Introduction to Power System Protection by Unknown

Author:Unknown
Language: eng
Format: epub
Published: 2022-06-25T06:56:05+00:00

Figure 6 shows an unloaded transformer being switched on to an ac supply.

Figure 6. Inrush phenomenon: switching on an unloaded transformer.

Let the flux in the transformer be written as

The induced voltage can then be written as

The applied voltage is exactly equal to the induced voltage. Thus, the flux in a transformer lags the applied voltage by 90” in the steady state as shown in Figure 7.

Figure 7. Flux lags the applied voltage by 90º

Therefor., when voltage is passing through zero and becoming positive the flux should be at its negative maxima and increasing as shown in Figure 7. In a time equal to T/2 (half cycle), the flux changes from

as shown in Figure 8. This is the steady-state picture.

Figure 8. Inrush phenomenon

Let us assume that the transformer is switched on at positive zero crossing of the voltage waveform as shown in Figure 8. Further, assume that the residual flux is zero. Thus, the initial value of flux is zero but subsequently the flux must have the same rate of change and same waveform as it has in the steady-state. Thus, the flux must reach a -peak value of,

in half a cycle. Since power transformers operate near the knee of the saturation curve, a flux demand of

, drives the transformer core deep into saturation, causing it to draw a very large magnetizing current with a peaky non-sinusoidal waveform. The magnetizing current is, therefore, very high, of the order of 8 to 30 times the full-load current. This current is known as inrush current. The time constant of this transient component of current could be of the order of a few seconds at worst.

The inrush phenomenon can be explained mathematically as follows: Let the voltage be represented as

The variable ϴ in the above expression controls the switching instant. Let Ф be the instantaneous value of the flux. Then we can write:

Thus, the flux in the transformer is a function of the following three factors:

Residual flux

Instant of switching

Magnetic properties of core, i.e. the amount of magnetizing current required to produce a given amount of flux.

Inrush is also experienced whenever there are sudden changes in the system voltage such as sudden recovery of system voltage on clearing of a fault, somewhere in the system.

While an unloaded transformer, which is being switched on, experiences an inrush, an adjacent transformer, which is in service, may also experience a smaller degree of inrush. This is known as sympathetic inrush.

Further, as such a high current flow only on one side of the transformer (on the side which is being connected to the supply), it looks like an internal fault to the differential scheme and ends up as spill current.

A short circuit at the terminals of a transformer causes similar magnitudes of currents to flow. Hence, the percentage differential relay is likely to maloperate on magnetizing inrush.

Percentage Differential Relay with Harmonic Restraint:

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