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capcitor energy vs pwr factor




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From:  Antonio Carlos M. de Queiroz [SMTP:acmq-at-compuland-dot-com.br]
Sent:  Saturday, February 07, 1998 2:14 PM
To:  Tesla List
Subject:  Re: capcitor energy vs pwr factor

Jim McVey wrote:

> Some say that E/I is the inductive reactance of the secondary and that
> matching this with capacitive reactance -at-60 HZ produces resonance.

True, if the inductive reactance of the secondary is used for current
limiting, as in a typical NST. E is the open-circuit voltage and I is
the short-circuit current. Assuming that all the current limitation is
due to the inductance, L=E/(I*2*PI*60), and a capacitance C=I/(E*2*PI*60)
results in resonance at 60 Hz. (The transformer insulation doesn't like
this...)
 
> Wouldn't the resonance  actually be due to the sum of the transformer
> secondary leakage reactance and the series choke?  The transformer
> presents an in phase and therefore resistive component to the model which
> limits Q. Right?

Assuming E=15 kV and I = 30 mA, for example: E/I=500 kOhm and L=1326 H.
L is much larger than any reasonable filter choke inductance, and the 
secondary wire resistance is certainly much smaller that 500 kOhm. It
limits the Q, yes.
 
> Others say that the current is cosine with sine voltage and the T/4
> instantaneous
> energy is the integral of these function's product. 

This assumes steady-state conditions, and is exactly what happens with
the primary capacitor in this situation. Actually, this would happen
exactly only if there is no firing of the spark gap for several cycles.

> If this is the case,
> the absorbed power is    absolutely dismal compared to an "in phase
> system".

No. The spark gap fires and all the energy in the capacitor is put to
use. The system operates very far from steady-state sinusoidal conditions,
and so any consideration about phase angles, power factors, etc. is
not exactly correct. The voltage and the current in the primary of the
power transformer can be considered as approximately sinusoidal in most
cases, because of the heavy filtering caused by the large series inductance
of a NST secondary, and measurements of simulations of this would show a 
high power factor (See the ROTJIT program), with efficient energy transfer
from the power line. Tesla was aware of this, certainly.

> Thus I propose that we consider the secondary resistive, which yeilds a
> 45 degree phase angle when the capacitive reactance is equal to the
> E/I "resistance" and this approaches zero as the leakage and choke
> reactances are considered.

This can happen if you use a normal transformer with low series inductance
and a resistive ballast as current limiter at the primary side. This is
very inefficient, however, as the ballast dissipates great part of the energy.

Antonio Carlos M. de Queiroz
mailto:acmq-at-compuland-dot-com.br
http://www.coe.ufrj.br/~acmq