Owen Duffy wrote:
Considering the steady state...

If we accept the P(t) is the product of instantaneous voltage and
current, then there will be some points on any mismatched line where P(t)
is always positive. In between those points, P(t) will have positive and
negative excursions.

I think that it is a reasonable interpretation that at those points where
P(t) is always positive, then there is never at any instant, a flow of
energy away from the load, energy is never exchanged during a cycle
across those points, it always flows from source to load.

I'd make a small addition, that . . .there is never at any instant a
*net* flow of energy away from the load. . .

The problem is that I don't know of any way to keep track of a
particular bundle of energy -- it gets mixed together. So you could have
energy constantly flowing both ways through a point while maintaining a
net flow (power) in one direction and it would look just the same as
energy going only one way. Keith's DC thought experiments illustrate
these different approaches and some of their logical -- and illogical --
consequences.

Quite some time ago I wrote and made available a little graphic program
showing the voltage, current, power, and energy on lines under several
conditions. When a complete standing wave exists, there are points of
zero voltage and current and hence zero power. For one half the cycle
you can see energy moving into those points equally from both directions
(obviously being stored at the node), and during the other half, energy
is moving out of those points in both directions (being retrieved from
storage). One interpretation is that the energy arriving from the left
exits to the right, and vice-versa, and that fits neatly into the
concept of waves of energy simultaneously moving in both directions. Or
you can decide that the energy which came in from the right exits to the
right, and in from the left exits to the left. If that's your
interpretation, then you conclude that no energy ever crosses the
boundary. I think this is the genesis of Cecil's view that energy waves
somehow bounce off the standing wave node. Both interpretations fit
equally well with the observed net flow of energy but, like Keith's DC
thought experiments and Cecil's writings show, take you down quite
different paths when trying to divine some concept of what's
fundamentally happening.

. . .

Roy Lewallen, W7EL