Power Factor by Two Wattmeter Method:

When we talk about the power factor in three-phase circuits, it applies only to balanced circuits, since the power factor in a balanced load is the power factor of any phase. We cannot strictly define the power factor in three-phase unbalanced circuits, as every phase has a separate power factor. The two wattmeter method, when applied to measure power in a three-phase balanced circuits, provides information that help us to calculate the power factor of the load.

Figure 9.47 shows the vector diagram of the circuit shown in Fig. 9.46. Since the load is assumed to be balanced, we can take Z₁ ∠Φ₁ = Z₂ ∠Φ₂ = Z₃ ∠Φ₃ = Z ∠Φ for the star-connected load. Assuming RYB phase sequence, the three rms load phase voltages are V_RN, V_YN and V_BN. I_R, I_Y and I_B are the rms line (phase) currents. These currents will lag behind their respective phase voltages by an angle Φ. (An inductive load is considered).

Now consider the readings of the Two Wattmeter Method in Fig. 9.46. W_R measures the product of effective value of the current through its current coil I_R, effective value of the voltage across its pressure coil V_RB and the cosine of the angle between the phasors I_R and V_RB. The voltage-across the pressure coil of W_R is given as follows.

It is clear from the phasor diagram that the phase angle between

Similarly, W_Y measures the product of effective value of the current through its current coil I_Y, the effective value of the voltage across its pressure coil, V_YB and the cosine of the angle between the phasors V_YB and I_Y.

From Fig. 9.47, it is clear that the phase angle between V_YB and I_Y is (30° + Φ).

Since the load is balanced, the line voltage V_RB = V_YB = V_L and the line current I_R = I_Y = I_L

Adding W_R and W_Y gives total power in the circuit, thus

From the two wattmeter readings, it is clear that for the same load angle Φ, wattmeter W_R registers more power when the load is inductive. It is also connected in the leading phase as the phase sequence is RYB. Therefore, W_R is higher reading wattmeter in the circuit of Fig. 9.46. In other words, if the load is capacitive, the wattmeter connected in the leading phase reads less for the same load angle. So, if we know the nature of the load, we can easily identify the phase sequence of the system. The higher reading wattmeter always reads positive. By proper manipulation of Two Wattmeter Method readings, we can obtain the power factor of the load.

Taking the ratio of the above two values, we get

Thereafter, we can find cos Φ