Time domain fault analysis
Time-domain fault analysis pertains to techniques that allow for the calculation of the shortcircuit current as a function of time from the moment of the fault inception.

For large electric power systems, with many machines and generators contributing to the fault current, the contributions of many machines will have to be taken into account concurrently.

Machine models have been developed that let predictions of considerable accuracy be made regarding the behavior of any machine for a fault either at or beyond its terminals.

These models are rather complex because they tend to represent in detail not only the machine itself but also several nonlinear controllers, such as excitation systems and their related stabilization circuitry, with nonlinearities.

It can therefore be seen that the calculating requirements could be stupendous, because the problem is reduced to simultaneously solving a large number of differential equations.

Despite its inherent power, the use of time-domain fault analysis is not very widespread and is only used for special studies because it is data-intensive (data requirements can be at least as demanding as transient stability analysis) and it requires special software.

Quasi-steady-state fault analysis
Quasi-steady-state fault analysis pertains to techniques that represent the system at steady state. Phasors are used to represent system voltages, currents, and impedances at fundamental frequency.

System modeling and the resulting computational techniques are based on the assumption that the system and its components can be represented by linear models.

Retaining linearity simplifies considerably the necessary calculations (Anderson [B1], Arrilaga, Arnold, and Harker [B2], Blackburn [B3] Stevenson [B10], Wagner and Evans [B13]).

Furthermore, linear algebra theory and the numerical advances in matrix computations make it possible to implement very elegant computer solutions for relatively large systems. These techniques have been favored by the various industry standards and will be briefly examined next.

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