Trade-off between computation time and solution quality for integrated generation and transmission expansion planning with N-1 security criterion

The generation and transmission (G&T) expansion planning of large-scale systems is usually carried out hierarchically due to the high complexity of the problem. However, this hierarchical plan may be more expensive than a fully integrated (co-optimized) G&T plan that, on the other hand, requires high computation time. Therefore, the trade-off between computation time and solution quality is of great importance, especially with the integration of renewable generation. This paper proposes and assesses alternative formulations of the integrated G&T planning problem, also considering the system operation simulation under the N-1 security criterion, seeking to balance solution optimality and computational effort. The assessments are illustrated for the Chilean electrical system. The main outcome is that one of the proposed methods, in which the future cost function is maintained fixed during the generation and transmission optimization and is recalculated only in the final simulation of the system operation, achieves results very close to the fully integrated generation, transmission, and operation optimization method. This method presents a cost reduction of 8 % compared to a hierarchical approach, which represents savings of around 700 million dollars, and 50 % less computation time compared to the fully integrated method. For the same proposed method, the preliminary calculation of an optimal solution without applying the N-1 security constraint as a starting point, followed by re-optimization with active N-1 security constraints, contributes to a 65 % reduction of the computation time without significantly impacting the quality of the solution.