THE PHYSICS of . . . . MAGNETIZATION-CURRENT INRUSH

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Phil Corso

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THE PHYSICS of . . . . MAGNETIZATION-CURRENT INRUSH

1, Scope.
A number of posts related to Magnetization-Current Inrush contain misunderstood concepts, expressions, and definitions. My goal, for those members and visitors of this forum (especially newbies) that choose to accept, is to provide some enlightenment, without malice, without scorn, without prejudice! And, for those who don?t accept my goal, so be it! Who cares as long as you?re happy!

2. Root Cause of Phenomenon; Iron-Core Saturation
This and additional topics will be presented as time permits!

Regards, Phil Corso
 
Phil Corso said:
THE PHYSICS of . . . . MAGNETIZATION-CURRENT INRUSH

1, Scope.
A number of posts related to Magnetization-Current Inrush contain misunderstood concepts, expressions, and definitions. My goal, for those members and visitors of this forum (especially newbies) that choose to accept, is to provide some enlightenment, without malice, without scorn, without prejudice! And, for those who don?t accept my goal, so be it! Who cares as long as you?re happy!

2. Root Cause of Phenomenon; Iron-Core Saturation
This and additional topics will be presented as time permits!

Regards, Phil Corso
Click to expand...

Why would inrush current be higher than the current at any other time? The field completely reverses itself 120 time a second.
 
140407-1550 EDT

Following is a part of what I had started as a reply to the other thread.

150405-1412 EDT

GoldDigger:

On reflection I want to try to clarify flux or flux density in a ferromagnetic material in relation to current thru a coil coupled to the ferromagnetic material. So possibly more readers can follow what happens relative to inrush for an unloaded or loaded transformer.

In free space or air it is true that B (flux or flux density) = u (a constant) * i (current thru a coil).

When a ferromagnetic material is coupled to the coil, then this is not true internal to the ferromagnetic material. "u" is no longer a constant and thus "B" is not necessarlily zero when current is zero. This is where a hysteresis curve comes into play. There is no one single curve, but many different ones dependent upon the magnitude of "i", the ferromagnetic material, and the prior history of the magnetic flux.

There is no clean simple equation to substitute for "u". To a large extent one uses graphical means to determine what happens based upon experimental measurements.

An example hysteresis curve from "Electric and Magnetic Fields", 3rd Edition, 1949, Wiley, Stephen S. Attwood, is :
PICT3792.JPG]

For this graph --- Initially there is 0 flux in the core, point O. The rising characteristic is from "O" to "M" as current is increased from "O" to "T". As current is reduced from "T" to "O" the flux curve goes from "M" to "N". "N" is the residual flux point when current has been returned to zero.



To others:

Repeating some of my previous comments.

1. The conditions of initial flux density in a transformer core just before turn-on where created at the last turn-off of the transformer.

2. For a solid-state switch, such as an SCR pair, or Triac, the turn-off will occur at a current zero-crossing. For a mechanical switch turn-off will be approximately at a current zero-crossing when switching an inductive load. This is because the inductor will try to maintain current flow until all energy is dissipated. Thus, an arc occurs at the contacts until the current is near zero.

At this point I was trying to work on a description that would include a loaded and unloaded transformer. It is tax season and i don't have time to go further at this moment.

.
 
Part Deux

2. Root Cause of Phenomenon; Magnetic-Core Saturation
Although the term iron?core is always used in discussion a Xfmr?s magnetic-core is actually made of very thin sheets of steel, not iron (the latter being unsuitable as core-material!) The magnetomotive force (mmf) driving ?flux? (more aptly flux-density) is produced by excitation current in the form of a winding of ?N?-turns encircling the ?Core; and carrying I, amperes. The units of ?Excitation? are expressed as N?I or Ampere-Turns, or simply AT!

The behavior between excitation applied and flux-density produced is represented in a graph called magnetization-curves, B-H curves, or Saturation-curves! The vertical-axis, representing B, is called Flux-Density, while the horizontal-axis, representing H, is called Magnetic-Field-Intensity, or AT. Clearly, the resultant curve has two zones; one linear; the other non-linear!

Obviously, steady-state operation is when Field-Intensity is proportional to Flux-Density; but, transient-operation occurs in the non-linear zone when intensity is severely increased (I refer to it as exaggerated) due to a flattening of the curve! Finally, the curve transition from linear to non-linear is called the ?knee?! It is the latter situation that is responsible for Magnetic-Inrush-Current phenomenon!

Part 3 will cover "Normal" energization of Xfmr!

