# Measurement of Power in Three Phase Systems

Power in three-phase loads may be measured by the following methods :

### One-wattmeter method for a balanced load

Wattmeter connections for both star and delta are shown in Fig.

Total Power = 3 × wattmeter reading

### Two-wattmeter method for balanced or unbalanced load

A connection diagram for this method is shown in Fig for a star-connected load. Similar connections are made for a delta-connected load.

Total power = sum of wattmeter readings

= P1+ P2

The power factor may be determined from:

$\tan \phi=\sqrt{3}\left(\frac{P_1-P_2}{P_1+P_2}\right)$

It is possible, depending on the load power factor, for one wattmeter to have to be ‘reversed’ to obtain a reading. In this case it is taken as a negative reading.

### Three-wattmeter method for a three-phase, 4- wire system for balanced and unbalanced loads

Total power = P1 + P2 + P3

Advantages of three-phase systems over single-phase supplies include:

For a given amount of power transmitted through a system, the three-phase system requires conductors with a smaller cross-sectional area. This means a saving of copper (or aluminium) and thus the original installation costs are less.

Three-phase motors are very robust, relatively cheap, generally smaller, have self-starting properties, provide a steadier output and require little maintenance compared with single-phase motors.