Re: NST power rating -- another perspective

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Terry Fritz <teslalist-at-twfpowerelectronics-dot-com>

Hi Gerry,

At 11:36 PM 10/4/2003, you wrote:
>A different perspective:
>
>I have a 4500 Vrms 22ma transformer (100VA).  The primary resistance is 
>17W.  The secondary resistance is 22.1KW.
>
>The issue of power transfer, I believe, can better be understood by 
>starting from a simple model and progressing from there.  I will thevenize 
>the transformer to start.
>
>First the turns ratio is 4500/120 or 37.5.  The open circuit output 
>voltage is 4500 Vrms and the short circuit output current is 22ma.

I think NST manufacturers could possibly over-wind the secondaries by about 
5% to make up for core losses in these leaky transformers.  I note that 
more complex models usually need to have added secondary inductance to 
maintain the OC output voltage.  Probably a trivial don't care point here 
but you may run into that too.

>The thevenin output impedance is 4500Vrms/22ma or 205KW.  I will transform 
>the primary resistance to the secondary 17W * n^^2 or 23.9KW and add this 
>to the secondary resistance of 22.1KW for a total thevenin resistance of 
>46KW.  The primary leakage flux has already been accounted for by the 
>short circuit current measurement.

Hmmmm...  Ok, I'll assume that is ok ;-))

>Next, I will decompose the 205KW into its reactive and resistive 
>component. Xl will be 200KW (or 530 heneries) and Rs is 46KW.  Therefore, 
>the simplified NST model will be:
>
>     Vs = 4500 Vrms
>     Ls = 530
>     Rs = 46KW

Interesting that you now also know the "Q" at this point.  Q = R/Xp = 46000 
/ (2 x pi x 60 x 530) = 4.34  So the open circuit voltage with a resonant 
cap should be 19500VAC.  Could be tested with a variac but the low voltage 
losses and variac my disturb things too...  Also interesting that this 
agrees with our "wild estimate" of 80kV for a 15/60 resonant system in a 
runaway state which also has a "Q" of ~~4.

BTW - A trust you have seen the papers at:

http://hot-streamer-dot-com/TeslaCoils/OtherPapers/TeroRanta/CurrentLimitedTransformers/NSTModel.htm

http://hot-streamer-dot-com/TeslaCoils/OtherPapers/TeroRanta/NSTCapMatching/ResonantCapacitorMatch.htm



>
>The next step is to add a linear load (a pure ideal C with no esr).  I 
>will not (at this time) add a sparkgap nor a load resister.  I will pick C 
>to resonate with Ls at 60 hertz.  Xc and Xl will cancel and the current 
>will be limited only by Rs.  The output current will be 4500V/46KW or 
>~100ma (note much greater than the 22ma rating).  Question: what is the 
>power across C.  Answer:  Zero real power, it is all reactive power.  At 
>peak voltage, there is zero current.  At zero voltage, there is peak 
>current.  If one were to calculate the instantaneous power vs time, it 
>would go positive and negative and the average power would be zero. Now, 
>lets get maximum real power transfer.

The ESR of "real" Tesla coil primary caps is a critical thing.  But does 
not mater for the analysis here.

>
>Realizing in a linear circuit, the only time one can get real power is 
>with resistance (I^^2 R). The maximum real power transfer will be with Rl 
>matched to Rs.  If we add Rl (=Rs) in series with C, the reactances will 
>again cancel and the power transfered into Rl will be 1/2 * V^^2 / (Rs + 
>Rl).  For this case, the power into Rl is 110 watts (higher that the VA 
>rating of the transformer because we are running at resonance - not what 
>it was spec'd for).

Real coils do have some slight RF and field losses to surrounding 
objects.  But they are of no mater here.

>
>Now comes the complexity.  We add an ideal sparkgap that we can control 
>"the when" and "how long" it fires.

I would submit that there is no such thing as an "ideal spark" 
gap.  Consider an ideal cap charged to 20,000 volts and an ideal switch 
across it in an ideal circuit with no resistance.  If you close the switch, 
ideally no power is expended. :o)))  You can ask our quarter crushing 
friends to verify that :-D  You can only push the ideal stuff so far.  In 
this case, the ideal current is infinite and the analysis fails on highbrow 
theoretical grounds.  But again, for the purpose of your analysis and since 
you do have Rs which should take into account gap loss too (IMHO) I will 
let it go ;-))  As long as no currents or voltages approach infinity, you 
should be fine.

