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Induction Machines & Variable Frequency Drives
Introduction
The objectives of laboratory 3 are threefold:
 Understand the relationship between starting voltage, in-rush current, and run up time for
an induction machine. The concept is to limit in-rush current to avoid negative
consequences of large currents while providing a quick start to steady state time.
 Investigate the limitations of constant frequency control.
 Elucidate the advantages of variable voltage/frequency control.
Analysis
PART I. REDUCED VOLTAGE STARTING TO LIMIT STARTING CURRENT
Lab Data
20 %
30 %
40 %
46Vl-l
69Vl-l
92Vl-l
7.4A
11.4A
16A
4.5sec
1.6sec
0.9sec
No
load
speed
1720
1772
1783
50%
115Vl-l
19.6A
0.6sec
1788
applied voltage
(% of Vrated)
No load
voltage
inrush
current
run up
time(sec)
1) Argue possible advantages and disadvantages of Induction machines over Dc machines.
Advantages: Induction machines can move faster.
Disadvantages: Speeds are not as easily controlled as in DC machines.
2) (i) Plot the inrush current in A units vs. voltage in V units, and estimate the full-voltage
inrush current.
Estimate of full voltage is 40.37A
(ii) Explain why we did not carried out this test at 100% voltage.
Power is proportional to the square of the current and since the current is rising with increasing
applied voltage, we could have high power consequences such as thermal degradation of the
components.
(iii) But, why would we want to apply as high voltage as possible at the start-up?
At the start up we need a high voltage so we can increase the slip so that the motor gets spinning
quicker. This is shown by decrease in ramp up time as the stator voltages increase.
3) (i) Does the inrush current depend on the load torque? Explain why.
Inrush current is independent of the torque because it is proportional only to the applied voltage
at the start.
Geurts/Wabiszewski/Sanfilippo
(ii) Does the run-up time change depending on the applied voltage? Explain why.
2
Yes, it deceases with increasing voltage. The reason the run-up time decreases when the voltage
increases is because the voltage causes the motor to spin faster and therefore reduces the runup time.
(iii) Does the run-up time vary depending on the load torque?
No, it depends on applied voltage.
4) Plot the input impedance (Zin) vs. slip (s) over the range of 0 to 1
Zin = V/I
Slip = (rated speed – no load speed)/rated speed
Impedence vs. Slip
6.3
6.2
Impedence (ohm)
6.1
6.0
5.9
5.8
-1.000
-0.800
-0.600
-0.400
-0.200
5.7
0.000
0.200
0.400
0.600
0.800
1.000
Slip
5) Explain why no-load speeds from the lab data vary depending on the stator voltages (Vs-an).
In the lab when more voltage is applied, the magnitude of the current vector increases.
PART II. MEASURING MOTOR CHARACTERISTICS UNDER CONSTANT 60 HZ VOLTAGE EXCITATION
Lab Data
motor torque
(N•m)
0
-2.0
shaft speed (rpm)
230 V
184 V
138 V
1794
1795
1791
1784
1788
1770
stator current Is (Amp)
230 V
184 V
138 V
2.9
2.3
1.8
3.1
2.6
2.3
Geurts/Wabiszewski/Sanfilippo
1)
-4.0
1781
1770
1746
3.3
3.1
3.1
-5.0
1777
1764
1733
3.5
3.3
3.6
3
(i) Plot the motor torque vs. shaft speed curves for the various voltages on the same plot.
Torque vs. Speed
6
5
Torque (Nm)
4
230 V
184 V
3
138 V
2
1
0
1720
1730
1740
1750
1760
1770
1780
1790
1800
Speed (rpm)
(ii) What is the relation between motor torque and shaft speed at the given voltage?
They are inversely proportional, as torque goes up, speed goes down.
(iii) What is the relation between voltage and shaft speed under the given torque?
They are proportional, as voltage goes down, speed goes down
(iv) Do the (ii) and (iii) make sense to you, compare your results to Figure 2 in the lab
handout? Make brief comments.
Looking at the fan load line, as you follow it up from zero, you can see that as the percent of
maximum voltage increases, the speed increases. Similarly, it can be seen that the torque
will go down in this same fashion.
1)
plot.
(i) Plot the motor torque vs. stator current (Is) curves of all voltage levels on the same
Geurts/Wabiszewski/Sanfilippo
4
Torque vs. Current
6
5
Torque (Nm)
4
230 V
3
184 V
138 V
2
1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Current (A)
(ii) Calculate the slip (s) at V=230V and V=138V.
Slip (s)
Motor Torque
(Nm)
V =230V
V=138V
0
0.50
0.50
-2
0.50
0.51
-4
0.51
0.52
-5
0.51
0.52
(iii) As you can see from (ii), slip more rapidly rises at lower voltage in order to increase the
motor torque. Describe why IM with lower voltage supply needs to boost the slip in order to
increase the torque?
At a lower voltage, there is less current, which leads to less torque production. Therefore the slip
must be boosted or increased to increase the torque production.
Geurts/Wabiszewski/Sanfilippo 5
PART III. MEASURING MOTOR CHARACTERISTICS UNDER VARIABLE VOLTAGE FREQUENCY
EXCITATION (CONSTANT TORQUE CONTROL)
Lab Data
shaft
speed
nr mech
motor torque 0 Nm
Vs-an
one cycle period
excitation
frequency
fe
1500rpm
185.2 V
19.96 ms
50.07 Hz
1000
125.1 V
29.95 ms
33.38 Hz
500
61.8 V
60.15 ms
16.70 Hz
0
7.5 V
Inf ms
0 Hz
shaft
speed
nr mech
motor torque -2.5 Nm
Vs-an
1500rpm
one cycle period
excitation
frequency
fe
184 V
20.22 ms
49.45 Hz
1000
122.2 V
30.20 ms
33.10 Hz
500
59.3 V
61.40 ms
16.40 Hz
0
5.3 V
Inf ms
0 Hz
shaft
speed
nr mech
motor torque -5 Nm
Vs-an
one cycle period
excitation
frequency
fe
1500rpm
182.8 V
20.22 ms
49.44 Hz
1000
120.0 V
30.46 ms
32.82 Hz
500
57.4 V
62.46 ms
16.13 Hz
0
7.1 V
Inf ms
0 Hz
Geurts/Wabiszewski/Sanfilippo 6
1) (i) Plot the shaft speed (n r mech) vs. stator voltage (Vs-an) for all motor torque levels on
the same plot, and briefly comment on the relation between n r mech and Vs-an.
Shaft Speed vs. Stator Voltage
1600
1400
Shaft Speed (rpm)
1200
1000
0 Nm
800
2.5 Nm
``
5 Nm
600
400
200
0
0
20
40
60
80
100
120
140
160
180
200
Stator Voltage (V)
Shaft speed and stator voltage are positively associated and fairly linear.
Linear fits have been calculated for all torque levels and are as follows:
T=0 Nm
Shaft Speed [rpm] = 8.3762[rpm/V]*(Stator Voltage)[V] - 44.898[rpm]
T= 2.5 Nm
Shaft Speed [rpm] = 8.3379[rpm/V]*(Stator Voltage)[V] - 22.919[rpm]
T= 5 Nm
Shaft Speed [rpm] = 8.4563[rpm/V]*(Stator Voltage)[V] - 26.502[rpm]
Additionally, all data series display a similar slope and a slight leftward shift as torque
increases.
(ii) Estimate the required stator voltages to keep the steady state motor speed constant to
750 rpm at the motor torque of 0Nm, 2.5Nm and 5Nm, respectively.
Geurts/Wabiszewski/Sanfilippo
7
We may estimate this value by rearranging the linear equations developed in the last question.
shaft  A V  B  V 
shaft  B
A
where A is the slope of the graph and B is the y-intercept.
Motor Torque
(Nm)
0.0
Estimated Vs-an
(V)
94.9
2.5
92.7
5.0
91.8
2(i) The voltage control approach introduced in Part 2 is not capable of allowing the speed of
the induction motor to become slower than the speed at the peak torque. (approx. 1200 rpm as is
shown in Fig.2 of the lab handout). However, the control method of this part enables one to
maintain the induction motor at any speed from 0 to 1500 rpm. Explain what makes it possible
to attain this wider controllable speed range.
The voltage control approach only allows for movement up or down the torque vs.
shaft speed curve at a speed where the torque peak will occur (constant speed). This
happens as a result of only controlling the magnitude of voltage and not the frequency
at which it may activate the rotor in the induction motor (ie, the separation between
the current and magnetic field vector). The motor is essentially locked into a certain
speed where the voltage (ie power) necessary is a function of where the torque peak
occurs for a curve of constant power. However, by having control of frequency, one
is able to specify the rate at which the current vector leads the magnetic field vector.
This is essentially analogous to moving left or right on a curve of constant
voltage/power on the shaft speed vs. torque curve.
Geurts/Wabiszewski/Sanfilippo
2(ii)For the torque at 0Nm and -2.5Nm divide the voltage by the excitation frequency at each
shaft speed (ie: Vs-an/fe). Why do you think that this ratio is almost constant for a given motor
torque (hint: what does V/f represent from Faraday’s law).
Torque [Nm]
0
-2.5
-5
Shaft Speed
[rpm]
Stator
Voltage [V]
1500
1000
500
0
1500
1000
500
0
1500
1000
500
0
185.2
125.1
61.8
7.5
184
122.2
59.3
5.3
182.8
120
57.4
7.1
Excitation
Frequency
[Hz]
50.07
33.38
16.7
0
49.45
33.1
16.4
0
49.44
32.82
16.13
0
8
Vst/fe
[V/Hz]
3.70
3.75
3.70
inf
3.72
3.69
3.62
inf
3.70
3.66
3.56
inf
The idea behind the relationship between Vst and fe is that more voltage is present with an
increase in excitation frequency due to an increase in the angle between the current and
magnetic field vectors.
Conclusion
Lab 3 introduced the concept of balancing input voltage or power with the need to have a small
run-up time. Increasing the voltage or power provided to the motor decreases this run-up time
but may also result in higher initial currents that are harmful to the induction machine. The lab
also presented the shortcomings of speed/torque regulation with a fixed frequency. A promising
alternative seemed to be a variance of the input frequency for a given torque value. This method
seems all the more plausible with the ubiquity of cheap, reliable, and almost instantaneous
controllers on the market. It allows for simultaneous voltage and speed control without locking
in one particular speed related to a given load.