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Power system protection

How Differential Protection WorksANSI 87

The scheme that compares current in against current out of a protected zone — and trips the instant they stop matching. Toggle the scenarios below to see why it stays quiet through heavy external faults but trips instantly on an internal one.

Protected zone — live scenario

Illustrative CT ratio 400:1 → 1 A rated secondary. Figures are for teaching, not a specific relay's actual settings.

Protected zone CT1 CT2 I1 I2 87 RESTRAIN Ia Ib
I1 (primary)400 A
Ia = I1 / n1.00 A
I2 (primary)400 A
Ib = I2 / n1.00 A
Differential Id0.00 A
Restraint Ir1.00 A
Relay statusRestrain
Normal load: current flows straight through the zone. Both CTs see (almost) the same current, so the secondary currents cancel at the relay — differential current stays near zero.

Step-by-step calculation

The principle, in order

01

Measure both ends

A CT at every boundary of the protected zone converts primary current to a proportional secondary signal, wired so the two secondaries oppose each other around a common loop.

02

Compare, don't just measure

Kirchhoff's current law says whatever flows in must flow out — for any current outside the zone, however large. Through current: Id = |Ia − Ib|. Internal fault: Id = Ia + Ib.

03

Operate only on imbalance

An internal fault is fed from both ends at once, so the secondaries stop opposing and start adding. Id spikes, crosses the bias characteristic, and the relay trips — typically in under 20 ms.

Percentage bias (restraint) characteristic

Plain differential relays would false-trip on CT mismatch during heavy through-faults. Biasing the trip threshold against restraint current — the average of Ia and Ib, the CT secondary currents — fixes that: the boundary rises exactly where CT error is largest.

RESTRAINT CURRENT Ir = (Ia + Ib) / 2 [A secondary] DIFFERENTIAL CURRENT Id [A secondary] OPERATE RESTRAIN
Normal load Through-fault (external) Internal fault

Commissioning notes

CT ratio & polarity

Both CTs must present matched secondary currents to the relay for a healthy through-current. Wrong polarity on either CT reads every through-fault as internal — verify polarity before energizing.

Vector group compensation

On a transformer, Dyn11 (or similar) shifts current phase 30° across the winding. Modern relays compensate digitally; on electromechanical schemes it's done with interposing CTs.

Inrush restraint

Energizing a transformer draws magnetizing inrush that looks like an internal fault to a naive relay. 2nd-harmonic restraint blocks tripping during that transient.

Where it's used

Transformers (87T), generators (87G), busbars (87B), and feeders/cables (87L via pilot wire or communications channel) — any zone with clearly defined, measurable boundaries.