Keith Dysart wrote:
Is this a standard ideal voltage source ...

Let's save that discussion for later by dropping
Vs out of the example. The specific characteristics
of the source need not be known for the following
subset problem which, I believe, is the source of
our disagreement, having nothing to do with Vs.
In fact, Vs can be located one wavelength away from
Rs and steady-state conditions will be the same.
Let's take a close look at what is happening only
on each side of Rs in this previous example.

100v Vg
Gnd---Vs--x--Rs--+----45deg-50ohm---------short

The following are given:

A 100% 50 ohm environment by definition.
Reference Voltage = 100v RMS at point 'x'
Rho = 0.4472 @ 63.4 deg at point 'x'

Rho^2 = 0.2 and an ideal 50 ohm directional wattmeter
will provide the following indications.

100v Rs=50ohms Vg
------------x---/\/\/\/\/---+--------------
Pf1=125w-- Prs=100w Pf2=50w--
--Pr1=25w --Pr2=50w

These are the energy components that you say do not
balance. But I didn't see Pf1(t) or Pr1(t) in any
of your previous equations. I suggest you will
discover that the destructive interference on one
side of Rs is exactly balanced by the constructive
interference on the other side.
--
73, Cecil http://www.w5dxp.com