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.
Step-by-step calculation
The principle, in order
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.
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.
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.
Commissioning notes
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.
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.
Energizing a transformer draws magnetizing inrush that looks like an internal fault to a naive relay. 2nd-harmonic restraint blocks tripping during that transient.
Transformers (87T), generators (87G), busbars (87B), and feeders/cables (87L via pilot wire or communications channel) — any zone with clearly defined, measurable boundaries.