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 VRY is equal to the phasor difference of ERN and EYN. To subtract EYN from ERN, reverse the phasor EYN find its phasor sum with ERN shown in the phasor diagram in Fig. (a). The two phasors ERN and E-YN are equal in magnitude (= EPh) and are 60° apart.
By geometrical method. We have used graphical method and phasor algebra to prove therelation: VL = -√Eph . 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 Eph.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.
Line voltage, VL = BD + DY
= Eph cos 30° + Eph cos 30°
= 2 Eph cos 30° = √3Eph
Hence in a balanced 3-phase Y-connected supply system
(1) Line voltage, VL = √3Eph ....... in magnitude
(2) All line voltages are equal in magnitude (i.e. = √3Eph ) but displaced 1200 from one another (See phasor diagram in Fig. (a).
(3) Line voltages are 30° ahead of their respective phase voltages.
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