In this paper, a new methodology to assist system planners is proposed, which is able of providing a set of good solutions to the addition of new transmission lines, in order to reinforce the sub-transmission network. To circumvent the combinatorial explosion of reinforcement alternatives, a constructive heuristic algorithm is used for adding new branches to the sub-transmission grid. Based on performance indices to measure the attractiveness of new branches and using an expansion tree, the proposed algorithm is able to capture the combined effect of reinforcement additions. For selecting the best alternative, from the set of good reinforcement solutions, the planned network performance in meeting the future load demand is evaluated, considering the following operational aspects: ohmic losses, reliability, branch loading condition, and voltage profile. The evaluation of the performance indices and all operational aspects is achieved by applying a non-linear AC model-based power flow. For the reliability assessment, an enumeration technique is used to select system states. A large sub-transmission Brazilian system belonging to CEMIG utility is used to validate the methodology and the results are presented and extensively discussed.