Electrical Engineering ⇒ Topic : 3-Voltmeter Method of Determining Phase Angle

3-Voltmeter Method of Determining Phase Angle

It is sometimes very convenient to determine the phase angle between two voltages V₁₂ and V₂₃with no equipment other than 3 a.c. voltmeters connected as shown in Fig. a (i). The method may be used to determine the phase angles between line voltages of 3-phase circuits by connecting the lines directly to the junctions of the voltmeter leads as shown in Fig. a (ii).

                                                                              figure (a)

By Kirchhoff's voltage law, the phasor sum of the three voltmeter readings is zero. We can thus obtain the graphical solution as shown in Fig.(B). First, the base line is drawn proportional in length to one of the voltmeter readings, in this case V₃₁. Next two arcs are drawn ; one having a radius originating at point 1 and proportional in length to V₁₂, and the other having a radius originating at point 3 and proportional in length to V₂₃. The intersection of the two arcs becomes point 2 and locates the ends of phasors V₁₂ and V₂₃. From familiar principles of trigonometry, we have

                                                figure (b)