Keith obviously understands the requirements for energy flow, but a
casual reader might draw the wrong conclusions. . .

Keith Dysart wrote:
. . .

This is quite incorrect. Energy flows must balance, otherwise energy
is being created or destroyed to sustain a difference in flow.

On the average, yes. But not moment-by-moment. Energy can be stored and
retrieved from storage, resulting in unequal energy flow (power) into
and out of a point. For a while. This was explicitly stated earlier when
discussing a capacitor, but I think it's important to make the
distinction here between instantaneous and average requirements. In
steady state, the average condition (energy flow balance) must be met
each cycle. That is, the total energy into a node over a cycle has to
equal the energy out of a node over a cycle.

. . .

Unfortunately wrong. Energy flows must balance as well. Otherwise,
energy is coming from nowhere to sustain the flow.

Ditto.

. . .

Yes, indeed. At that instant, zero energy is flowing from the inductor
to the capacitor. But very soon, energy will be flowing from the
capacitor to the inductor. The balance is that the energy flowing
out of the capacitor is always and exactly equal to the energy flowing
in to the inductor. That is the energy flow balance. The only way for
this not to be true is for energy to be created or destroyed.

Ditto.

. . .

Instead, think that at every instant, the energy flow between the
entities in the experiment must balance.

No, it doesn't, unless I'm misunderstanding the statement. At a given
instant, more energy can flow into a component (e.g., a capacitor or
inductor) than is flowing out, or vice-versa. But in steady state,
whatever flows in during one part of the cycle must flow out during the
remainder of the cycle.

Every time one of your instantaneous power curves crosses the zero
axis, power has been destroyed. Every time one of your instantaneous
power curves reaches a peak, power has been created.

I think you may be confused because you are only looking at the
flow in and out of a single entity. This is clearly not conserved.
Nor for that matter is the energy within that entity. It is the
total energy within the system that is conserved, just as it is
the total of the flows of energy between the entities within the
system that must be conserved.

Put more strictly: The sum of all the energy flows in to all of
the entities within the system must equal the energy flow in to
the system.

Again, only on an average or steady-state cycle-by-cycle basis. Great
inequalities can exist for shorter periods.

. . .

Like Keith, I firmly believe that an instantaneous time-domain analysis
is essential in understanding what really happens to the energy in an AC
system. Averaging reduces the amount of information you have -- if all
you know is the average value of a waveform, you have no way of going
back and finding out what the waveform was, out of an infinite number of
possibilities. If averaging is to be done, it should be done after you
calculate and understand what's going on at each instant, not before you
begin the analysis.

But it's also essential to make absolutely clear what conditions must be
met every instant, such as p(t) = v(t) * i(t), and which must be met
only on the average, such as energy in = energy out.

Roy Lewallen, W7EL