Transformer Differential Protection (ANSI 87T): Biased Slope, Inrush Restraint, and CT Saturation

Dual-slope percentage restraint differential protection, 2nd harmonic magnetizing inrush restraint (I_2nd > 15%), 5th harmonic overexcitation blocking, and CT k

1. Transformer Differential Protection (ANSI 87T) Principles

Per IEC 60255-187-1, percentage biased differential protection (ANSI 87T) serves as the primary unit protection for power transformers against internal short circuits.

2. Dual-Slope Operating Characteristic Equations

Idiff = |ĪHV + ĪLV_referred|
Ibias = (|ĪHV| + |ĪLV_referred|) / (2)

Trip Regions:

  • Slope 1 (K1 = 20% - 30%): Sensitive tripping for internal turn-to-turn and low-current ground faults during normal load.
  • Slope 2 (K2 = 60% - 80%): High restraint preventing false tripping during severe through-faults with CT saturation.

3. Harmonic Inrush & Overexcitation Restraint

Harmonic ComponentThreshold RatioRelay ActionPhysical Root Cause
2nd Harmonic (100 Hz)I2nd / Ifundamental > 15%Block Differential TripMagnetizing inrush current during energization
5th Harmonic (250 Hz)I5th / Ifundamental > 35%Block / AlarmCore overexcitation from system overvoltage

4. Current Transformer (CT) Knee-Point Voltage (Vk) Sizing

To prevent CT saturation during maximum external through-fault current (If_max):

Vk ≥ 2 · Isec_max · (Rct + 2 · Rlead + Rrelay)

Where Rct is CT secondary winding resistance and Rlead is one-way lead wire resistance.

*Reference: IEC 60255-187-1:2021; IEC 61869-2:2012; IEEE Std C37.91-2021.*