Worked example · CT Secondary Burden · Lead-burden method

The Copper Was the Load — One Burden Budget, One CT Within Rating, One Busted by Its Own Leads

The relay draws 2.50 VA. The leads draw 6.90 VA. The same burden budget walked both ways: a 400/5 feeder circuit that clears its 15.00 VA core at 62.6%, and an 800/5 run whose 45 m of copper exceeds the entire rating before the relay is connected — then rescued by a 1 A secondary. A worked demonstration of the method, not a specific site installation.

Published 2026-08-02 · EI Portal

The relay was never the load. A CT drives its whole secondary loop — the connected device plus the two-wire lead run back to the panel — and on a 5 A secondary the copper usually draws more VA than the relay it feeds. Here is the budget worked through both ways on the same method: one circuit that sits comfortably inside its rating, one whose leads alone exceed the entire core, and the one-line change that rescues it.

The method

Every number below comes from one chain, referred to the secondary:

lead loop           = 2 × one-way length
      lead resistance     = ρ × loop / area        (ρ Cu 0.017241 Ω·mm²/m at 20 °C)
      lead burden VA      = Isec² × lead resistance
      total burden        = connected + lead
      utilisation %       = total / rated × 100
      max one-way length  = (available VA ÷ Isec²) × area ÷ (2ρ)
      

The verdict compares utilisation against the rated VA and returns "Within rating", "Near limit" or "Over burden" — the boundaries sitting at ≥85% for near limit and >100% for over burden.

Case 1 — the 400/5 feeder circuit (within rating)

A feeder protection circuit: 400/5 CT, 15.00 VA rated burden, a numerical relay drawing 2.50 VA, and 20 m one-way of 2.5 mm² copper.

The chain:

• Two-wire loop: 2 × 20 m = 40.0 m
• Lead resistance: 0.017241 × 40.0 ÷ 2.5 = 0.276 Ω
• Lead burden: Isec² × R = 25 × 0.276 = 6.90 VA
• Total: 2.50 + 6.90 = 9.40 VA = 62.6% of 15.00 VA

Verdict: "Within rating" — margin 5.60 VA, equivalent burden 0.376 Ω, secondary loop voltage 1.88 V, and a maximum one-way lead length of 36.3 m.

Note what just happened: the relay contributed 2.50 VA and the copper contributed 6.90 VA. Work the division — 6.90 ÷ 9.40 — and the leads are 73.4% of the total burden. The circuit passes, but the thing filling the core is the wiring.

The knife edge

Hold every input and stretch only the lead run, and the verdict walks through all three states:

• 20 m → 62.6% → "Within rating"
• 30 m → 85.6% → "Near limit" — past the ≥85% line, so a marginal circuit never reads as a confident pass
• 40 m → "Over burden" — total 16.29 VA, margin −1.29 VA

No surprise where the edge sits: the 20 m readout already reported a maximum one-way length of 36.3 m, and 40 m is beyond it. Ten metres of extra containment route is the difference between a comfortable pass and a busted core.

Case 2 — the 45 m long run (over burden)

Now the same method on the tool's long-run preset: an 800/5 CT, 15 VA rated, a 3.00 VA relay, and 45 m of 2.5 mm² copper.

It fails before the relay is even counted:

Lead burden alone: 15.52 VA — more than the entire 15 VA rating. Total 18.52 VA = 123.4% → "Over burden", margin −3.52 VA. The maximum run on this core was 34.8 m; the design asks for 45 m.

Nothing about the relay caused this — a 3.00 VA device is modest. The cable did it: at 5 A, every ohm of loop resistance costs 25 VA, and 45 m of 2.5 mm² copper is enough resistance to spend the whole budget on its own.

The rescue — swap the secondary to 1 A

Go back to the feeder circuit and change one thing: the secondary rating. Same 20 m, same 2.5 mm² copper, same relay — 1 A instead of 5 A. The lead resistance is unchanged; the current through it is not, and lead burden scales with Isec²:

• Lead burden: 0.28 VA — versus 6.90 VA at 5 A, exactly 25× less, because (5/1)² = 25
• Total: 2.78 VA = 18.5% utilisation
• Maximum one-way lead length: 906.3 m

The same copper that dominated the 5 A circuit becomes a rounding error, and the reach grows from 36.3 m to 906.3 m. This is the whole argument for 1 A secondaries on long runs and large substations, in three lines of arithmetic.

The lesson

The relay's VA is the small, honest number on the nameplate; the burden that actually loads the core is mostly in the wiring, and it scales with the square of the secondary current. A burden check that ignores the leads counts about a quarter of the truth — and a run that looks unremarkable on a drawing can exceed the entire rating by itself. Total both terms, read the maximum lead length before you route the cable, and check the circuit both ways in the CT Burden Quick Checker — the method itself is unpacked in the companion article.

This is a rated-burden quick check, not a CT design. It does not assess CT accuracy class, ALF, knee-point voltage, excitation current, remanence, saturation, transient offset or relay operating thresholds — that depth is the EI Portal CT Selection tool. Lead burden is estimated from a two-wire loop at 20 °C; resistance rises with temperature, so use project cable data where available, and confirm the core against the manufacturer's / IEC 61869-2 ratings. Not a CT certification, and there is no PDF or report export.