Roger Sparks wrote:

I can see why you find "no power" at the zero voltage point, but does that imply that there is no energy flow and no power from every perspective? As I write, I am struggling how to clearly differentiate between "power" as "work done" and energy as "capacity to do work", and what "network" are we defining.

Power at a particular point on the line is the rate of energy flow past
that point. It does no imply that any work is done anywhere, since any
energy flowing past the point can be stored. That is, in fact, exactly
what happens with the open circuited line in my analyses and illustrated
with TLVis1. You can see from the TLVis1 demo 4 that power is present at
all times and places along the line except a few select points. No work
is being done; energy is simply moving back and forth along the line and
between the E and H fields.

. . .

I personally define power as a state/condition where "work 'is being' done", . Power must act over time and have a physical movement component. Voltage by itself does not fulfill this definition because no movement is observed. Current is movement, voltage is only an indication of where a concentration of charges is found.

Of course you're free to define anything in any way you choose. But
you've chosen a definition that's different from the one accepted in all
of electrical circuit analysis and all textbooks. So you can expect to
have a good deal of difficulty communicating with people who are
acquainted with the universally understood definition and assume that's
what you mean, rather than your own personal definition. To them, power
is the time rate of energy flow, dE/dt, period.

. . .

Roy Lewallen, W7EL