Networks of Networks: The Last Frontier of Complexity by Gregorio D'Agostino & Antonio Scala

Author:Gregorio D'Agostino & Antonio Scala
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(8.3)

As the voltage and current have the sinusoidal form at steady state, it is convenient to express the magnitude and phase angle of the voltage in a complex number form called a phasor. A phasor is developed using the Euler’s identity as follows:

(8.4)

The terms and are the real and imaginary parts and they are denoted by and , respectively. Therefore, the voltage and current can be written in the phasor form as follows

(8.5)

(8.6)

Since both the voltage and current have the same frequency, the component becomes less important, and for convenience it is enough to express the voltage and current in terms of their magnitude and phase shift using the following form

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