TWO-WATTMETER METHOD (BALANCED LOAD)

The two-wattmeter method can be explained somewhat more clearly by considering a balanced load. In this case, we shall prove that power measured by the two wattmeters (i.e.,sum of two wattmeter readings) is equal to V_LI_L cosɸ, which is the actual power consumed in a three- phase balanced load.

The connection diagram for a three-phase balanced load (connected in star) is shown in Figure 8.37(a). Considering load to be an inductive one, the phasor diagram is shown in Figure 8.37(b). The three-phase voltages V_RN, V_YN,and V_BNdisplaced by an angle of 120° electrical are shown in phasor diagram. The phase currents lag behind their respective phase voltages by an angle ɸ.

Fig. 8.37  (a) Connection of two wattmeters for power measurement in balanced 3-phase load (b) Phase diagram

Current through current coil (c.c.) of W₁ = I_R

Potential difference across potential coil (p.c.) of 

To obtain V_RB, reverse the phasor V_BNand add it vectorially to phasor V_RN, as shown in Figure 8.37(b).

The phase difference between V_RBand I_Ris (30° − ɸ).

Power measured by wattmeter

W₁ = V_RBI_R cos(30 − ɸ)

Current through c.c. of W₂ = I_Y

Potential difference across p.c. of 

To obtain V_YB, reverse the phasor V_BNand add it vectorially to phasor V_YNas shown in Figure 8.37(b).

The phase difference between V_YBand I_Yis (30° + ɸ).

Power measured by wattmeter, W₂ = V_YB= V_BR= V_L

Wattmeter reading, W₁ = V_L I_Lcos (30° − ɸ)

Wattmeter reading, W₂ = V_L I_Lcos (30° + ɸ)

Sum of the two wattmeter readings,

 

W₁ + W₂ = V_L I_Lcos (30° − ɸ) + V_L I_Lcos (30° + ɸ)

= V_L I_L[cos (30° − ɸ) + cos (30° + ɸ)]

= V_L I_L[cos 30° cos ɸ+ sin 30° sin ɸ+ cos 30° cos ɸ− sin 30° sin ɸ]

= V_L I_L(2 cos 30° cosɸ ) 

= Total power absorbed by a three-phase balanced load (P)

P = W₁ + W₂

Thus, the sum of the readings of the two wattmeters is equal to the power absorbed in a three-phase balanced load.

8.16.1  Determination of Power Factor from Wattmeter Readings

We have seen that

W₁ + W₂ = V_LI_Lcosɸ        (8.1)

W₁ − W₂ = V_LI_L(cos(30° − ɸ) − cos(30° + ɸ))

=2V_LI_Lsin30sinɸ= V_LI_Lsinɸ        (8.2)

Dividing Equation (8.2) by (8.1), we get

or

Power factor

cosɸ = cos tan⁻¹ɸ = 

8.16.2  Determination of Reactive Power from Two Wattmeter Readings

Multiplying Equation (8.2) by , we get

(W₁ − W₂) =  V_LI_Lsinɸ = P_r

Reactive power,

P_r = (W₁ − W₂)

8.17  EFFECT OF POWER FACTOR ON THE TWO WATTMETER READINGS

For lagging power factor, the wattmeter readings are

 

W₁ = V_L I_Lcos (30° − ɸ) and W₂ = V_L I_Lcos (30° + ɸ)

 

It is clear that the readings of the two wattmeters do not only depend upon load, but they also depend upon the phase angle ɸor the power factor of the load.