Mathematical modelling of multi-terminal VSC-HVDC links in power systems using optimal power flows

An advanced mathematical model of the Voltage Source Converters (VSC) suitable for optimal power flow (OPF) solutions using Newton’s method for augmented Lagrangian functions has been developed in this research, using first principles – this model is far more flexible and realistic than the existing VSC models aimed at fundamental frequency power systems studies. The nodal active and reactive powers of the VSC are suitably modified to accommodate more complex models corresponding to back-to-back, point-to-point and multi-terminal High Voltage Direct Current (HVDC) transmission links, within Newton’s OPF algorithm – the various model representations of the HVDC links use two or more VSC models, resulting in a new and more powerful way of VSC-HVDC representation. These models are subsequently used to interconnect otherwise independent AC systems. The new models are developed and presented in quite a comprehensive manner throughout the thesis. System simulations are carried out in order to illustrate the VSC-HVDC modelling flexibility in representing various modes of VSC-HVDC operation by selecting a range of control modes. It should be noticed that a straightforward extension of the VSC model yields a new STATCOM model of unrivalled modelling flexibility. It has been observed that the new models do not impair the strong convergence characteristics exhibited by Newton’s iterative method. As an integral part of this research, a computer program written in MATLAB has been developed to perform OPF system simulations. The program is capable of solving conventional power systems of an arbitrary complexity, multi-terminal VSC-HVDC transmission links and combined AC/DC transmission systems. It follows that less complex systems comprising one or more STATCOM, back-to-back and point-to-point VSC-HVDC can be solved with ease, using the Newton OPF computer program. It should be brought to attention that existing power systems commercial or distribution free packages with OPF facilities do not possess the advanced modelling capabilities exhibited by the new VSC model and its extensions, presented in this thesis