A mixed integer linear programming model for minimum backbone grid

Developing a minimum backbone grid in the power system planning is beneficial to improve the power system's resilience. To obtain a minimum backbone grid, a mixed integer linear programming (MILP) model with network connectivity constraints for a minimum backbone grid is proposed. In the model, some constraints are presented to consider the practical application requirements. Especially, to avoid islands in the minimum backbone grid, a set of linear constraints based on single-commodity flow formulations is proposed to ensure connectivity of the backbone grid. The simulations on the IEEE-39 bus system and the French 1888 bus system show that the proposed model can be solved with higher computational efficiency in only about 30 min for such a large system and the minimum backbone grid has a small scale only 52% of the original grid. Compared with the improved fireworks method, the minimum backbone grid from the proposed method has fewer lines and generators.