Convex Flexible Branch Model for Steady-State Operational Modelling, Analysis and Optimisation of Hybrid AC/DC Networks

This thesis research introduces a new mathematical modelling framework for solving short-term operational planning formulated as steady-state computational problems for active hybrid AC/DC networks. Specifically, the research aims to address the increasing modelling and computational complexity of such problems (e.g., the OPF problem) for such networks and specifically when applied in both transmission and radial Distribution Networks (DNs). With the increasing level of adoption of Renewable Energy Source (RES) based Distributed Generation (DG) as a viable means to advance decarbonisation targets within energy systems, new hybrid technologies, such as Voltage Source Converter (VSC)-interfaced generation resources as well as active control devices, High-Voltage DC (HVDC) transmission, and Multi-Terminal DC (MTDC) networks, are being explored and implemented in power networks. This shift is driven by the need for advanced controls and coupling conditions for the RES. However, existing mathematical models and management frameworks used for steady-state analysis and operational planning in power networks can become computationally expensive due to the increased complexity of the network. This is mainly because many existing mathematical models are based on the non-convex non-linear AC OPF problem formulation, which can easily become intractable for larger cases, especially when considering a defined time horizon and dealing with the stochastic nature of the RES. To this end, the Convex Flexible Branch Model (CFBM) is presented in this thesis. The CFBM is a new flexible convex OPF framework based on the semidefinite formulation of the OPF and is capable of modelling both passive and active electrical elements, including VSCs, for forming hybrid networks. Moreover, the CFBM is flexible to allow for modelling a variety of AC/DC elements such as VSCs, Static Compensators (STATCOMs) and Static Synchronous Series Compensators (SSSCs). The CFBM is tested and validated using other proven frameworks that use non-convex and convex formulations of the OPF to solve hybrid networks. Simulations and numerical tests demonstrated that the CFBM is capable of obtaining comparable, if not identical, results in terms of operating points to those of the other frameworks. Additionally, it ensures tight objective function values (i.e., negligible relaxation gaps) and reduced solving times compared to its non-convex, non-linear counterpart. Furthermore, the CFBM is used to obtain a fully convex formulation of a proposed Active Network Management (ANM) framework for Network Reconfiguration (NR) through Back-to-Back (BTB)-VSC arrangements (acting as soft open points) for mitigating the inherent operational challenges in radial DNs related to voltage deviations, power curtailment, power congestion, and generation uncertainty.