# Re: Power Factor Correction methods

```Hi Terry, and all,

Power factor is something which I have spent some time investigating
with regard to TCs,  as I am trying to optimise my rotary and charging
system efficiency.

Yes,  it is possible to calculate the required capacitor value for best
power factor correction on a practical system.  You don't need to run
a simulation but I find it is useful to check if I did the maths right !

Any system with poor power factor is drawing real power AND reactive
power from the supply. The fundamental frequency component of the supply
current is actually out of phase with the supply voltage.  For best
power factor the TC should appear as a pure resistive load to the supply.
However for less than unity power factor the system appears slightly
capacitive or slightly inductive.  This is due to an imbalance between
the transformer leakage inductance and the tank capacitance in the
charging circuit.  This means that a small amount of "reacitive power"
merely sloshes back and forth in the supply cables (causing heating etc.)
To improve the power factor we need to cancel out the reactive power bit,
so that only the useful real power is left.

In order to calculate the required Power Factor Correction (PFC)
capacitance,  you need to know two things about your TC:-

1. The VA drawn by the system form the supply.  This one is easy.  You
just measure the supply voltage and current and multiply them.

2. The Real Power being drawn from the supply.  This is a little harder.
You need to use a WATT METER.  (It is possible to get an approximate
value for the real power by calculating the "Tank Cap Watts" if you
know the break rate and peak tank cap voltage.  This method is less
accurate however, as it does not take resistive losses into account.)

When measuring these make sure your system is set up correctly,  as any
change in ballasts, capacitors or rotary phase will change these values!

Now the maths bit:  (Don't panic, only 3 steps.)

P = Real power,  Q = Supply VA,  R = Reactive VA, Z = Impedance of PFC,
V = RMS supply voltage,  pf = Power factor,  F = Supply frequency,
C = PFC correction capacitance.

pf = P / Q,     and     Q = sqrt ( (P*P) + (R*R) )

To get unity power factor we need to make the reactive power R = 0, so
that Q = P  and pf = 1.

STEP 1:  Calculate the reactive power R.

R = sqrt ( (Q*Q) - (P*P) )

A large reactive power R here indicates that the TC is either highly
inductive or highly capacitive,  and will have poor power factor.

STEP 2:  Now we need calculate the required PFC impedance Z to
cancel the reactive power R.

R = V * V / Z   (this is from ohms law  p = v*v/r)

rearranges to give:

Z = V * V / R

STEP 3:  Calculate the correction capacitance C to give the required
impedance Z accross the line, (just like when choosing a mains
resonant cap for a neon.)

C = 1 / 2 / pi / F / Z		(Remember C is in Farads)

The PFC capacitor should be connected as close as possible accross the
LV supply side of the step-up transformer.  You should repeat the two
measurements of supply VA and real power.  If the PFC value is correct
the real power will be the same as before,  but the supply VA should
have dropped to little more than the real power value.

I have tried to make this somewhat confusing subject of power factor as
clear as possible,  by showing the steps involved.  However I still get
confused so someone please check my maths !

I think there are simpler, "rule of thumb" type calculations around,
however this method will give "perfect" power factor correction. The
accuracy depends only on how accurately you can measure P and Q.

If you don't want to go through the maths,  try adding progressively more
and more PFC capacitance until you begin to notice very little decrease
in current drawn from the supply.  This is pretty close.  If you add too
much PFC capacitance the current will start to increase again.

Also, remember that using a PFC cap only reduces the supply cord current,
it does not make life any easier for the transformer and ballast parts.

Comments and corrections welcome,

- Richie,

- In Sunny Newcastle.

```