# Transformer Inrush Current: Calculation & Theory

When a transformer is switched on from the primary side while keeping its secondary circuit open, it acts as a simple inductance. When the electrical power transformer runs normally, the flux produced in the core is in quadrature with applied voltage as shown in the figure below.

The flux wave will reach its maximum value, 1/4 cycle or π/2 angle later, reaching the maximum value of the voltage wave. As per the waves shown in the figure below, at the instant when the voltage is zero, the corresponding steady state value of flux should be the negative maximum (i.e. minimum value). But it is not practically possible to have flux the instant you switch on the supply to the transformer. This is because there will be no flux linked to the core prior to switching on the supply. The steady state value of flux will not be reached instantly. Although it’s very fast from our perspective – it takes a non-zero amount of time. The speed of this process depends on how fast the circuit can take energy.

This is because the rate of energy transfer to a circuit cannot be infinity. So the flux in the core also will start from its zero value at the time of switching on the transformer. According to Faraday’s law of electromagnetic induction the voltage induced across the winding is given as e = dφ/dt. Where φ is the flux in the core. Hence the flux will be integral of the voltage wave, which can be calculated using the formula below:

If the transformer is switched on at the instant of voltage zero, the flux wave is initiated from the same origin as voltage waveform, the value of flux at the end of first half cycle of the voltage waveform can be calculated using:

Where φm is the maximum value of the steady-state flux. The transformer core is generally saturated just above the maximum steady state value of flux. But in our example, when switching on the transformer the maximum value of flux will jump to double its steady state maximum value.

After the steady state maximum value of flux, the core becomes saturated and the current required to produce the rest of flux is very high. So the transformer primary will draw a very high peak current from the source. This is known as the transformer inrush current or magnetizing inrush current of the transformer.

Magnetizing inrush current in transformer is the current which is drown by a transformer at the time of energizing the transformer. This current is transient in nature and exists for few milliseconds. The inrush current may be up to 10 times higher than normal rated current of transformer.

Although the magnitude of inrush current is so high but it generally does not create any permanent fault in transformer as it exists for very small time. But still inrush current in power transformer is a problem, because it interferes with the operation of circuits as they have been designed to function. Some effects of high inrush include nuisance fuse or breaker interruptions, as well as arcing and failure of primary circuit components, such as switches. High magnetizing inrush current in transformer also necessitate over-sizing of fuses or breakers. Another side effect of high inrush is the injection of noise and distortion back into the mains.

## Transformer Inrush Current Video 