Differential (87) and distance (21) protection

Reference notes

Use Next → on the narrator above to step through the two workhorse "fast-acting" protections: differential (ANSI 87) for unit equipment, and distance (ANSI 21) for transmission lines.

Differential protection — ANSI 87

87 applies Kirchhoff's current law (Σ-of-currents = 0) to the protected zone. CTs at every boundary measure the current flowing into and out of the zone. For external loads or external faults, ΣI_in = ΣI_out and the difference is ideally zero:

For an internal fault, the fault current bypasses the output CT — I_op becomes large and the relay trips.

Percentage-restraint characteristic

Real CTs are not perfect — at high through-currents they saturate and produce ratio errors of several percent. A fixed pickup would nuisance-trip on external faults. The fix is the percentage-restraint (bias) characteristic:

Slope is typically 20–40 %. Modern relays add a second slope above an inflection point (~3× rated) to ride through severe CT saturation during external faults.

Transformer differential: the 2nd-harmonic trick

Energizing a transformer produces magnetizing inrush — 6–10× rated, all on the primary side with no secondary current. To a plain differential relay this looks identical to an internal fault. The fix exploits the harmonic content: inrush is rich in 2nd harmonic; fault current is not. Transformer differential relays block tripping when 2nd-harmonic content exceeds ~15 % of the fundamental.

Where 87 is used

• Transformers: 87T, with phase-shift compensation for Δ-Y windings and 2nd-harmonic restraint for inrush.
• Generators: 87G, the primary protection for stator faults. Very high sensitivity (pickup ~0.1 pu).
• Buses: 87B, with low-impedance or high-impedance schemes. Fast (one cycle) clearing of bus faults.
• Motors: 87M for large motors (typically above 1000 hp).

Distance protection — ANSI 21

21 measures the impedance from the relay terminal to the fault:

For a fault at the far end of the line, Z_relay equals the full line impedance. For a closer fault, Z_relay is smaller. The relay trips when the measured impedance falls within its operating characteristic on the R-X impedance plane.

Mho characteristic

The classic mho is a circle on the R-X plane passing through the origin, with diameter Z_reach along the protected line's angle (typically 75–85° for HV transmission lines). The geometry naturally:

• Trips faults along the line angle (line impedance is mostly inductive: small R, large X).
• Rejects load impedance (load PF is near unity, so load impedance sits at low angle — outside the mho circle).

Modern numerical relays often use a quadrilateral (quad) characteristic with adjustable R and X reach boundaries for finer control, especially on lines with significant arc-fault resistance.

Three zones

• Z1: reach 80 % of the protected line, instantaneous (1 cycle + breaker time). Cannot reach 100 % because of measurement errors that could overreach into the next line section.
• Z2: reach 120 % of the line, delayed ~300 ms. Covers the 20 % of line not seen by Z1 AND backs up the next station's Z1.
• Z3: reach 250 %+, delayed ~1 s. Backup for the next station's Z1 and Z2.

Pilot schemes — eliminating the 20 % Z1 gap

For lines where instantaneous clearing of the full 100 % is required (HV / EHV), pilot schemes use a communication channel between line ends:

• POTT (permissive overreach transfer trip): each end's Z2 trips its breaker only if the other end also sees a fault in its Z2.
• DCB (directional comparison blocking): each end trips its Z2 unless the other end signals a "block" indicating the fault is behind it.
• Differential line protection (87L): sends actual current values between ends and applies differential math across the line. Effectively 87 for a transmission line.

87 vs 21 — when to use which

Keyboard shortcuts

• → next step  ·  ← previous step
• R replay narration  ·  M mute / unmute  ·  F fullscreen
• On step 2: click "Inject fault →" to simulate an in-zone fault and watch I_op rise.
• On steps 4–6: click anywhere on the impedance plane to move the fault location and see which zone trips.