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An isolated synchronous generator with transient reactance of 0.1 pu on a 100 MVA base is connected to the high voltage bus through a step up transformer of reactance 0.1 pu on a 100 MVA base. Fault level at the bus is
1000 MVA
500 MVA
50 MVA
10 MVA
500 MVA
The fault level at a bus is defined as the product of the base MVA and the reciprocal of the total per-unit reactance (subtransient) looking into the fault point. In this case, the generator and transformer are in series, so their reactances add up, resulting in a total equivalent reactance of 0.2┬аpu.
The fault level at a bus is defined as the product of the base MVA and the reciprocal of the total per-unit reactance (subtransient) looking into the fault point. In this case, the generator and transformer are in series, so their reactances add up, resulting in a total equivalent reactance of 0.2┬аpu.
SfaultтАЛ=Xtotal(pu)тАЛSbaseтАЛтАЛ тАФ Formula to calculate fault MVA
XtotalтАЛ=XgenтАЛ+XtransтАЛ тАФ Series addition of reactances
The short-circuit capacity (Fault Level) is calculated as SfaultтАЛ=Xeq(pu)тАЛSbaseтАЛтАЛ. Since the generator is connected to the bus through a transformer, the total reactance seen from the bus during a fault is XgenтАЛ+XtransтАЛ=0.1+0.1=0.2┬аpu. Dividing the 100 MVA base by 0.2 gives 500 MVA.
Fault level is inversely proportional to the per-unit impedance.
Per-unit values remain consistent only when calculated on the same MVA base.
The transient reactance is used to calculate the subtransient fault level for standard breaker rating studies.
Simplifies complex multi-machine system analysis.
Allows direct comparison of fault severity across different voltage levels.
Does not account for resistance (R), which is often ignored for simplicity.
Transient behavior varies over time (subtransient vs transient vs steady state).
Rating of circuit breakers and switchgear.
Design of protective relaying systems.
Determining the capacity of busbars and bus-ducts.
Standard procedure: Always check if the base MVA is consistent for all components.
If reactance was given on different bases, we would first convert them to a common MVA base.
B is correct тАФ The total reactance is 0.2┬аpu, and dividing 100┬аMVA by 0.2┬аpu yields 500┬аMVA.
Always ensure the MVA base is the same for all components before adding per-unit impedances; otherwise, perform a base conversion.