From: Paul
Date: Sun, 28 Apr 2002 10:06:52 +0100
Subject: [TSSP] Secondary voltage stress factor
Hi All,
Here's an idea for your consideration.
If a uniform secondary voltage gradient is assumed, ie a constant
volts/turn all along the coil, then the volts/turn is simply Vtop/N
where N is the number of turns.
In practice, the voltage distribution is non-uniform and therefore
the highest volts/turn on the coil must be something in excess of
the value Vtop/N. The naive value of Vtop/N is thus a lower limit
for voltage stress. We can characterise a particular coil by
indicating what its maximum voltage stress is, in units of Vtop/N,
in other words by specifying a 'voltage stress factor' which is the
ratio of the highest V/turn on the coil, to the value Vtop/N.
For example, a particular coil with h/d=6 and 1200 turns has a peak
top voltage of 520 kV, and a max gradient of 0.63kV/turn (at 22%
height). Thus the uniform gradient is 520/1200 = 0.43 kV/turn and
we have a 'stress factor' of 0.63/0.43 = 1.46, so that for this
coil, naive estimates of the insulation requirements need to be
uprated by at least this factor. These figures were calculated for
CW steady state resonance, and this provides a lower limit for the
voltage stress, since in a primary-driven coil the primary induction
must be added, along with the contributions of higher modes.
I'm wondering whether it would be helpful and possible to produce a
table of these voltage stress factors, as a function of the shape of
the secondary.
Consider an arbitrary secondary coil, in cross-section in
http://www.abelian.demon.co.uk/tmp/vcoil.gif
and with no loss of generality we can say that the 'r1' end of the
coil is the grounded end.
The shape of this coil can be described by two parameters, for
example, let d be the average diameter, ie
d = r1 + r2
then we could choose the two parameters
A = h/d
and
B = (r1 - r2)/d
to describe the shape of the coil independently of its overall size.
Then cylindrical secondaries will have B = 0 and A between say 1 and
say 8. Flat secondaries with center-ground will have A = 0 and B
between -1 and 0. Center-hot flat secondaries will have A = 0 and B
between +1 and 0. Cone shaped coils, as per the diagram will have
A between say 1 and 8, and B between 0 and 1. Inverted cones would
have the same range of A but with B between 0 and -1.
The voltage stress factors could then be tabulated thus,
B
-1 -0.8 -0.5 -0.3 0 0.3 0.5 0.8 1
A 8
6 1.46
4
3
2.5
2
1.5
0 1.75 1.0 2.14
in which cylindrical coils occupy the center column, flat coils
occupy the bottom row, and the rest of the table covers the various
cone shapes.
Whether this would work or not depends on whether the voltage
stress factor is mostly independent of the number of turns on the
coil, and of the overall size and position of the coil.
If it turned out that this was the case, ie the stress factor was
mainly a function of the coil's shape, then such a table would be
meaningful, and could be potentially useful to coilers.
I propose we run a series of coils through the model to test
whether the voltage stress factor can be characterised as a
function of shape only, and if so, to fill in the above table.
This would require processing of a few hundred coils.
Terry, would your Sun computer be available for this, by any chance?
The program could be set to run at low priority to avoid slowing
down the qvar results processing. About 600Mbyte of disk space would
be needed, and about 200-300 hours of CPU time.
Cheers All,
--
Paul Nicholson,
--
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.