On Jun 29, 10:13*am, Cecil Moore wrote:
On Jun 28, 5:33*pm, Keith Dysart wrote:

Do you reject *P(t)=V(t)*I(t) ?

I certainly reject as a moronic method for attempting to track
instantaneous energy.

Dodging the question again! It is not that hard.

I agree completely. And my analysis does successfully track all the
energy at all times.

That is obviously false. You have tracked the *power* after assuming a
one-to-one correspondence between power (watts) and energy (joules).
Your assumption is most likely false. You usually cannot use
instantaneous watts to track joules within a fraction of a cycle.

Of course you can. It is just like water flowing from multiple pipes
in to a tank. The sum of the instantaneous flows is exactly equal
to the rate at which the volume of water is increasing in the tank.

Not hard at all.

If
the voltage and current are out of phase, some of the joules are
occupied as reactive power, and not available as watts of real power.

Mostly true. But this is accurately accounted for by using the
instantaneous voltage and current and not the RMS. This is an
important difference expressed in

P(t) = V(t) * I(t)

and why I do not use

Pavg = Vrms * Irms

which has all the problems you mention.

Why do you think the power companies spend so much money trying to
balance the power factor?

Not for this reason. The energy meter at my house accurately
measures the power (using P(t) = V(t) * I(t)) and integrates
so that they bill me for the energy I have used. And so they do.

Poor power factor does not affect this, but increases the losses
experienced by the power company when delivering the energy to me.
They want the customer to pay for these losses so they monitor
VAR.

....Keith