SIEMENS
SINAMICS DCM
Engineering information
Harmonics
5/28
Siemens D 23.1 · 2014
5
■
Overview
Line-side harmonics produced by converter units in a
fully-controlled three-phase bridge circuit B6C and
(B6)A(B6)C
The majority of converter units for medium-power applications
have a fully-controlled three-phase bridge circuit. Below is an
example of the harmonics that can be found in a typical system
configuration for two firing angles (
α
= 20° and
α
= 60°).
The values have been taken from a previous publication,
"Oberschwingungen im netzseitigen Strom sechspulsiger
netzgeführter Stromrichter (Harmonics in the Line-Side Current
of Six-Pulse, Line-Commutated Converters)" by H. Arremann
and G. Möltgen, Siemens Research and Development Division,
Volume 7 (1978) No. 2, © Springer-Verlag 1978.
In addition, the formulas are specified which, depending on
the actual operating data in use, line supply voltage (no-load
voltage
V
V0
, line frequency
f
N
, and DC current
I
d
), can be used
to calculate the short-circuit power
S
K
and armature inductance
L
a
for the motor to which the specified harmonics spectrum
applies.
If the actual line short-circuit power and/or actual armature
inductance deviate from the values calculated in this way, then
they will need to be calculated on a case-by-case basis.
The harmonics spectrum shown below is obtained if the values
for the short-circuit power
S
K
at the point where the unit is con-
nected and the armature inductance
L
a
of the motor, calculated
using the following formulas, match the actual values of the plant
or system. If the values do not match, the harmonics will have to
be separately calculated.
The fundamental component of current
I
1
as a reference variable
is calculated using the following formula:
I
1
=
g
×
0.817
×
I
d
I
d
DC current of the operating point being investigated
g
Basic fundamental content
The harmonics currents calculated according to the table only
apply for:
a) Short-circuit power
S
K
at the point where the converter
unit is connected
S
K
=
V
V0
2
/
X
N
(VA)
where
X
N
=
X
K
–
X
D
= 0.03536
×
V
V0
/
I
d
– 2
π
×
f
N
×
L
D
(
Ω
)
V
V0
No-load voltage at the point where the converter unit is
connected in V
I
d
DC current of the operating point being investigated in A
f
N
Line frequency in Hz
L
D
Inductance of the commutating reactor being used in H
b) Armature inductance
L
a
L
a
= 0.0488
×
V
V0
/(
f
N
×
I
d
) (H)
If the actual values for the short-circuit power
S
K
and/or armature
inductance
L
a
deviate from the values calculated using the
formulas above, a separate calculation will need to be made.
Example
:
Let us assume a drive with the following data:
V
V0
= 400 V
I
d
= 150 A
f
N
= 50 Hz
L
D
= 0.169 mH (4EU2421-7AA10) with
I
LN
= 125 A
where
X
N
= 0.03536
×
400/150 – 2
π ×
0.169
×
10
–3
= 0.0412
Ω
The following short-circuit power of the line supply required at
the point where the converter is connected:
S
K
= 400
2
/0.0412 = 3.88 MVA
and the following armature inductance of the motor required:
L
a
= 0.0488
×
400/(50
×
150) = 2.0 mH
The harmonics currents
I
ν
(with
I
1
=
g
×
0.817
×
I
d
for firing
angles
α
= 20° and
α
= 60°) that can be taken from the tables,
only apply for the values
S
K
and
L
a
that have been calculated in
this way. If the actual values deviate from these, a separate
calculation will have to be made.
For the purpose of dimensioning filters and compensation
equipment with reactors, it is only possible to draw on the
information provided by the harmonic values calculated in this
way if the calculated values
S
K
and
L
a
match the actual drive
values. In all other cases, a separate calculation will have to be
made (this particularly applies when using compensated motors
as they have very low armature inductance levels).
n
I
ν
/
I
1
at
α
= 20°
fundamental factor
g
= 0.962
at
α
= 60°
fundamental factor
g
= 0.953
5
0.235
0.283
7
0.100
0.050
11
0.083
0.089
13
0.056
0.038
17
0.046
0.050
19
0.035
0.029
23
0.028
0.034
25
0.024
0.023
29
0.018
0.026
31
0.016
0.019
35
0.011
0.020
37
0.010
0.016
41
0.006
0.016
43
0.006
0.013
47
0.003
0.013
49
0.003
0.011
© Siemens AG 2014