Characteristics of Measurement of Criterion Values and Adaptive - Digital Signal Processing in Power System Protection and Control - page 189

Fig. 9.12 Complex
characteristic of impedance
measurement for additive
component of frequency
f/f 1 = 2.5

X

1

0.8

0.6

0.4

0.2

0

0 0.2 0.4 0.6 0.8 1

R

From ( 9.29 )to( 9.31 ) follows that the highest measurement errors are
approximately equal to higher value of filter gains for given frequency.
The investigation results shown in Fig. 9.11 also confirm this observation.
Generally, one can say that the shape and level of deviations can be identified
with the characteristics of applied orthogonal filters. One can also notice that the
relationship between the algorithms' spectra and characteristics for additive
distortions is rather weak. It should be mentioned that the measurement errors
due to distortion components, here quite high because of assumed level of
additive components, will be much lower in reality, where expected harmonics
and other components are usually much smaller than the fundamental frequency
component.
There exist also other possibilities of presenting expected measurement errors.
For instance, in order to show both module and phase error of a complex
variable one can present the results on a plane R-X or P-Q. An example of such
a characteristic is shown in Fig. 9.12 for selected impedance measurement
algorithm and frequency of the current/voltage signals. The accurate value
amounts R = X = 0.707, whereas the measured values surround this point along
an ellipse, showing both module and argument deviations. Quite big size of the
ellipse results from relatively low frequency of the additive component and its
unit magnitude. In practice the size of the curve should always be much more
limited.
The frequency characteristics of measurement algorithms presented in this
chapter illustrate the frequency features of considered algorithms. The way of
algorithms evaluation can be further transmitted to assessment of other algorithms,
e.g. for impedance measurement. Interested reader can perform similar analyses
himself, one can also reach for available references, e.g., [ 5 , 11 ].