Does Choice of Power Flow Representation Matter in Transmission Expansion Optimization? A Quantitative Comparison for a Large-Scale Test System

Power transmission network reinforcements must be carefully evaluated to ensure economic, secure, and reliable delivery of electricity. Transmission expansion planning (TEP) models, which seek to optimize the timing, location, and voltages of new transmission lines, can be useful for this task. In general, such models can be mixed-integer nonconvex models due to the discrete nature of investments and AC power flow representations. The original nonconvex TEP model (i.e., ACTEP) is approximated as a linear model (i.e., DCTEP) in most studies. However, the accuracy of this TEP approximation has not been quantified for large-scale power systems. In this article, we first propose a large-scale test system for ACTEP studies, which addresses drawbacks of existing test systems. An ACTEP global solver (i.e., Global-TEP) is used to obtain global solutions of the proposed test system with a guaranteed optimality gap, which allows it to serve as a benchmark for future ACTEP studies. Then, differences among solutions of four TEP models (i.e., DCTEP, local solution of ACTEP, global solution of ACTEP, and global solution of ACTEP with reactive power compensator expansion) are quantified. To our knowledge, this is the first quantitative comparison of DCTEP vs. ACTEP global solutions on a large-scale system. Since a significant difference is observed between the DCTEP and ACTEP solutions, and since the DCTEP solution's performance is significantly worse when verified by an AC load flow model, considering the exact AC power flow representations in TEP studies is recommended.