**Two wattmeter method **

In this article, we are going to explain a method used in electrical systems to measure quantities, which is the two-wattmeter method.

It is simply a method used at the 3phase load to measure the overall power, this is not a simple process, and we need to connect two wattmeters at the 3phase wire in two connections such as star and delta.

In this post, we try to explain some of the pieces of information about the two wattmeter methods.

**The two wattmeter method is applicable for **

Two wattmeter method is applicable for the 3 phase, 3 wire star or delta connected the balanced or unbalanced load.

- And the two-wattmeter method is used to measure the power at these connections.
- The wattmeter consists of two coils, which are the current coil and pressure coil.
- The two of the wattmeters are well connected in a way that, the current coil of the wattmeter is connected with any two lines say R and Y.
- And the potential coil of each wattmeter is joined on the same line or connected across the load circuit.

**Two wattmeter method of power measurement **

For to measure the power on the two wattmeter method, we need to consider both the two wattmeter connections, which are star and delta connections.

**Star connection**

A star connection of two wattmeter method, wattmeter one produce phase current and voltage difference……..** (V _{2}-V_{3})**

And at the same time, wattmeter two produce current and voltage…….. **(V _{2}-V_{3})**

The total sum of power is,

**P= P _{1} + P_{2} = I_{1} (V_{1} + V_{2}) + I_{2} (V_{2}-V_{3})**

**Delta connection**

At two wattmeter delta connection, the wattmeter one can be

**P _{1} = -V_{3} (I_{1} – I_{3})**

And also wattmeter two will be,

**P _{2} = -V_{2} (I_{2} – I_{1})**

Total power is,

** P= P _{1} + P_{2} = V_{2} I_{2} + V_{3} I_{3} – I_{1} (V_{2} + V_{3})**

**Two wattmeter method power factor formula**

**V _{RB} = V_{RN} – V_{BN}**, this is the phase difference shown by the two wattmeter method.

V_{RB} and I_{R} is (30°- Φ)

W_{R} = V_{RB} .I_{R} cos (30°-Φ)

V_{YB} = V_{YN} – V_{BN}

W_{Y} = V_{YB}. I_{Y} cos (30° + Φ) (V_{RB} = V_{YB} = V_{L}) (I_{R} = I_{Y} = I_{L})

W_{R} = V_{L}.I_{L} cos (30°-Φ)

W_{Y} = V_{L} I_{L} cos (30°+Φ)

W_{R} + W_{Y} that is,

W_{R} + W_{Y} = √3 V_{L} I_{L} cos Φ

P= √3 V_{L} I_{L} cos Φ

W_{R} + W_{Y} = √3 V_{L} I_{L} cos Φ

W_{R} – W_{Y} = V_{L} I_{L} sin Φ

W_{R} – W_{Y}/W_{R} + W_{Y} = tanΦ/√3

tanΦ = √3 [W_{R} – W_{Y}/ W_{R}+W_{Y}]

** Φ = tan ^{-1} √3 [W_{R}-W_{Y}/W_{R}+W_{Y}]**

This is the formula of two wattmeter method power factor.