Resilient Operation of Microgrids: Optimisation Models for Steady-State and Transiently Secure Operation

Recent years have seen electric power systems transitioned to become more sustainable through the incorporation of Renewable Energy Resources (RES), such as wind and solar. RESs interfaced to the grid via fast-acting Power Electronic (PE) converters are therefore gradually replacing conventional generators. Unlike Synchronous Generators (SGs) that have well-defined mechanisms for frequency and voltage support provision, Converter-Interfaced Generators (CIGs) lack these support features inherently. This leads to more volatile system dynamic response when faced with contingencies due to the lack of reactive power support and the low inertia levels. The large excursions in frequency and voltage during such events affect the operational stability and security, potentially resulting in cascading failures and total system collapse. Therefore, there is a great necessity for mechanisms to increase the resilience of power systems. In this respect, Microgrids (MGs) present a revolutionary step in the electric power system infrastructure and operation due to their ability to split from the bulk network and form self-sufficient islands. MGs can enhance the system resilience by forming islands during extreme conditions in the bulk grid, thus ensuring power supply continuity to customers. However, this can only be achieved if MG security is ensured before, during and after an islanding event. The MG should be able to survive the system transients, preventing generator disconnections due to action of device protection systems -- a scenario that can result in cascading disconnections. This thesis proposes a set of optimisation-based algorithms for investment and operation planning of MGs that ensure the security in grid-connected mode, islanded mode, as well as the transitions between the two. The first part of the thesis investigates various formulations of Optimal Power Flow-based (OPF) planning models for MGs. Convex relaxations, restrictions and approximations are investigated for tractability and their applicability to MG networks is assessed. Moreover, the issues of uncertainty due RES and load demand variations are analysed and tackled using two proposed methods, a stochastic approach incorporating machine learning clustering techniques and a distributionally robust technique using linear decision rules. Finally, the proposed MG optimisation models are then enhanced to include security requirements for both steady-state operation as well as transient frequency and voltage response during islanding. Using an analytical formulation for the transient frequency response metrics, an iterative bound-tightening strategy is first proposed to solve a MG planning model consisting of both static and transient security metrics. The same problem is also tackled with a decomposition-based approach using dual cutting planes and sensitivities to frequency support parameters of the different generators. Finally, a dynamic optimisation approach with sequential transient constraint transcription based on time-domain simulations of the MG operation is proposed, incorporating security constraints for both frequency and voltage transient operation in an operational planning problem. All three algorithms investigate both infrastructural enhancement and operational flexibility mechanisms that can be adopted to enhance system performance. Moreover, the algorithms developed ensure cost effective and secure operation of the MG in the pre-islanding, post-islanding and during the event-triggered unscheduled transition to islanded state. The proposed algorithms are tested on MG networks with both CIGs and SGs. The computations and simulations are performed on benchmark low-voltage and medium-voltage distribution networks, as well as the real MG network of Alderney Island.