Peterson coil for 33 kV 60 km line

A Peterson coil (arc suppression coil) is an iron-cored reactor connected between the system neutral and earth, tuned to the line-to-earth capacitance so that the earth-fault current is neutralised.

Principle: during an earth fault on one phase, the healthy phases send a capacitive current I_C = 3 V_ph ωC into the fault. The Peterson coil in the neutral sends an equal inductive current I_L = V_ph / (ωL) through the fault, which cancels I_C, so the arc goes out. For resonance:

I_L = I_C
V_ph/(ωL) = 3 V_ph ωC
        L = 1 / (3 ω² C)

Rating of the coil = V_ph × I_L (the coil sees phase voltage during the fault).

Data

• Line voltage V_L = 33 kV, f = 50 Hz, ω = 2π × 50 = 314.16 rad/s
• Capacitance per phase C = 0.015 μF/km × 60 km = 0.9 μF = 0.9 × 10⁻⁶ F

Inductance of the coil

L = 1 / (3 ω² C)
  = 1 / (3 × 314.16² × 0.9 × 10⁻⁶)
  = 1 / 0.26648
  = 3.753 H

kVA rating

V_ph = 33000/√3          = 19052.6 V
I_L  = I_C = 3 V_ph ω C
     = 3 × 19052.6 × 314.16 × 0.9×10⁻⁶
     = 16.16 A
Rating = V_ph × I_L
       = 19052.6 × 16.16
       = 307.9 kVA

Answer: Inductance of Peterson coil = 3.753 H; kVA rating ≈ 307.9 kVA (coil current 16.16 A at 19.05 kV).