Distribution systems reliability uncertainty evaluation using an interval arithmetic approach

Reliability evaluation is considered a very useful tool in the planning of a distribution system because one can evaluate the performance of several configurations based on their reliability indices. These values are obtained both from analytical or simulation models, using system components data such as component failures, repairs and restoration times. One difficult problem therein is the quantification of the model parameters. If they are available, e.g., from measurement, they are not accurate and are subject to uncertainty. The study of a system with parameters over a possible range of variations (due to uncertainty) can be approached by evaluating the effects of such variations. There are two classical ways of dealing with uncertainty parameters: sensitivity analysis and repeated simulations (trial and error or Monte Carlo). In this paper we propose the use of interval arithmetic to evaluate reliability uncertainty in distribution systems. Interval arithmetic takes into consideration the uncertainty of all of the parameters and is able to provide strict bounds for indices, with only one evaluation. The final interval will contain all possible solutions due to the variations in input parameters. It is also shown that it is possible to perform sensitivity analysis by using interval arithmetic.