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.