ELC-32

Power factor

pf = P/S = cosφ for linear sinusoidal loads.

Reading speed

PowerIEEE 1459

Governing equation

\mathrm{pf}=P/S=\cos\varphi

$Q \in \left[-1500, 1500\right]$

where

P: Active power (kW)
Q: Reactive power (kvar)
S: Apparent (kVA)
\mathrm{pf}: Power factor (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\mathrm{pf}=P/S=\cos\varphi

$Q \in \left[-1500, 1500\right]$

$Q = -1500$ $S = 0.053$

Along the curve

②

Domain of the variable — blue

Q_{\min} = -1500,\quad Q_{\max} = 1500

$Q \in \left[-1500, 1500\right]$

$Q = -1500$ $Q = -1500$

Along the curve

③

Response curve — green

\mathrm{pf}=P/S=\cos\varphi

$Q \in \left[-1500, 1500\right]$

$Q = -1500$ $S = 0.053$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}S}{\mathrm{d}Q}

$Q \in \left[-1500, 1500\right]$

$Q = -1481.1$ $S^{\prime} = 3.63\times 10^{-5}$

Along the curve

Lecture brief

Historical brief

Ohm (1827), Kirchhoff (1845) and Maxwell’s circuit reduction still run every board: RLC transients, transformers, skin effect and three-phase power. The sheets are those network laws, not a SPICE deck. This sheet (ELC-32 — Power factor) is the form associated with IEEE 1459. Working symbols: $P$ , $Q$ $\rightarrow$ $S$ , $\mathrm{pf}$ . Apparent power S = VI is the hypotenuse of the P–Q triangle. A lagging pf means inductive Q.

Purpose

Purpose: compute

S

\mathrm{pf}

from

P

Q

in Electrical via

\mathrm{pf}=P/S=\cos\varphi

pf = P/S = cosφ for linear sinusoidal loads. Use it when a real electrical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

P = 80.000\,\mathrm{kW}

Q = 40.000\,\mathrm{kvar}

, the governing relation

\mathrm{pf}=P/S=\cos\varphi

yields

S = 89.44\,\mathrm{kVA}

\mathrm{pf} = 0.8944\,\mathrm{—}

. A P–Q triangle, a pf cosine, a φ arc. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Active power P80 kWReactive power Q40 kvar

Outputs

Apparent S89.44 kVA
Power factor \mathrm{pf}0.8944 —

Reading speed

Watch on YouTube

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Narration of this film

A P–Q triangle, a pf cosine, a φ arc.

Apparent power S = VI is the hypotenuse of the P–Q triangle. A lagging pf means inductive Q.

Reading speed

Watch on YouTube