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Inrush Current

By E.S. Barker – Chief Engineer

When a transformer is switched on, a transient current flows. The value of this current over the first half cycle of mains voltage exceeds the normal magnetizing current by a very large factor, and is often sufficient to blow the primary fuse or lead to excessive tripping of the input circuit breaker. This current decays exponentially over several cycles until normal magnetizing current flows. An explanation of this phenomenon, is rather involved but is presented below.

During normal transformer operation a sinusoidal flux is set up in the magnetic core of the transformer. The value of the flux density within the core is set by the designer, and appears 90 degrees out of phase with the impressed primary voltage which causes it.
Inrush
During normal operation of the transformer the flux swings between +Bmax and -Bmax over each cycle this represents a total flux swing of 2Bmax. If the transformer primary voltage is switched on to the primary at the worst instant i.e. when the flux would normally be at one of the extreme values,(+Bmax or -Bmax) then the additional swing of 2Bmax adds to any flux already present in the core.

When a transformer is switched off, the flux density follows the hysteresis loop of the core material and remains at a level termed the ‘residual’ value of the flux density. In modern transformer steels this value can be as much as 80% of Bmax. Thus if the switch off and switch on of the transformer have each occured at the least favourable time we have a worst case flux density of (Bres + 2Bmax) established in the core. The core material itself can only absorb a flux density of Bsat before saturation of the steel occurs. Any flux density in excess of this value flows in the air space (between the core and the inside of the primary winding) since this flux is flowing in a non-magnetic medium, very large values of magnetizing current are necessary causing the excessive values of magnetizing current which are the subject of this short note.

In practical terms, if we assume a normal value of 1.4 tesla for the core flux density, and a saturation value of 2.1 tesla for the core, a flux density of approximately 1.8 tesla flows in the air gap. It must be stessed that these absolute values are in fact hardly ever encountered in practice, due to various factors such as supply impedance, primary winding resistance, etc..

Many, often inexpensive, ploys may be used to decrease the inrush current on any transformer, these will generally involve the lowering of the maximum levels of the residual and/or working flux densities, or the deliberate increasing of the resistance, or air cored inductance of the primary coil. Other techniques such as switching in an extra resistance, in the primary are sometimes employed. Of prime importance to the transformer user is the knowledge that these inrush currents do exist and if restraints are put on the transformer design early enough then trouble with circuit protection can often be eliminated.

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