0195136047.pdf

10.2 SINGLE- AND THREE-PHASE SYSTEMS 457

Quadrant II Quadrant I

Quadrant III Quadrant IV

V

I

(positive)

(leading)

θ

Reference

(a)

Figure 10.2.2Leading 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(negative)

(b)

Qleading PF

Pleading PF
−P

+Q

−Q

+P

S,VA

θ

(c)

P,W

Q,VA R

where

P 3 φ=

√

3 VLILcosθP (10.2.4)

Q 3 φ=

√

3 VLILsinθP (10.2.5)

S 3 φ=

√

3 VLIL=

√

P 32 φ+Q^23 φ (10.2.6)

+

−

I

V

SVI*PjQ==+

(a)

+

−

I

V

SVI*PjQ==+

(b)

Figure 10.2.3Convention for positive power flow.(a)Generator case. IfPis positive, then real power is

delivered. IfQis positive, then reactive power is delivered. IfPis negative, then real power is absorbed. If

Qis negative, then reactive power is absorbed.(b)Load case. IfPis positive, then real power is absorbed. If

Qis positive, then reactive power is absorbed. IfPis negative, then real power is delivered. IfQis negative,

then reactive power is delivered.