Stability analysis of offshore HVDC power systems

The ongoing transition from conventional fossil fuel-based power plants to renewable energy sources, coupled with the continued electrification of the industry, transportation, residential, and commercial sectors, is enabled by substantial transformations within the electrical power system. New means of generating electricity, such as wind farms, are frequently located at considerable distances from population centres, whereas rooftop photovoltaic panels are often integrated into urban landscapes, bringing them closer to end-users. These advancements are significant, marking not only a departure from the conventional centralised power generation paradigm of the past century, but also from the reliance on the large synchronous generators of traditional power plants, as renewable sources are typically connected to the grid through power-electronic converters. Moreover, to mitigate the intermittent and uncertain nature of renewable energy production, there is a growing need for enhanced cross-border and long-distance grid interconnections. In this context, high-voltage direct-current (HVDC) transmission technology plays an increasingly pivotal role and is expected to become the backbone of modern power systems. Naturally, HVDC systems need to interface with existing AC systems, a task primarily accomplished through large-scale power-electronic converters.

What merits particular attention is the distinct dynamic behaviour of power-electronic converters in contrast to that of synchronous generators. Relying on switched semiconductor devices with little to no intrinsic energy storage, power-electronic converters are also capable of reacting to disturbances within very small time frames and over broad frequency ranges. Consequently, in today's technology mix, new forms of adverse interactions between converters and their nearby electrical environment have started to emerge, some of which may have severe consequences. A comprehensive investigation and better understanding of the mechanisms underlying these interactions is crucial in taking proactive measures to prevent undesirable dynamic phenomena from deteriorating the proper and stable operation of modern and future power systems.

Among the various types of converters, the modular multilevel converter (MMC) stands out due to its enhanced efficiency and scalability, which come at the cost of an elaborate topology and complex control structures. While multiple methodologies exist for studying potential adverse interactions involving power-electronic converters, methods that were suitable for the previous generations of the power system start to lack accuracy when addressing the particular features of the MMC, such as the multi-harmonic time-periodic nature of its variables in steady state as well as non-negligible delays in its control structure.

In this thesis, mathematical frameworks are studied and developed to enable more accurate small-signal stability assessments specifically addressing unsolved challenges of MMC-based HVDC systems. An overview of periodic trajectory calculation techniques motivates the development of a Fourier-based collocation method to efficiently calculate the steady-state harmonic content of the MMC while accounting for nonlinearity in its dynamic equations. In combination with linearisation, an in-depth review of approximation and transformation methods from time-periodic to time-invariant models demonstrates the advantages of frequency-lifting approaches, such as the harmonic state space, in terms of flexibility and accuracy. Lastly, a generalisation of the harmonic state space is established to enable modal analysis of systems involving the MMC and accounting for both its time-periodic and time-delayed characteristics while discarding common delay approximations.