Electrical Steel curves and magnetizing current 1

[Mondy]

Dear Experts

Can anyone tell me how I can calculate the rms magnetizing current of a transformer when the only information I have for the core steel are curves for Watts Loss per Kg and Peak Magentic Field strength(A/meter) for any given value of flux density. As far as I can see, using the A/meter curves would be fine at low flux densities as the magnetizing current is nearly a sinewave, but as the flux approaches material saturation, the magnetizing current becomes very peaky. So how can I deduce the rms current value from peak H values when the waveform shape is unknown?

Many thanks
Mondy

 

[edison123]

mondy,

Transformer no-load current (which is the basically the magnetizing current + core loss current) is provided in the test certificate of the individual unit. Normally, it varies from 1% (for big ones) to even 5% (for small ones) of the full load current.

As for as the saturation is concerned, the transformer designer will design the flux density to be below saturation levels. Normal design values rarely exceed 1.5 T at 50 Hz with modern materials. This is to avoid harmonics at saturation levels.

 

[Mondy]

Thanks Edison

I am not looking at this from the viewpoint of evaluating a transformer. I need to know the magnetizing current and watts loss of coils wound on a core of the steel material. I have the curves for the material but I cannot see how the magnetizing current at high flux densitites can be obtained from the pk H curves. If the mag current were sinusoidal then I could use

(Hpk (from curves) * 0.707 * Magnetic path length)/turns

But as the mag current waveform would be peaky at high flux densities I would have no way of knowing the pk/rms factor. There must be a way of doing this as Hpk is a very common curve given for electrical steel grades.

Have you any ideas?

Once again thanks for your reply

Mondy

 

[jbartos]

Comment: To obtain magnetizing current theoretically, the engineering and design of the transformer will have to be performed. The transformer will have certain ratings:
kVA
Z
Vprim
Vsec
Iprim
Isec
Np/Ns
EFF
PF
Temp Rating
BILL
Primary Winding Connection
Secondary Winding Connection
Number of Windings
Material B-H curve
etc.
Also, the magnetizing current is related to Exciting Current and Core Loss Current. If the latter ones are known the magnetizing current can be obtained.

 

[cuky2000]

The transformer magnetizing (Inrush) current could be determine using transient computer program such as PSPICE, EMTP, etc.
For less sophisticated method, there are two practical approaches commonly used in the industry to draw the protective device selectivity coordination curve passing between the equipment damage curve and the Inrush criteria describe as follow:
1- One Inrush point at 0.1 sec:
I_inrush= K.FLC
_{Were:
FLC = Full load current of transformer
K= 12 for sizes above 3MVA self cooling rating or
K=8 for <3 MVA rating.}

2- Set of points or Inrush curve:
For modeling purposes the following relation provide an approximated Inrush transformer curve as follow:
I_inrush= I_pu. FLC
_{Were:
Ipu=6.t^-0.31 for t<5.
Ipu=5.t^-0.6 – 1.8. for t>5 .}

The enclose IEEE sites provide a template and additional information in this topic.

http://grouper.ieee.org/groups/transformers/info/F01/inrush_saturation_model.xls

http://grouper.ieee.org/groups/transformers/info/F01/Inrush01.pdf

 

[electricpete]

Great info as usual, cuky.

I may be wrong and maybe the original poster can clarify. I was under the impression the term magnetizing current refers to the steady state current, rather than magnetizing inrush current which refers to energization transient.

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[cuky2000]

Thanks Electricpete,

I concur with you that we do need clarification from Mondy in the original post.

To determine the rms value the first step requires determining H as a function of t. This is not an easy task since H is a random value that depends of various factors such as the closing time, saturation level, etc.
In general, the rms value of any variable expressed in function of time could be calculated as

H_rms = (1/T)^1/2*[Integral₀^t.(H(t)².dt]^1/2

 

[darwin513]

Mondy,

I'm a transformer design engineer and the maximum peak inrush current is a function of (2) variables: flux density and the air core inductance of the excited coil (typically the primary). Because transformer cores are typically soft-iron material, it will have some memory or remnant flux. This remnant flux can potentially be at Bmax at turn-off. If the core is excited at a point where the flux density is at Bmax, the core will be effectively saturated at 2*Bmax. This in effect greatly reduces the permeability of the iron resulting in a large increase in magnetizing current. Apart from designing a transformer with nominal Bmax less than 15kG, it is also important to introduce impedance in the excited winding that will limit the magnetizing current.

The self-inductance of the winding is partially dependent upon the mean-length-turn of the winding. By increasing the mean-length-turn of the winding (by winding the primary last), the inductance of the winding increases. This increase in inductance opposes the magnetizing current, thus in many cases, reducing the effective value of inrush current to < 20 times load current. This level, for many applications, is sufficient, especially when used with slo-blow fuses.

Therefore, it is a function of transformer design based upon the application. However, for standard off the shelf transformers, most transformers are designed for inrush currents less than 20 times the primary load current.

Hope this helps..

Sergio

 

[electricpete]

I did a numerical simulation of transformer inrush transient at teh following link:

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

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[Mondy]

Hi everyone

Many thanks for all your replies. I was not originally concerned with inrush current (I am however very keen on learning a little more about this...)

