arXiv:2610.30011v1 Announce Type: new Abstract: Deploying voltage source converter (VSC)-based multi-terminal DC (MTDC) networks in existing AC grids offers a promising solution for alleviating transmission congestion, enhancing power-transfer capability, and improving operational economy. However, constructing an MTDC network requires participation from merchant investors. Therefore, the transmission system operator (TSO) responsible for the AC grid must provide an adequate economic incentive that enables merchant investors not only to recover the MTDC investment cost but also to earn a reasonable return commensurate with their risk and expectations. An insufficient incentive may fail to attract merchant investment, whereas an excessive incentive may unnecessarily reduce the economic benefits retained by the TSO. Determining an appropriate incentive that balances these competing interests therefore becomes a critical issue. To address this issue, this paper formulates a sharing-rate-parameterized mixed-integer second-order cone programming (MISOCP) model that jointly optimizes VSC siting and sizing while coordinating AC/DC system operation. A straightforward search procedure is then employed to identify the benefit-sharing rate that meets the investor's expectations while preserving sufficient benefits for the TSO. Case studies demonstrate the operating-cost benefits of MTDC integration and validate the proposed search strategy for seeking such a benefit-sharing rate.