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Abstract-The recent rise of electricity generation based on renewable energy sources increases the demand for transmission capacity. Capacity expansion via the upgrade of transmission line capacity, e.g., by conversion to a high-voltage direct current (HVDC) line, is an attractive option. In this paper, it is shown that if the upgrade to HVDC is applied systematically to selected transmission lines across the grid, a hybrid architecture is obtained that enables an efficient and globally optimal solution of the optimal power flow (OPF) problem. More precisely, for conventional meshed AC transmission grids the OPF problem is nonconvex and in general NP-hard, rendering it hard to solve. We prove that after the upgrade to the proposed hybrid architecture, the same mesh topology facilitates an exact convex relaxation of the OPF problem, enabling its globally optimal solution with efficient polynomial time algorithms. This OPF method is then employed in simulations, which demonstrate that the hybrid architecture can increase the effective transmission capacity and substantially reduce the generation costs, even compared to the AC grid with optimal transmission switching.Index Terms-Congestion management, convex relaxation, economic dispatch, HVDC transmission, optimal power flow, optimal transmission switching, power system design, power system management, semidefinite program, transmission capacity.

Recently, we proposed a capacity expansion approach for transmission grids that combines the upgrade of transmission capacity with a transition in system structure to improve grid operation. The key to this concept is a particular hybrid AC/DC transmission grid architecture, which is obtained by uprating selected AC lines via a conversion to HVDC. We have shown that this system structure improves optimal power flow (OPF) solvability and that it can reduce the total generation costs. In this work, we study the benefits of this hybrid architecture in the context of a deregulated electricity market. We propose an efficient and accurate nodal pricing method based on locational marginal prices (LMPs) that utilizes a second-order cone relaxation of the OPF problem. Applicability of this method requires exactness of the relaxation, which is difficult to obtain for conventional meshed AC transmission grids. We prove that the hybrid architecture ensures applicability if the LMPs do not coincide with certain pathological price profiles, which are shown to be unlikely under normal operating conditions. Using this nodal pricing method, we demonstrate that upgrading to the hybrid architecture can not only increase the effective transmission capacity but also reduce the separation of nodal markets and improve the utilization of generation.Comment: IEEE Transactions on Power System

High-voltage direct current (HVDC) systems are increasingly incorporated into today's AC power grids, necessitating optimal power flow (OPF) tools for the analysis, planning, and operation of such hybrid systems. To this end, we introduce hynet, a Python-based open-source OPF framework for hybrid AC/DC grids with point-to-point and radial multiterminal HVDC systems. hynet's design promotes ease of use and extensibility, which is supported by the particular mathematical model and software design presented in this paper. The system model features a unified representation of AC and DC subgrids as well as a concise and flexible converter model, which enable the compact description of a hybrid AC/DC power system and its OPF problem. To support convex relaxation based OPF solution techniques, a state space relaxation is introduced to obtain a unified OPF formulation that is analogous to the OPF of AC power systems. This enables the direct generalization of relaxation-related results for AC grids to hybrid AC/DC grids, which is shown for the semidefinite and second-order cone relaxation as well as associated results on exactness and locational marginal prices. Finally, hynet's object-oriented software design is discussed, which provides extensibility via inheritance and standard design patterns, and its robust and competitive performance is illustrated with case studies.