My main concern was just calculating with reasonable accuracy the no load rms current of transformers/coils wound on a particular grade of steel.

It is (or was!) common for core material suppliers to supply two curves for power use namely Watts/Kilogram and VA/Kilogram for a given frequency and a range of flux densities (say 0.1 to 2 tesla) To calculate the no-load current you just looked up the VA/kg at the corresponding working flux, multiplied it by the weight of the core and divided the rms working voltage into this figure to come up with the no-load current. Now however it seems that the Watts/kg is given as usual (and arguably the most important curve) but instead of VA/kg, they provide an AC Magnetization curve that represents Peak Magnetic Field Strength (in Amps per meter) as a function of Peak Flux density. To me this would be OK if it was RMS Magnetic Field strength as all you would need to do was to Multiply this figure by the Magnetic Path length of the core and divide this by the turns to get the RMS no-load current. However as it shows only peak values, how can you determine the RMS value as towards the higher flux densities (and the nearer you get to saturation) the no-load current departs from a sinusoidal shape and gets strongly peaky. How then can you establish the rms value of the no-load current?

Sergio, could you give me your method of calculating the Inrush current of transformers so that you can ensure that it is at least below a certain level? I have never really seen a method to do this. I have always been shown to calculate the approximate coil inductance using 20 as the permeability of the material (?!), and then add the resulting impedance at the working frequency to the coil DC resistance (in quadrature) to come up with the lump impedance and then just dividing this by the peak voltage applied to the coil. To my mind this seemed a little too rule of thumb and although the majority of "practical" transformer equations are of this sort, I thought that a better method should be sought, but so far no luck. The majority of customers of small transformers just need to know a worst-case scenario.

It seems that on the net and in general there is an awfull lot of theoretical information and very little practical application information regarding all spects of transformer design.

Once again thanks all for your replies it is ver much appreciated.

Mondy

 

[jbartos]

Suggestions/comments to the previous posting marked ///\\Mondy (Electrical) May 4, 2004
Hi everyone

My main concern was just calculating with reasonable accuracy the no load rms current of transformers/coils wound on a particular grade of steel.
///Usually, the fundamental sinusoidal waves are used since the transformer is supposed to operate in the linear region. The nonlinear region is left to transients, overloads, inrushes, etc.\\It is (or was!) common for core material suppliers to supply two curves for power use namely Watts/Kilogram and VA/Kilogram for a given frequency and a range of flux densities (say 0.1 to 2 tesla) To calculate the no-load current you just looked up the VA/kg at the corresponding working flux, multiplied it by the weight of the core and divided the rms working voltage into this figure to come up with the no-load current. Now however it seems that the Watts/kg is given as usual (and arguably the most important curve) but instead of VA/kg, they provide an AC Magnetization curve that represents Peak Magnetic Field Strength (in Amps per meter) as a function of Peak Flux density. To me this would be OK if it was RMS Magnetic Field strength as all you would need to do was to Multiply this figure by the Magnetic Path length of the core and divide this by the turns to get the RMS no-load current.
///The given magnetization curve is supposed to be used in its linear portions for the transformer operation in the linear region.\\ However as it shows only peak values, how can you determine the RMS value as towards the higher flux densities (and the nearer you get to saturation) the no-load current departs from a sinusoidal shape and gets strongly peaky. How then can you establish the rms value of the no-load current?
///The linear portion suffices. The nonlinear portion will provide additional results for the transformer operations in the nonlinear region.\\Sergio, could you give me your method of calculating the Inrush current of transformers so that you can ensure that it is at least below a certain level? I have never really seen a method to do this. I have always been shown to calculate the approximate coil inductance using 20 as the permeability of the material (?!), and then add the resulting impedance at the working frequency to the coil DC resistance (in quadrature) to come up with the lump impedance and then just dividing this by the peak voltage applied to the coil.
///Taking the worst case in some parameters is often done in the design process. By obtaining the more accurate lower values, the design is more accurate; however, the margin due to most conservative value is not there.\\ To my mind this seemed a little too rule of thumb and although the majority of "practical" transformer equations are of this sort, I thought that a better method should be sought, but so far no luck. The majority of customers of small transformers just need to know a worst-case scenario.
///Yes, this seems to be the case, namely, to get the most for their money.\\It seems that on the net and in general there is an awfull lot of theoretical information and very little practical application information regarding all spects of transformer design.
///This is just to have a good insight, which phenomena take place, how good is the worst case or more conservative value, etc.\\

 

[wilkin]

The basic formula for Voltage is E = 4.44fBsAN volts
B = Peak FLUX DENSITY
A = area
N = turns
s = space factor
The constant 4.44 is 4 x 1.1 where 1.1 is the form factor for a sine wave.
A square wave would be 4 x 1 = 4

E/4.44fsAN = B = Peak FLUX DENSITY.
This may clear your vision ?

 

[wilkin]

The basic formula for Voltage is E = 4.44fBsAN volts
B = Peak FLUX DENSITY
A = area
N = turns
s = space factor
The constant 4.44 is 4 x 1.1 where 1.1 is the form factor for a sine wave.
A square wave would be 4 x 1 = 4
E/4.44fsAN = B = Peak FLUX DENSITY.
This may clear your vision ?