A CT can fail from too little burden: the secondary check in calculator #006

Everybody checks that the connected burden is below the rated burden. Almost nobody checks the other end. IEC 61869-2 states its accuracy limits for a burden "from 25 % to 100 % of the rated output" — a floor as well as a ceiling — and a modern digital meter draws about 0,03 VA. Put one on a 5 VA metering core through 45 m of 2,5 mm² and the connected burden lands at 16 % of rated, outside the window in which the class is guaranteed. The answer is a smaller CT, which is the opposite of the instinct. This guide runs the current transformer check through both of its sides. The worked example is a real run — every figure below was taken from the calculator, not typed in by hand.

What the tool is for

A multi-winding current transformer, checked per core: the protection cores against saturation and the metering cores against their burden window, both against the thermal withstand of the analog input they feed.

Each winding carries its own class, ratio, rated burden, ALF or FS, secondary winding resistance Rct, knee-point voltage, remanence assumption, list of connected devices, and list of cable segments. The station carries the fault scenarios, and each winding names which of them apply to it. Classes are grouped the way the standard groups them: 0,1 · 0,2 · 0,5 · 1,0 · 0,2S · 0,5S · 3 · 5 are measuring, 5P · 10P · PX · PXR · TPX · TPY · TPZ are protective, and C · K are the ANSI/IEEE ratings.

How the burden is assembled

Zb_connected = Is² × (ΣR_cable + ΣR_terminal + R_test-switch) + Σ(device VA × qty)

R_cable    = ρ(θ) × length × loop / section
ρ(θ)       = 0,0175 × (1 + 0,00393 × (θ − 20))     → 0,02128 Ω·mm²/m at 75 °C
R_contact  = (n_terminals × R_terminal + R_test-switch) × ageing factor

Three things in that are worth naming. The loop factor is explicit — a two-wire run is 2 × length of copper, and the field mistake is to enter the route length once. The copper temperature is 75 °C by default, not 20 °C, and the tool prints the resistivity it used beside the result. And the ageing factor applies to the contacts, not to the conductor: it is the terminals and the test switch that degrade.

Device burdens are summed as scalars. IEC 61869-2 specifies the test burden at a power factor of 0,8 lagging — 1,0 when the burden is under 5 VA, with a minimum of 1 VA — so a scalar sum is the conservative simplification, and the tool says so rather than implying a vector sum it does not perform.

A worked feeder CT: 1200/1, two cores

Core 1 — class 5P, 1200/1 A, rated burden 15 VA, ALF 20, Rct 4,2 Ω, knee point 180 V, remanence assumed 60 %. It feeds a feeder overcurrent and earth-fault relay through 75 m of 4 mm² copper, two-wire loop, eight terminals at 1,5 mΩ each and a 3 mΩ test switch, ageing factor 1,25.

The cable is 98 % of the burden. That is the normal situation on a 1 A core and the reason the marshalling route belongs in the calculation rather than in an allowance.

Now the saturation check. IEC 61869-2 defines, in clause 3.4.209, the secondary limiting e.m.f. of a class P core:

E_ALF = ALF × Isr × |(Rct + Rb) + jXb|

That e.m.f. is a property of the core, so if the connected burden is smaller than the rated burden, the same e.m.f. is reached at a higher current multiple. Holding E_ALF constant gives the operative number:

ALF_actual = ALF × (Rct + Sr/Is²) / (Rct + Zb_connected)
           = 20 × (4,2 + 15) / (4,2 + 0,8468)
           = 76,09

against a fault-current multiple of 23,33 — so the core does not saturate, with a wide margin that came from the light burden, not from the nameplate. Read in the other direction, the same relation is the warning: load that 15 VA core to its rated burden and the accuracy limit factor falls back to 20, and 20 × 1200 = 24 kA is uncomfortably close to the fault current.

Which fault governs — and the one it refuses to assume

The station in this run carries three scenarios: F1, a 25 kA three-phase fault at the CT with X/R 20; F2, a 28 kA single-phase-to-earth fault with X/R 22; F3, a 3,5 kA remote-end minimum fault for sensitivity. Both F1 and F2 have a 0,5 s clearing time and a 40 ms required saturation-free time.

Select only F1 on a core whose function is overcurrent and earth fault, and the tool returns NOT READY with the reason: an EF/REF/residual function requires a single-phase-to-earth scenario, because the three-phase fault is not automatically the governing one. On this station it is not — the earth fault is the larger current. Adding F2 changes every governing figure:

The 272,2 A²s is compared with the short-time withstand of the relay's analog input — the terminal, not the CT — because that is a rating a CT check routinely forgets and a relay manual routinely states.

