Inrush - inductors and capacitors

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gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
141213-2009 EST

I constant see comments on this forum that there is high inrush because the load is inductive. This is a totally incorrect statement.

A true pure inductor can not have its current instantaneously changed. If the initial current in the inductor is zero, and you apply a large voltage to that inductor, then the instant after the application of the voltage the current is still 0. With the voltage maintained constant (applies to AC or DC) the peak current will never exceed its steady state value. True perfect inductor means an invariant value of inductance.

The above will also be true for a real air core inductor with any amount of eqivalent internal series resistance.

Motors and transformers do not fall into the category of true perfect inductors.

In a motor at stand still there is no counter-EMF generated. When a motor is first started if looks like an iron core (ferromagnetic) inductor with series resistance. If the rotor is kept locked, then the current variation with time would behave as defined by the the characteristics of the particular electro-magnetic circuit. When the rotor is released then it spins up to its full speed value. The rotation of the rotor produces a counter-emf (a voltage that opposes the source voltage) that is approximately proportional to speed. Thus, at full speed there is only a small voltage applied across the series resistance-inductance circuit and current is much less than at locked rotor.

In an iron core transformer with a non-zero flux state at the time of application of a voltage, and the applied voltage forces the flux to a greater value, then the core is driven more toward saturation, and the magnetizing current increases. Essentially the inductance is lowered. High inrush currents will result. The closer the initial flux is to saturation at turn on the greater is the peak in rush current.

A pure capacitor can not have its voltage changed instantaneously. Assuming no internal series resistance in the capacitor, then the application of a large voltage to a capacitor with zero initial charge (0 volts on capacitor) will have a large inrush current defined by the internal impedance of the voltage source. This current decreases to its steady state value with time. We can not define what happens with a theoretically perfect voltage source connected to a perfect capacitor.

The inrush current of motors and transformers is not because these are loosely classified as inductive, but as a result of other factors.

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winnie

Senior Member
Location
Springfield, MA, USA
Occupation
Electric motor research
I absolutely agree with your general point: that inrush current into an inductive load is not because of its inductance per se, but rather because of the saturation of that inductor.

I have a small nit to pick:
In an iron core transformer with a non-zero flux state at the time of application of a voltage, and the applied voltage forces the flux to a greater value, then the core is driven more toward saturation, and the magnetizing current increases.

It is not the initial non-zero flux of the core, but rather the point in the AC cycle when voltage is applied, with a small input from any non-zero flux on the core.

The residual flux in a good transformer steel is small; ideal steel would have zero permanent flux but you can't buy it :) (Ideal steel would also not saturate, so we can't use ideal steel as an example:)

In steady state operation, zero flux is found in the core at the _peak_ of the applied AC voltage. Over the course of 1/2 AC cycle, when the applied voltage is of a single polarity, the flux changes from maximum value to maximum value of the opposite sign. So if you start with a core that has a bit of residual flux, and you apply voltage at the peak of the AC cycle, you will 'drop in' to almost steady state operation.

On the other hand, if you apply voltage right at zero crossing, then the core would have to support a flux change to 2x its steady state peak value. You would see saturation and inrush current.

The initial flux state of the core would of course influence this, but imho would be a second order contribution.

-Jon
 

gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
141214-0811 EST

winnie:

The residual flux state in an iron core inductor is a function of the hysteresis curve and the current turn off point. In an unloaded transformer driven by a sine wave voltage and with turn off at near zero current there will be a large residual flux. Heavily loaded with a resistive current at turn off and zero current turn off the residual flux will be lower.

Even with a mechanical switch the turn off in an inductive circuit tends to be near a current zero. In a single Triac or back-to-back SCRs the turn off is at a zero current point.

The voltage turn on point in relation to the resudual flux will determine whether the flux level is driven further into saturation or away from saturation.

It should be noted that in most iron core (ferromagnetic) circuits that there is a rounded shape to the hysteresis curve, and, therefore, no precise saturation point. In special square loop materials there is a very sharp corner in the hysteresis curve.

At my website http://beta-a2.com/EE-photos.html photos P6 and P7 graphically show the difference in initial current resulting from a difference in residual flux in a standard transformer. In P7 the initial peak current is relatively close to the steady state peak current in comparison to P6.

If I knew the residual flux state, and based on that the voltage was turned on at exactly the correct point, then there would be no peak current at all different than the steady state value.

.
 
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winnie

Senior Member
Location
Springfield, MA, USA
Occupation
Electric motor research
Gar:

cool, actual data that refutes my gut :)

If I am reading the description of your setup, in both photos P6 and P7 the AC voltage was applied at exactly the same spot in the AC cycle, right at zero crossing. In both photos, the current spikes show up at the latter half of the + portion of the AC cycle, but the peak magnitude of the initial spike is quite different.

Is there any chance that the AC was applied at a different point in the cycle?

Would you be interested in a series of tests showing the difference in transient current with application of AC at different parts of the cycle?

Thanks
Jon
 

meternerd

Senior Member
Location
Athol, ID
Occupation
retired water & electric utility electrician, meter/relay tech
Just to add to the "techno-babble"....inrush current on a power transformer contains a high amount of second harmonic. That's how transformer differential relays keep from tripping during energization. It's called "harmonic restraint". Don't remember the math behind why it happens, though.
 
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gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
141215-1502 EST

winnie:

The reason is different initial residual. One residual was negative of the other. I have to leave at the moment. I will be back later this evening.

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gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
141215-2147 EST

winnie:

I do not remember exacly how I switched the transformer primary. The secondary was unloaded. and the transformer I used was an A41-175-16 made by Signal Transformer.

