In this article we will discus about:- 1. Introduction to Re-Striking Voltage Transient 2. Expression for Re-Striking Voltage Transient 3. Classification 4. Characteristics 5. Factors Affecting.

**Introduction to Re-Striking Voltage Transient****: **

Electrically a power system is an oscillatory network so that it is logical to expect that the interruption of fault current will give rise to a transient whose frequency depends on the constants of the circuit.

Let us consider a simple circuit, having a circuit breaker CB, as illustrated in Fig. 6.7 (a) and that a short circuit occurs on the feeder close to the bus-bars. The equivalent circuit is shown in Fig. 6.7 (b). Let L be the inductance per phase of the system up to the fault point, R be the resistance per phase of the system up to the fault point and C be the capacitance to earth of circuit-breaker porcelain bushing.

Consider the opening of a circuit breaker under fault conditions shown in simplified form in Fig. 6.7 (b). Before current interruption, the capacitance C is short circuited by the fault and the short-circuit current through the breaker is limited by resistance R and inductance L of the system. If R is negligible compared to L, the short-circuit current i will lag behind the system voltage v by 90°, as illustrated in Fig. 6.7 (c).

With the contacts opened and the arc broken, current i is diverted through capacitance C so that the voltage v, which has so far been effective only across the inductance L, is suddenly applied to the inductance L and capacitance C in series which form an oscillatory circuit, having a natural frequency.

The initial charging current surge tends to carry the voltage across the capacitor, and therefore across the circuit breaker contacts to double its equilibrium value i.e., 2 V_{max}; this is the re-striking voltage transient which tends to re-establish the arc in the circuit breaker.

These frequencies are of the order of 10 Hz to 10 kHz depending upon the values of L and C. The actual power system is composed of distributed capacitances and inductances. The circuit configuration is also complex. The re-striking voltage transient for such circuits can have several component frequencies ranging from a few Hz to several kHz.

**Expression for Re-Striking Voltage Transient****: **

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When the breaker contacts are opened and the arc finally extinguishes at some current zero, a voltage v is suddenly applied across capacitor and therefore, across the circuit breaker contacts. The current i which would flow to the fault is not injected in the capacitor and inductor. Thus –

Assuming zero time at zero currents when t = 0, and further –

v = V_{max }cos wt

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i = V_{max}/wL sin wt before opening of circuit breaker

Substituting in Eq. (6.9) we have –

The solution of this standard equation is –

The above expression is the expression for re-striking voltage where V_{max} is the peak value of recovery voltage (phase-to-neutral), t is time in seconds, L is inductance in henrys, C is the capacitance in farads and v is the re-striking voltage in volts.

The maximum value of re-striking voltage is 2 V_{max} and occurs at t = π /w or t = π √LC .

**Classification of Re-Striking Voltage Transients****: **

**Re-striking voltage transients, and consequently their respective circuits can generally be placed under two main categories:**

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**(i) Single Frequency Oscillatory Transients: **

The single frequency re-striking voltage transient is produced in the circuit illustrated in Fig. 6.7 (b). The voltage waveform is shown in Fig. 6.7 (c).

**(ii) Double Frequency Transients: **

It is quite possible that the circuit breaker may have L and C on its both sides, as illustrated in basic circuit given in Fig. 6.8 (a). Before clearing the fault, both terminals 1 and 2 are at the same potential. After the fault is cleared, i.e., the arc has been extinguished, both the circuits oscillate at their own natural frequencies and a composite double frequency transient appears across the circuit breaker pole. This is illustrated in Fig. 6.8. (b).

**Characteristics of Re-Striking Voltage****:**

**The important characteristics of re-striking voltage which affect the performance of the circuit breaker are:**

(i) Amplitude factor and

(ii) Rate of rise of re-striking voltage, abbreviated as RRRV.

**(i) Amplitude Factor: **

The amplitude factor is defined as the ratio of the peak of transient voltage to the peak system frequency voltage.

**(ii) Rate of Rise of Re-Striking Voltage (RRRV): **

It is the rate of rise of re-striking voltage and is expressed in kV/µs. It may be defined as the slope of the steepest tangent to the re-striking voltage curve. For a re-striking voltage having a single frequency transient component the RRRV is obtained by dividing the maximum amplitude of the oscillation by the duration of the first half wave. Higher values of natural frequencies can be related with higher rates of rise of re-striking voltage.

It is clear that other things being equal, the duty of circuit breaker is much more severe when employed in a network of higher natural frequency than on a network of low natural frequency. This is because the average RRRV is much greater in the former case. In the latter case the voltage across the circuit breaker contacts rises slowly thereby giving longer time for building up of the dielectric strength.

**Expression for RRRV****: **

It is given as –

**Factors Affecting Re-Striking Voltage Characteristics:**

After current zero, the initial rate of rise and peak value of the re-striking voltage stressing the contact gap depend upon the configuration of the network, its natural frequency and on the relative position of the resistances (in series or in parallel with the circuit main capacitance). Because of presence of resistance dampening of the rate of rise of re-striking voltage is quite logical. The true nature of attenuation is quite complicated because the losses depend on several factors such as conductor resistance, iron loss, dielectric loss, corona, etc. These factors depend on frequency and voltage in different ways.

In a network consisting of generators, transformers, reactors and transmission line, each of them exerts its own damping. Usually the attenuation due to them is too small to be relied upon for improvement in the breaker performance. Where high RRRV are expected circuit breakers with shunt resistances are employed.

Now for ensuring exponential build-up of voltage across the breaker to the 50 Hz recovery voltage, without overshoot, instead of exhibiting the oscillatory doubling effect associated with an un-damped circuit, the value of resistance R_{P} required to achieve critical damping is ½ √L/C.

It can thus be inferred that the shunt resistance across the breaker modifies the oscillatory re-striking voltage into a periodic wave. This entails the arc to be extinguished even though the dielectric strength of the gap increases only relatively slowly as a result of severe short circuit. Inclusion of the shunt resistor thus increases the rupturing capacity of the breaker.

Figure 6.11 shows the relation of RRRV and rupturing capacity of an air-blast circuit breaker with and without shunt resistors as a function of natural frequency. Without shunt resistance RRRV is directly proportional to the natural frequency of the circuit, and the rupturing capacity of the breaker, therefore, drops rapidly with the increase in frequencies. In the case of breaker with shunt resistance the RRRV cannot exceed a certain value determined by the resistor and hence the rupturing capacity does not drop to that extent. For higher values of natural frequencies the advantage gained in the rupturing capacity is more.