symbolic dynamic models for highly varying power system loads

15
Fractional occurrence: Fractional occurrence is the ratio of frequency of a word to the
total number of words in that dictionary. ƒ xi denotes the fractional occurrence of i th word
in dictionary X.
Common signal index (CSI): The common signal index is a measure of distortion in two
signals. A separate two-dimensional array is formed by taking all the common words and
their frequencies in both dictionaries. For these common words, a common signal index
is defined by using the fractional occurrences of the words in both dictionaries. The
following five CSIs are considered,
CSI 1 = ∑
i=
1
CSI 2 = ∑
i=
1
N
CSI 3 = ∑
i=
1
N
CSI 4 = ∑
i=
1
N
CSI 5 = ∑
i=
1
(ƒ xi *ƒ yi )/(ƒ xi +ƒ yi )
(ƒ xi *ƒ yi )/(1+⎥ƒ xi -ƒ yi ⎥)
⎥ƒ xi -ƒ yi ⎥/(1+ƒ xi +ƒ yi )
(ƒ xi *ƒ yi )/(1+ƒ xi +ƒ yi )
(ƒ xi *ƒ yi )/(ƒ xi +ƒ yi +ƒ xi *ƒ yi )
where N is the total number of different words in the common dictionary.
Considering the results of various synthetic tests to be described in Chapter 3,
CSI 1 was found to be the most appropriate. Therefore all the other CSIs were used only
for comparative purposes in connection with synthetic tests.
2.3 Coding a signal in Symbolic Dynamics