# Swith in transients

1. Oct 17, 2010

### djsourabh

hello,i am se electrical student. I want to know why in a transformer at start up the flux through the core is doubled?

Last edited: Oct 17, 2010
2. Oct 17, 2010

### m.s.j

When a transformer is disconnected from a power source, the current is interrupted and the magnetic field or mmf driving flux through the core is reduced to zero. As we have seen in the preceding section, the core retains a residual induction which is called the remanence when the hysteresis path is on the positive descending (negative ascending) branch of a normal loop. In other cases, there could also be a residual induction but it would not have as high a magnitude. In order to drive the core to the zero magnetization state, it would be necessary to gradually lower the peak induction while cycling the field. Since the intrinsic normal hysteresis loops for oriented Si-Fe have fairly flat tops (or bottoms), the remanence is close to the peak induction. However, the presence of gaps in the core reduces this somewhat. When the unit is re-energized by a voltage source, the flux change must match the voltage change according to Faraday’s law. For a sinusoidal voltage source, the flux is also sinusoidal, where øp is the peak flux. Assuming uniform flux density, we have

øp=Bp.Ac

where Ac is the core cross-sectional area. Hence the peak voltage, using w=2пf, where f is the frequency in Hz, is

Vp=2пf.N.Bp.Ac

Thus to follow the voltage change, the induction must change by ± Bp over a cycle. If, in a worst case scenario, the voltage source is turned on when the voltage is at a value which requires a -Bp value and the remanent induction has a positive value of nearly Bp, then the induction will triple to nearly 3 Bp when the voltage reaches a value corresponding to +Bp. Since Bp is usually ~10 to 20 % below saturation in typical power transformers, this means that the core will be driven strongly into saturation, which requires a very high exciting current. This exciting current is called the inrush current and can be many times the normal load current in a transformer.

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Creative thinking is breezy, Then think about your surrounding things and other thought products. http://electrical-riddles.com

3. Oct 17, 2010

### Bob S

Normally when a transformer (without load) is running steady state on a sinusoidally varying voltage, the voltage leads the current by 90 degrees (e.g., V = L dI/dt). So during steady state operation, when the voltage is zero, the current is at a negative maximum. But at startup, both the voltage and the current are initially simultaneously zero (i.e., not 90 degrees apart). When the voltage is switched on at a phase where applied voltage is maximum, there is a transient current surge that wants to double the maximum core flux. If the inductance L is a nonlinear function of current, the current surge is worse.

Bob S

4. Oct 18, 2010

### m.s.j

Excuse me my dear friend, I think vice versa the increasing of flux (saturation condition) is origin of inrush magnetizing current, also mentioned phenomenon is related to transformer magnetizing characteristics (core material) not angle difference between voltage and current.

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Creative thinking is breezy, Then think about your surrounding things and other thought products. http://electrical-riddles.com

5. Oct 18, 2010

### Bob S

I thought I was careful to state that the "surge that wants to double the maximum core flux". In addition, if the core saturates (i.e., dL/dI is negative), the current surge is much larger. I have one transformer that will often create so much current surge that all the lights in the building flicker when I switch it on.

Bob S

6. Oct 19, 2010

### m.s.j

Dear Bob S,

Your description is related to RL circuit transient behavior due to circuit switching in time frame about milliseconds to a seconds which is an electromagnetic phenomenon regardless transformer magnetizing characteristics. As you know inrush current of transformer can be very huge ( up to 14*In ) with several times of mentioned time frame.

Best Regards
m.s.j