# What is Restriking Voltage and its Calculation ?

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Restriking voltage is the transient voltage appearing across the breaker contacts immediately after the opening of breaker contacts. also called Transient Recovery Voltage.

When the current across the contact of the circuit breaker is zero, a high-frequency transient voltage develops in the whole breaker contact and is produced by the sudden distribution of energy between the electric and magnetic field. This transient voltage is called restriking voltage. The voltage appears across the breaker contacts at the moment of final current has a serious influence on the arc extinction process. Under the influence of this voltage, the arc tries to restrike and hence it is named as the restriking voltage.

# Calculation of Restriking Voltage

Let’s take the some Assumption, at the maximum restriking voltage after the removal of fault by breaker contact opening. to Calculate the Restriking Voltage,

• Current interruption is assumed to be taking place at natural current zero.
• Assumed the whole is system is lossless.
• The fault does not involve any arcing. Example, the fault is solid one.
• Effect of corona and saturation is ignored. Corona and saturation of machine attenuates the voltage surge during breaker contact opening by dissipating energy.

Figure below shows the simple Circuit of system consisting of a source connected to a bus bar. The  capacitance and inductance of the system is lumped together and connected in  parallel and series with the source respectively. The voltage across CB contact will be equal to the multiplication of fault current and the system impedance as seen from the CB contacts with voltage source shorted. Let us assume this voltage to be v(t). For making calculations easy, it will be a smart way to consider every parameter in laplace domain.

Therefore,

I(f) = Fault Current
V(s) = Supply Voltage
Z(s) = System Impedance as seen from CB contacts

Hence,
V(s) = I(f)Z(s) ………….(1)
But source voltage is VmSinωt, hence source voltage at natural current zero i.e. when breaker contact open will be Vm. Therefore V(s) = Vm /s and impedance is mainly offered by inductance, this means Z(s) = Ls

Thus from (1),

Vm/s = I(f)Z(s)
I(f) = Vm / Ls2 ………..(2)

Now let us find the Z(s). Z(s) will be parallel equivalent of inductance L and capacitance C when viewed from breaker contact. Therefore,

Z(s) = [(Ls)(1 / Cs)] / [Ls + 1/Cs]
= Ls / [Ls + 1/Cs]
= (s / C) / [s2 + 1/LC]

Now from (2),

V(s) = Voltage across CB contact immediately after opening
= Restriking Voltage
= Transient Recovery Voltage
= I(f)Z(s)
= [(Vm/s)(1/sL) (s / C)] / [s2 + 1/LC]
= Vm [1/s – s / (s2 + 1/LC)]
Taking inverse laplace transform, we get

v(t) = Vm[1 – cosω0t] ………(3)

where ω0 = 1 / √LC and hence f0 = (1/2π√LC) where f0 is the natural frequency of oscillation. The maximum value of TRV = 2Vwhen ω0t = π

t = π / ω0
= π / (1 / √LC)
= π √LC

Expression no. 3 is the restriking or transient recovery voltage. It can be seen from the expression that TRV is of sustained oscillating nature. But it’s not true. The above expression has been arrived at by assuming some conditions which eliminates the damping effect. In real scenario, Restriking voltage die out due to damping effect of corona, arc involved in faults etc.