Two-Wattmeter Method Formulas

Two-wattmeter method formulas: the total power of a three-phase load from two readings, the reactive power, the power angle and the power factor.

The formulas

W1 and W2 are the readings of the two wattmeters, connected in two lines with their voltage coils to the third line, for a three-wire three-phase load. The method works for a balanced load whatever the power factor. W1 is the larger reading. At a power factor of 0.5 the smaller reading is zero, and below 0.5 it is negative, so keep the sign when you add. The formula for Q and the angle assumes a balanced load, and the total P holds also for an unbalanced load on three wires. The readings here are examples.

Worked example: W1 = 8 kW and W2 = 4 kW

1. P = 8 + 4 = 12 kW
2. Q = √3 × (8 − 4) = 6.928 kVAR
3. tan φ = 6.928 / 12 = 0.5774, so φ = 30°
4. pf = cos φ = 0.866

Worked example: W1 = 6 kW and W2 = −2 kW

1. P = 6 + (−2) = 4 kW
2. Q = √3 × (6 − (−2)) = 13.86 kVAR
3. tan φ = 13.86 / 4 = 3.464, so φ = 73.9°
4. pf = cos φ = 0.2774

Ratio of the readings W2 / W1 by power factor

Frequently asked questions

Why can one reading be negative?

Below a power factor of 0.5 the angle is above 60°, and one wattmeter sees a negative power. Reverse its connection to read it and count the reading as negative.

Why two wattmeters and not three?

For three wires the sum of the line currents is zero, so two instruments are enough to find the total power.

Does the method need a balanced load?

The total power does not. The reactive power and the angle from these formulas do.

What if the neutral is connected?

Then the load has four wires and the sum of the currents need not be zero, so use three wattmeters.

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