Two wattmeter method connection diagram

Principle: The total power in a three-wire three-phase circuit (star or delta, balanced or unbalanced) can be measured with two wattmeters. The algebraic sum of their readings is the total power.

Connection diagram

 R ──[ W2: CC ]───────────┬──► load
        PC ──────┐        │
 Y ──────────────┴────────┼──► load
        PC ──────┐        │
 B ──[ W1: CC ]───────────┴──► load

• The current coils (CC) are in series with two of the lines (R and B).
• One end of each pressure coil (PC) is connected to the line of its own current coil, and the other ends of both are joined to the third line (Y).
• Each wattmeter measures the average of (line-to-Y voltage) × (current in its own line).

Readings (balanced load, lagging power factor cos φ)

• W₁ = V_L I_L cos(30° − φ)
• W₂ = V_L I_L cos(30° + φ)

Total power P = W₁ + W₂ = √3 V_L I_L cos φ

Also: tan φ = √3 (W₁ − W₂)/(W₁ + W₂), so the power factor of the load can be found from the readings. Reactive power Q = √3 (W₁ − W₂).

Notes

• At unity power factor both wattmeters read the same.
• At cos φ = 0.5, one wattmeter reads zero and the other reads the total power.
• For cos φ < 0.5, one wattmeter reads negative. Its pressure-coil connection is reversed to get a deflection, and that reading is subtracted.
• It cannot be used for a four-wire system with a neutral current, where three wattmeters are needed.