Introduction

Introduction to phasors

    Introduction

Library

Modelica/Electrical/QuasiStationary/UsersGuide/Overview

Description

The purely sinusoidal voltage

v=\\sqrt{2}V_{\\mathrm{RMS}}\\cos(\\omega t+\\varphi_{v})

in the time domain can be represented by a complexrms phasor

\\underline{v}=V_{\\mathrm{RMS}}e^{j\\varphi_{v}}.

For these quasi stationaryphasor the following relationship applies:

\\begin{displaymath}v=\\mathrm{Re}(\\sqrt{2}\\underline{v}e^{j\\omega t})\\end{displaymath}

This equation is also illustrated in Fig. 1.

phasor_voltage.png
Fig. 1: Relationship between voltage phasor and time domain voltage

From the above equation it is obvious that for t = 0the time domain voltage is v = cos(φv).The complex representation of the phasor corresponds with this instance, too, sincethe phasor is leading the real axis by the angle φv.

The explanation given for sinusoidal voltages can certainly also be appliedto sinusoidal currents.

See also

AC circuit, Power, Reference system