LS Industrial Systems Metasol Series, Technical Catalogue

Page: 52 / 156

51
D
Frequency Measurement and Harmonics Calculation for P, S Type
X(k) : The complex number of k degree’s harmonics
(ex k 1 fundamental wave, k 2 : 2 harmonics)
N : Sampling cycle ( The square number of 2, 2^5, 2^6.....)
x1(m) : x(2m). m=0, 1, 2.....(N/2)-1 even variable sampled
x2(m) : x(2m+1). m=0, 1, 2.....(N/2)-1 odd variable sampled
1. Frequency Measurement
1) P and S type frequency is measured through the Zero-Crossing method based on hardware style.
2) Zero-Crossing method has a fatal disadvantage for the harmonics, hence frequency detecting circuit is arranged
by passing Low-Pass Filter to make Cut-Off under 100Hz.
3) Frequency ensures the accuracy from 45Hz to 65Hz.
4) The corresponding Hardware Circuit operates at R phase voltage.
5) Frequency detection operates when R phase voltage which is input into voltage dividing module is more than
80V at least. For the voltage below the value, the operation could be unstable and it indicates a frequency with
‘0 ‘Hz in case the voltage value is below 50V.
2. Harmonics Calculation
1) S type can measure the 63 rd degree harmonics through 128 samplings per cycle.
2) Harmonics spectrum bar on display indicates values up to 31 st degree, and the detailed value of harmonics
includes all values up to 63 rd degree.
3) Frequency spectrum bar and the value of THD is indicated when R, S, T phase turns over.
4) It displays the shape of waveform used for harmonics analysis after capturing the waveform as it is.
5) For 3P 4W type harmonics are analyzed with phase-to-phase voltage and for 3P 3W harmonics are analyzed
with line-to-line voltage.
X(k) = x
1
(
m)W
N / 2
+
W
N
x
2
(
m)W
N / 2
Σ
N
2
- 1 ( )
m= 0
Σ
N
2
- 1 ( )
m= 0
mk mk k
W
N / 2
= e = cos( ) - j sin( )
2
π
N / 2
km - j ( )
2π km
N / 2
2π km
N / 2
mk
Low-Pass
Filter
Analogue Signal
Digital Signal
CPU Comparer
Digital Trip Relay
5. Measurement Function