# Two-Wattmeter Method

The two-wattmeter method is generally used for measurement of power in 3-phase, 3-wire load circuits. The current coils of two-wattmeters are inserted in any two lines, and the pressure coil is connected from its own current coil to the line without a current coil.

Let V1, V2, V3, and I1, I2, and I3 be the voltages and currents of the three loads connected across three different phases at any particular instant. Thus, the power at the instant under consideration is equal to the sum of their products, regardless of power factor.

## Measurement of Power by Two Wattmeter Method in Star Connection System

According to Kirchhoff`s first law, the algebraic sum of three instantaneous currents is Zero as all three phases meet at a star point.

since i1 is the instantaneous current flowing through the current coil  and (v1-v3) is the instantaneous potential difference across the pressure coil of wattmeter W1,

is the instantaneous power measured by Wattmeter W1

since i2 is the instantaneous current flowing through the current coil  and (v2-v3) is the instantaneous potential difference across the pressure coil of wattmeter W2,

is the instantaneous power measured by wattmeter W2.

## Measurement of Power by Two-Wattmeter Method in Delta Connection System

In delta connected system the three phases form a closed loop. According to Krichhoff`s second law,

since -v3 is the instantaneous potential difference across pressure coil and (i1-i3) is  the instantaneous current flowing through the current coil of wattmeter W1,

is the instantaneous power measured by wattmeter W1.

since v2 is the instantaneous potential difference across the pressure coil and (i2-i1) is  the instantaneous current flowing through the current coil of wattmeter W2,