Two Wattmeter Method – Balanced Load Condition

The Two Wattmeter Method is explained, taking an example of a balanced load. In this, we have to prove that the power measured by the Two Wattmeter i.e. the sum of the two wattmeter readings is equal to root 3 times of the phase voltage and line voltage (√3VLIL Cosϕ) which is the actual power consumed in a 3 phase balanced load.

The connection diagram of a 3 phase balanced load connected as Star Connection is shown below.

TWO-WATTMETER-METHOD-BALANCED-LOAD-FIG-1

Contents:

The load is considered as an inductive load, and thus, the phasor diagram of the inductive load is drawn below.

TWO-WATTMETER-METHOD-BALANCED-LOAD-FIG-2The three voltages VRN, VYN and VBN, are displaced by an angle of 120 degrees electrical as shown in the phasor diagram. The phase current lag behind their respective phase voltages by an angle ϕ.

Now, the current flowing through the current coil of the Wattmeter, W1 will be given as

two-wattmeter-balance-condition-eq1

Potential difference across the pressure or potential coil of the Wattmeter, W1 will be

two-wattmeter-balance-condition-eq2

To obtain the value of VYB, reverse the phasor VBN and add it to the phasor VYN as shown in the phasor diagram above. The phase difference between VRB and IR is (30⁰ – ϕ)

Therefore, the power measured by the Wattmeter, W1 is

two-wattmeter-balance-condition-eq3

Current through the current coil of the Wattmeter, W2 is given as

two-wattmeter-balance-condition-eq4

Potential difference across the Wattmeter, W2 is

two-wattmeter-balance-condition-eq5

The phase difference VYB and IY is (30⁰ + ϕ).

Therefore, the power measured by the Wattmeter, W2 is given by the equation shown below.

two-wattmeter-balance-condition-eq6

Since, the load is in balanced condition, hence,

two-wattmeter-balance-condition-eq7

Therefore, the wattmeter readings will be

two-wattmeter-balance-condition-eq8

Now, the sum of two Wattmeter readings will be given as

two-wattmeter-balance-condition-eq9The above equation (1) gives the total power absorbed by a 3 phase balanced load.

Thus, the sum of the readings of the two Wattmeters is equal to the power absorbed in a 3 phase balanced load.


Determination of Power Factor from Wattmeter Readings

As we know that,

two-wattmeter-balance-condition-eq10

Now,

two-wattmeter-balance-condition-eq11Dividing equation (3) by equation (2) we get,

two-wattmeter-balance-condition-eq12

Power factor of the load is given as

two-wattmeter-balance-condition-eq13

Determination of Reactive Power by Two Wattmeter Method

To get the reactive power, multiply equation (3) by √3.

two-wattmeter-balance-condition-eq14

Therefore, the Reactive Power is given by the equation shown below.

two-wattmeter-balance-condition-eq15For the Measurement of the Three Phase Power, you can also refer the two topics given below.

Also See: Measurement of Three Phase Power: Three Wattmeter Method

Also See: Two Wattmeter Method of Power Measurement.

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