Problems in connection with three-phase star loads

It is known that the value of the power factor of a balanced three-phase load obtained by the two-wattmeter and the three-wattmeter methods are not always the same. It is known also that the ratio of the mesh voltage to the star voltage to earth is not always equal to ¿3. The author investigates the reasons for these variations and with the help of solid geometry develops a pictorial method of considering the problem. It is proved that ¿3 is the maximum value of the ratio of the mesh voltage to the potential difference between a terminal and earth. It is also proved that a star inductive load only has an equivalent mesh load when the time constants of the arms of the star load are all equal.