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capacitor voltage transformer (CVT) transients in the voltages. The device uses a combination of a 1/4 cycle filter
using 12 coefficients, a 1/2 cycle filter using 24 coefficients, and a single cycle filter using 48 coefficients. The
device automatically performs intelligent switching in the application of the filters, to select the best balance of
removal of transients with fast response. The protection elements themselves then perform additional filtering,
implemented for example, by the trip count strategy.
The following figure shows the frequency response of the 12, 24 and 48 coefficient filters, noting that all have a
gain of unity at the fundamental frequency:
E00308
Filter Response
Gain
Harmonic
Full
Quarter
Half
0 18
15
12 9 6 3
0.5
1
2
1.5
0
21
2.5
Figure 26: Frequency response of FIR filters
5.5 FOURIER SIGNAL PROCESSING
All backup protection and measurement functions use single-cycle fourier digital filtering to extract the power
frequency component. This filtering is performed on the main processor board.
When the protection and control task is re-started by the sampling function, it calculates the Fourier components
for the analog signals. Although some protection algorithms use some Fourier-derived harmonics (e.g. second
harmonic for magnetizing inrush), most protection functions are based on the Fourier-derived fundamental
components of the measured analog signals. The Fourier components of the input current and voltage signals are
stored in memory so that they can be accessed by all of the protection elements’ algorithms.
The Fourier components are calculated using single-cycle Fourier algorithm. This Fourier algorithm always uses
the most recent 48 samples from the 2-cycle buffer.
Most protection algorithms use the fundamental component. In this case, the Fourier algorithm extracts the power
frequency fundamental component from the signal to produce its magnitude and phase angle. This can be
represented in either polar format or rectangular format, depending on the functions and algorithms using it.
The Fourier function acts as a filter, with zero gain at DC and unity gain at the fundamental, but with good
harmonic rejection for all harmonic frequencies up to the nyquist frequency. Frequencies beyond this nyquist
frequency are known as alias frequencies, which are introduced when the sampling frequency becomes less than
twice the frequency component being sampled. However, the Alias frequencies are significantly attenuated by an
anti-aliasing filter (low pass filter), which acts on the analog signals before they are sampled. The ideal cut-off point
of an anti-aliasing low pass filter would be set at:
(samples per cycle)
´
(fundamental frequency)/2
At 48samples per cycle, this would be nominally 1200 Hz for a 50 Hz system, or 1440 Hz for a 60 Hz system.
The following figure shows the nominal frequency response of the anti-alias filter and the Fourier filter for a 48-
sample single cycle fourier algorithm acting on the fundamental component:
Chapter 4 - Software Design P446SV
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