Preventing Critical Edges when Designing Transmission Networks.

When designing an electric transmission grid, it is important to ensure that the resulting grid is reliable. In particular, it should remain operable if one piece of equipment fails (N - 1 criterion). In this work we focus on the failure of single transmission lines. We consider a criticality measure by Witthaut et al., which captures the dynamic behavior of failing lines. The criterion itself is based on maximum graph-theoretic flows in suitably defined residual networks. In a first step, we compare it to the N - 1 criterion and find that networks without critical edges tend to satisfy the N - 1 criterion. We then formulate the criticality measure as set of linear constraints, which may form a building block in transmission network design problems. In particular, we introduce these constraints into a basic Transmission Network Expansion Planning (TNEP) formulation, obtaining models for the two problems Criticality-Constrained Transmission Network Expansion Planning (CC-TNEP) and Criticality Minimal Expansion (CME). We study the effects of adding these constraints on the time needed for solving the models. Moreover, we provide a simple heuristic for CME, which often finds optimal solutions but in less time.