3-phase systems

AN3157

18/26

Doc ID 17105 Rev 1

A.1

Power in 3-phase AC circuits

Let's assume that the angle between the phase voltage and the phase current is

θ, which is

equal to the angle of the load impedance. Considering the load configurations given in

Figure 13, the phase power and the total power can be easily estimated.

In the case of Figure 13 (a), the total active power is equal to three times the power of one

phase:

Equation 1

Equation 2

Since the line current in the balanced delta-connected loads is:

Equation 3

If Equation 3 is substituted into Equation 2, the total active load becomes:

Equation 4

Figure 13.

Per-phase powers in (a) delta-connected load and (b) wye-connected load.

θ

=

=

=

=

cos

I

V

P

P

P

P

phase

line

3

2

1

θ

=

=

cos

I

V

3

P

3

P

phase

line

Total

phase

line

I

3

I

=

θ

=

cos

I

V

3

P

line

line

Total