>We remove Rl and neglect the TC primary inductance for charging 
>purposes.  The only components for this consideration is Vs, Ls, Rs, C, 
>and the sparkgap (standard topology).  The TC primary in reality, will 
>control the discharge rate of C and affect the energy transfer time.
>
>This is a non linear circuit that often results in a lot of confusion 
>(myself included so don't fret).  First, we realize that a charging 
>interval (at 60 Hz) is 8.3ms, so we will fire the ideal sparkgap every 
>8.3ms when Vc reaches peak.

Trivial point, but in real models one should use 8.33333333... mS or the 
timing will slip in the model.

>For my coil, the energy transfer time is 18us (to 1st primary notch) and 
>we realize this is much less than a percent of the charging time.  Lets 
>assume all of the 1/2 CV^^2 energy goes thru the sparkgap and into the 
>secondary never to be seen again.

Watch out!  If you store all the energy in the primary coil (lossless with 
no R) and open the switch, the voltage across it goes to infinity hitting 
my ideal warning condition above!   That can invalidate the rest...

>Otherwords, lets open the sparkgap 18us after it fires.  Now we have a 
>pseudo linear circiut that would normally not have any real power 
>delivered (remember we removed the R in the load) but now we are removing 
>real energy at a rate of 1/2 CV^^2 times the break rate (BPS).

With infinite voltage across the primary coil, it may not be right to go 
further.  Maybe try modeling this.  Or try adding 0.0001 ohms of resistance 
and running models on "almost ideal" circuits.  You can't have an ideal 
switch switching infinite voltages without such an analysis going 
invalid...  I think you need to add the secondary L-C just to store the 
energy so the energy stored in the primary coil at gap opening is zero and 
the voltage at opening is also zero so as to keep things happy.  Then you 
need to discharge the secondary energy "magically" to keep the circuit sane 
(if you add resistance, that messes up you primary side model.  But it 
should be ok to assume the secondary energy is "somehow" dissipated).

>This real energy transfer rate is REAL POWER and has to be replaced by the 
>charging circuit.  The hard question is how much is this REAL POWER, how 
>do you optimize for it, and what other constraints do you need to consider 
>(like not overvolting the transformer at resonance).

One big one (30% of a coil's power loss) is that nasty old spark gap.  All 
that bright light and noise can't be neglected.  Solid state spark gaps 
also run into areas and conditions where they are going to "spark" 
regardless of how wonderful they are.  MY OLTC plays many tricks to be able 
to open it's solid state gap at "bad" times...  Mostly by burning off 
energy like mad...

>I'm still learning the answer to this but believe the best way is by 
>simulation.

Yes!! :-))))  But try to think of and have us do experiments to keep the 
models on the right track.

>I DO believe the real metrix for spark length is the REAL POWER transfered 
>thru the sparkgap and not the VA rating for the transformer (at least NST 
>types).  This REAL POWER will certainly be porportional to VA (everything 
>else being the effectively the same), will vary with Cp, the sparkgap 
>setting, and the resultant BPS (static gaps).

I too think this.  John's formula suggests streamer length is directly 
proportional to the square root of streamer power.  You have to optimize 
all the impedances (from wall plug to streamer) and then reduce all the 
losses except those of the streamer.  One things that really gets messy is 
that spark gaps and especially streamer impedance is very dynamic through 
the firing cycle.  I "sneak" around that by using equivalent resistances 
assuming they are "one number"  But the range of the "right number" varies 
over many orders of magnitude and I think I loose a lot there in modeling.

>It will probably be very close to the POWER measured in the line cord 
>using a WATT meter (I^^2 R loses in the transformer would need to be 
>factored out).  The actual line cord VA could be significantly larger than 
>the VA rating of the transformer and will ultimately depend on your chosen 
>operating point.

If you get into the frightening SLTR mode, you could probably pull a few 
thousand watts out of an NST until it blows the secondary windings.

Neat that you are working on all this!!  There are many many unanswered 
questions.  Try to think up real experiments that can be performed that 
could help verify or test things.  I found that real experiments and data 
were crucial to keeping models on the right track.  Goodness knows we have 
the stuff to do such testing.

>
>Hope this adds some clarity to a very muddy subject.

When ever this subjects seems clearer or simpler, I think I must be doing 
something wrong :o)))  Only when it gets worse and worse and the problems 
become intractably complex, am I sure that I am doing it right :-)))

Cheers,

         Terry


>
>Gerry R
>Ft Collins, CO