1. During fault behavior of circuit breaker
A circuit breaker has two contacts – a fixed contact and a moving contact. Under normal conditions these two contacts remain in closed position.
When the circuit breaker is required to isolate the faulty part, the moving contact moves to interrupt the circuit.
On the separation of the contacts, the flow of current is interrupted, resulting in the formation of arc between the contacts. The contacts are placed in a closed chamber containing some insulating medium (liquid or gas) which extinguishes the arc
Making current: It is the peak (maximum) value of current during the first cycle of current wave after the closure of circuit breaker contacts
Breaking current: It is RMS value of current at the instant of contact separation

2. The voltage drop across the arc is called arc voltage
The voltage drop across the arc is called arc voltage. As the arc path is purely resistive, the arc voltage is in phase with the arc current.
The magnitude of the arc voltage is very low,amounting to only a few per cent of the rated voltage.
A typical value may be about 3 per cent of the rated voltage.
There are two methods of arc interruption:
1. High Resistance Interruption
2. Current Zero Interruption
In this method of arc interruption, its resistance is increased so as to reduce the current to a value insufficient to maintain the arc.
The arc resistance can be increased by cooling, lengthening, constraining and splitting the arc.

3. High Resistance Interruption
When current is interrupted the energy associated with its magnetic field appears in the form of electrostatic energy.
A high voltage appears across the contacts of the circuit breaker.
If this voltage is very high and more than the withstanding capacity of the gap between the contacts, the arc will strike again.
Therefore, this method is not suitable for a large-current interruption. This can be employed for low power arc and dc circuit breakers.

4. Current Zero Interruption
This method is applicable only in case of ac circuit breakers.
In case of ac supply, the current wave passes through a zero point, 120 times per second at the supply frequency of 60 Hz.
This feature of ac is utilized for arc interruption. The current is not interrupted at any point other than the zero current instant, otherwise a high transient voltage will occur across the contact gap. The current is not allowed to rise again after a zero current occurs.

5. Restriking voltage: It is the resultant transient voltage which appears across circuit breaker contact at the instant of arc extinction
Recovery voltage: It is power frequency RMS voltage which appears across the circuit breaker contacts after transient oscillation die out and final extinction of arc has resulted in all the poles
Amplitude(crest) factor: It is the ratio of peak of transient voltage to the peak system frequency voltage
Rate of Rise of Restriking Voltage (RRRV):It is defined as the slope of steepest tangent to the restriking voltage curve.it is expressed in kilovolts per microsecond.
Arc voltage: It is the voltage that appears across the circuit breaker contacts during he arcing period.arc voltage becomes system voltage when the arc is extinguished.

6. Expression for Restriking Voltage and RRRV
Figure (a) shows a short circuit on a feeder beyond the location of the circuit breaker.
Figure (b) shows an equivalent electrical circuit where L and C are the inductance and capacitance per phase of the system up to the point of circuit breaker location, respectively.

7. When the circuit breaker is closed, the short circuit current flows through R, L and the contacts of the circuit breaker, the capacitance C being short-circuited by the fault.
When the circuit breaker contacts are opened and the arc is extinguished, the current is diverted through the capacitance C, resulting in a transient condition.
The voltage across the capacitance which is the voltage across the contacts of the circuit breaker can be calculated in terms of L, C, fn and system voltage.

8. The mathematical expression for transient condition (neglecting resistance) is as follows.
Where E is the system voltage at the instant of arc interruption. As the transient oscillation is a fast phenomenon, E can be regarded as a constant for a short duration.

11. Example: For a 132 kV system, the reactance and capacitance up to the location of the circuit breaker is 3 ohms and μ F, respectively. Calculate the following:
a. The frequency of transient oscillation.
b. The maximum value of restriking voltage across the contacts of the circuit breaker
c. The maximum value of RRRV

13. Resistance Switching
To reduce the restriking voltage, RRRV and severity of the transient oscillations, a resistance is connected across the contacts of the circuit breaker. This is known as resistance switching. The resistance is in parallel with the arc. A part of the arc current flows through this resistance resulting in a decrease in the arc current and increase in the deionization of the arc path and resistance of the arc. This process continues and the current through the shunt resistance increases and arc current decreases. Due to the decrease in the arc current, restriking voltage and RRRV are reduced. The resistance may be automatically switched in with the help of a sphere gap as shown in Fig. The resistance switching is of great help in switching out capacitive current or low inductive current.

