# Re: Latest MMC Calculations...

```At 09:20 PM 7/20/99 +0200, you wrote:
>Hi Jim, Terry, Reinhard, all,
>
>If we use 100 caps in an MMC, will the total lifetime be
>reduced by the factor of 100? Well, I think NOT.

100 caps will have a little less life than one cap.  Since you have one
hundred chances of failure, the life will stop when the first one fails.
So instead of counting on the time it takes for 50% to fail you would use
the time it takes for just 1% to fail.  But in general, such statistical
games are not important in our case.

>
>Of course, the caps will not fail at the same time, but
>they also will not fail evenly distributed over the time
>as they ALL degrade more or less evenly over the time.
>So the lifetime of an MMC buildt out of 100 caps WILL be
>shorter than the lifetime of one cap alone - but how much
>shorter?

I am sure someone has found the shape of that curve.  However, I am also
sure no one has done the curve for our type of use.  I think there may be a
chance of infant mortality but after that, the caps will endure a long long
time before we reach the first 1% failure rate point.

>
>Statistic is a very complicated thing, especially if you
>don't know the exact functions to describe the problem.
>I.e. we don't know how the dU/dt affects the lifetime factor.
>which depends on the corona.

Actually, that is probably the best known.  I think it is a Weibule (sp)
function/distribution.  L : (U0/U1)^15  Perhaps a math expert could fill in
the details.

>
>So we can test each special type of small cap we want to
>use in an EMMC-arrangement and calculate the lifetime from
>the first dead cap. But this gives only a very bad (rough)
>approximation as you need a 'high' number of events for a
>'good' statistics.

I think if "mine" lasts a long time I'll be happy :-))  Although, since you
can run off simple 60Hz ac high voltage, this testing IS rather easy to do.
Be a great science fair project...  State of the art cap lifetimes with
wiebul statistics should win...  Or get you a job...

>
>Seems to me as if the only way to exactly determine the
>lifetime of the _COMPLETE_ MMC, is to build a complete MMC
>and try how long it will last before the first small cap
>fails and how often you have to replace one of them.
>
>
>One thing we all should have a look at is the setting of
>the safety gap (or the static main system spark gap). If
>you allow a too high voltage buildup, the MMC will die
>very fast because of the 15th power law. Of course one
>spike every now and then will not harm, but if your
>voltage level is constantly higher than expected, your
>MMC lifetime will go down rapidly.
>As Terry pointed out, if you apply 1.17 (1.36) times the
>voltage, the lifetime will decrease by the factor 10 (100)
>due to the 15th power law.

I think for most of us, if our caps last a few hours we will be happy.  We
just don't want to push our luck too far.  However, with just a few more
caps a few hour life could be extended for years.  Since we all use
different caps, from different sources, it is hard to pin down the exact
magic number.  One must be careful not to worry too much about one life
number and let another life factor sneak up on you.  I guess I don't think
we should make this too complex or scientific.  Just use a reasonable
number of caps in a reasonable number of strings and you should be fine.
The equations I have posted should get you pretty close without going too far.

www.peakpeak-dot-com/~terryf/tesla/misc/MMCPower4.html

If anybody has any suggestion or improvements to these calcs...  I have two
other life calculations for Dv/Dt and Temperature but they are REALLY
guesses :-)  They are in the MathCad docs:

www.peakpeak-dot-com/~terryf/tesla/misc/MMCcalc.MCD

Or a JPG version for those without MathCad:

www.peakpeak-dot-com/~terryf/tesla/misc/MMCCalc1.jpg
www.peakpeak-dot-com/~terryf/tesla/misc/MMCCalc2.jpg

I have never heard of any other calculations but I am all ears...

I think some people are working on computer programs to simplify all this a
bit.  such a design tool would really help everyone...

Cheers,

Terry

>
>
>Cheers, Stefan
>     \_            _    _/\_________________________________
>       \_______  _/ `--'                                    |