Note that the flux linkages – and hence the magnetizing current – are continuous at t = 0, when
the switch is closed. Equation (8.7) assumes that there is no remnant flux in the core. Any remnant
flux must be added to the right-hand side of this equation.
In reality, the magnetizing inductance of the transformer is nonlinear. Consider the two-slope
approximation of a magnetizing characteristic shown in Figure 8.6(a). As the flux linkages go above
the saturation knee point, a much larger current is drawn from the source. The magnitude of this
current is determined by the slope of the magnetizing characteristic in the saturated region, and
by the leakage inductance of the transformer. It is obvious that magnetizing inrush currents of the
order of fault currents are possible. Because of the losses in the circuit, the magnetizing current
will decay to its nominal small value as shown in Figure 8.6(b). Time constants of several seconds
are common in most modern power transformers.
It should be clear that in most modern transformers very large inrush currents are possible,
depending upon the instant of energization, and the remnant flux in the transformer core. Since the
inrush current flows only in the primary and not in the secondary winding of the transformer, it
is clear that it produces a differential current which is 200% of the restraining current, and would
cause a false operation.