Excercises Electric Machinery Fundamentals

Chapter 6

Problem 6-25


In [1]:
%pylab inline


Populating the interactive namespace from numpy and matplotlib

Description

In this chapter, we learned that a step-down autotransformer could be used to reduce the starting current drawn by an induction motor. While this technique works, an autotransformer is relatively expensive. A much less expensive way to reduce the starting current is to use a device called $Y - \Delta$ starter (described earlier in this chapter). If an induction motor is normally $\Delta$-connected, it is possible to reduce its phase voltage $V_\phi$ (and hence its starting current) by simply re-connecting the stator windings in Y during starting, and then restoring the connections to $\Delta$ when the motor comes up to speed. Answer the following questions about this type of starter.

(a)

  • How would the phase voltage at starting compare with the phase voltage under normal running conditions?

(b)

  • How would the starting current of the Y-connected motor compare to the starting current if the motor remained in a $\Delta$-connection during starting?

SOLUTION

(a)

The phase voltage at $Y$-starting divided by the phase voltage under normal $\Delta$-running conditions would be:


In [2]:
Vstart_Vrun = 1/sqrt(3)
print('''
Vstart_Vrun = {:.1f} %
===================='''.format(Vstart_Vrun*100))


Vstart_Vrun = 57.7 %
====================

I.e., $V_{\phi,Y\text{-start}} = V_{\phi,\Delta\text{-run}}/\sqrt{3}$

(b)

The starting phase current will also decrease to same percentage of the normal starting current as the phase voltage does.

  • For the $\Delta$-connection: $I_{L,\Delta} = \sqrt{3}I_{\phi,\Delta}$

  • For the Y-connection: $I_{L,Y} = I_{\phi,Y}$

But, $I_{\phi,\Delta} = \sqrt{3}I_{\phi,Y}$ because of $V_{L_Y} = \sqrt{3}V_{\phi_Y}$ gives:

$$I_{L,\Delta} = \sqrt{3}I_{\phi,\Delta} = \sqrt{3} \cdot \sqrt{3}I_{L,Y} = \mathbf{3} \cdot I_{L,Y} $$

In [3]:
Ild_Iphid = sqrt(3)
Ily_Iphiy = 1
Iphid_Iphiy = sqrt(3)
Ild_Ily = Ild_Iphid * Iphid_Iphiy / Ily_Iphiy
print('''
Ild = {:.0f} Ily
==========='''.format(Ild_Ily))


Ild = 3 Ily
===========