Electrical Engineering ⇒ Topic : Relation between line voltage and phase voltage

Relation between line voltage and phase voltage. Considering the lines R and Y, the line voltage V_RY is equal to the phasor difference of E_RN and E_YN. To subtract E_YN from E_RN, reverse the phasor E_YN find its phasor sum with E_RN shown in the phasor diagram in Fig. (a). The two phasors E_RN and E_-YN are equal in magnitude (= E_Ph) and are 60° apart.

                                                                figure (a)

By geometrical method. We have used graphical method and phasor algebra to prove therelation: VL = -√E_ph . The same result can also be obtained bygeometrical method as shown in  . (b). The distance of the neutral N to any line R, Y or B represents the phase voltage E_ph.The triangle RYB will be an equilateral triangle with N at the centre of the triangle. The sides of this triangle represent the three line voltages. It is clear that if we produce RN, it will bisect the 120° angle as well as the base BY.

                                            figure (b)

Line voltage, V_L = BD + DY

                           = E_ph cos 30° + E_ph cos 30°

                           = 2 E_ph cos 30° = √3E_ph

Hence in a balanced 3-phase Y-connected supply system

(1) Line voltage, V_L = √3E_ph                   ....... in magnitude

(2) All line voltages are equal in magnitude (i.e. = √3E_ph ) but displaced 120⁰ from one another (See phasor diagram in Fig. (a).

(3) Line voltages are 30° ahead of their respective phase voltages.