Amprobe ACD-30P Podręcznik użytkownika - Strona 8

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Notes on Displacement Power Factor & True Power Factor

●Introduction: Power is the rate of change of energy with respect to time (in terms of

voltage V and current A). Instantaneous (real) power w = vi where v is the instantaneous

voltage and i the instantaneous current. The average (real) power is the mean of vi and

is given by:

W = ω/2π∫vi dt , over the interval from 0 to 2π/ω

●Displacement Power Factor (more traditional): Assuming V and A are pure

sinusoidal waveforms without harmonics (as in most traditional cases), that is, v = V sin

ωt and i = I sin (ωt -θ), the expression can be simplified to:

W = 1/2 x V x I x Cosθ where V and I are the peak values, θ is the displacement

power factor angle, and Cosθ is the displacement power factor. Using RMS values, it is

written as:

W = V

x A

rms

Practically, in such cases without harmonics, θ is also called the phase-shift angle of

the current A to the voltage V. An inductive circuit is said to have a lagging power factor

since current A lags voltage V (phase-shift angle θ and thus Sinθ are both "+"), and a

capacitive circuit is said to have a leading power factor since current A leads voltage V

(phase-shift angle θ and thus Sinθ are both "-").

●True Power Factor (encountering harmonics): When encountering distorted

waveforms with the presence of harmonics, however, the simplified power expression

should not be used since substituting the above mentioned pure sinusoidal V and A

functions cannot fulfill the actual conditions. Cosine of phase-shift angle (Cos

displacement power factor, is no longer the only component constituting the overall

power factor. Harmonics do increase apparent power and thus decrease the overall

power factor. That is, the True Power Factor is actually affected by both phase-shift

angle and harmonics, and is given by the expression:

True Power Factor (PF) = Real Power (V

)

trms

In order to improve overall system power factor, nowadays power-system engineers

need to address both phase-shift and harmonics problems. Practically, harmonics

should be dealt with (e.g. filtering out) before phase-shift to be corrected (e.g. installing

capacitors in parallel with inductive loads).

Power function

Set the slide-switch function-selector to the Power position.

●Default at last selected function. Press SELECT button momentarily selects between

W (real power), VAR (reactive power) & VA (apparent power) measurement functions.

x Cosθ

rms

x A

x Cosθ)/Apparent Power (V

rms

), or the

trms