RRRV from short circuit test (132 kV)

The rate of rise of restriking voltage (RRRV) is the slope of the transient voltage across the CB contacts after current zero; it decides whether the arc re-ignites.

Method

• Peak phase voltage: V_m = √2 × V_L/√3.
• At current zero the instantaneous system voltage is V_m sin φ (fault current lags by φ, cos φ = fault p.f.).
• Active recovery voltage: V_r = k × sin φ × V_m, where k is the recovery voltage factor (0.9 of full line value).
• For an ungrounded symmetrical fault the first pole to clear sees 1.5 times this (first-pole-to-clear factor 1.5).
• Restriking voltage peak = 2 V_r, reached at t = 1/(2f_n).
• RRRV (average up to the peak, the usual textbook value) = 2V_r / t = 4 f_n V_r. The maximum instantaneous rate is ω_n V_r.

Data

V_L = 132 kV, cos φ = 0.4, k = 0.9, f_n = 16 kHz.

sin φ = √(1 − 0.4²) = 0.9165
V_m   = √2 × 132/√3 = 107.78 kV
t     = 1/(2 × 16000) = 31.25 μs

i) Fault grounded

V_r   = 0.9 × 0.9165 × 107.78 = 88.90 kV
Peak  = 2 × 88.90             = 177.80 kV
RRRV  = 177.80 kV / 31.25 μs  = 5.69 kV/μs
(max instantaneous = ω_n V_r
 = 2π×16000×88.90 kV = 8.94 kV/μs)

ii) Fault not grounded (first-pole factor 1.5)

V_r   = 1.5 × 88.90           = 133.35 kV
Peak  = 2 × 133.35            = 266.71 kV
RRRV  = 266.71 kV / 31.25 μs  = 8.53 kV/μs
(max instantaneous = 13.41 kV/μs)

Answer: RRRV ≈ 5.69 kV/μs with a grounded fault and ≈ 8.53 kV/μs with an ungrounded fault (average up to the first peak).

An ungrounded fault therefore puts 50% more stress on the breaker.