RRRV from short circuit test (220 kV)

The RRRV is the rate at which the voltage across the CB contacts rises after the arc is extinguished at current zero.

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 would see 1.5 times this (first-pole-to-clear factor 1.5); here the fault is grounded, so the factor is 1.
• 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 = 220 kV, cos φ = 0.45, k = 0.9, f_n = 18 kHz, fault grounded (factor 1).

sin φ = √(1 − 0.45²)          = 0.8930
V_m   = √2 × 220/√3           = 179.63 kV
V_r   = 0.9 × 0.8930 × 179.63 = 144.37 kV
Peak restriking = 2 V_r       = 288.75 kV
t = 1/(2 f_n) = 1/(2×18000)   = 27.78 μs
RRRV = 288.75 kV / 27.78 μs   = 10.39 kV/μs

Maximum instantaneous rate (at t = 1/(4f_n) = 13.9 μs):

ω_n V_r = 2π × 18000 × 144.37 kV
        = 16.33 kV/μs

Answer: RRRV ≈ 10.39 kV/μs (average up to the first peak of 288.75 kV); maximum instantaneous RRRV ≈ 16.33 kV/μs.