Phil
 
150411-0844 EDT

Phil:

Obviously, steady-state operation is when Field-Intensity is proportional to Flux-Density;
Click to expand...
This is not obvious and not correct, if I understand what you said. Refer to Attwood's hysteresis graph that I presented in post #6.

Under steady-state AC excitation conditions the flux density vs excitation current follows the relationship shown by the hysteresis curve, and this is not linear and not even the same path when when current is increasing vs when current is decreasing. That is why it is called a hysteresis curve.

For those unfamilar with the word hysteresis see:
http://encyclopedia2.thefreedictionary.com/Hysteresis
http://en.wikipedia.org/wiki/Hysteresis

The relationship of current and voltage, where voltage is a sine wave, in a circuit with a resistance, and either an invariant inductance or capactance, produces a hysteresis curve. With no inductance or capacitance the curve is a straight line, a linear relationship. As reactance is added the straight opens to an ellipse and finally a circle.

.
 
3. Identifying the Main Players: Exciting-Current (Ie); Magnetization-Current (Im)!
First, I would like to clear-up a major misunderstanding? they are not the same. Upon energization, an unloaded Xfmr?s behavior is like that of an iron-core reactor. From an electrical circuit viewpoint, energization-current (Ie), has two components; one resistive (Ir), the other, inductive (Im)! The former is related to winding-loss (and it?s in phase with supply-voltage). The latter is, of course, the Magnetization-current (but it lags the supply-voltage by 90?).
If Ir is neglected (in general its influence is nil) then, the resultant flux value has two values; one steady-state, the other transient.

4. Influence of PoW on Transient Flux!
Transient-flux depends upon the instant (Point-on-Wave) at which the Xfmr is energized. When the supply voltage is near 0?, Transient-flux is maximum. When PoW is somewhat distant from 0?, Transient-flux is zero!
If operating in the linear part of the B-H curve the Xfmr?s magnetizing current and flux would vary in direct proportion to supply voltage! Magnetizing-current would be sinusoidal and in phase with flux! Unfortunately, economy dictates it operate in the ?knee? part of the curve!

Next: Part 5,
How operation in ?saturation? zone impacts inrush.
 
Actually, the period symbol looks like this: .

The one your keyboard keeps substituting - ! - is actually called an "exclamation mark" and informs the reader that extra emphasis is given to a word or group of words similar to shouting, ex.:

Stop! In the name of the law.

Greetings Earthlings!

I love you, man!

You love me! You really, really love me!



Using an exclamation mark the way you are makes it sound like Crazy Eddie is reading your text:

4. Influence of PoW on Transient Flux!
You won't find PoW cheaper anywhere! When your Transient Flux is zero, your payment is zero! Nobody beats Craaaaaaaazy Eddie!
 
140411-1706 EDT

Phil:

At 60 Hz eddy current (also called Foucault current) and hystersis losses are about equal. This is achieved by the selection the core material and the lamination thickness. Losses are effectively resistive, but not necessarily a linear resistance. These core losses are in addition to the i^2*R loss of the coil winding resistance, and for an unloaded transformer the coil loss is insignificant, but the core loss is not insignificant.

The incremental (instantaneous) inductance of of a ferromagnetic core transformer is not a constant thru an AC cycle.

When the supply voltage is near 0?, Transient-flux is maximum.
Click to expand...
If a transformer has been at rest, no power applied, and an arbitrary voltage is applied the instantaneous current after application of the voltage is zero independent of the magnitude of the voltage. And, thus, at that instant there is no change in the core flux density. Thus, your statement of "Transient-flux is maximum" is not correct.

So far your discussion seems to ignore the ferromagnetic hysteresis loop of the core material. How you can do this and describe transformer inrush current I don't know.

.
 
Phil Corso said:

4. Influence of PoW on Transient Flux!
Transient-flux depends upon the instant (Point-on-Wave) at which the Xfmr is energized. When the supply voltage is near 0?, Transient-flux is maximum. When PoW is somewhat distant from 0?, Transient-flux is zero!
If operating in the linear part of the B-H curve the Xfmr?s magnetizing current and flux would vary in direct proportion to supply voltage! Magnetizing-current would be sinusoidal and in phase with flux! Unfortunately, economy dictates it operate in the ?knee? part of the curve!
Click to expand...


