remnant flux maximum values?
remnant flux maximum values?
(OP)
I have a question for the experts,
I read in a couple of white papers that the remnant flux Br inside a Xformer is the value of the last flux before d-energizing as it takes days to decay. My question is if we d-energize the Xformer at B(t) = Bmax =1.0 PU then the Br should equal 1.0 pu?? However according to the BH curve and some white papers the Br-max is around 0.7 P.U never to reach 1.0pu. Any explanation to this?
thx
I read in a couple of white papers that the remnant flux Br inside a Xformer is the value of the last flux before d-energizing as it takes days to decay. My question is if we d-energize the Xformer at B(t) = Bmax =1.0 PU then the Br should equal 1.0 pu?? However according to the BH curve and some white papers the Br-max is around 0.7 P.U never to reach 1.0pu. Any explanation to this?
thx






RE: remnant flux maximum values?
RE: remnant flux maximum values?
http://info.ee.surrey.ac.uk/Workshop/advice/coils/...
which illustrates remnance and core hysteresis. Although the curve is not real world data (its width is exaggerated to illustrate the loss area), the relationship between P2 and P3 is pretty good.
RE: remnant flux maximum values?
I see some confusion on B,H and Φ here. At zero magnetic field B=0, the flux density H on hysteresis B-H curve is not zero, 0.7 pu of the max. But remnant flux should symbolized as Φr, Br is confusing.
RE: remnant flux maximum values?
pwrtran,
At Zero magnetic field H=0, the Br is the remnant flux B = Phi / A, where phi is the flux in Wb and B is magnetic density in Tesla so remnant flux could be either Br or PHIr where is the confusion? am I missing something :)
Assuming I want to compensate for a known remnant flux in a controlled switching algo for a transformer is there an relationship between the BH curves and the optimal angle?
thx,
RE: remnant flux maximum values?
Optimal angle? and for 3 phases - theoretically yes, but practically difficult to control. Gradually increase the voltage from zero and gradually decrease to zero will do the job.
RE: remnant flux maximum values?
1- Ok I get it, you meant when we mention a "remnant flux" It is better to refer as Φr instead of Br. As Br would be the remnat flux density if that's even a term.
2- Regardying the optimal angle for the three phases... elaborating more on the same question, if I know my volt-seconds which is approx equal to Φr at de-energization time I should optimize my angle as in:
angle = arcsin( Φr / Φmax) blabla something like that...
Is knowing the BH curves data come into play at all when computing that angle? It hard for me to belive that I can compensate based on the formula above alone without knowing the BH characteistics of the core? so is that all needed?
RE: remnant flux maximum values?
RE: remnant flux maximum values?
RE: remnant flux maximum values?
"Remnant flux" is indeed a misnomer for Br. It should be called remnance (or residual flux density in full). The reason we can typically avoid the confusion between B and φ is that for a certain transformer they are proportional. Same story for H (field strength) and I (current). Which is why you might see the B-H curve for a transformer is actually labelled flux vs current. As long as you don't change the magnetic path area (the constant of proportionality between B and φ) or the winding length (the constant of proportionality between H and I), the curve will look the same.
I think juleselec and PHovnanian have covered the reason why remnance is less than max B.
As for calculating an optimal angle, you ask:
I think you'll find that the B-H curve is not relevant. It is relevant if you're trying to determine maximum remnance, but your assumptions is that the actual remnance is "known". Note that that is a big assumption - of course, it will change depending on where in the cycle de-energisation occurred and it is very difficult to measure in practice. So let's assume it's known!
The only other thing you really need to know to determine the angle for re-energisation is the "prospective flux" that would result from application of the primary voltage. It is proportional to the integral of the voltage (I think this is the volt-seconds you refer to). In an ideal world the constant of proportionality is equal to 1/N where N is the number of turns. Non-ideal effects will likely dominate so you'd probably need to measure the maximum flux during operation at nominal volts to get the proportionality right. Note that this max flux will not be the same as on the B-H curve since in normal operation you want to keep flux below the maximum (saturation) point of the B-H curve. Let's call this max operating flux φm.
Once you have your prospective flux, you'll find it is a sine wave 90 degrees lagging the line voltage (due to the integration) with an amplitude of φm. The optimal angle then is simply when the prospective flux is equal to the residual flux. Note that this will occur a couple of times per cycle - either will do. If you define θ as the angle of the line voltage, then prospective flux φ = φm * sin(θ - 90°) = -φm * cos(θ). For φ equal to the residual flux φr, θ = arccos(-φr/φm).
