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Transmission Network Expansion Planning (TNEP) problems find the mosteconomical way of expanding a given grid given long-term growth in generationcapacity and demand patterns. The recent development of Flexible ACTransmission System (FACTS) devices, which can dynamically re-route power flowsby adjusting individual branches' impedance, call for their integration intoTNEP problems. However, the resulting TNEP+FACTS formulations are significantlyharder to solve than traditional TNEP instances, due to the nonlinearity ofFACTS behavior. This paper proposes a new mixed-integer formulation forTNEP+FACTS, which directly represents the change in power flow induced byindividual FACTS devices. The proposed formulation uses an extended formulationand facet-defining constraints, which are stronger than big-M constraintstypically used in the literature. The paper conducts numerical experiments on asynthetic model of the Texas system with high renewable penetration. Theresults demonstrate the computational superiority of the proposed approach,which achieves a 4x speedup over state-of-the-art formulations, and highlightthe potential of FACTS devices to mitigate congestion.

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