Typical impedances for a generator might be Xd= 2.00 pu, Xd"=0.15 pu.
The Xd synchronous reactance determines the steady state fault current. The Xd" sub-transient reactance determines the fault current for the first few cycles of the fault.
Using the values above, the long term short circuit = I=V/Xd = 1/2.0 = 0.5 per unit. But the fault starts at the instantaneous fault level of I= V/Xd" = 1/0.15 = 6.67 per unit.
For a solid three phase fault the current will start at 660% of full load and decay to 50% of full load. The transition between these two extreme values is determined by the generator's short circuit time constants and the response of the excitation system.
To graph this generator's short circuit current on time-current curve, put a mark at 660% current on the bottom axis and a mark at the top axis at 50%. Draw a "knee" curve between the two points similar in shape to a thermal breaker curve. If the generator has a long short circuit time constant, the knee will be up in tens of seconds range or higher. For small generators with "short" or fast short circuit time constants, the knee will be down in the seconds range, meaning the generator’s short circuit output will rapidly decay from 600%+ to less than 100%. (Most coordination programs can graph this curve given the generator data.)
The time-current tripping curve for a standard overcurrent device or relay set at 125% or higher pickup will never intersect the generator output curve unless the generator has a long time-constant with a "high" knee. An overcurrent relay set high enough to allow normal load may never see the fault as current decays to 50% of full load current.
The standard solution is to apply a 51V voltage controlled or restrained relay with a pickup of 50-80% of full load. The overcurrent element is inactive unless the voltage also drops below set point as it would during a fault.
If the generator has a long time constant, it may be possible to set a regular 51 overcurrent relay or low voltage breaker to intersect the generator curve and provide protection. Otherwise, a 51V, or 21 impedance protection is needed. 51 V is cheaper.