Page 72 - Power Quality in Electrical Systems

Harmonics and Interharmonics 55

Truncated square wave
1.5
1

0.5

0
−0.5

−1

−1.5
0 0.005 0.01 0.015 0.02 0.025 0.03
Figure 4.15 A truncated square wave Fourier series result with first, third, fifth, and
seventh harmonics. The THD is 41.4 percent.

Example 4.2: Neutral current in three-phase systems. In this example, we’ll
show that the neutral current in three-phase systems with balanced
linear loads is zero. Shown in Figure 4.16a is a balanced three-phase
system with linear resistive loads. The three-phase voltages have the
form:

5 Vsin svtd
v an
v bn 5 Vsinsvt 2 1208d
v cn 5 Vsinsvt 2 2408d

, v , v ) is the phase voltage to neutral.
where each of the voltages (v an bn cn
The phase currents are:
V
i 5 a b sinsvtd
a
R
V
i 5 a b sinsvt 2 1208d
b
R
V
i 5 a b sinsvt 2 2408d
c
R
The neutral current is the vector sum of the three-phase currents.

V
i 5 i 1 i 1 i 5 a b[sinsvtd1 sinsvt 2 1208d 1 sinsvt 2 2408d] 5 0
a
n
b
c
R