METREL Energy Master MI 2883, Инструкция по эксплуатации

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MI 2883 Energy Master Theory and internal operation
133
FFT
Voltage harmonics and THD
10 periods
t
n
1 2 3 4 5 6 50
U
FFT
10 periods
t
n
1 2 3 4 5 6 50
I
Uhn
Ihn
Current harmonics and THD
Figure 5.6: Current and voltage harmonics






   


k
k
k
t f
k
c c t u
 
1
1024
1
0
2
10
sin ) (
(41)
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 (42)
n
th
current harmonic:

 
 

1
1
2
) 10 ( ,
k
k n C n p
I h I p: 1,2,3 (43)