14. Current Chopping
When low inductive current is being interrupted and the arc quenching force of the circuit breaker is more than necessary to interrupt a low magnitude of current, the current will be interrupted before its natural zero instant. In such a situation, the energy stored in the magnetic field appears in the form of high voltage across the stray capacitance, which will cause restriking of the arc.

16. If the value of v is more than the withstanding capacity of the gap between the contacts, the arc appears again. Since the quenching force is more, the current is again chopped. The phenomenon continues till the value of v becomes less than the withstanding capacity of the gap. The theoretical value of v is called the prospective value of the voltage.

17. Interruption of Capacitive Current
The interruption of capacitive current produces high voltage transients across the gap of the circuit breaker. This occurs when an unloaded long transmission line or a capacitor bank is switched off. Figure shows an equivalent electrical circuit of a simple power system. C represents stray capacitance of the circuit breaker. CL represents line capacitance. The value of CL is much more than C.

18. Rating of Circuit Breakers
In addition to the rated voltage, current and frequency, circuit breakers have the following important ratings. (i) Breaking Capacity (ii) Making Capacity (iii) Short-time Capacity Breaking Capacity The breaking capacity of a circuit breaker is of two types (i) Symmetrical breaking capacity (ii) Asymmetrical breaking capacity

19. Symmetrical breaking capacity
It is the rms value of the ac component of the fault current that the circuit breaker is capable of breaking under specified conditions of recovery voltage.
Asymmetrical breaking capacity
It is the rms value of the total current comprising of both ac and dc components of the fault current that the circuit breaker can break under specified conditions of recovery voltage.

20. The short-circuit current contains a dc component which dies out gradually as shown in the figure. In the beginning, the short-circuit current is asymmetrical due to the dc component. When dc dies out completely, the short-current becomes symmetrical

21. The line X-X indicates the instant of contact separation.
AB is the peak value of the ac component of the current at this instant.
Therefore, the symmetrical breaking current which is the rms value of the ac component of the current at the instant of contact separation is equal to current AB/√2.
The section BC is the dc component of the short-circuit current at this instant. Therefore, asymmetrical breaking current is given by

22. The breaking capacity of a circuit breaker is generally expressed in MVA. For a three-phase circuit breaker, it is given by Breaking capacity = √3 x rated voltage in kV x rated current in kA. The breaking capacity will be symmetrical if the rated current in the above expression is symmetrical (British practice). The breaking capacity will be asymmetrical if the rated current is asymmetrical (American practice). The rated breaking current is taken by designer as 1.6 times the rated symmetrical current.

23. Making Capacity
The possibility of a circuit breaker to be closed on short-circuit is also considered. The rated making current is defined as the peak value of the current (including the component) in the first cycle at which a circuit breaker can be closed onto a short-circuit. Ip in Fig. is the making current. The capacity of a circuit breaker to be closed onto a short-circuit depends upon its ability to withstand the effects of electromagnetic forces

24. Making current = √2 x 1. 8 x symmetrical breaking current
Making current = √2 x 1.8 x symmetrical breaking current. The multiplication by √2 is to obtain the peak value and again by 1.8 to take the dc component into account. Making capacity = √2 x 1.8 x symmetrical breaking capacity =2.55 x symmetrical breaking capacity

25. Short-time Current Rating
The short-time current rating is based on thermal and mechanical limitations. The circuit breaker must be capable of carrying short-circuit current for a short period while another circuit breaker (in series) is clearing the fault. The rated short-time current is the rms value (total current, both a.c and d.c components) of the current that the circuit breaker can carry safely for a specified short period.

26. According to British standard, the time is 3 seconds if the ratio of symmetrical breaking current to rated normal current is equal to or less than 40 and 1 second if this ratio is more than 40. According to ASA there are two short-time ratings; one is the current which the circuit breaker can withstand for 1 second or less. Another is rated 4-second current which is the current that the circuit breaker can withstand for a period longer than 1 second but not more than 4 seconds.

27. Three phase Fault calculations

28. Three phase fault calculations Eg is generator per phase prefault voltage