Strong Mixed-Integer Formulations for Transmission Expansion Planning with FACTS Devices

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.