Phasor

A phasor is a complex number that represents the magnitude and phase angle of a sinusoidal quantity in alternating current (AC) power systems. By transforming time-varying sinusoidal waveforms into static complex numbers, phasors allow engineers to analyze steady-state AC circuits using algebraic operations instead of differential equations.

Key Aspects of a Phasor:

• Complex Representation: A phasor is written as V = |V|∠θ (polar form) or V = a + jb (rectangular form), where |V| is the RMS magnitude and θ is the phase angle relative to a chosen reference, typically the slack bus voltage or one of the phase voltages.
• Time-Domain Link: The instantaneous value of a sinusoidal signal v(t) = √2·|V|·cos(ωt + θ) is fully captured by its phasor V = |V|∠θ, because frequency ω is common to all quantities in a steady-state system and can be factored out.
• Phasor Diagrams: Graphical representations of phasors as rotating vectors in the complex plane are widely used to visualize phase relationships between voltages and currents, making it easy to see leading/lagging conditions and power factor at a glance.
• Power Calculations: Complex power S = P + jQ is computed directly from voltage and current phasors as S = V·I*, where I* is the complex conjugate of the current phasor. This compact formulation underpins all power flow analysis.
• Symmetrical Components: Phasor analysis extends to unbalanced conditions through symmetrical components (positive, negative, and zero sequence), where unbalanced three-phase phasors are decomposed into three balanced sets for fault analysis and protection design.