Civil Engineering Reference
In-Depth Information
, being for high frequency, is the average of the
subtransient inductance in the d and q axes, that is as follows:
harmonic inductance L
n
(
)
LL
′′ + ′′
d
q
L
=
(14-10)
n
2
and the reactance for the harmonic of order n is given by the following:
X
=π⋅ =π
2
f
L
2
nfL
(14-11)
n
n
n
n
where f
= n
harmonic frequency
th
n
f
= fundamental frequency.
In single-phase or three-phase AC currents having positive and negative
portions of the cycle symmetrical, the odd number of harmonics are absent.
That is, I
= 0 for n = 2, 4, 6, 8, and so on. In three-phase load circuits fed by
transformers having the primary windings connected in delta, all triple
harmonics are absent in the line currents, that is I
n
= 0 for n = 3, 9, 15, and
n
so on.
In the inverter circuit having m-pulse full bridge circuit, the harmonics
present are of the order n = mk ± 1, where k = 1, 2, 3, 4, and so on. For
example, the harmonics present in a 6-pulse inverter are 5, 7, 11, 13, 17, 19.
On the other hand, the harmonics present in 12-pulse inverter are 11, 13, 23,
25. The magnitude and phase of the harmonic currents are found to be
inversely proportional to the harmonic order n, that is as follows:
I
n
I
=
1
(14-12)
n
where I
is the fundamental current. This formula gives approximate har-
monic contents in 6 and 12-pulse inverters as given in the first two columns
of
Table 14-1
,
which clearly shows the benefits of using 12-pulse converters.
1
TABLE 14-1
Harmonic Contents of the 6-pulse and 12-pulse Converters
Harmonic
Order
n
6-Pulse
Converter
Eq. 14-12
12-Pulse
Converter
Eq.14-12
3-pulse and 6-pulse
Converters
(IEEE Standard 519)
5
20
—
17.5
7
14.5
—
11.1
11
9.1
9.1
4.5
13
7.7
7.7
2.9
17
5.9
5.9
1.5
19
5.3
5.3
1.0
