CT hysteresis losses 1

[veritas]

As I understand it the B-H curve follows a different trajectory on the increase and subsequent decrease of the excitation current. Briefly, when the current is reduced to zero, there is a remnant flux remaining and negative H is required to return the core flux to 0. Since energy is required to reduce the flux to zero I have seen hysteresis losses being mentioned. What is this loss exactly? Resistive? If it is energy required to re-align magnetic domains (and the associated frictional losses) to their original position then surely hysteresis exists at all times during a complete cycle as the domains are being aligned all the time (assume no saturation). What is the difference between the energy requirements to overcome hysteresis and the energy required to align the magnetic domains?

 

[Warpspeed]

Current is really irrelevant to the BH curve.

It is volts per turn (and frequency plus cross section) that decides the flux in the core. Faraday's law makes no mention of current.

With a current transformer the load resistance and the volts per turn are always kept extremely low, and so is flux density.

 

[electricpete]

The energy per cycle is related to the area inside the hysteresis curve.

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[light1]

The energy needed to overcome hysteresis is governed by the Steinmetz Law
According to C.P. Steinmetz, the heat energy due to hysteresis released per cycle per unit of iron volume is approximately
Wh=eta x Bmax^1.6
where
Bmax is the maximum of flux density in T
eta is the hysteresis coefficient
The energy to align the magnetic domain is associated with the initial magnetization curve in the first B-H quadrant.

 

[veritas]

Thanks for the replies. I understand that the energy per cycle is given by the area of the hysteresis loop (this I understand to be the hysteresis loss per cycle). What I am really asking (and I apologise if I was clear enough initially) is what is the difference between the energy required in the 1st quadrant to align the magnetic domains and the hysteresis energy in the 2nd quadrant? As I see it BOTH deal with aligning the domains. Does it not imply that when domains are aligned frictional losses are always involved?

I suspect that this question touches on what inductance is all about. The alignment of the magnetic domains in essence results in the establishment of a magnetic field. If there were no ferrous core (air cored inductor) the field would be pretty weak (as much energy is required to align the domains of air). Ignoring eddy current losses for now, this leads to the two parameters in the magnetisation part of the equivalent circuit of a CT, viz. magnetising inductance, Xm, and the hysteresis losses, Rh. The Xm part is associated with inductance which tells me what I put in on the +ve half cycle I get back on the -ve half cycle. Rh tells me there is an irreversible resistive losses. But somehow I cannot connect this to my original question stated above? Maybe someone can help?

 

[electricpete]

The hysteresis energy associated with losses from re-aligning dipoles discussed above.

The energy associated with the field is stored energy in the magnetic field. It will be much larger as we know the reactive power required to magnetize an iron-core inductor is much larger than the resistive loss from hysteresis.

Some other ways to look at energy stored in the field:

E = 0.5*Integral B*H dV = 0.5*mu*Integral H^2 dV

Another way look at basic inductor relationship:
voltage v = L di/dt
power p = i v = i * L di/dt
Energy = integral p dt = integral i * L di/dt dt
= integral i*L di = 0.5 * L * i^2/2

I think a fitting analogy would be a mass on a spring. It has stored energy oscillating between kinetic and potential (analogous to reactive magnetizing power). There is also small portion of energy lost each cycle due to damping present in real-world spring. The energy lost per cycle is typically much less than the energy stored per cycle for low-damped system. I believe the Q factor represting the sharpness of the frequency-response resonant peak can be formulated as ratio of energy stored over energy lost in one cycle.

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[sreid]

Parendse,

I think that you had it correct in your original post. Ideally for transformers one would like a material with a high permeability and low hysteresis losses. Iron is cheap and comes close. The hysteresis loss is the energy required to align magnetic domains. The higher you drive the magnetizing flux the more domains are aligned. When the magnetic field is reversed it takes more energy to flip the domains from one direction to the other direction. In a transformer core, of course, this happens twice per cycle.

Inductance has little or nothing to do with hysteresis. Coils in a vacuum have inductance and a vacuum has little hysterisis.

Electric fields are created by charge. Magnetic fields are created by moving charge (current). Electromagnetic fields are created by accelerating charge. My primary point here is that Faradays law, if closely inspected, really relates current to magnetic field strength.

