To Whom it May Concern

MEMORANDUM

Page 29 March 2005

Page 3

9 March 2005

To:To Whom it May Concern

From:Mark Stockton - Senior Product Management Engineer

Date: 9 March 2005

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Subject:24 Sample DFT for Frequency Tracking

This document looks to explain the basic principles of the frequency tracking algorithm used by most of the Px4x relays. Slight variations exist on some products depending upon application (notably the P94x).

The frequency tracking is based upon a 1 cycle, 24 sample DFT that is used to calculate and subsequently control the time between samples. With this information and knowing the number of samples per cycle, it is possible to calculate the fundamental frequency of the system.

The DFT uses a number of formulae to actually calculate the magnitude and angle of the fundamental component of the waveform. For the purposes of the frequency tracking it is the angle calculation that is important. The DFT uses the following formulae based upon 24 samples per cycle, where k is the sample number (0 to 23):-

Based upon these equations, every other sample the peak magnitude and angle of the fundamental frequency component of the sampled waveform is calculated. Between each sample, the angular difference is calculated and used to correct the time between samples (TS) based upon the following calculation:-

This forces the sampling period to constantly re-align to 24 samples per cycle. As a by-product of this frequency tracking, we also get the fundamental frequency of the system, which is calculated as:

Additional checks are performed regarding changing of tracking channels, initial start-up procedure, validity of input waveform (amplitude), etc.. For most products (other than the P94x) a limit of 10Hz/s is placed on the change in system frequency between samples. This has been removed on the P94x to allow faster reaction to rapid changes in frequency (such as test conditions where step changes are applied).

T&D

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