Now in reality this is very difficult to put into practice. Firstly remnance is difficult to measure and it will change every time the transformer is de-energised. Secondly, energising one phase will affect the remnance in the other phases, so the optimal angle for them changes. Thirdly, the actual moment a contactor makes the circuit is subject to unpredictable variation due to closing time and prestrike.
I found these references useful:
A. Ebner, M. Bosch, R. Cortesi, "Controlled switching of transformers - effects of closing time scatter and residual flux uncertainty," Universities Power Engineering Conference, 2008. UPEC 2008. 43rd International , vol., no., pp.1-5, 1-4 Sept. 2008
J. H. Brunke, K. J. Fröhlich, “Elimination of Transformer Inrush Currents by Controlled Switching – Part I: Theoretical Considerations,” IEEE Transactions on Power Delivery, vol. 16, no. 2, pp. 276-280, April 2001
A. Ebner, "Transient Transformer Inrush Currents due to Closing Time- and Residual Flux Measurement- Deviations if Controlled Switching is used"
RE: remnant flux maximum values?
Thank you for the detailed explanation, I have a good understanding of all that now. The problem that I am facing right now is that I am looking at an algorithm that continuously integrates the line voltage to get the flux and assumes the flux at DE-energization is the remnant then does something like:
degrees to adjust the optimal angle in case there is a remnant flux density:
adjust(degrees) = a*Φr^2 + b*Φr + offset
Where a and b: some constants and,
offset : to model the hysteresis loss depending on the polarity of flux and voltage.
My questions are:
1-If you use the equation above that should approximate either I or H ( since they are both proportional to each other) because that's another way of coming up with (H or I) = f(Φ) is that correct?
2-How do you relate an adjust angle directly to I if the above is correct?
it should be -as you mentioned- some inverse trigonometric function(acos or asin) of the flux, I can't find any literature or formula stating that I or H =~ some f.factor * angle...
am I missing something here?
thx,
RE: remnant flux maximum values?
2. If I take your assumptions, then the relationship between I and angle can be derived using the inductor equation:
CODE --> maths
So you can see that the relationship between I and θ is not linear, but sinusoidal.
That all said, can you not just skip the excursion via I? What if your original equation was used to approximate θ = arccos(-φr/φm)? φm is a constant, and arccos can be approximated by a second order polynomial (though the question arises - why bother?), so can't you just use θ = a*φr^2 + b*φr + offset as your approximation?
RE: remnant flux maximum values?
thanks for taking the time to follow my train of thoughts.
The conclusion you came to is the same as mine, the equations can only be used if they are approximating acos/asin.
I think the offset is some constant tweaked through measurement that represent the Br??? because (maybe)
at I=H =0 we have φ =φr =offset.
After adding the offset they came up with four lookup tables (depending on flux voltage polarity) which represent the adjustment angle vs remnant flux...
My only concern with θ = arccos(-φr/φm) is that it seams you don't need to know the BH characteristics and the effect of hysteresis on that angle θ.
RE: remnant flux maximum values?
I don't think your concern is necessary - it turns out the hysteresis has no effect on the choice of angle. Sure, it is the cause of the remnance in the first place, but once it is there you are just interested in the prospective flux at the instant of reapplication of voltage on the primary. Turns out that the prospective flux is just the sinusoidal relationship. Once you get going the B-H curve comes into effect again, but not at the moment of re-energisation.
RE: remnant flux maximum values?
flux= flux_max= 1.0pu, now the φr =1 pu which gives you an adjust angle of acos( 1 ) = 0 that does not make sense.
Plus I read from white papers that φr is always around 0.6 ish pu so the maximum adjuct angle at flux_max would always be around 53~60 degrees...hmmm
RE: remnant flux maximum values?
RE: remnant flux maximum values?
This leads to a method that can be used to leave the core at remnant flux density 0 Vs/m2 (or Tesla): If practical, connect a capacitor parallel to the winding (secondary preferred) and let the swinging take place. It doesn't always work, a load reduces the Q factor so the oscillations dies too quickly for a demagnetization to occur.
This is a project for a rainy day. And, since it has been raining for a while, I shall do some measurements. Stay tuned!
Gunnar Englund
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.
RE: remnant flux maximum values?
I wonder what practical benefit that would have at the end of the day though - it doesn't sound particularly safe to encourage an oscillation after power is removed and apart from the difficulty in measuring it, what's the harm in having non-zero remnance?
RE: remnant flux maximum values?
Gunnar Englund
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.
RE: remnant flux maximum values?
RE: remnant flux maximum values?
Please, find attached a paper on this subject.
Regards,
Herivelto
Best Regards,
Herivelto S. Bronzeado
Ministério da Integração Nacional - MI
Brasília, Brazil