Percentage bias in differential relay

Percentage bias means that the operating current needed to trip a differential relay is not a fixed value but a set percentage of the through (restraining) current. The relay operates only when

|I₁ − I₂| ≥ K × (I₁ + I₂)/2 + I_min

where K is the bias (slope), typically 10–40%.

Need for bias

In a simple differential relay, the CTs at the two ends are never perfectly matched. During heavy through faults the CTs may saturate unequally, and the transformer tap changer also causes mismatch. The resulting spill current may exceed a fixed setting and cause a false trip. With bias, the operating level rises as the through current rises, so the relay remains stable.

How it is achieved in practice

• The relay has a restraining (bias) coil and an operating coil.
• The restraining coil is connected in the pilot wire circuit, with its mid-point tapped; it carries the average through current (I₁ + I₂)/2 and produces restraining torque.
• The operating coil is connected between the mid-point of the restraining coil and the CT star point; it carries the differential current (I₁ − I₂) and produces operating torque.
• In an induction or balanced-beam relay the two coils act on the same moving element in opposite directions. The ratio of the turns of the restraining and operating coils sets the percentage slope.
• In static/numerical relays the same rule is applied in software, often with a dual slope (low slope at low current, steeper slope at high current). Transformer relays also add harmonic restraint (2nd harmonic for magnetising inrush, 5th for over-excitation), because inrush current flows on one side only and bias alone cannot stop it from tripping the relay.

 CT1 ──────┬────R/2────●────R/2────┬────── CT2
           │      restraining      │
           │           │ mid-point │
           │       [Operating]     │
           │           │           │
           └───────────┴───────────┘

Characteristic

 Operating │          /  trip
 current   │        /
 I₁ − I₂   │      /  slope = K %
           │    /
           │__/      restrain (no trip)
           └──────────────────────
             through current (I₁+I₂)/2

When a percentage differential relay is preferred

• When the protected unit carries heavy through-fault currents that may saturate CTs (large generators, transformers).
• When CT ratios cannot be matched exactly (e.g. transformer ratios that do not match standard CT ratios).
• On transformers with on-load tap changers, where the ratio changes with tap position.
• Where long pilot leads or unequal CT burdens cause unbalance.
• In general, whenever high sensitivity to internal faults must be combined with high stability for external faults.