Andrew,
I have another qeustion after read your web page. When you demostrate
the concepts, your were using the areas of the curve. The areas (red,
grean), i think, are energes. And, I feel it can be decuded from your
tratement, that
VAH = kWh + kvarh (1)
where,
* kWh is (red area) - (green area)
* kvarh = (green area)
* VAH = (red area)
Am I right?
No. It's simply red area is energy drawn from supply (quadrants I and
III in your original post), and green is energy returned to supply
(quadrants II and IV in your original post). So red includes
both real and reactive energy draw, but green can only be reactive.
Since the reactive energy returned to the supply (green) will be
same as reactive energy drawn from supply, you can assume that a
part of the red area equal in size to the green area is also reactive
energy, and the remainder of the red is real power. However, it
doesn't make any sense to try and identify that part because you can't
sensibly say which particular bit of the energy drawn from the supply
(red) is reactive and will be returned, verses another bit of the red
which is not reactive and will be burned in the load. i.e. at a phase
angle of 60° (PF=0.5), 1/3rd of the red area is reactive and 2/3rds
is real, but there's no way to say which of the red pixels is reactive
or which is real.
So:
Wh is fixed in this example. It's same as red area at phase angle = 0.
VAh will be red + green.
VArh will be 2*green.
However, we know
S^2 = P^2 + Q^2 (2)
where, S is apparent power, P is real power or true power, Q is reactive
power.
That comes from the vector diagram equalatral triangle.
It should be same result, but at 01:05 in the middle of the night
here, I can't immediately think how you could prove it.