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

Daniel
 
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 3phase Yconnected 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 120^{0} from one another (See phasor diagram in Fig. (a). (3) Line voltages are 30° ahead of their respective phase voltages.  
 
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