
other working voltage and frequency combinations, the speed still appears to decline linearly
as the amount of torque is increased.
Speed
Torque 40V 5Hz 80V 10Hz 200V
25Hz
400V,
50hz
560V
70Hz
0 15.7 31.36 78.47 156.9 219.7
10 14.4 30.29 77.42 155.9 218.7
20 12.43 28.99 76.38 154.9 217.7
30 7.508 27.39 75.19 153.8 216.6
40 Does not
stabilize
25.26 73.91 152.7 215.5
50 Does not
stabilize
22.02 72.51 151.5 214.4
60 Does not
stabilize
Does not
stabilize
70.95 150.2 213.2
7
Part 4B
The new machine is even more unstable. With the same set of voltages and load torques as in
the previous part, the machine reaches instability much more often. This can be seen in the
table and plot below.
Speed
Torque 40V 5Hz 80V 10Hz 200V
25Hz
400V,
50hz
560V
70Hz
0 31.25 62.58 156.5 312.9 438.1
10 DNS 54.57 150.1 307 432.2
20 DNS DNS 141.7 300 425.6
30 DNS