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# displacement power factor

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## displacement power factor

(OP)
I'm looking for the correct assignment of polarity to displacement power factor for each of the four power quadrants.

### RE: displacement power factor

The power factor is defined as the cosine of the angle between the real power (kW) and the apparent power (kVA), (otherwise, the cosine of the angle by which the load current lags the bus voltage).  As I remember it, the cosine is positive in the first and fourth quadrants, negative in the second and third.

### RE: displacement power factor

There is a related issue that is always confusing and that is the terminology "lagging" and "leading" power factor.  The best way to remember this is as follows:

When reactive power is in the same direction as the real power, it is **lagging**.  When reactive power is in the opposite direction from the real power, it is **leading**.  This works for any load or generator.  So a generator operating at a power factor of 0.9 and producing vars is **lagging**.

Hope this helps.

### RE: displacement power factor

Good answers so far.

There are lots of ways to say the same thing.

The angle of S is the same as the angle of Z,
since S = VI* = V (V/I)* = VV*/(I*) = |V|^2/I  with angle of I

The horizontal axis is typically defined as real portion, vertical axis defined as imaginary portion.

Things that lie in the right half of the plane have positive power factor (as per peterb's definition). This includes loads (they have positive P = power flowing in... equivalently they have positive resistance... they may have positive or negative Q and reactance).

Things that lie in the left half of the plane have negative power factor.  This would inclde sources (they have negative P = power flowing out... equivalently negative resistance... may have positive or negative Q and reactance).

We haven't said anything about leading or lagging yet... but using dpc's recipe you see that lagging is when P and Q are both positive (top left) or both negative (bottom left).

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