Measurement Algorithms for Digital Protection - Digital Signal Processing in Power System Protection and Control - page 161

Fig. 8.9 Relative error of
frequency measurement for
Example 8.17

0.03
Δ [] Hz

0.02

0.01

0

-0.01

-0.02

-0.03

45 50 55

fH []

frequency. When the real value of frequency amounts to 48 Hz the measured
frequency deviation is:

¼ 1 : 99866

Df ¼ 100
p

48p
100

cos

and for f md = 45 Hz:

¼ 4 : 979 :

Df ¼ 100
p

45p
100

cos

Therefore one gets:

D 48 ¼ f 1 þ Df f md ¼ 50 1 : 99866 48 ¼ 0 : 00234 Hz

D 45 ¼ 50 4 : 979 45 ¼ 0 : 021 Hz

The course of this error as a function of measured frequency is shown in
Fig. 8.9 .

8.2.6 Filtering of Symmetrical Components

Transformation of three phase sinusoidal variables to symmetrical components is
realized according to known matrix equation of complex variables:

x 012 ¼ S x L1L2L3 ; ð 8 : 159 Þ

h i T

where x L1L2L3 ¼ x L1 ; x L2 ; x L3 is a vector of three phase sinusoidal variables,

h i T

x 012 ¼ x 0 ; x 1 ; x 2 is a vector of symmetrical components, i.e., zero, positive and

negative sequence components.