Importance of radiality constraints formulation in reconfiguration problems

Obtaining accurate solutions in an acceptable computation time for the problem of distribution systems reconfiguration is very important because the topology of real distribution systems needs to be changed several times a day in online applications. In this way, the processing time of reconfiguration models must be short enough for quick response to power demand changes and performing the next switching action. One of the most important parts of the reconfiguration problem that significantly affects the computation time is the radiality constraints, in which the best radial topology must be determined quickly without the appearance of loops or isolated buses in reconfigured networks. However, this issue does not happen easily because if the radiality constraints are not defined well, the reconfiguration algorithm finds wrong solutions (non-radial configurations) or acquires the optimal topologies after intensive computations (high CPU time). Therefore, the method of modeling the radiality constraints to find proper solutions in a short computational time is so important. To address this challenge, various formulations of radiality constraints are reviewed in the current study, and their efficiencies are compared in several distribution systems according to the results presented in specialized literature. The investigations done in this paper allow the researchers and operators to better understand the importance of formulating radiality constraints for reconfiguration problems. The results analysis indicates that the adoption of the radiality constraints (64)–(68) for analytical reconfiguration methods is more appropriate while considering the constraint (76) and the fundamental loops are more suitable for metaheuristic reconfiguration algorithms.