Page 202 - Decision Making Applications in Modern Power Systems

Adaptive estimation and tracking of power quality disturbances Chapter | 6 165

analytic signal gives phase spectrum. From these spectrums, features, such as
standard deviation of amplitude, standard deviation of phase, and signal
energy, are extracted. For a real-valued signal a(t), the HT is defined by the
principal value integral [23].

1N
1 ð aðt Þ
0
bðtÞ 5 dt 0 ð6:42Þ
π t 2 t 0
2N
cðtÞ 5 aðtÞ 1 jbðtÞ 5 dðtÞexpðjθðtÞÞ ð6:43Þ
where d(t) and θ(t) are, respectively, the amplitude and phase of analytic
function whose expressions are as

p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
dðtÞ 5 a ðtÞ 1 b ðtÞ ð6:44Þ
2

bðtÞ
θðtÞ 5 arctan ð6:45Þ
aðtÞ
The instantaneous frequency is then defined by ω(t) 5 dθ(t)/dt. Both the
instantaneous amplitude and the instantaneous frequency are the function of
time which can be calculated for every IMF at every time-step.

6.3.3 Artificial neural network
In various power system applications and for PQ event classification pur-
pose, the artificial neural network has been mostly utilized. Data clustering,
classification, function approximation, and optimization are the capabilities
of ANN technique [24]. The methodologies that are based on ANN have
been proved efficient for resolving the problems in real time. The patterns
are regularly used based on learning from examples for the classification.
For each type of ANN, the learning rules are different until they are able to
recognize pattern features from a set of training data, and on the basis of fea-
tures, it uses to classify the new data. The capabilities of self-tuning and
self-learning are the salient features of ANN. Fig. 6.6 shows architecture of
ANN. The ANN is flexible, which can be used in real-time applications for
the classification of PQ events [25].

6.3.4 Probabilistic neural network classifier

A PNN is a kind of feed-forward neural network, which is suitable for classi-
fication and pattern recognition problems [26]. This model is composed of
two layers, that is, the radial basis layer and the competitive layer. The
operations are organized into a multilayered feed-forward network with four
layers, followed by input layer, hidden layer, pattern layer, and output layer,
which is shown in Fig. 6.7.