I have a problem with this description as applied to the turn on transient itself, possibly just because I am not understanding the way you are using the terminology.
I agree that during the steady state regime of a constant sine wave voltage source connected to the Xfmr the current will be greatest at the voltage zero crossing and the current will be essentially zero at the voltage maximum. Is this what you call the steady state current and the corresponding steady state flux?
If this is what you are talking about, then the application of power to the Xfmr will involve a near step change in applied voltage with zero current before turn on and the applied voltage and a varying current after turn on with a (probably exponentially decaying) wave form over the next cycle or two.
If you make the connection at the voltage zero crossing, then the transient current is at its maximum as it is essentially just the difference between the real current of zero and the steady state current of Imax. And at the voltage maximum the transient current starts out at zero because the total current and steady state current are both zero.
But this should not be taken to imply that the observed inrush current, which will happen at some point after time t0, will be maximized or minimized for those two situations. That will depend on the actual waveform of the transient current and its effect after t0.

Now your description referred instead to transient flux, and that will be further modified by the point on the hysteresis curve at which you are operating rather than directly following the current waveform, especially near saturation. I suppose that could also be approached by just working with the transient flux equations, but in that case there would have to be a third term which brings in the initial (residual) flux.
 
5. How Operation in ?Saturation? Zone Influences Inrush.
For the case above the Xfmr was energized at some point other than zero-volts. Furthermore, residual flux was zero. Then, neglecting supply variation, total flux magnitude becomes twice the steady-state value. However, if closure occurs when supply voltage is maximum, and current-change results in flux-increase in a direction reinforcing residual-flux, then total flux crests at 2.6 times (theoretically) the steady-state value. The magnetic-core is saturated, flux-change relative to time decreases, and counter-emf decreases, resulting in a larger inrush-current magnitude! In-closing (excuse the pun) the phenomenon is a random event!

References:
1) Westinghouse Corp, Electrical Transmission and Distribution Reference Book.
2) C.I, Hubert, Electric Machines.
3) EE Staff, MIT, Magnetic Circuits and Transformers.
4) A.E Guile, Electrical Power Systems (Vol-1).

Regards, Phil Corso
 
150413-1514 EDT

Phil:

Please describe your statement
For the case above the Xfmr was energized at some point other than zero-volts. Furthermore, residual flux was zero. Then, neglecting supply variation, total flux magnitude becomes twice the steady-state value.
Click to expand...
What were the initial conditions for the "case above". From this very loose statement how do you conclude "twice"?

What is the meaning of total flux magnitude?
What does "steady-state" mean?

.
 
gar said:
150413-1514 EDT

Phil:

Please describe your statement What were the initial conditions for the "case above". From this very loose statement how do you conclude "twice"?

What is the meaning of total flux magnitude?
What does "steady-state" mean?

.
Click to expand...

Hmm. As they used to say at MIT, "IOTTMCO".
(Intuitively Obvious To The Most Casual Observer). These days we would add "Not!" to that. :)
 
Phil Corso said:
Part Deux

2. Root Cause of Phenomenon; Magnetic-Core Saturation
Although the term iron?core is always used in discussion a Xfmr?s magnetic-core is actually made of very thin sheets of steel, not iron (the latter being unsuitable as core-material!) The magnetomotive force (mmf) driving ?flux? (more aptly flux-density) is produced by excitation current in the form of a winding of ?N?-turns encircling the ?Core; and carrying I, amperes. The units of ?Excitation? are expressed as N?I or Ampere-Turns, or simply AT!

The behavior between excitation applied and flux-density produced is represented in a graph called magnetization-curves, B-H curves, or Saturation-curves! The vertical-axis, representing B, is called Flux-Density, while the horizontal-axis, representing H, is called Magnetic-Field-Intensity, or AT. Clearly, the resultant curve has two zones; one linear; the other non-linear!

Obviously, steady-state operation is when Field-Intensity is proportional to Flux-Density; but, transient-operation occurs in the non-linear zone when intensity is severely increased (I refer to it as exaggerated) due to a flattening of the curve! Finally, the curve transition from linear to non-linear is called the ?knee?! It is the latter situation that is responsible for Magnetic-Inrush-Current phenomenon!

Part 3 will cover "Normal" energization of Xfmr!

Phil
Click to expand...

Isn't steel made from iron? Why can't the core be made from iron?

This also a question, not a challenge.
 
Last edited:
Bugman1400 said:
Isn't steel made from iron? Why can't the core be made from iron?

This also a question, not a challenge.
Click to expand...
The magnetic properties of iron are quite suitable for use as a transformer core. Unfortunately a solid block of iron has good electrical conductivity in all directions and that allows eddy currents to form and waste power.
The solution to the eddy current problem is to use thin laminations that are insulated from each other. Pure iron is not the best material in terms of mechanical properties for making strong thin laminations, so steel is used instead.

The magnetic properties of steel depend heavily on the additives used in the allow. Most stainless steel formulations, for example, are not ferromagnetic at all.
 