I might have used a relay, mechanical or solid-state, or just a two prog plug.

If one does not control the turn off time, then the probability is 50% relative to whether turn off is on a positive or negative slope current zero, and, thus, the residual flux polarity. I am assuming that almost any mechanical or SCR (Triac) switch will usually actually turn off near a current crossing with a high inductive load.

If you have existing equipment to run controlled tests it would be interesting to see the results. The turn off current zero crossing will be shifted from near 90 deg to near 0 by simply fully loading the transformer secondary with resistance. There should be some voltage turn on phase angle for a particular magnitude of residual flux that would produce an initial current pulse not much different than the steady state current.

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gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
141216-1217 EST

Some additional experiments:

Same transformer primary. DC excitation of primary. Hall device on transformer side in position that provides the greatest signal. 5 V excitation to Hall, and about 2.45 V relative to common for zero flux density.

The core can be demagnetized by application of an AC voltage and gradually lowering the voltage to 0. All readings are the Hall output voltage. Lower than mean is one flux polarity, and above mean is the opposite polarity.

*****************************************

0.9 A about 2 V.
While excited ---- Residual
----- 1.642 ------ 2.417
----- 1.642 ------ 2.417

Opposite polarity of excitation current
----- 3.226 ------ 2.485
----- 3.266 ------ 2.487

Average of 2.417 and 2.487 = 2.452 = estimate of zero flux point for the Hall device.
Values with mean substracted
----- 0.810 ------ 0.035

Opposite polarity
----- 0.814 ------ 0.035

*****************************************

*****************************************

2.32 A
----- 0.645 ------ 2.401

Opposite polarity
----- 4.244 ------ 2.504


Average of 4.244 and 0.645 = 2.445 = estimate of zero flux point for the Hall device.
Average of 2.504 and 2.401 = 2.453 = estimate of zero flux point for the Hall device.

Values with mean substracted
----- 1.800 ------ 0.044

Opposite polarity
----- 1.799 ------ 0.051

*****************************************

With a 2.58 times increase in excitation current the leakage flux increased by a factor of 2.22 . And the residual flux ratio was 1.26 .

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gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
141220-1502 EST

An additional experiment. This is an AC experiment in contrast to the previous one that was DC. Goal to see how leakage flux relates to saturation. Three measurements relative to AC input voltage were obtained, and one calculated value.

The Hall sensor was located in a fixed position relative to the transformer to obtain a relatively high signal from the leakage flux. Measured were Hall voltage, RMS and full wave rectified average. Calculated was the percentage of full voltage. If the apparent inductance and series rersistance of the unloaded transformer were constant, then current would be proportional to voltage. But it is not because core saturation reduces inductance. The inductance variation is really an instantaneously varying value thru the cycle, but for convenience one can describe an average value.

Code:
Volts     mVolts  mVolts   mAmps     Normalized Volts
RMS       RMS     Avg      RMS       Ratio
Input     Hall    Hall     Input

    0         3       2        .2       0
   20         7       7       7        14
   40        12      12      11        29
   60        19      19      17        43
   80        32      31      30        57
  100        94      79      77        71
  120       233     197     196        86
  140       585     448     455       100
At 80 V input we start to see a deviation from linear tracking resulting from the peak magnetic flux density moving into the core saturation region and distortion of the magnetizing current from a sine wave.

Note that the leakage flux is increasing more rapidly than magnetizing current as magnetization moves into saturation.
 

winnie

Senior Member
Location
Springfield, MA, USA
Occupation
Electric motor research
Gar,

Thanks for continuing to play with this while I've been mulling your results.

As I understand your experimental setup, you have an SCR which will 'turn on' the AC applied to your transformer right at the zero crossing, and your scope records a trace starting at that same point.

In the pictures on the web page that you linked ( http://beta-a2.com/EE-photos.html ) , you have two different traces of inrush current, one with a 40A peak, one with a 7A peak. Since the applied AC was in exactly the same phase and the same voltage in the two cases, the difference in the peak value can only be ascribed to residual flux.

You also have the tools to zero out the residual flux (by applying smoothly reduced AC) and applying a specific DC current to create a specific residual flux.

My question: can you apply AC to the primary starting exactly at the _peak_ of the AC cycle, rather than at zero crossing?

If you look at your traces, the inrush spikes all starts roughly 90 degrees into the applied AC cycle. In the condition of zero residual flux, minimum 'inrush' current would be realized if the AC were applied at the peak of the AC cycle. In this way the core would be reaching saturation just as the applied AC voltage crosses zero and starts magnetizing in the opposite direction.

Your data clearly shows that residual flux is a very significant contributor to the level of the inrush current. I still contend that the phase of the applied AC right at the start will have a larger effect on the level of inrush...but it seems to me that you have the tools to measure this directly :)

Thanks
Jon
 

gar

Senior Member
Location
Ann Arbor, Michigan
Occupation
EE
141222-1127 EST

winnie:

If we know the magnitude and direction of the residual flux, then we should be able to choose the phase angle of voltage turn on such that the volt-time integral from the applied voltage will take us on a path that would be approximately equal to the flux change path had we not turned the excitation off. How well I can demonstrate this I don't know,

Generally I have the ability to turn on a back-to-back pair of SCRs at any phase angle. My idea of using DC to set residual flux was new to this experiment during this present discussion. Six years ago when I did the other experiments I just used the random turn off time as a means to get the two different initial residual flux levels.

I am some what handicapped in that my good scope of six years ago failed. I will see what I can do. The experiment won't be done immeadiately.

.
 
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