Page 299 - Industrial Power Engineering and Applications Handbook

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same as that of the impedance of a motor during a start, Stator minimum heat
in a balanced supply system. Thus, the current effect
during normal running of a negative sequence voltage This occurs in the other two windings, which are 120"
will be the same as that of the starting current effect on phase apart (Figure 12.5). Hence
a balanced supply system.
The effect of voltage unbalance is, therefore, more I,,(min.) = $I: + I: + 21, x I, cos 60"
pronounced than the percentage of unbalance itself. For = J7-c
instance, a voltage unbalance of 3% may cause a current
unbalance of 18-30%, which is detrimental to the life of
the motor. The effective current in the stator windings and the minimum heat generated,
would depend upon the relative positions of the positive
and the negative sequence components. In one of the H,, (min.) = ( I,' + 1,2 + I, x I,
windings they may be in phase, producing the maximum
current and the associated heating effect, and in the other (Figure 12.3, curve 2) (12.5)
two they may be 120" apart. In Figure 12.5 we have
drawn the maximum and the minimum effective currents Example 12.3
which the stator windings may experience on an un- The minimum heat generated in the above case
balanced supply system. Heq (min.) = (1' + 0.4' + 1 x 0.4)
or = (1 + 0.16 + 0.4)
Stator maximum heat
i.e. 1.56 or 156%
This occurs when the positive and negative sequence
components fall in phase in which case the equivalent Stator average heat
stator current will become
- - In practice the temperature attained by the stator windings
I,, (max.) = I, + I,
will be significantly below the maximum or even the
and the maximum heat generated, Heq(max.) ..(I, + IJ2 minimum heats as determined above due to the heat sink
(Figure 12.3, curve 1) effect. The heat will flow from the hotter phase to the
cooler phasedarea (see curve 3 of Figure 12.3). But for
or H,,(max.) 0~ (I,? + I,' + 21, x I, ) (12.4) protection of the motor windings against negative sequence
components, the average heat curve is of no relevance,
Example 12.2 for it will take a considerable time for the heat to stabilize
Consider a negative sequence component of 40% of the at this curve, and much more than the thermal withstand
rated current. Then the maximum heat generated as in equation capacity of the winding most affected.
(1 2.4) It is therefore essential to provide adequate protection
Heq (max.) = (1' + 0.4' + 2 x 1 x 0.4) for the motor to disconnect it from the mains quickly
before any damage is caused to the most affected winding.
or = (1 + 0.16 + 0.8) The protection is based on the maximum heat that may
i.e. 1.96 or 196% be generated in the motor windings in the event of a
negative sequence component in the system.

Magnitudes of negative sequence components
for protection
The additional heat generated by a negative sequence
component may vary from six to ten times the theoretical
heat produced by that amount of a positive sequence
component, as analysed above. It is therefore more relevant
to consider a factor of 6 to represent the effect of such a
component. The heat generated can be rewritten as

He, = (I,? +6Z,') (12.6)
and the current on unbalance,

The factor 6 is a design parameter for all future reference.
In fact, this empirical factor has been established over
many years of experience and field data collected on the
behaviour and performance of a motor in such an
Figure 12.5 Equivalent stator currents during unbalanced voltage unfavourable operating condition.