Maximum motor inrush current resulting from voltage waveform switching

[philly]

Can someone please explain to me or point me to a good reference as to why the maximum transient inrush current when energizing a motor (or I believe transformer as well) is maximum when one of the phases is closed near or at the zero crossing on the voltage waveform?

In my other thread where I posed transient current plots for a motor inrush I noticed that the maximum transient current appeared on the voltage phase that was closest to zero crossing when closing the contactor.

Can someone please explain the theory behind this?

 

[realolman]

I would not see why this would be the case.
The only thing I can think of is that for a very small period of time it would be similar to a single phase situation

Solid state relays are often made to switch ON the zero crossing point to reduce noise.

If switching on the zero crossing caused higher inrush, it seems to me that would increase noise... but those are usually energizing single phase relays or the like.

I don't see why something that happens on one part of one cycle... especially when the voltage was lowest.... would affect total inrush current very much.

If this is true, I will look forward to the explanation also.

 

[richxtlc]

The only time that I have seen maximum transient inrush was when we energized an autotransformer that had been out-of-service for several weeks, the inrush was high enough to trip the protective relays. When we analyzed the cause, after testing the transformer and finding nothing, we calculated that if the circuit breaker was closed at the peak of the sine wave and the core lost its residual magnetism there would be sufficient current to operate the relays. (The relays were set on the sensitive side).
This same phenomenon would happen with a motor that has been out-of-service for a long period of time.

 

[gar]

100615-0740 EST

The magnetic flux produced is a function of the volt-time integral.

If you turn off the excitation to a ferromagnetic material when it is at its maximum positive flux density, and suppose this is near saturation for the core. Of course different core materials have different shapes to their magnetization curves, and therefore what defines saturation.

If you apply a voltage to this inductor of a polarity such that it continues to raise this flux level, then the magnetizing current will increase very much. Suppose a positive changing voltage causes this increase in flux, then starting at a maximum negative peak voltage and increasing to a maximum peak positive voltage will give the maximum integrated volt-time change and thus the greatest peak current.

If the volt-time integral went in the opposite direction you would diminish the flux level and not cause an increase in current.

The residual flux level for an uncontrolled turn off time is a random value. So also is the turn on time relative to the last turn off a random value. a priori peak turn on current is unpredictable.

.

 

[rcwilson]

For a pure inductive load, current lags voltage by 90 degrees. Transformer inrush is almost purely inductive. To close the breaker when current = zero, close it 90 electrical degrees after the voltage is zero, which is when the voltage is at maximum positive or negative.

This is counter-intuitive, but it works.

On our high-current circuit breaker test sets, the solid state contactor is triggered when output voltage is at maximum peak to minimize the DC offset. This gives a very repeatable current waveform for testing the instantaneous setting on circuit breakers.

On a recent substation job with 240 MVA, 230 kV transformers, the voltage dip caused by transformer inrush might affect a nearby electronics facility so the utility required the circuit breakers to have either pre-insertion resistors (like a reduced voltage starter) or a Point-On-Wave controller to minimize inrush current. The POW device closed each circuit breaker pole when that phase voltage was at a peak. (Each phase had its own closing and tripping mechanism.) The fancy controller accounted for the breaker closing time even including measurements of the applied voltage, temperature of the hydraulic oil, time since the last operation and other factors that affect the breaker closing speed.

I watched the tests on the waveform recorders. When we closed at voltage near zero, inrush was about 6,700 amps and we could feel the transformer?s loud thump 50 yards away. When the timing got adjusted and closed the first phase at peak voltage, the inrush was 600 amps, no thump, just a 60 Hz hum.

Close at voltage peak, open at current zero.

 

[realolman]

1. Does this hold true using a contactor as the OP posted?
Does a contactor bounce as do relay contacts?

2. The inrush of current that is being described and questioned due to energizing the inductor during the "wrong" part of the cycle... is this something that is under consideration or measured for more than 90 deg. of one cycle?

3. I would like to try to understand how the beginning of the first cycle the inductor is energized could cause high current that lags the voltage waveform, when the voltage waveform began at zero.

How could there be any current at all with zero voltage at the beginning of the energizing waveform? It seems to me it would have to start lagging the voltage waveform at a later point in time than at the initial "turn on " point when the voltage was zero.

My low level understanding of the current through an inductor is that the peak of current is caused by the lines of flux collapsing around the inductor AFTER the voltage has peaked. In the initial energizing of the inductor, there would be no lines of flux, because the inductor was not yet energized.

 

[winnie]

Simplify the question, and just ask about what happens when AC is applied to a simple inductor.

First consider 'steady state' operation. With an inductor, the rate change of the current through the inductor is equal to the applied voltage (less any resistance loss) divided by the inductance. The total change in current between any two points in time is equal to the integral of rate change in current. During normal steady state operation of the inductor, when the applied voltage is at its zero crossing, the current through the inductor will be at a _peak_. When you get to the next zero crossing, the current will have changed its maximum amount, and will now be at the opposite peak.

With this in mind, look at the inrush. This inrush current doesn't happen right at the instant of switch closure; at T=0 current is zero, and as with any inductor will start to change. The current will keep changing in the same direction until you get to the next zero crossing. So if you start at T=0 with I=0 right at a zero crossing, then by the time you get to the next zero crossing the _change_ in current through the inductor would be equal to the full normal change from -max to +max.

If you had a perfect inductor (no saturation, no resistance) and you connected it to a perfect voltage source (no resistance), and switched it on at the voltage zero crossing at T=0 with I=0, then the current would start at zero, rise to the '2x' peak by the next zero crossing, and then fall back to zero at the end of the AC cycle...only to repeat. In the case of the perfect inductor, the startup conditions will determine the steady state conditions for all time.

In the case of a real inductor with a real voltage source, resistance will act to cause the average current to drop to zero, so that the long term steady state operation is nice and balanced from -max to +max and back. Any imbalance in current flow would show as unbalanced voltage drop, tending to push the average current to zero.

In the case of a real inductor, _saturation_ means that the inductance is not constant, but actually drops as the current goes up. As the current passes its normal peak, the rate change in current for a given applied voltage starts to go up. The real current peak will be much greater than 2x normal if the inductor gets extremely saturated...on the other hand, an air core inductor (with no saturation effect) will only have a maximum current peak that is 2x normal. This is one of the reasons that inductors are sometimes 'gapped', built with intentional air gaps in the core.

-Jon