Optimal Planning of Embedded VSC-HVDC for Urban Power Grids with High Load Density

The rising load density and increasingly uneven spatial distribution in urban AC grids are undermining power flow controllability. Congestion in AC corridors and short-circuit limits have become dominant constraints. To address these challenges, an optimized planning approach for embedded voltage source converter based high voltage direct current (VSC-HVDC) is developed, by adding converters and DC lines to form a hybrid AC/DC architecture, which enables rapid inter-area power flow redistribution and mitigates AC bottlenecks. A mixed-integer linear programming (MILP) model minimizes total planning-period cost by unifying DC terminal siting, converter sizing, generator dispatch, load-shedding decisions, and line power flow control within a single decision framework. Nonconvex couplings between DC terminal siting and DC line connectivity are handled via linear relaxation. The total-cost objective integrates capital expenditures of converters and DC lines with operating costs from generation and load shedding. Case studies on the IEEE 30-bus system compute planning solutions at several discrete load levels and demonstrate that optimized DC configurations effectively relieve AC congestion, ensure secure operation, and minimize planning-period cost. These findings highlight the potential of embedded VSC-HVDC for precise power flow steering and improved techno-economic performance, offering both theoretical support and a practical pathway for flexible interconnection upgrades in high-load-density urban grids.