Types of AC power P, Q, S and PF

[RoGeorge]

Latest QUCS 0.0.20 simulator includes a type of probe for measuring power.

I was trying to understand how it works, so I fed the power probe with two AC sources, one for current and the other for voltage.  Both I and V sources are the same frequency, but with the phase angle between them adjustable.

The AC current source I1 has 1.2A RMS and the AC voltage source V1 has 1.5V RMS.  The phase of the voltage relative to current, Ph, is swept between -180 and 180 degrees.



PF (dimensionless) - power factor, yellow trace
P (W) - active power, red trace
Q (VAR) - reactive power, blue trace
S (VA) - apparent power, magenta trace

I was expecting the apparent power S to change with the phase, too, just like the others.

Why is S constant no matter the phase between V and I? 

[HackedFridgeMagnet]

I was expecting the apparent power S to change with the phase, too, just like the others.

Why is S constant no matter the phase between V and I? 

? The definition of apparent power is Vrms * Irms if you ignore the phase difference.
So it will be flat and not vary with phase.

[WattsThat]

VA = Volts * Amps

Phase angle does not mater, Cos/PF always equals one. Think DC. P = E *I.

[RoGeorge]

Now it makes sense, thank you!
At first I thought it was a software bug.   

Easy to agree S should be constant even intuitively, without pencil and paper if I visualize the triangle of powers:


Source:  https://en.wikipedia.org/wiki/AC_power

From the simulation plot, P and Q behave like two quadrature sinusoidal signals when varying the angle between I and V, but P and Q are always perpendicular, which forces S to stay constant.

S will rotate while varying the angle between I and V, but the length of the S vector will stay the same.

[T3sl4co1l]

Pythagorean identity.  Take the magnitude of S = P + iQ.

Tim

[RoGeorge]

Trivial indeed when it's put like that.   

But still, some aspects of AC power are very bamboozling and counter intuitive, IMHO.  For example, the max power transfer.  If we have a given voltage source of a fixed voltage and a fixed internal resistance, then the maximum active power can be extracted only when the load is the same resistance with the internal resistance of the voltage source.  That given said, when the R load is different from the source's internal R, there's no way to extract the max possible power in DC.

However, in AC we can make a trick and push in any load the max possible active power a source can deliver.  We call this impedance matching, and it's done by adding some reactive elements to the circuit, in order to match the impedance between the source and the load.  Since reactive elements does not dissipate any active power, all the active power a source can deliver will end up into the load.  This wouldn't be possible in DC.

If we step back and take a bird's eye view about maximizing the transfer of active power, say for example lighting up an incandescent light bulb, that's quite intriguing:  If it's DC power then it's not possible to push the max available power into an arbitrary load.  But wiggle that power up and down to make it AC, and suddenly there's a way to push the max available power in any load!   

One can not disobey the laws of physics, but can circumvent them.