Linear Formulations for Topology-Variable-Based Distribution System Reliability Assessment Considering Switching Interruptions

Continuity of supply plays a significant role in modern distribution system planning and operational studies. Accordingly, various techniques have been developed for reliability assessment of distribution networks. However, owing to the complexities and restrictions of these methods, many researchers have resorted to several heuristic optimization algorithms for solving reliability-constrained optimization problems. Therefore, solution quality and convergence to global optimality cannot be guaranteed. Aiming to address this issue, two salient mathematical models are introduced in this paper for topology-variable-based reliability evaluation of both radial and radially-operated meshed distribution networks. Cast as a set of linear expressions, the first model is suitable for radial networks. The second model relies on mixed-integer linear programming and allows handling not only radial networks but also radially-operated meshed distribution grids. Therefore, the proposed formulations can be readily incorporated into various mathematical programming models for distribution system planning and operation. Numerical results from several case studies back the scalability of the developed models, which is promising for their further application in distribution system optimization studies. Moreover, the benefits of the proposed formulations in terms of solution quality are empirically evidenced.