Two-wattmeter method (Aron connection) — power measurement in a three-phase three-wire network without a neutral

The guide on measuring power and cosφ with a three-phase clamp meter covers the practice of power measurement with modern clamp meters, which typically measure all three phases and the neutral conductor separately. This article covers a classic measurement technique that correctly determines the total power in a three-phase three-wire network using two measuring elements instead of three — a principle that still underlies many older panel meters and some modern energy-metering setups.

The problem: a three-phase three-wire network has no accessible neutral

In a three-phase four-wire network (with a neutral conductor), power can be measured per phase separately (phase voltage × phase current × cosφ per phase) and then summed. In a three-phase three-wire network — for example, a delta-fed motor connection without a neutral conductor — the reference point (the star point) that a conventional per-phase power measurement would normally measure against is missing.

The Aron connection: two wattmeters, three lines

The Aron connection (also known as the two-wattmeter method) solves this with two wattmeters:

The current coil of each wattmeter is placed in series with one of two of the three line conductors (for example L1 and L2).
The voltage coil of each wattmeter is connected between that line conductor and the third, common line conductor (L3) — so not against a neutral conductor or star point, but against the third phase wire.

The total active power of the three-phase system is then simply the algebraic sum of the two wattmeter readings:

P_total = P1 + P2

This formula holds for the total active power regardless of whether the load is balanced or unbalanced — this is the method's main practical strength: with just two measuring elements, the total power is determined correctly, even with an unevenly loaded three-phase load.

Reactive power: valid only for a balanced load

From the difference between the two wattmeter readings, for a balanced load, the total reactive power can also be derived:

Q_total = √3 × (P1 − P2)

and from that the power factor (cosφ) of the system. This difference formula relies on the assumption that the three phase currents are equal in magnitude and shifted by 120° relative to each other — an assumption that no longer holds for an unbalanced load. For an unevenly loaded three-phase load, the simple difference formula therefore does not give a reliable value for the reactive power, even though the sum formula for the active power (P1 + P2) does remain valid.

Note: which of the two wattmeter readings is the larger one, and whether either reading can even become negative at a low power factor, depends on the phase angle of the load; a negative reading on one of the two wattmeters with a strongly inductive or capacitive load is normal behaviour for the Aron connection and not a measurement error in itself.

Practical relevance

When assessing an older panel setup with two analogue wattmeters on a three-phase three-wire connection — for example, an older motor supply without a neutral conductor — it is important to recognise that the sum of both readings gives the correct total active power, even with an unbalanced load, while any derived power factor or reactive-power value from the difference of the two readings is only reliable if the load is actually balanced. When in doubt about load symmetry, a modern three-phase clamp meter with three separate measuring channels (see the related guide) is the more reliable choice.

Common mistakes

Applying the reactive-power difference formula (Q = √3 × (P1 − P2)) to an unbalanced load — this formula is only valid for a balanced load.
Treating a negative reading on one of the two wattmeters as a measurement error — this is normal behaviour with a strongly inductive or capacitive load within the Aron connection.
Thinking the Aron connection requires a neutral conductor — the method is precisely designed for a three-phase three-wire network without an accessible neutral.
Doubting the total-power formula (P1 + P2) for an unbalanced load — unlike the reactive-power formula, this sum formula for the active power remains valid even under imbalance.