AN3157

3-phase systems

Doc ID 17105 Rev 1

19/26

Equation 5

Therefore, the phase active power and the total active power are:

Equation 6

Equation 7

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

power becomes identical to Equation 4. This means that the total power in any balanced 3-

phase load (

Δ or Y-connected) is given by Equation 4.

Similarly, the total reactive and the total apparent power in the 3-phase balanced AC circuits

can be given by:

Equation 8

Equation 9

A.2

Power measurement techniques

In 3-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 combined in the

between the voltage and current. Therefore, a wattmeter has two voltage and two current

terminals, which have + or - polarity signs. Three power measurement methods utilizing the

wattmeters are described next, and are applied to the balanced 3-phase AC load.

A.2.1

Two-wattmeter method

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

may be connected to

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

shown in Figure 14.

3

V

V

line

θ

=

=

=

=

cos

I

V

P

P

P

P

line

phase

3

2

1

θ

=

=

cos

I

V

3

P

3

P

line

phase

Total

θ

=

sin

I

V

3

Q

line

line

Total

line

line

Total

I

V

3

S

=