# Two Wattmeter Method of Power Measurement

All electrical devices run on electrical power, the consumed energy is measured in terms of watts. the device used to measure consumed power is called a watt meter. to measure three-phase power mainly two methods are used namely two wattmeter method and three wattmeter method.

In this article, we will discuss two wattmeter method of power measurement.

In 2 watt meter method, the current coils of two watt meters are connected in series with R and Y lines. The potential coil of each watt meter is connected to the third line B.

The algebraic sum of the reading of two watt meters gives the total power consumption of the connected load even if the load is balanced or unbalanced.

Total power=W_{1}+W_{2}

## Two WattMeter Method

As shown in two wattmeter method connection diagram, two watt meters are connected to three phase star connected load for power measurement.

Wattmeter current coils are connected in series with two lines of load R & Y and the pressure coils (potential coil) of two wattmeters jointed to third line B.

The instantaneous power consumed by three phase load is indicated by W_{1} and W_{2}.

The instantaneous potential difference across W_{1}=e_{RB}=e_{R}-e_{B}

Instantaneous current through W_{1 }=I_{R}

Instantaneous current through W_{2 }=I_{Y}

The instantaneous potential difference across W_{2}=e_{YB}=e_{Y}-e_{B}

Instantaneous power consumed by load=W_{1}+W_{2}

=I_{R}e_{RB}+I_{Y}e_{YB}

=I_{R}(e_{R}-e_{B})+I_{Y}(e_{Y}-e_{B})

=I_{R}e_{R}-I_{R}e_{B}+I_{Y}e_{Y}-I_{Y}e_{B}

=I_{R}e_{R}+I_{Y}e_{Y}-e_{B}(I_{R}+I_{Y})

=I_{R}e_{R}+I_{Y}e_{Y}+I_{B}e_{B} …… as the load is balanced I_{R}+I_{Y}+I_{B}=0 and I_{R}+I_{Y}=-I_{B}

Hence,

W_{1}+W_{2}=P_{1}+P_{2}+P_{3}

Where,

P_{1}=power consumed by load L_{1}

P_{2}=power consumed by load L_{2}

P_{3}=power consumed by load L_{3}

P= total power consumed=W_{1}+W_{2}

## 2 Watt Meter Method For Balance Load

Total power absorbed by three phase load can be calculated using two watt meters

When load is considered as inductive then the vector diagram for star connected balance load is

Let three phase rms voltages are E_{R } E_{Y} and E_{B} and rms currents are I_{R}, I_{Y} and I_{B}

As considered load is inductive in nature, current lags behind the voltage by angle Φ

Current through wattmeter W_{1}=I_{R}

The potential difference across the potential coil of W_{1} is

W_{1}=E_{RB}=E_{R}-E_{B}

From the vector diagram value of E_{RB} is obtained by compounding E_{R} and E_{B} reversed. and phase difference between E_{RB} and I_{R} is (30^{0}-Φ)

Wattmeter W_{1} reading=W_{1}=E_{RB}*I_{R}*cos (30^{0}-Φ)

Current through wattmeter W_{2}=I_{Y} and potential difference across pressure coil of W_{2}

=E_{YB}=E_{Y}-E_{B}

E_{B} is derived by compounding E_{Y} and E_{B} in reversed.

the phase angle between E_{YB} and I_{Y} is cos (30^{0}+Φ)

but the load is balanced

E_{RB}=E_{YB}=E_{L} and I_{R}=I_{Y}=I_{B}

W_{1}=E_{L}*I_{L}*cos (30^{0}-Φ)

W_{2}=E_{L}*I_{L}*cos (30^{0}+Φ)

P=W_{1}+W_{2}

=E_{L}*I_{L}*(cos (30^{0}-Φ)+cos (30^{0}+Φ))

using cos (A)+cos (B) formula and solving this we get equation

P=*√3* *E_{L}*I_{L}*cos (Φ)