Efficient handling of radiality constraints for large-scaled power distribution networks

Power distribution networks are usually characterized by a radial topology and therefore the related optimization problems require radiality constraints in their formulations. However, practical instances may have very large size, and the number of radiality constraints { may grow faster than} the size of the instance. Hence, the arising optimization models may become computationally intractable due to their huge dimension. This work proposes a combinatorial optimization approach to overcome this issue. Our approach is based on the combinatorial formulation of the radiality constraints and their delayed and efficient generation in the model, following a separation-optimization scheme. We find an optimal acyclic spanning subgraph subject to both technical side constraints and topological radiality requirements on a graph representing the distribution network. This can be done without considering all the exponentially many radiality constrains from the beginning of the model solution, but introducing only the ones that are needed to make the solution feasible. It turns out that the number of required constraints is much smaller than the number of all possible radiality constraints, also because some of the electric constraints already favor the elimination of infeasible configurations. Computational experiments on reconfiguration benchmarks from the literature show the effectiveness of the proposed approach.