OLTC inductances

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Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Hi:

I made an adaptation in my "Inca" inductance calculator to allow
the analysis of transformers with all the primary turns in parallel,
as those used in the recent OLTC coils.
The procedure is as follows:
1)The program computes the inductance matrix of the system, considering
v circular turns in the primary, that can be a general conical coil,
and a solenoidal secondary coil. Explicit precise formulas by Maxwell
and John Viriamu Jones, based on elliptic integrals, are used.
This keeps high precision even for very strange coils, and is fast.
The matrix has v+1 rows and columns, with the last corresponding to
the secondary coil and its coupling to the individual turns. The matrix
is listed if the number of turns is small.
2)The matrix is inverted, and the first v lines and columns are added.
This corresponds to the application of a common voltage over all the
primary turns, and the addition of the currents in all the primary
turns.
3)The resulting 2x2 matrix is inverted again. The result is the two
equivalent inductances and the final mutual inductance.

So far, the results look consistent. The coupling coefficient is
about the same for a spiral primary coil, but the inductance of the
primary coil is smaller than an one turn inductance. It tends to
a current sheet inductance with 1 turn, that Wheeler's formula
approximates quite well. A curiosity is that the secondary inductance
is slightly decreased, due to the "shorted turn" effect caused by the
different mutual inductances between the interconnected primary
turns and the secondary coil.

A problem is that uniform secondary current is still assumed.
The effective coupling coefficient in a real coil will be a bit
higher due to current concentration at the bottom section of the
secondary coil.

The program is at: http://www.coe.ufrj.br/~acmq/programs

Antonio Carlos M. de Queiroz