Hello All

I was wondering if anyone knows of a reasonably accurate way to calculate the leakage inductance of toroidal windings in small (<100KVA)power transformers. I have come accross plenty of information relating to conventional EI core designs, but to date I have found absolutely nothing based on toroidal geometry.

Everyone I speak to just says the leakage is so small in a well designed toroidal winding that it can be neglected. Can anyone help?

Many thanks
Mondy

You can calulate the leakage inductance of a toroidal transformer with primary and secondary wound in two layers (and not on separate sectors of the core) using the same equations as for EI-cores when you substitue the length of the leg by the mean circumference of your toroidal core.

Many thanks for your relpy electricuwe

Do you have any experiance with this method of calculation with toroids? I have not tried it yet as I need to get some information together first (and dig out the formula for the EI calculation!) but I will give this a go and see what it comes up with.

The formula I remeber has the winding length and winding depth on the bobbin involved (secondary wound over primary) and the thickness of insulation between them. When you say mean circumference, are you refering to the circumference of each winding or the final wound component circumference?

Once again thank you kindly for your reply, it is much appreciated


Cheers
Mondy

I have never used that formula myself. It's derived from theory in analogy to the derivation of the formula for the EI-core.

The mean diameter is the mean diameter of the core.(imagine you would cut the core, bend it to straight shape and close the magnetic circuit again)

Monday,

I am skeptical about the advice to substitute EI core design leakage inductance specs for toroidal specs.  An EI core is generally made up of open ended laminations that are put together after inserting the bobbin.  The laminations for a toroid generally consist of a single strip of steel tightly wound up like a clock spring.  The winding(s) for a toroid must be applied using a shuttle.  Because of this basic difference in design, the leakage inductance for an EI design transformer is normally many times greater than a toroidal design of the same VA rating.

In many applications, the larger leakage inductance of an EI design transformer is not important.  Since cost is often the major consideration, the EI design will be chosen.

Re "<100kVA" — Are even 50kVA toroidal transformers available?  
  

busbar,

Yes.  There are some monsters available for special applications.

The leakage flux in toroidal power transformer is negligable.
The inrush current at switch on can be very high (limited by primary resistance only) if core saturates.
To counter this the operating flux can be lower or a starting resister can be used.
The fault current is limited by resistance only

Thanks for your replies

20KVA is generally the limit for a single core but banks of toroids are used upto about 100KVA. As you mentioned switching on any toroid over about 5 - 10KVA is a nightmare due to the switch on surges. This is the main reason why I am trying to find a reasonably accurate equation or method of calculating the leakage L. The reactive voltage drop on the secondary windings etc. due to leakage L is pretty small and can be neglected in most cases, but when it comes down to these enormous toroidal inrush currents, every little bit of impedance counts.

As I said lots of calculation methods for EI and distribution transformers, but nothing on toroids. Does anyone know of a method or formula for it's calculation that is accurate enough to be of practical use?

Hi Mondy.

I am not clear as to if your main concern is with leakage inductance or inrush current caused by core saturation ?

The main reason these toroids have such a fearsome reputation, is that there is no magnetic gap, and most often they use a grain oriented silicon steel core which although it has a higher saturation flux, will saturate far more suddenly.

Or is your leakage inductance concern to do with secondary voltage regulation ?



 

Suggestion: Visit
http://members.aol.com/Marcttpapers2/Induct1.pdf
for "Brute Force" method of toroid magnetic analysis
http://www.ipst.org/TechPapers/2001/IPST01Paper046.pdf
for superconducting area toroid leakage equation
etc. for more info
The superconducting areas and fusion areas have toroids pretty much under the controls.

Hi All

The main reason I need to calculate the Leakage L is for short-circuit current calculations, % reactance etc, and for calculations of (approx.) switch on surge current. The principal impedance of the toroid at switch on (say worst case, zero crossing point, maximum negative remanence)is the DCR of the winding and the LL, as the primary winding shunt inductance is reduced to zero at hard core saturation. Without the LL put into the equation it is not possible to calculate accurate short-circuit characteristics and overall transformer Z used in predicting overload currents etc.

Thanks for the likns Jbartos, I am not sure if these are of any help to me as I am not too good at extracting formula from laws and primary equations (not too good at sums I'm afraid!)

Can anyone help me here??

Thx

Mondy: if you go to page 5 of jbartos' first link you'll find a complete answer to your question.

The inductance of the toroid is approximately given by:

L=(m*N*N*A)/d

where:

m=magnetic permeability of the core material
N=number of turns
A=cross sectional area of the toroid
d=circumference of the toroid (d=2*pi*radius)

Thanks for your help

I think this article is for general calculation of Inductance?

It's not the inductance of the transformer windings I require, It's the leakage inductance I need.

As I can predict the transformer's overall magnetizing current for any given primary input voltage and Bmax accurately enough, I generally use the following to calculate the series Inductance of the primary:

SQRT(Pri Volts^2/(Magnetizing amps^2*(2*PI*Frequency)^2)-(Pri Ohms^2/(2*PI*Frequency)^2))

This then transfers to to the secondary windings by the square of the turns ratio

This generally works well (the Mag amps covers the variance of core steel perm. with peak flux density)

The leakage inductance is a function of the primary and secondary winding proximity, mag length, core geometry & Bmax etc. and I just can't seem to find any references to toroidal geometry in works on the subject. Come to mention there seems precious little on toroidal geometry in any transformer theory works.

I really hope someone can come to my rescue!

Thanks

twosockets,

I didn't talk about leakage inductance specification, but about calculating leakage inductance based on dimensions for a toroidal transformer.

This calculation will lead to a much lower leakage inductance for a toroidal transformer compared to a EI-transformer with typical design and a comparable rating.

mondy,

if your problem is inrush current you should keep in mind that the common formulas for calculating leakage inductance
are based on the assumption that the iron is not saturated. This will not be true during inrush ! For the EI-transfomer the difference will be significant (leakage will get lower) whereas for the toroidal transformer leakage inductance will change not much.

electricuwe

Thanks for your reply and soory about the delay in mine.  

When calculating primary *Series Inductance* for inrush current approximations, the usual calculations seem to work if an effective permeability of around 20 is used (inrush current can generally only be an approximation, as there are so many things involved such as line impedance, supply voltage droops during the inrush etc.)

I was thinking that maybe a standard formula for *Leakage Inductance* could be used to find the normal running LL and then apply the same percentage inductance reduction to come up with the LL during inrush surges?

I am very interested in finding a good Leakage Inductance formula for toroids under normal working conditions as well for more accurate calculation of secondary voltage drop. Do you or any one know of such a formula? If so I would love to find out!!

Cheers