Page 300 - Industrial Power Engineering and Applications Handbook

Protection of electric motors 12/279
The heat derived from this equation may be less than i.e. 2.5 or 250%
the minimum heat (equation (12.5)) or even more than which is even more than the maximum heat obtained from
the maximurn heat (equation (1 2.4)) depending upon the equation (12.4). Equation (12.6) is thus more appropriate for
se\perity and the phase disposition of the negative a protective device and reflects the effect of a negative
component with reference to the positive component. sequence component in a motor winding more precisely.
This can be illustrated by the following examples.
Rotor power
Example 12.4
Referring to Examples 12.2 and 12.3 above, the heat produced The negative sequence voltage sets up a reverse rotating
according to the empirical formula is as follows: field and the slip of the rotor becomes '2 - S', compared
to the positive sequence slip S. The motor will thus operate
Hes = (1' + 6 x 0.4') under the cumulative influence of these two slips, where
1.e. 1.96 or 196% power output P can be expressed by (see also Section
2.3).
which is the same as that derived in Example 12.2.
Corollary

One can thus easily obtain the significance of the factor 6 to where
represent the status of the most affected winding of the motor I,, = positive sequence current in the rotor circuit, and
in the event of a voltage unbalance resulting in a negative I,, = negative sequence current in the rotor circuit
sequence current component. For more clarity, consider
equations (12.4) and (12.6) to ascertain the similarity in both
these equations. Since both must represent the maximum Rotor heat
heating effect
The unbalanced voltage will produce an additional rotor
:. I: + 6I: = I: + I,' + 2. I, x I, current at nearly twice the supply frequency. For example.
for a 2% slip, i.e. a slip of 1 Hz, the negative sequence
or 51,' = 21, x I" stator current, due to an unhalanced supply voltage, will
or I, = 215 x I,, Le. 0.4 I, induce a rotor current at a frequency of (2f- 1) = 99 Hz
for a 50 Hz system. These high-frequency currents will
Thus these two methods will yield the same result for a negative produce significant skin effects in the rotor bars and
sequence component of 40%. If the negative sequence current cause high eddy current and hysteresis losses (Section
I, is lower than 40%, the heat produced from equation (12.6) 1.6.2(A-iv)). Total rotor heat may be represented by
will be lower than the minimum heat obtained from equation
(12.5). In contrast, for a negative sequence component of
more than 40%, the situation is likely to be reversed, since =(I; + 3;") (1 2.9)
the heat produced as in equation (12.6) will be higher than
the maximum heat produced by equation (12.4). See the (refer to curve 4 of Figure 12.3) and cumulative rotor
following example for more clarity. current

Example 12.5
Consider a negative sequence component of 15% and 50%
respectively.
Example 12.6
For example 12.2, the rotor heat at 40% stator negative
(a) For a 15°/0 negative sequence component: sequence current
From equation (12.5) = (1' + 3 x 0.4')
He,(min.) = (1'+ 0.15' + I x 0.15) i.e. 1.48 or 148%
i.e. 1.1725 or 117.25%
Refer to curve 4 of Figure 12.3.
and from equation (12.6)
He, = (1' + 6 x 0.15')
12.3 Fault conditions
i.e. 1.135 or 113.5%
which is even less than the minimum heat obtained from These are conditions in which overheating of the machine
equation (12.5). may not trace back to its own thermal curves as in the
(b) For a 50% negative sequence component: first case. The temperature rise may now be adiabatic
(linear) and not exponential and hence rapid. Now a
From equation (1 2.4) normal thermal protection device may not be able to
He,(max.) = (1' + 0.50' + 2 x 1 x 0.5) respond as in the previous case. Some conditions causing
overheating may not recessarily be fault conditions.
i.e. 2.25 or 225%
Nevertheless, they may require fast tripping, and hence
and from equation (12.6) are classified in this category for more clarity. Such
Heq (1' + 6 x 0.5') conditions may be one or more of the following: