AC/multi-terminal DC (MTDC) hybrid power systems have emerged as a solution for the large-scale and long-distance accommodation of power produced by renewable energy systems (RESs). To ensure the optimal operation of such hybrid power systems, this paper addresses three key issues: system operational flexibility, centralized communication limitations, and RES uncertainties. Accordingly, a specific AC/DC optimal power flow (OPF) model and a distributed robust optimization method are proposed. Firstly, we apply a set of linear approximation and convex relaxation techniques to formulate the mixed-integer convex AC/DC OPF model. This model incorporates the DC network-cognizant constraint, enabling DC topology reconfiguration. Next, generalized Benders decomposition (GBD) is employed to provide distributed optimization. Enhanced approaches are incorporated into GBD to achieve parallel computation and asynchronous updating. Additionally, the extreme scenario method (ESM) is embedded into the constructed AC/DC OPF model to provide robust decisions to hedge against RES uncertainties. ESM is further extended to align the GBD procedure. Numerical results are finally presented to validate the effectiveness of our proposed optimization method.

The distribution network (DN) reconfiguration is a well-known optimal power flow (OPF) problem. However, with the transition of DN from 'passive' to 'active', new technical challenges arise in DN reconfiguration. This article addresses two key issues in this regard. Firstly, the integration of local renewable generation (LRG) introduces uncertainty into the system-wide power flow of the DN. Secondly, the coupling between DN and the external power grid (EPG) affects the determination of DN root voltage. Consequently, a novel DN reconfiguration approach is proposed in this article. To begin with, an explicit mixed-integer convex OPF model is constructed that incorporates both the EPG and DN sides. Notably, the OPF model embeds the function of local droop control that is provided by LRG. Subsequently, the original OPF model is decomposed, and the distributed optimization methods based on the augmented Lagrangian relaxation are employed. The article comprehensively discusses parallel processing and asynchronous implementation as parts of the distributed optimization procedure. Furthermore, to address the uncertainty related to LRG integration, the extreme scenario method is used to provide a robust decision regarding DN reconfiguration. The application of the extreme scenario method in the distributed OPF model concerning DN reconfiguration is successively developed. Finally, numerical results are presented to demonstrate the acceptable performance of the distributed optimization methods, in terms of optimality and convergence. Also, these are validated that the proposed DN reconfiguration approach exhibits robustness to LRG integration, the system-wide voltage profile is improved, and the active power loss is effectively reduced using the proposed DN reconfiguration approach.