
Three-Phase Electric Power Systems 34-11
If the system is balanced, it is straightforward to show that (Figure 34.10)
V I V I t
V
an bn cn3
2
φ
θ ω α β
( ) ( )
= ⋅ ⋅ + ⋅ ⋅ + +
+ ⋅
cos cos
II V I t
V I V I t
⋅ + ⋅ ⋅ + + °
+ ⋅ ⋅ + ⋅ ⋅ + −
cos cos
cos cos
( ) ( )
( ) (
θ ω α
θ ω α
2 240
2 240°°
)
(34.28)
Hence, we see the second advantage to balanced three-phase systems. The three-phase instanta-
neous power is constant!
Contrast this with the single-phase instantaneous power, which is oscillatory with radian frequency
2ω. Continuing, it is straightforward to show that
S V I
S V I
V
I
V I
P V I
an a
L
L
L
L L
L L
3
3
3
3
3 3
3
3
3
φ
φ
φ