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

TL;DR

This paper addresses Transmission Network Expansion Planning (TNEP) with Flexible AC Transmission System (FACTS) devices by introducing a strong mixed-integer linear programming formulation that directly represents FACTS-induced changes in power flows. It replaces weak big-M approaches with an extended disjunctive formulation and facet-defining inequalities, enabling tighter relaxations and faster solution times. On a synthetic Texas TX123BT system with high renewable penetration, the proposed FACeTS formulation achieves roughly a 4x speedup and a 40x reduction in branch-and-bound nodes compared with prior methods, while reducing unserved energy and curtailed renewables. These results demonstrate the practical potential of FACTS to mitigate congestion and improve long-term planning reliability, with implications for broader grid optimization and market applications.

Abstract

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.

Figures (11)

• Figure 1: Domain Space of $(\mathbf{p}^{\text{f}}, \theta)$
• Figure 2: The 123-bus Texas 345kV backbone topology. Circles indicate the location and size (scaled nameplate capacity, in MW) of renewable generators.
• Figure 3: Evolution of optimality gap (in %) over time, shown in log-scale. The red dashed line indicates the optimality tolerance of 0.01%.
• Figure 4: Evolution of each formulation's primal bound (in M$) over time. The red dashed line indicates the optimal objective value.
• Figure 5: Evolution of each formulation's dual bound (in M$) over time. The red dashed line indicates the optimal objective value.

Theorems & Definitions (4)

• Theorem 1
• proof
• Lemma 1
• proof