  Transmission Network Expansion Planning (TNEP) problems find the most
economical way of expanding a given grid given long-term growth in generation
capacity and demand patterns. The recent development of Flexible AC
Transmission System (FACTS) devices, which can dynamically re-route power flows
by adjusting individual branches' impedance, call for their integration into
TNEP problems. However, the resulting TNEP+FACTS formulations are significantly
harder to solve than traditional TNEP instances, due to the nonlinearity of
FACTS behavior. This paper proposes a new mixed-integer formulation for
TNEP+FACTS, which directly represents the change in power flow induced by
individual FACTS devices. The proposed formulation uses an extended formulation
and facet-defining constraints, which are stronger than big-M constraints
typically used in the literature. The paper conducts numerical experiments on a
synthetic model of the Texas system with high renewable penetration. The
results demonstrate the computational superiority of the proposed approach,
which achieves a 4x speedup over state-of-the-art formulations, and highlight
the potential of FACTS devices to mitigate congestion.
