3PhasePhasorDiagram - Setting up 3-Phase Phasor diagram and demonstrating Animations Ean:= 120 volt e j 0 deg Dr M Giesselmann Ebn:= 120 volt e j 120

k 0 1 .. := E CA E an e j θ ⋅ ⋅ E cn e j θ ⋅ ⋅       := E BC E bn e j θ ⋅ ⋅ E cn e j θ ⋅ ⋅       := E AB E bn e j θ ⋅ ⋅ E an e j θ ⋅ ⋅       := E CN 10 3 − volt ⋅ E cn e j θ ⋅ ⋅       := E BN 10 3 − volt ⋅ E bn e j θ ⋅ ⋅       := E AN 10 3 − volt ⋅ E an e j θ ⋅ ⋅       := θ 0 deg ⋅ 5 deg ⋅ FRAME ⋅ + := arg E LL ( ) 30 90 − 150       deg = E LL E ab E bc E ca         := arg E ph ( ) 0 120 − 120       deg = E ph E an E bn E cn         := 1 2 1 2 + 2 1 ⋅ 1 ⋅ cos 120 deg ⋅ ( ) ⋅ − 3 = Law of Cosines applied to calculate line to line voltages: http://hyperphysics.phy-astr.gsu.edu/hbase/lcos.html Law of Cosines: The Line-Line Voltages in 3-Phase Systems are 3 larger than the line to Neutral Voltages Confirms Eq. 2.5.6., Page 59, Glover, Sarma, Overbye, 4 th ed. arg E ab ( ) 30 deg = E ab 207.85 V = E ca E cn E an − := E bc E bn E cn − := E ab E an E bn − := E cn 120 volt ⋅ e j 120 ⋅ deg ⋅ ⋅ := E bn 120 volt ⋅ e j − 120 ⋅ deg ⋅ ⋅ := E an 120 volt ⋅ e j 0 ⋅ deg ⋅ ⋅ := Dr. M. Giesselmann, Jan 18, 2008 Setting up 3-Phase Phasor diagram and demonstrating Animations: