Instrument transformer sizing: CT ratio, accuracy class, burden and thermal rating

What CT/VT sizing is

An instrument transformer does not measure power — it scales the primary current or voltage down to a safe, standardized secondary (5 A, 1 A or 115 V) that meters and relays can read. Sizing one is therefore a triple decision: the transformation ratio that fits the primary quantity, the accuracy class that bounds the error for the duty, and the burden the secondary circuit imposes. Get any of the three wrong and the device that depends on it — a revenue meter, an overcurrent relay, a distance relay — reads a number that is no longer the truth.

The split between metering and protection cores runs through everything below. A metering core must be accurate around the service current and must stop passing current on a fault, to protect its instruments. A protection core must do the opposite: stay linear far above the nominal current, all the way up to the fault, so the relay sees the real disturbance. The same physical window cannot serve both, which is why CTs carry separate cores.

The current transformer (CT)

Ratio and standard primary

The primary current rating cannot be any number — it is picked from the standard series (5, 10, 15, 20, 25, … 5000 A). The method takes the loaded current at the point, applies a sizing margin (headroom above the nominal current), and rounds up to the next standard value:

Ipn = next_standard(max(margin · In, 1))

The transformation ratio is then RTC = Ipn / Isn, with Isn equal to 5 A or 1 A. A 200 A feeder with a 1.25 margin needs at least 250 A, which is itself a standard value, giving a 250/5 ratio.

Burden and the effective factor

The secondary circuit — meters, relays, the cable run back to the panel — loads the core. That load is the burden, given in VA at rated current or as an impedance:

Zb = VA_nom / Isn²

A 15 VA core at 5 A presents 0.6 Ω. The subtle point is what happens when you wire less burden than the core is rated for. The accuracy class is guaranteed at the rated burden; with a lighter load, the same secondary current produces a smaller secondary voltage, so the core stays linear up to a higher current. The effective security or accuracy factor scales:

factor_ef = factor · (VA_nom / VA_real)

For a protection core this is free headroom against saturation. For a metering core it is a warning: under-burdening pushes the real FS above the nameplate, so instruments are protected only at a higher fault multiple than you specified.

Metering vs. protection

A metering CT is specified as, for example, 0.5 — 15 VA — FS5: class 0.5, 15 VA rated burden, and a security factor of 5 that caps the secondary current to protect the meters. A protection CT is specified as 15 VA 5P20: 15 VA, class 5P (5 % composite error) at an accuracy limit factor of 20. The 5P20 core stays faithful up to 20 times its rated primary — which must be enough to cover the fault.

Will the protection core saturate?

The decisive protection check expresses the fault as a multiple of the rated primary:

factor_req = (Ik · 1000) / Ipn

and compares it with the effective limit factor:

saturation OK ⇔ factor_ef ≥ factor_req

If the effective ALF reaches the fault multiple, the composite error stays within class throughout the fault and the relay measures a faithful current. If it falls short, the core saturates: the secondary current collapses into a distorted, undersized waveform and the protection may under-reach or operate late.

Thermal and dynamic withstand

Independently of its accuracy duty, the CT must survive the short circuit physically:

Ith = Ik (for the stated duration t) ; Idyn = 2.5 · Ith

Ith is the rated short-time thermal current — the RMS fault the windings carry for the specified time (usually 1 s) without overheating. Idyn is the rated dynamic current, the mechanical peak the windings withstand against electromagnetic forces, taken as 2.5×Ith per IEC 61869-2. Both must exceed the prospective short-circuit at the CT location.

The voltage transformer (VT)

A VT scales the system voltage down to a standard secondary, typically 115 V (or 115/√3 for a phase-earth connection). The primary rating depends on the connection:

Vpn = U (phase-phase) or Vpn = U/√3 (phase-earth)

and the ratio is RTP = Vpn / Vsn. The burden, as for a CT, is an impedance:

Zb = Vsn² / VA

The voltage factor

The distinctive VT parameter is the voltage factor Fv, the per-unit over-voltage the unit must tolerate. It is 1.2 continuously in all systems. For the short-duration over-voltage during an earth fault, it depends on the neutral treatment:

• Effectively (solidly) earthed system: Fv = 1.5 for 30 s.
• Isolated or impedance-earthed system: Fv = 1.9 for up to 8 h.

The reason is physical: on an isolated-neutral network, an earth fault on one phase raises the two healthy phases toward the line voltage — a √3 increase — and the VT must not saturate while it sustains that for the time the fault may persist. Choosing the 1.5 factor on an isolated system is a classic specification error.

How to read the result

• Ratio: confirm Ipn (or Vpn) is a standard value and that the margin leaves headroom for foreseeable load growth without pushing the meter off-scale.
• Burden: the wired VA must be at or below the rated VA; if it is well below, recompute the effective factor before trusting the class.
• Effective vs. required factor (protection): factor_ef ≥ factor_req is the saturation gate — the single most important protection check.
• FS (metering): verify the security factor is low enough to protect the instruments at the real burden, not just at the rated burden.
• Thermal/dynamic: Ith and Idyn must clear the prospective fault and its peak.
• Voltage factor (VT): match Fv to the actual system grounding.

Practical specification notes

• Never share a core between metering and protection — their accuracy windows are opposite. Specify separate cores on the same CT.
• Watch the cable run. On long secondaries the cable burden dominates; a 1 A secondary cuts it 25-fold versus 5 A and may let a smaller VA core keep its class.
• Size for the fault you computed. The protection ALF check is only as good as the short-circuit study feeding Ik.
• Align standard and duty. IEC 61869-2 / NBR 6856 govern current transformers; IEC 61869-3 / NBR 6855 govern inductive voltage transformers; IEEE C57.13 is the ANSI counterpart.

Worked end to end — ratio, burden, effective factor, saturation check and short-circuit ratings for the CT, and ratio plus voltage factor for the VT — this method turns a one-line point into a complete, buyable instrument-transformer nameplate.