Restriking voltage numerical (6.6 kV, 8 mH)

When the CB current passes through zero, the voltage across its contacts oscillates at the natural frequency of the system and can reach twice the peak system voltage.

Method (resistance neglected)

• Peak phase voltage V_m = √2 × V_L/√3.
• Restriking voltage v = V_m(1 − cos ωₙt); maximum across contacts = 2V_m.
• Time to first peak t = π√(LC) = 1/(2f_n).
• Average rate of rise up to first peak = 2V_m / t.

Data

L = 8 mH, f_n = 10.273 kHz, V_L = 6.6 kV, 50 Hz.

i) Maximum voltage across contacts

V_m = √2 × 6600/√3 = 5389 V
v_max = 2 V_m = 10 778 V ≈ 10.78 kV

ii) System capacitance per phase

f_n = 1/(2π√(LC))  →  C = 1/(4π² f_n² L)
C = 1/(4π² × 10273² × 8×10⁻³)
  = 3.0 × 10⁻⁸ F = 0.03 μF

iii) Average rate of rise up to first peak

t = 1/(2 f_n) = 1/(2 × 10273) = 48.67 μs
Average RRRV = 10 778 V / 48.67 μs
             = 221.4 V/μs ≈ 0.221 kV/μs

Answer: i) 10.78 kV; ii) C = 0.03 μF per phase; iii) 0.221 kV/μs (2.214 × 10⁸ V/s).