Probabilistic Short-Circuit Analysis by Monte Carlo Simulations and Analytical Methods

The probability distribution of short-circuit currents in a bus or a section of a line represents basic information in planning, reliability, and risk assessment studies. This paper presents two methods for the development of the probability distribution of fault currents. The first one is based upon a Monte Carlo simulation while the second utilizes analytical expressions derived from probability theory. The Monte Carlo approach is more general but requires an extensive computational effort; the analytical method is only applicable to three-phase faults, but provides an accurate determination of short-circuit currents at a much reduced computational cost. For both approaches, a method has been developed to determine short-circuit currents for faults along various points by recalculating elements of the bus impedance matrix without a need to invert, each time, the bus admittance matrix. This technique allows for the analysis of large systems by limiting considerably the computation time. For example, computational effort was reduced approximately by a factor of four for a 16 bus system and by a factor of six for a 24 bus system.