Three-phase power measurement: A 3-phase balanced supply feeds a 3-phase unbalanced load. Which measurement methods can correctly measure total power?

Introduction / Context:
In three-phase systems, practical power measurement often uses wattmeter methods. The choice depends on whether the system is 3-wire or 4-wire, whether loads are balanced or unbalanced, and whether line voltages are balanced. This question considers a balanced 3-phase supply feeding an unbalanced 3-phase load.

Given Data / Assumptions:

• Supply is balanced (line voltages equal in magnitude and 120° apart).
• Load is unbalanced.
• Standard 3-wire connection unless otherwise specified.

Concept / Approach:

The two-wattmeter method measures total power accurately in any 3-phase, 3-wire system regardless of load balance (provided the supply is balanced). The three-wattmeter method measures total power in both 3-wire and 4-wire systems and works for any balance condition by summing per-phase powers. A single wattmeter is insufficient for general unbalanced 3-phase power unless special connections or restrictions exist (e.g., symmetrical load and specific phase).

Step-by-Step Solution:

Verification / Alternative check:

Derivations of the two-wattmeter method show W1 + W2 = total real power for any power factor and even unbalanced loads when supply is balanced; three-wattmeter trivially sums each phase power, confirming the answer.

Why Other Options Are Wrong:

• 1 and 2 / 2 and 3 / 3 alone: Include the inadequate one-wattmeter case or exclude a valid method.

Common Pitfalls:

• Assuming two-wattmeter works only for balanced loads; it works for unbalanced loads with a balanced 3-wire supply.

Final Answer:

1 and 3