Phasors
The key idea
A phasor is one arrow that stands for a full sine wave. The length of the arrow is the size of the wave. The angle of the arrow is the timing of the wave. Two numbers replace an entire curve.
The idea
Everything on an AC network — every voltage, every current — is a wave that repeats 50 or 60 times each second. Drawing waves is slow, and comparing two waves by eye is hard.
Engineers use a shortcut. Picture an arrow that rotates at the system frequency, like the hand of a very fast clock running backward. Track the height of the arrow tip, moment by moment: that height traces out a sine wave — exactly the wave the arrow stands for.
Because every wave in the network rotates at the same frequency, the rotation itself carries no information. So we freeze the picture and keep just the arrow: its length (the magnitude) and its angle (the phase). That frozen arrow is the phasor.
Try it
The height of the arrow tip, moment by moment, is the wave. Grab the tip and move it — shorter arrow, smaller wave; different angle, shifted wave. That is all a phasor is: the arrow that stands for the wave.
Why it matters
- Comparing waves becomes comparing arrows. "Current lags voltage by 30°" is one glance at two arrows. On two overlapping curves, it is a careful measurement.
- Wave arithmetic becomes arrow arithmetic. Adding two waves point by point is tedious. Adding two phasors is tip-to-tail arrow addition — one triangle.
- The whole toolbox depends on it. Bus voltage angles in a power flow, the phase shift of a transformer vector group, and the 120° spacing of a three-phase system are all statements about phasors.
The software you are reading about is named after this idea.
The math, if you want itOptional — the page reads completely without it
A wave becomes a phasor by keeping only its size and its timing:
the wave, and the phasor that stands for it
v(t) = Vm sin( ωt + φ ) ⟶ V = V ∠ φ
where V is the RMS magnitude (Vm/√2) and φ is the phase angle. Formally the phasor is a complex number:
complex form
V = V ( cos φ + j sin φ ) = V ejφ
The rotation ejωt is dropped because it is common to every quantity in the network. All AC circuit laws then work with complex arithmetic exactly as they do with real numbers in DC circuits:
Ohm's law, phasor form
V = Z · I
See it in Phasor
Every voltage and current that Phasor solves is a phasor: the power flow reports each bus voltage as a magnitude in per unit and an angle in degrees. The rotating field on the Phasor home page is this exact diagram, drawn for three phases.