Two-wattmeter method in 3-phase systems: Under what condition will one wattmeter show a negative reading when measuring total power of a 3-phase load?

Introduction / Context:
The two-wattmeter method measures total power in a 3-phase, 3-wire system irrespective of load balance, provided the supply is balanced. A well-known characteristic is that one wattmeter may read negative at low power factors. Recognizing the condition for a negative wattmeter helps diagnose load characteristics and power factor.

Given Data / Assumptions:

• Balanced 3-phase source; load can be balanced or unbalanced.
• Two wattmeters connected in the standard manner.
• Power factor angle φ relates to PF by PF = cos φ.

Concept / Approach:

Two-wattmeter readings for a 3-phase system are W1 = V_L I_L cos(30° − φ) and W2 = V_L I_L cos(30° + φ). One reading becomes negative when its cosine term is negative. For W2, cos(30° + φ) becomes negative when 30° + φ > 90°, i.e., φ > 60°, which corresponds to PF < 0.5. This condition applies whether the power factor is lagging (inductive) or leading (capacitive); it depends only on the magnitude of φ exceeding 60°.

Step-by-Step Solution:

Verification / Alternative check:

Vector diagrams confirm that the current phasor moves far enough relative to the wattmeter voltage reference to flip the sign of one cosine term beyond φ = 60°, producing a negative torque and reading.

Why Other Options Are Wrong:

• “Less than 0.5 lagging”: too restrictive; leading also produces the effect.
• “Greater than 0.5 lagging” and “unity”: both lead to positive readings for both meters.
• “Only purely capacitive”: incorrect; inductive loads with PF < 0.5 also cause negativity.

Common Pitfalls:

• Assuming the sign depends on lag vs lead; it depends on the magnitude of φ.
• Misapplying formulas for 4-wire systems in which the method is different.

Final Answer:

when power factor is less than 0.5