We will discuss here in details the concept of Arc Voltage, Recovery Voltage, Restriking Voltage, RRRV
Basic Concept of Arc Voltage, Recovery Voltage, Restriking Voltage, RRRV
When contacts of a circuit breaker open under current carrying condition, electric arcs form in the gap between the contacts. This is due to ionization of the surrounding medium. During the natural zero crossing of the alternating current waveform, the arc current becomes zero. Since the current is zero, at this instant, the circuit can not supply any further energy to maintain the arc. Consequently, the electrons and ions in the arc plasma begin to recombine and the medium starts to deionize.
This process helps restore the dielectric strength (insulating capability) between the contacts. However, if the reestablishment of dielectric strength does not happen quickly enough, the gap may not regain sufficient dielectric strength. The open contact gap may not withstand the system voltage. Mainly, this is the voltage appearing across the contact gap just after the extinguishment of the arc. So, the open contact gap may not withstand the system voltage appearing across the contact gap just after extinguishment of the arcs. As a result, the arc can reignite. We call this phenomenon as restriking. Hence, to prevent this restriking after current zero, the dielectric strength of the contact gap must recover rapidly.
The removal of the residual charge carriers (free electrons and ions) from the arc path can accelerate the recovery of dielectric. Techniques like forced cooling and high-velocity gas flow sweep out the ionized particles, ensuring a faster dielectric recovery. When this process is effective, the arc does not reignite. Hence, permanently interrupts the current.
Restriking Voltage
In inductive circuits, the current lags behind the voltage. Therefore, at the instant when the current becomes zero, the system voltage may still be at or near its peak. Now, suppose, the medium in the contact gap does not get fully deionized. Also it has not gained sufficient dielectric strength at that moment. Then the high voltage appearing across the contacts can cause the arc to restrike. This high voltage that appears immediately after current zero and may cause arc reformation is known as the restriking voltage. In other words, the restriking voltage is the voltage that appears across the contacts of a circuit breaker immediately after the current interruption.
The magnitude of the restriking voltage depends primarily on two factors. The first one is the phase angle between the current and voltage. In other words, this is the power factor of the system. The second one is the reactive part of the system. The reactive part includes inductance and capacitance of the power system. In general, a lower power factor and higher inductive reactance increase the severity of restriking voltage. This is because the peaks of the voltage appear nearer to the current zero when the circuit is highly inductive. The amplitude of the system voltage at the instant of current zero governs the voltage appearing across the contact gap at current zero.
Arc Voltage
During arcing, the voltage across the arc is quite small because the arc presents a low-resistance path. Typically, the arc voltage is only about 2% to 3% of the system voltage. However, just after the arc extinguishment and hence the current interruption, the system voltage appears across the open contacts. If the system is inductive, this voltage may be at its peak precisely at current zero.
The sudden transition from low arc voltage to peak system voltage causes a rapid voltage rise across the contact gap. This abrupt change can induce oscillations in the voltage waveform across the contacts due to the interaction of inductive and capacitive elements in the power system. Because of these elements, the circuit effectively becomes an LC (inductor-capacitor) resonant circuit with minimal resistance. As a result, the voltage across the contacts oscillates with a natural frequency determined by the system’s inductance and capacitance values.
In summary, successful interruption of current in a circuit breaker depends on the ability of the contact gap to quickly recover its dielectric strength after the arc quenching. If this recovery is not fast enough and restriking voltage exceeds the dielectric strength, the arc may reignite, defeating the interruption. Therefore, the control of arc extinction and dielectric recovery is critical for effective circuit breaker operation.
Recovery Voltage
A steady-state voltage appears across the open contacts after damping out the oscillating restriking voltage. We refer this voltage as the recovery voltage.
Rate of Rise of Restriking Voltage (RRRV)
The is a rate at which the restriking voltage rises to its first peak of oscillation. We refer this as the Rate of Rise of Restriking Voltage (RRRV). It indicates how quickly the restriking voltage increases from its initial value to the peak value.
Equation of Restriking Voltage and Rate of Rise of Restriking Voltage (RRRV)
The standard equation for restriking voltage is given as:
After damping out the accelerating restriking voltage, the steady-state voltage appearing across the open contacts of the circuit breaker is known as the recovery voltage.
The restriking voltage is expressed as: \[ v\left(t\right) = V_m \left( 1 – \cos\omega t \right) \]Where \( \omega \) is the natural angular frequency of the LC network:\[ v\left(t\right) = V_m \left( 1 – \cos\frac{t}{\sqrt{LC}} \right) \]The rate of rise of restriking voltage is:\[\frac{dv(t)}{dt} = \frac{V_m}{\sqrt{LC}} \cdot \sin\left(\frac{t}{\sqrt{LC}}\right)\]Maximum RRRV value:\[\text{RRRV}_{\text{max}} = \frac{V_m}{\sqrt{LC}}\]