CHARACTERISTICS OF TIME-VARYING INDUCTANCE

When an ac current pushes an inductor into saturation for part of each cycle, the inductor presents two values of inductance to the rest of the circuit. This situation can arise either deliberately, as in the o peration of a fluxgate magnetometer, or unintentionally, as with the s aturation of power transformers by geomagnetically induced currents. A nalyzing such a circuit can be laborious, but often all that is requir ed is knowledge of how the changing inductance affects slowly varying components of the current. It is shown that the effective inductance s een by slowly varying currents flowing through a time-varying inductan ce is given by 1/L(eff) = theta/L1 + (1 - theta)/L2, where theta is th e proportion of time for which the inductance has value L1. This expre ssion is comparable to that for the effective inductance of two uncoup led inductors in parallel, but allowing for the proportion of time tha t each one is seen by the rest of the circuit. For power transformers, where the unsaturated inductance is considerably greater than the sat urated inductance, the term involving the larger inductance quickly be comes negligable as the proportion of time in saturation increases. Th us, beyond very mild saturation, the effective inductance seen by slow ly varying currents flowing through the transformer is inversely relat ed to the proportion of time in saturation.