A binary formulation of SAIDI for the predictive reliability assessment of radial distribution systems with tie-lines

Distribution system engineers can optimize distribution system reliability through the optimal placement of reclosers, fuse-blow fuses, fuse-save fuses, switches, and tie-lines. However, the lack of an objective function formulation that is explicitly expressed as a function of the locations of these devices presents a barrier to the application of mathematical methods for reliability optimization. This paper presents such a formulation: a binary formulation of the System Average Interruption Duration Index (SAIDI) explicitly expressed as a function of the placement of reclosers, fuse-blow fuses, fuse-save fuses, switches, and tie-lines in a radially operated distribution system. This formulation can be used (1) for predictive reliability assessment as an alternative assessment methodology and (2) for reliability optimization as an objective function that is compatible with deterministic, heuristic, and stochastic optimization approaches. We were able to validate this formulation against published results and an established predictive reliability assessment method. Furthermore, we demonstrated that this formulation could be used in finding the global optimal SAIDI of distribution systems.