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Notes on Displacement Power Factor & Total 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

sinωt 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

rms

x A

rms

x Cosθ

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 “-”).

●Total 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

), or the 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 Total Power Factor is actually

affected by both phase-shift angle and harmonics, and is given by the expression:

Total Power Factor (PF) = Real Power (W) / Apparent Power (VA)

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

needs 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.