The transient number, and why a 5P core is not failed against it

For the same core the tool also computes the transient duty, using the transient factor of IEC TR 61869-100:2017, clause 6.1.3, Equation (14):

Ktf,dc(t) = ω · Tp·Ts/(Tp − Ts) · (e^(−t/Tp) − e^(−t/Ts)) + 1        Tp = (X/R)/ω

Ktd = Ktf × M          (the report's own relation; M is a stated margin, not a hidden constant)

V_required = If_sec × (Rct + Zb) × Ktd / (1 − Kr)

With X/R 20, a 40 ms time to accuracy limit and a non-gapped core (Ts not stated, taken as the conservative Ts → ∞ branch, where the expression collapses to 1 + ωTp(1 − e^(−t/Tp))), that gives Ktf = 10,33; with M = 1,2, Ktd = 12,40; and with 60 % remanence, a required secondary voltage of 3258 V against a knee point of 180 V — a margin of 0,055.

The tool prints that number and does not fail the core on it. A class 5P core is dimensioned in the steady state, by E_ALF; the transient dimensioning factor belongs to the TP classes, or to a core where the engineer has explicitly asked for the check. Enforcing Ktd on every 5P core would fail every ordinary feeder CT in the world against a requirement its class was never designed to meet, which is a false alarm, not a finding. What the number is genuinely good for is the conversation it starts: if your protection actually needs 40 ms of saturation-free time under a fully offset fault with 60 % remanence, a 5P/180 V core is not the answer and a TPY core is.

IEC TR 61869-100 is explicit that this is the relay engineer's number to set: "it is common practice that the relay developers stipulate the required overdimensioning of the protection current transformers". That is why M is a field in the form rather than a constant in the code.

The metering core, and the floor nobody checks

Core 2 — class 0,2S, 1200/1 A, rated burden 5 VA, feeding a revenue meter through 45 m of 2,5 mm². Connected burden 0,811 VA.

Clause 5.6.201.3 of IEC 61869-2 sets the burden range over which the class holds: 25 % to 100 % of rated output for classes 0,1 / 0,2 / 0,5 / 1 and for 0,2S / 0,5S, and 50 % to 100 % for classes 3 and 5. At 0,811 VA on a 5 VA core the burden is 16,2 % of rated — below the floor — and the tool returns FAIL with the clause quoted.

Specify the same core at 2,5 VA instead and the burden becomes 32,4 % of rated, inside the window, and the verdict clears. Nothing about the installation changed. The over-specified rated burden was the defect, and it is a common one: 5 VA and 10 VA metering cores are ordered out of habit from an era when a meter was an induction disc with a real coil.

The verdict ladder

Four states, and they are not decorations:

• FAIL — a check that was performed did not pass
• NOT READY — a check could not be performed: no applicable fault scenario, no earth-fault scenario on an earth-fault function, no stated analog-input I²t withstand
• PRELIMINARY — every check passed, but at least one input is not yet traceable
• PASS — everything passed on traceable data

A metering core is always at most PRELIMINARY, because the accuracy class itself cannot be confirmed without manufacturer ratio-error and phase-displacement data, and no formula substitutes for a test certificate. So does any core whose device burden came from a database row marked as a template, or from a manual entry with no datasheet attached.

That matters for how you should read the built-in device database, which holds 1040 rows: 784 of them are explicitly marked as generated templates to be replaced by the exact factory value from the manual or order code, and the remainder are CT catalogue families used for manufacturability screening, which carry no burden figures at all. In other words the database will get you a defensible screening run and it will not get you a PASS, and it says which of the two you are holding. That is deliberate. A burden figure invented for a relay you have not opened the manual for is worse than no figure, because it looks like an answer.

What it does not do

• Confirm an accuracy class. Ratio error and phase displacement come from the manufacturer's test report, against Tables 201 to 203 of IEC 61869-2. The tool checks the burden window the class is defined over, which is a precondition, not the class.
• Speak for IEEE C57.13. The ANSI C/K mode computes the terminal voltage at 20 × Is against the C rating and reports the internal e.m.f. behind Rct for information, and it says on the result that C57.13 is not held in our standards library and the clause must be confirmed before issue. An honest screening beats a fabricated citation.
• Replace an excitation curve. The saturation curve drawn from Vk and Ie at Vk is a calibrated shape for sanity-checking, and the note under it says to replace it with the manufacturer's excitation test curve for final design.
• Settle differential or REF stability. PX/PXR screening confirms that Vk, Rct and Ie are available and consistent; the stability equation itself belongs to the relay manual for the scheme you are actually using.
• Sum burdens vectorially, or account for CT lead capacitance, or judge the mechanical and insulation design of the transformer.

Where this leaves you

The CT is the one component in a protection chain that is specified before the relay is chosen, installed before the cable route is final, and impossible to change afterwards without an outage. It is also the component whose datasheet is most often read as if the rated burden were the operating burden.

Two numbers decide almost everything, and neither is on the nameplate: the burden your marshalling actually presents, and the fault current your system actually produces at that location. Get those two into the same calculation and the class either works or it does not.

Check your own cores →