An AC Mathematical Model for Solving Complex Restoration Problems in Radial Distribution Systems in a Treatable Runtime

A restoration problem in a radial electrical distribution system (EDS) is solved to restore de-energized loads downstream of sectors affected by a permanent fault, transferring loads among primary feeders through switching operations. As it is a computationally complex problem, its resolution by exact optimization techniques in a treatable runtime is a difficult task. The complexity is related to the number of switches available for solution. To reduce investment costs, a typical EDS has switches only in a portion of the branches, but the number of switches tends to be expressive in larger systems. In this context, less complex restoration problems have been successfully solved in the literature by exact methods, but they tend to be prohibitive in highly complex problems. In this paper, a mathematical model with an enhanced approach solves, through exact techniques, the restoration problem in a relatively large radial EDS with the aim of evaluating its ability to obtain optimal operationally reliable solutions with low computational effort. The problem is solved without simplifying the topological structure of the system and using only two types of binary variables. The model minimizes the demand not supplied with a minimum number of switching operations, allowing considering the influence of priority loads and remotely controlled switches, and ensures a feasible and radial operation. Tests were carried out on a radial 417-bus EDS adapted to have switches at strategic locations and the results show that the model effectively provides optimal solutions and can be applied for larger systems mainly in an offline or preventive way.