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186 Decision Making Applications in Modern Power Systems
(A)
Signal maximum value instant
X rms
θ
Zero time instant
(B)
Imaginary X rms Phasor (X p)
θ
Real
FIGURE 7.3 (A) An ideal sinusoid signal and (B) phasor representation an ideal sinusoid
signal.
the rms value of the sinusoid signal. In power system, most of the signals are
corrupted with noise and other frequencies. In such cases, only the principal
frequency is considered for phasor representation. The extraction of this fre-
quency is done with Fourier transform. For discrete data, discrete Fourier
transform or fast Fourier transform is used [16].
For synchrophasor concept, consider two sinusoid signals of different
magnitude and angle as shown in Fig. 7.4A. The equivalent phasor represen-
tation of the two signals is represented in Fig. 7.4B. It can be seen that at a
