Linear and quadratic optimal power flow models of a hybrid network based on VSC-MTDC

Optimal Power Flow (OPF) models are essential tools not only from the daily operational point of view, but also for medium-term and long term studies. In this case, when it is necessary to consider future expansion planning, the size of the resulting problem can be intractable. This paper presents two approximated (linear and quadratic) formulations of the OPF considering a combination of a Voltage Source Converter based Multi-Terminal High Voltage Direct Current grid (VSC-MTDC) and an alternating current (AC) system. The models presented in the paper take into account both transmission losses and converter losses. The key technical limits of VSC are included in both models as constraints for VSC-MTDC system operation. All the study results are verified and compared with the full power flow solver based on MATPOWER. The models allow to obtain good approximations of power flows and voltage levels of all DC buses within a reasonable range of accuracy, as well as to model the interaction between AC and DC networks with a substantial lower computational burden compared with the state-of-the-art
non-linear OPF models.