150415-1933 EDT

Bugman1400:

I provided a portion of one B-H curve in post 6. This was a hysteresis curve. Basically there are two types of B-H curves generally presented. These are "Magnetization" and "Hysteresis" curves.

Magnetization curves are generated by initially demagnetizing the material, using a toroidial core with no air gap, and monotonically increasing the current to a coil around the core and measuring incremental flux changes. On p326 in Fig. 13.1 in the Attwood book that I previously mentioned in post 6 is shown a circuit for this measurement.

Hysteresis curves are generated by a non-monotonic cycling of the excitation current. Any sort of initial conditions could exist, but the curve I showed started with a demagnetized core. Many different hysteresis curves can be obtained from the same core. Usually of most interest is a repetitive curve under some specific steady-state set of conditions, like the core in a stabalized state after application of a 120 V RMS sine wave applied to a transformer primary. There is also interest in the transient result (inrush current) following the application of voltage to the transformer primary. Initial conditions of the core flux state and excitation voltage determine this result.

.
 
I will add my 2 cents by describing how current flows in a perfect inductor. This might help to understand how inrush current occurs in a real inductor.

Even in a perfect inductor, startup conditions can cause current flow in excess of the expected 'steady state' current flow. (More correctly, with a 'perfect' inductor steady state transients will persist; there is no unique 'steady state'.)

An inductor is simply a conductor arranged to interact with the magnetic field created when current flows in it. Every wire is somewhat an inductor. Inductors are usually set up as coils of wire, concentrating the magnetic flux and letting the same 'loop' of flux interact multiple times with the conductor.

In an inductor, current flow creates a magnetic flux. This magnetic flux stores energy. As with any circuit element, we can relate the current flowing through the inductor, the voltage applied to the inductor, and the energy stored in the inductor.

For a perfect inductor, the applied voltage sets the rate change of the magnetic flux coupled to the conductor. If you were to apply 1V to an inductor then the flux coupled to the conductor would be fixed at 1 Weber per second. Note that this doesn't say anything about the current flow! The applied voltage sets the rate of flux change.

Of course, since it is the current which creates the flux in the first place, the applied voltage is also indirectly setting the rate of current change for a given inductor. Each inductor will have a proportionality factor, called its inductance, which is the measure that relates current flow to flux coupled to the conductor.

In a 1 Henry inductor, 1 amp of current results in 1 Weber of flux coupled to the conductor. Apply 1V to a 1H inductor, and the coupled flux will change at 1Wb per second and current will change at a rate of 1A per second. Apply 1V to a 1uH inductor, and the coupled flux will still change at 1Wb per second, but now the _current_ changes at 1000000A per second.

What happens when you apply an AC voltage to a perfect inductor?

During the positive half of the AC cycle, total flux will become more positive (for a suitable sign convention). The flux will keep increasing for the entire positive half of the cycle. Similarly, during the negative half of the AC cycle the total flux will become more negative. The voltage and the duration of the AC half cycle determine the _change_ in flux experienced during that half cycle. The higher the voltage, the more the flux change. The longer the time the more the flux change.

Note that the above never tells us what the actual flux is; it simply tells us how the flux changes. It is necessary to know what the flux is at a given point in time to figure out what the flux will be later.

We can relate this to 'inrush' because it is the initial conditions of the inductor and the applied AC voltage that determine how the flux in and current through the inductor evolve over time.

So, for example, we could start with an inductor that has no flux in it (and no current flow), and apply an AC voltage. Depending upon where in the AC cycle we initially apply the voltage, we can figure out what the flux will do.

Say we take this inductor, with 0A flowing in it and zero flux, and apply AC right at the zero crossing going into the positive half cycle. The flux (and current) will increase to a maximum, and this maximum will be right at the end of the positive half cycle. Then on the negative half cycle the current (and flux) will drop back to zero. In this case, for a 'perfect' inductor, flux (and current) will cycle from 0 to + maximum and back to 0 again.

If instead we take this inductor and apply the AC voltage right at the peak of the positive half cycle, the flux (and current) will increase until the zero crossing...but because we have only carried half of a half cycle the peak flux (and current) will only be half that of the first example case. In the negative half cycle, the flux (and current) will drop from the positive maximum to zero and then go to the negative maximum, right at end of the negative half cycle.

In a nutshell: the peak flux coupling a 'perfect' inductor can vary by as much as 2x depending on where in the AC cycle an AC voltage is applied.

I am not going to continue the discussion to cover real inductor, but will add a point to consider: the applied voltage sets the _flux_ coupled by the inductor, not the current. If that flux is being carried by a core which can saturate, then this 2x variability in peak flux will make the difference between the core saturating or not.

-Jon
 
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