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ElectricalPower System
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Three phase short circuit MVA to be interrupted by a circuit breaker in a power system is given by

A

3├Ч\sqrt{3} \times3тАЛ├Ч post fault line voltage in kV ├Ч\times├Ч SC current in kA

B

3├Ч3 \times3├Ч pre fault line voltage in kV ├Ч\times├Ч SC current in kA

C

3├Ч\sqrt{3} \times3тАЛ├Ч pre fault line voltage in kV ├Ч\times├Ч SC current in kA

D

13├Ч\frac{1}{\sqrt{3}} \times3тАЛ1тАЛ├Ч pre fault line voltage in kV ├Ч\times├Ч SC current in kA

Correct Answer

тЪЩя╕П TE тАв Technical Concept & PrincipleElectricalPower System
Option C

3├Ч\sqrt{3} \times3тАЛ├Ч pre fault line voltage in kV ├Ч\times├Ч SC current in kA

Quick Summary:

The interrupting capacity of a circuit breaker in a three-phase system is defined by its ability to break the short-circuit MVA at a given voltage level. This is calculated using the product of 3\sqrt{3}3тАЛ, the pre-fault line-to-line voltage, and the short-circuit current.

тЪЩя╕ПTETechnical SolutionConcept & Principle
ЁЯТб Explanation

The interrupting capacity of a circuit breaker in a three-phase system is defined by its ability to break the short-circuit MVA at a given voltage level. This is calculated using the product of 3\sqrt{3}3тАЛ, the pre-fault line-to-line voltage, and the short-circuit current.

ЁЯФв Key Formulas

MVAsc=3├ЧVL├ЧIscMVA_{sc} = \sqrt{3} \times V_L \times I_{sc}MVAscтАЛ=3тАЛ├ЧVLтАЛ├ЧIscтАЛ тАФ Calculation of short circuit MVA

Isc=VphZeqI_{sc} = \frac{V_{ph}}{Z_{eq}}IscтАЛ=ZeqтАЛVphтАЛтАЛ тАФ Calculation of short circuit current

тЪЩя╕П Working Principle

During a symmetrical three-phase fault, the power system delivers maximum current to the fault point. The total apparent power (MVA) is calculated based on the system voltage prior to the fault and the steady-state fault current. Since the breaker must interrupt the total fault energy, the rating is defined as SMVA=3├ЧVline(kV)├ЧIsc(kA)S_{MVA} = \sqrt{3} \times V_{line(kV)} \times I_{sc(kA)}SMVAтАЛ=3тАЛ├ЧVline(kV)тАЛ├ЧIsc(kA)тАЛ.

ЁЯУМ Key Points
  • тЦ╕

    The voltage used is the rated pre-fault line-to-line voltage.

  • тЦ╕

    Short circuit MVA is a standard metric used to determine the interrupting rating of circuit breakers.

  • тЦ╕

    This formula assumes a balanced three-phase system under symmetrical fault conditions.

тЬЕ Advantages
  • тЦ╕

    Provides a simple, universal metric for comparing circuit breaker capabilities.

  • тЦ╕

    Directly relates fault energy to system voltage levels.

тЭМ Disadvantages / Limitations
  • тЦ╕

    Does not account for the DC offset component present in the transient period of a fault.

  • тЦ╕

    Calculations are based on steady-state values and may underestimate initial mechanical stress.

ЁЯЫая╕П Applications / Uses
  • тЦ╕

    Circuit breaker selection and sizing in power distribution networks.

  • тЦ╕

    Protection coordination studies in substation design.

ЁЯУД Additional Information
  • тЦ╕

    The term 'pre-fault' voltage is used because it represents the system condition before the voltage collapses due to the short circuit.

  • тЦ╕

    Option B is incorrect as it uses a factor of 3 instead of 3\sqrt{3}3тАЛ, and Option A uses post-fault voltage, which is nearly zero at the fault point.

ЁЯУК Diagram / Illustration
Short Circuit MVA Formula
3├ЧVline├ЧIsc\sqrt{3} \times V_{line} \times I_{sc}3тАЛ├ЧVlineтАЛ├ЧIscтАЛ
10┬│ (if using Volts and Amperes)
тЬЕ

C is correct тАФ The short-circuit MVA capacity is calculated as 3├ЧVpreтИТfault(line)├ЧIsc\sqrt{3} \times V_{pre-fault(line)} \times I_{sc}3тАЛ├ЧVpreтИТfault(line)тАЛ├ЧIscтАЛ.

Core Concepts Used
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Symmetrical Fault Analysis Circuit Breaker Rating Power System Stability
ЁЯТб EXAM TIP

Remember that for symmetrical faults, always use line-to-line voltage with 3\sqrt{3}3тАЛ, but if using phase voltage, the factor becomes 3.

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