0195136047.pdf

4.3 MEASUREMENT OF POWER 209

A

B

C

Potential coil

Current coil

Three-phase

load

Single-phase

wattmeter WC

Single-phase

wattmeter WA

+−

+−

+−

+−

Figure 4.3.1Connection diagram for two-wattmeter method of measuring three-phase power.

The significance of the algebraic sum will be realized in the paragraphs that follow. Two wattmeters
can be connected with their current coils in any two lines, while their potential coils are connected
to the third line, as shown in Figure 4.3.1. The wattmeter readings are given by

WA=VAB·IA·cosθA (4.3.2)

whereθAis the angle between the phasorsV ̄ABandI ̄A, and

WC=VCB·IC·cosθC (4.3.3)

whereθCis the angle between the phasorsV ̄CBandI ̄C.
The two-wattmeter method, when applied to thebalancedloads, yields interesting results.
Considering either balanced wye- or delta-connected loads, with the aid of the corresponding
phasor diagrams drawn earlier for the phase sequenceA–B–C(Figures 4.2.2. and 4.2.3), it can be
seen that the angle betweenV ̄ABandI ̄Ais (30°+φ) and that betweenV ̄CBandI ̄Cis (30−φ),
whereφis the load power factor angle, or the angle associated with the load impedance. Thus,
we have

WA=VLILcos(30°+φ) (4.3.4)

and

WC=VLILcos(30°−φ) (4.3.5)

whereVLandILare the magnitudes of the line-to-line voltage and line current, respectively.
Simple manipulations yield

WA+WC=

√

3 VLILcosφ (4.3.6)

and

WC−WA=VLILsinφ (4.3.7)

from which,

tanφ=

√

3

WC−WA

WC+WA

(4.3.8)