Current Transformer (CT) Analysis
Theory: exciting current causes error
Overview
A current transformer scales a large current down for meters. Doesn't it just follow the turns ratio?
Ideally, yes. But magnetising the core takes current, and the secondary current falls short by that amount. The magnetising requirement is set by secondary voltage, which rises with the connected meters or relays (the burden). So more burden means more error. During faults, current rises tens of times and may carry a DC offset, so the core can saturate and the secondary current collapse — directly affecting whether protective relays work. Let's calculate a 200/5 A CT.
Ratio error and phase displacement
$\mathbf{Z}_m$ is the magnetising impedance (secondary-referred), $R_2$ the secondary winding resistance, $\mathbf{Z}_b$ the burden. The more $\mathbf{Z}_m$ exceeds the burden, the smaller the error. The angle by which secondary current shifts from primary is the phase displacement, expressed in minutes (1/60 degree).
Core flux
$A_e$ is core cross-section. With a fully offset fault, the required flux can reach $(1 + X/R)$ times the AC-only peak; $X/R$ is the system reactance-to-resistance ratio, often 10 to 20 in transmission networks.
The birth of instrument transformers
As AC transmission spread in the late 19th century, currents of hundreds or thousands of amperes couldn't pass through meters directly, so current transformers were built to scale them down. In the 20th century they were used for system protection, and CT saturation preventing relay operation during faults became a major problem. In the later 20th century, standards for protection CTs accounting for DC-offset transient saturation were developed, and gapped cores to reduce remanence came into use. Rogowski coils and optical CTs, free of magnetic saturation, are now also in service.
Worked example: 200/5 A CT
Bar primary (1 turn, 40 secondary turns), 50 Hz. Toroid 20 cm² section, 0.30 m path, relative permeability 20,000 (8,000 assumed at 5% current), secondary resistance 0.15 Ω. Burden at power factor 0.8. Magnetising reactance 84 Ω (secondary-referred).
Burden and error
| Burden | Rated: ratio error | Rated: phase | 5%: ratio error | 5%: phase |
|---|---|---|---|---|
| 2.5 VA | −0.15% | 9 min | −0.26% | 23 min |
| 5 VA | −0.25% | 11 min | −0.46% | 30 min |
| 15 VA | −0.64% | 22 min | −1.28% | 59 min |
| 30 VA | −1.22% | 37 min | −2.49% | 102 min |
Class 0.5 limits are ±0.5% and ±30 minutes at rated current, ±1.5% and ±90 minutes at 5%. Up to 5 VA passes; at 15 VA the rated ratio error fails, and at 30 VA every point fails. At low current, core permeability drops, so error actually grows.
Fault current and saturation
| Burden | Flux density at rating | Multiple reaching saturation (1.8 T) |
|---|---|---|
| 5 VA | 0.093 T | 19× |
| 15 VA | 0.203 T | 9× |
| 30 VA | 0.368 T | 5× |
Transient saturation from DC offset
A fully offset fault on an X/R = 15 system with 5 VA resistive burden (no remanence):
| Fault current | AC-only flux | Worst with offset | Time to saturate |
|---|---|---|---|
| 5× rated | 0.49 T | 7.9 T | 11.5 ms |
| 10× rated | 0.98 T | 15.8 T | 8.2 ms |
| 20× rated | 1.97 T | 31.5 T | 6.2 ms |
AC-only it's a comfortable 0.49 T, but with DC offset even a 5× fault saturates in about half a cycle.
The DC component doesn't reverse, so it isn't cancelled like AC and keeps stacking flux in one direction. Its time constant, X/R divided by angular frequency, is 48 ms — plenty of time to saturate. Once saturated, secondary current appears only for part of each cycle, and distance or differential relays may underestimate the fault or mistake an external fault for an internal one. So protection CTs are chosen with margin to saturation based on X/R and relay operating time. Remanence from a previous fault makes saturation come even sooner.
Selection and analysis tips
- Sum meter, relay and wiring burden and keep it within the rated burden.
- Long secondary leads add burden; a 1 A secondary makes lead burden much smaller than 5 A.
- For protection, check time to saturation from maximum fault current and X/R.
- In transient analysis, include the core's B-H characteristic (hysteresis and remanence).
- Never open the secondary under load; nothing limits the flux and very high voltage appears.
“A differential relay tripped for an external fault”
At a substation, a fault outside a transformer caused its differential protection to trip it. Differential protection compares CT currents on both sides and treats any difference as an internal fault. Investigation showed that the CT on one side alone had saturated from DC offset, its secondary current dropping out and creating a spurious difference. Matching the CTs on both sides and adding saturation detection to block the relay fixed it. CT transient saturation is a classic cause of protection maloperation.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Forgetting lead burden | Out-of-class error | Include lead resistance |
| Saturation check on AC only | Transient saturation missed | Include X/R |
| Ignoring remanence | Earlier saturation | Assume worst remanence |
| Metering CT for protection | Saturates in faults | Use protection class |
| Open secondary | High voltage, burnout | Short before disconnecting |
I'd like to learn related topics.
Try magnetic circuits with the transformer magnetics tool. Related pages include transformer equivalent circuit, voltage transformers, core loss and leakage inductance.
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