  It is crucial for maintaining the security of supply that transmission
networks continue to operate even if a single line fails. Modeling $\mathcal{N}
- 1$ security in power system capacity expansion problems introduces many extra
constraints if all possible outages are accounted for, which leads to a high
computational burden. Typical approaches to avoid this burden consider only a
subset of possible outages relevant to a given dispatch situation. However,
this relies on knowing the dispatch situation beforehand, and it is not
suitable for investment optimization problems where the generation fleet is not
known in advance. In this paper, we introduce a heuristic approach to model the
fully secured $\mathcal{N}-1$ feasible space using a smaller number of
constraints in a way that only depends on the topology of transmission
networks. In our proposed approach, the network's security is modelled by
comparing the polytope of the feasible space of nodal net power obtained from
the security-constrained linearized AC optimal power flow problem. To
approximate this polytope, a buffer capacity factor is defined for transmission
lines in the $\mathcal{N}-0$ secure case, thereby avoiding the introduction of
many additional constraints. In this way, three approaches are introduced for
obtaining a buffer capacity factor consisting of approximate, robust and
line-specific approaches. Finally, the performance of our proposed approaches
is assessed in different scales of transmission networks for determining the
proposed buffer capacity factors, contingency analysis and economic evaluation.
Moreover, we find that our proposed heuristics provide excellent approximations
of the fully secured $\mathcal{N}-1$ solutions with a much lower computational
burden.
