Characteristics of Measurement of Criterion Values and Adaptive - Digital Signal Processing in Power System Protection and Control - page 180

(a) (b)

1.5

0.5

P, Q

R, X

P

0.4

1

R

0.3

0.5

0.2

X

Q

0

0.1

0 -0.5

0 5 10 15 20 25

0 5 10 15 20 25

n n

Fig. 9.6 Transient behavior of the algorithms without (dashed line) and with correction (solid
line) for: a power measurement, b impedance measurement

Having dynamically compensated algorithm measuring signal magnitudes and
power it is also possible to get algorithms for measurement of impedance or admit-
tance and their components. Very attractive solution appears when one synchronizes
the delays for the algorithms where it is required. Then all algorithms will start their
operation at the same instant having the same function of dynamical correction T(n).
The functions will be identical in numerator and denominator of impedance and its
components algorithms, which will allow canceling them as it is shown below:

R ð n Þ¼ 2T ð n Þ P

T ð n Þ I 2 ¼ R ;

ð 9 : 19a Þ

X ð n Þ¼ 2T ð n Þ Q

T ð n Þ I 2 ¼ X :

ð 9 : 19b Þ

It means that thanks to proper synchronization dynamically corrected algo-
rithms of impedance and its components without correction of calculated results at
consecutive samples are obtained. Impedance measurement algorithms ( 9.19a , b )
are thus the most attractive ones.
Simulation results of power and impedance measurement using presented
method are shown in Fig. 9.6 (solid line). It is seen that we can get steady state of
measurement much faster than with standard methods (dashed line). It should be
added that the delay of five samples can be further reduced even to one sample
delay, but at the cost of worse response to noise.

9.3 Frequency Characteristics of Measurement Algorithms

Frequency characteristics of protection measurement algorithms are of interest at
least for a couple of reasons. Firstly, for most of cases constant frequency of the
current and voltage signals is assumed, usually equal 50 or 60 Hz. In reality,