Phase balancing in a dwelling

Which phase do I connect each appliance to, so that L1, L2 and L3 come out as balanced as possible?

Calculation mode

Checks the whole connected load switched on at once — what the editor’s imbalance rule sees too. Quick, but pessimistic: every appliance on at the same time is not a real situation.

What you want to know

You start from scratch: the calculation picks each appliance’s phase. You can pin an appliance’s phase in its advanced parameters.

Split algorithm

GreedyThe largest appliance on the least loaded phase — the same principle as the editor’s automatic board design. Instant, but it can miss the optimum.OptimalSearches for the best split. In Simple it proves it; in Advanced it gives the best result found and the bound it cannot go below.

How it works

Greedy. Sorts the appliances by current, largest first, and puts each one on the phase that is least loaded at that point; in Advanced and Advanced+ it puts it where the peak of the situations grows least. It is fast and it is the principle behind the editor’s automatic board design, but it decides each appliance only once and never goes back on the choice — in small homes with a few large appliances it can miss the optimal split.

Optimal. In Simple it searches exhaustively, pruning the branches that can no longer beat the current solution; if it finishes within the computation budget, the result is “proven optimal”. In Advanced and Advanced+ it starts from greedy and from a few other splits, then moves and swaps appliances between phases as long as the peak goes down — the result is the best one found, shown together with the lower bound, so you can see how close it is to the theoretical optimum.

In both algorithms, lights and socket-outlets with no fixed appliance are first split across all three phases — for each kind (lighting, socket-outlets, other occasional-use appliances), at most one circuit more on any phase than on another — and then the rest is balanced. The algorithm still chooses which circuit goes on which phase.

With an equal peak, both pick the connection in which the phases are loaded more evenly at every moment and, in Advanced and Advanced+, across the whole connected load too (scaled to an ordinary moment, so that it does not drown out the rest). The peak remains the first criterion: if a lower percentage on the connected load would raise the peak, it is not taken.

Both algorithms optimise the arithmetic current per phase, Σ P/(230 V·λ): a quantity that adds up from appliance to appliance and comes out greater than or equal to the real current, so the peak and the verdict against In are on the safe side. The imbalance (max − min, the percentage) is calculated on the same quantity, not on the real current, so it is not a safe-side limit: the real imbalance can come out slightly higher or lower.

Service connectionMain protective device In (optional)A

Appliances in the home · 14 appliances

Result

Proposed split

Most loaded phase (L1), whole connected load37.3A

By phase, with the whole connected load on at once — the appliances and their position:

L137.3 A

8.40 kW

Induction hob → L1+L2
Air conditioner → L1
Outdoor lighting → L1occasional
Kitchen socket-outlets → L1
Kettle → L1

L236.5 A

8.25 kW

Induction hob → L1+L2
Oven → L2
Refrigerator → L2
Bedroom lighting → L2occasional
Bedroom socket-outlets → L2occasional

L336.7 A

8.40 kW

Washing machine → L3
Dishwasher → L3
Storage water heater → L3
Living area lighting → L3occasional
Living room socket-outlets → L3occasional

Lights and socket-outlets with no fixed appliance, circuits on each phase:

Lighting: L1 1 · L2 1 · L3 1
Socket-outlets: L1 0 · L2 1 · L3 1

Imbalance on the connected load2.3%

(max − min)/average. The 15 % / 30 % thresholds are the app’s convention (rule V43) — Art. 3.1.5.8 requires the phases to be loaded as evenly as possible, but gives no figure.

Max − min difference between phases0.8A

Neutral current I_N3.9A

At the fundamental, without harmonics. With different power factors it can exceed the phase current.

Phasor currents per phaseL1 37.0 · L2 36.1 · L3 36.5A

Sum with phase angles, for information only; the split is made on the arithmetic current above.

Proven optimal: among the splits that put lights and socket-outlets with no fixed appliance across all three phases, none gives a lower maximum phase current.

Greedy: 39.6 A · Optimal: 37.3 A (maximum phase, whole connected load)

Calculation assumptions

The result holds under the conditions below. If your situation differs, change the values in the advanced section.

the powers are the input powers from the appliance labels; while it is on, an appliance counts at full power
the split is optimised on the arithmetic current per phase, Σ P/(U·λ) — greater than or equal to the real current, because it ignores the phase angle between appliances (on the safe side)
the phasor currents and the neutral current are calculated at the fundamental (50 Hz), with cos φ = λ, without harmonics
230 V single-phase / 400 V between lines on three-phase
the 15 % and 30 % imbalance thresholds are the app’s convention (rule V43); I7-2011 Art. 3.1.5.8 requires the phases to be loaded as evenly as possible, without giving a figure
lights and socket-outlets with no fixed appliance are split across all three phases (at most one more on any phase than on another); in Advanced and Advanced+, at most as many as set under “In use at the same time” count as on at once on each phase, the largest ones, and in Simple all of them, at full power

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The results are indicative and do not replace a design checked by a registered electrician. Every tool states its assumptions.