Hybrid AC/DC OPF Model for Unbalanced Operation of Bipolar HVDC Grids

HVDC is a critically important technology for the large-scale integration of renewable resources such as offshore wind farms. Although to date mainly point-to-point and multi-terminal HVDC systems are in operation with the advancement of VSC-based converter technologies, future HVDC systems are foreseen to develop into meshed HVDC grids. While existing HVDC systems predominantly use monopolar configurations, bipolar HVDC systems offer additional benefits in terms of availability and flexibility. Bipolar HVDC grids can be intentionally operated in an unbalanced way during single-pole converter and dc branch outages or by design in the form of mixed monopolar and bipolar configurations. In order to study the steady state behaviour of such systems (optimal) power flow tools are needed capable of representing such system unbalance. For this reason, in this paper, we present a multiconductor OPF model for ac/dc grids with separate modeling of the positive pole, negative pole, metallic return conductors, and ground return to capture the dc grid unbalance. In order to avoid numerical issues due to the low voltage values of the neutral conductor, we formulate the OPF model in the current-voltage space for the dc grid. The model's capabilities are demonstrated using a small test case, including a monopolar tapping in a bipolar dc link. Numerical results are presented for multiple test cases with various system sizes, starting from an 11-bus system to a 3120-bus system to demonstrate the computational tractability of the chosen model formulation. Obtained results indicate that in edge cases converter loop flows can help to find a lower cost generation dispatch in unbalanced situations despite higher losses. Such behavior can only be captured using a multiconductor model as presented.