MI 2892 Power Master
Theory and internal operation
161
k
k
k
t
f
k
c
c
t
u
1
1024
1
0
2
10
sin
)
(
(57)
f
1
–
frequency of signal fundamental (in example: 50 Hz)
c
0
–
DC component
k –
ordinal number (order of the spectral line) related to the frequency basis
N
C
T
f
1
1
T
N
–
is the width (or duration) of the time window (T
N
= N*T
1
; T
1
=1/f
1
). Time window is that time
span of a time function over which the Fourier transformation is performed.
c
k
–
is the amplitude of the component with frequency
1
10
f
k
f
Ck
k
–
is the phase of the component c
k
U
c,k
– is the RMS voltage value of component c
k
I
c,k
–
is the RMS current value of component c
k
Phase voltage and current harmonics are calculated as RMS value of harmonic subgroup (sg): square
root of the sum of the squares of the RMS value of a harmonic and the two spectral components
immediately adjacent to it.
n
th
voltage harmonic:
1
1
2
)
10
(
,
k
k
n
C
n
p
U
h
U
p: 1,2,3
(58)
n
th
current harmonic:
1
1
2
)
10
(
,
k
k
n
C
n
p
I
h
I
p: 1,2,3
(59)
Total harmonic distortion is calculated as ratio of the RMS value of the harmonic subgroups to the RMS
value of the subgroup associated with the fundamental:
Total voltage harmonic distortion:
2
40
2
1
n
p
n
p
p
U
h
U
h
U
THD
, p: 1,2,3
(60)
Total current harmonic distortion:
2
40
2
1
n
p
n
p
Ip
h
I
h
I
THD
, p: 1,2,3
(61)
Spectral component between two harmonic subgroups are used for interharmonics assessment. Voltage
and current interharmonic subgroup of n-th order is calculated using RSS (root sum square) principle:
n
th
voltage interharmonic:
8
2
2
)
10
,(
k
k
n
C
n
p
U
ih
U
p: 1,2,3
(62)
n
th
current interharmonic:
8
2
2
)
10
,(
k
k
n
C
n
p
I
ih
I
p: 1,2,3
(63)
