AN4121

Three-phase systems

Doc ID 023243 Rev 1

20/26

If the relationship between the phase voltage and the line voltage is used, the total active

power becomes identical to

Equation 1 developed. This means that the total power in any

balanced three-phase load (

θ- or Y-connected) is given by Equation 1.

Similarly, the total reactive and the total apparent power in the three-phase balanced AC

circuits can be given by:

A.2

Power measurement techniques

In the three-phase power systems, one, two, or three wattmeters can be used to measure

the total power. A wattmeter may be considered to be a voltmeter and an ammeter

the angle between the voltage and current. Hence, a wattmeter has two voltage and two

current terminals, which have + or

θ polarity signs. Three power measurement methods

utilizing the wattmeters are described next, and are applied to the balanced three-phase AC

load.

A.2.1

Two-wattmeter method

This method can be used in a three-phase 3-wire balanced or unbalanced load system that

may be connected

θ or Y. To perform the measurement, two wattmeters are connected as

shown in

Figure 14.

Figure 14.

Two-wattmeter method in star- or delta-connected load

In the balanced loads, the sum of the two wattmeter readings gives the total power. This can

be proven in a star-connected load mathematically using the power reading of each meter

as:

θ

=

sin

I

V

3

Q

line

line

Total

line

line

Total

I

V

3

S

=