 

[veritas]

The 2nd posting of electricpete is 100% correct in my opinion. After some careful thought I would like to rephrase electricpete's posting in my own words :

Start off by ignoring hysteresis. Then the energy input (I) on the +ve half-cycle as the current increases is used to align the magnetic domains and so establish a magnetic field. As I decreases the magnetic field collapses and returns the energy to the system in that the domains are randomly aligned once more (i.e. the return to their original position when I = 0). The same happens on the -ve half-cycle except that the polarity of B is reversed. Overall there is no nett transfer of energy - a magnetic field cyclically rises and collapses - and this is exactly what inductance is all about. It is the ability of a device (or material) to store energy in the form of a magnetic field. It is quantified by the flux linkages per amp. This phenomenon is modelled by Xm in the magnetisation part of the CT equivalent circuit.

Hysteresis says that the domains tend to retain some of the magnetism once the source is removed. Extra energy is required to return the domains to their original position against friction. This is an irreversible process and is modelled by Rh (others may designate it differently). Its overall effect is to "fatten" the B-H loop. Hysteresis is present throughout the complete cycle.

Taking this a step further with CT saturation when all the domains are aligned (practically speaking) both Xm and Rh are about 0 for most of the cycle. They are only nonzero at the zero crossing of the primary current. This is the region where the CT output is a series of spikes.

Finally, this puts Rh in series with Xm in my model of the CT. I have seen textbooks lump Rh with Re (eddy current losses) and some that do not.

sreid - I agree with your comments on iron being used for CT cores but would not write off inductance so easily as having nothing to do with hysteresis. The way I see it hysteresis modifies the inductive process - even though very slightly.

Comments?

Thank you for all your valuable input so far.

 

[sreid]

Parendse,

In previous posts I interpreted some statements to mean that there was some intimate relationship between hysteresis and inductance. Clearly, anything that modifys the B-H curve changes the inductance. But as you say it's a minor one, certainly small compaired to the permiability of the iron vs. flux density for example.

 

[wilkin]

In an AC field the flux reverses in direction during each cycle. energy is lost in watts for this cycle and appears as heat.
If the cycle is interupted flux is left trapped in the core.
When a new cyle is started this remanent flux will effect the new cycle.
To prevent this when switching the cycle off the flux can be reduced slowly to zero.

 

[electricpete]

What do you mean about ct output being a series of spikes?

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[electricpete]

I am trying to understand the context of the comment that Rh is non-zero only at zero of exciting current. I know it is a conceptual/intuitive description, but I'm not sure what is the intent.

Hysteresis loss occurs only over a period of changing current. For constant (dc) current there is no hysteresis loss. So I cannot assign loss value based on a single current value corresponding to a point on the current waveform.

My only context for evaluating Rh as function of I would be to assume I represents a sinusoidal exciting current.

Start with low in linear region. Resistive losses are proportional to I. Rh is present for any ac current in the linear region.

As we increase current into the saturation region, there becomes less than linear increase of losses with current. Far above saturation there is no increase in losses with increase in current.

My rough model based on above reasoning.

- Rh is constant in the linear region of sinusoidal currents.
- The effective (linearized) Rh becomes less if we increase current into saturation region.
- Rh would approach zero for very high exciting currents far above saturation.


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[veritas]

Hi electricpete and others

To answer your first question : When in deep saturation there is only a rate of change of flux (a very high one at that) at the zero crossing of the primary current. Invoking Faraday's Law, there can only be a CT output (Es) when there is a rate of change of flux. Because of the high d(phi)/dt and also depending on the number of turns of the secondary winding the CT output is literally a series of spikes the spikes being manifested at the zero crossing of the primary current. There is practically no area under the spikes and so no energy is transferred to the secondary circuit.

This leads on to Rh. Your last posting actually correctly states my understanding of Rh as well. However, to be more correct, Rh only approaches zero when the core is into deep saturation as you correctly stated. This is because 99.9% of the magnetic domains are aligned. This is only valid though for the region between the zero crossings of the primary current when the core is in deep saturation. At the actual zero crossing, Rh is nonzero because the domains are moving and one actually has the maximum losses as the biggest possible B-H loop is being traversed. Consequently Rh is a maximum at the zero crossings and virtually zero elsewhere.

