0195136047.pdf

456 AC POWER SYSTEMS

PF=P/S=cosθ (10.2.2)

whereθ=tan−^1 Q/P. Inductive loads cause current to lag voltage and are referred to as lagging

power factor loads. Conversely, capacitive loads cause current to lead voltage and are referred to

as leading power factor loads.

For a case with lagging power factor, Figure 10.2.1(a) shows voltage and current phasors;

Figure 10.2.1(b) depicts the real, reactive, and apparent powers; and Figure 10.2.1(c) gives the

power triangle. The corresponding diagrams with leading power factor are shown in Figure

10.2.2. Loads on the electric power system are generally inductive, which will cause the phase

current to lag the corresponding applied phase voltage. The real power component represents

the components of voltage and current that are in phase, whereas the reactive power component

represents the components of voltage and current that are in quadrature (that is, 90° out of phase).

The convention used for positive power flow is described with the help of Figure 10.2.3, in

which Figure 10.2.3 (a) applies to a generator (source), and Figure 10.2.3 (b) applies to a load

(sink).

The power expressions for the three-phase case, in terms of the line quantities, are (see

Section 3.2)

S ̄ 3 φ=P 3 φ+jQ 3 φ (10.2.3)

Quadrant II Quadrant I

Quadrant III Quadrant IV

V

I

(Negative)

(Lagging)

θ

Reference

(a)

Figure 10.2.1Lagging power factor.(a)Voltage and current

phasors.(b)Real, reactive, and apparent powers.(c)Power

triangle.

Quadrant II Quadrant I

Quadrant III Quadrant IV

S

θ (Positive)

(b)

Qlagging PF

Plagging PF

−P

+Q

−Q

+P

S,VA

θ

(c)

P,W

Q,VA R