This, coupled with eddy current losses, I believe to be the reason why the core heats up when driven into deep saturation.

Does my explanation make sense?

Regards and thanks.

 

[electricpete]

Ah. I understand the spikes now and the description of Rh. It makes sense and I believe the whole subject of hysteresis is now a little more in focus for me thanks to your discussion.

I need to correct one statement I made earlier (before someone else does ;-). I believe losses increase linearly with current in the linear region. This actually would correspond to R~ (1/I) rather than constant R as I said previously.


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[veritas]

Hi electricpete and others (again)

I must say that I have benefitted a great deal from this discussion as well. Thanks to all those that have contributed.

electricpete : Did you not mean Rh ~ I (directly and not inversely proportional). To be even more correct I suppose it should be Rh ~ I^2, or not?

Regards.

 

[electricpete]

My thought is that the area of the loop increase in direct proportion to I within the linear range. This represents loss power (assuming frequency constant).

P = K*I = I^2 * Reffective
where
P is hysteresis losses
K K is proportionality constant
I is current

Reffective = K*I / I^2 = K/I



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[veritas]

electricpete & others

I've been thinking about this and realised my perception is not quite correct. I think the situation is analogous with current flow in a conductor. When a voltage is applied, electrons start moving. We consider current flow as the rate of change of charge (dQ/dt). If we had to plot current flow vs. applied voltage we get a line with a slope of dV/dt = R. Note that R is constant and the V, I relationship is a linear one.

Consider the following very rough approximation of a CT mag curve :
V /
/ /---------------------
/ /
/ /
/ /
//
----------------------------
I
The curve in essence consists of a linear portion and horizontal portion, the latter denoting the saturated region. Ignoring hysteresis for now, the slope of the linear portion (V/I) yield the magnetisation impedance Xm. Thus Xm is constant over the linear portion but then drops to zero when saturation starts.

I surmise that Rh pretty much follows the same behaviour. Thus Rh and Xm are constant impedances which drop to zero when saturation occurs.

Comments?

Thanks all for your valuable insights so far.

One last question - do you agree with Rh being in series with Xm in the CT model?

Regards.

 

[electricpete]

I agree effective Xm is constant in linear range and approaches zero in saturation range.

I am not positive but I think there may be difficulty in modeling that aspect with circuit analysis. Does your program interpret non-linear inductance to mean an inductance which varies over the course of a cycle? Or more likely I suspect a program like PSCPICE provides a simpler non-linear inductance used only in steady-state sinusoidal analysis which is just an ac analog of non-linear resistance in a dc circuit.

Certainly if you are programming a numerical solution using state space method (such as Matlab ode45) it would be easy to add flux as a state variable and there is no need to develop an equivalent circuit model. I have done example similar approach for power transformer here

http://geocities.com/pschimpf/temporary_stuff/transformer_inrush_simulation.htm

I did not model hysteresis and that would be more challenging, but I'm sure it can be done.

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[veritas]

Hi electricpete

No, I am not involved in any software modelling. I merely wish to correct my personal understanding of the CT model.

I am, however, most interested in your trfr inrush model. Two burning questions I have always had on this are :

1) How long exactly does the inrush current last?

2) I know that the inrush will be more prevalent in one of the three phases. If I have a star/delta trfr with the trfr being energised from the HV side and the HV side is solidly earthed will I have current flowing in the HV neutral and if so for how long?

These are pretty important questions when it comes to definite time earthfault protection on the HV side of trfrs.

Thanks and regards.

 

[electricpete]

Inrush current in a typical distribution application I believe lasts around 1- 10 seconds. For generating plant generator stepup transformers it is more than a minute. Higher L/R of the entire circuit from source means longer inrush current.

You are absolutely correct about current in the hv neutral during energization. Roughly speaking I believe the dc components of the three phase excitation currents cancel, the fundamentalc omponents of the three phase excitation currents cancel, but the excitation current spike that occurs on some or all phases once per cycle does not cancel and that spike current flows in the neutral. It lasts as long as the magnetizing inrush.

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