Modeling of the Modular Multilevel Converter using Dynamic Phasors: Reduced-Order Models for Small-Signal Stability Analysis

The decarbonization of the power system is becoming ever more urgent to limit global warming. Strengthening the electricity transmission networks is essential to enhance the proliferation of renewable energy sources (RES), which plays an integral role in the energy transition. High voltage direct current (HVdc) interconnections based on the voltage source converter (VSC) technology are proven candidates to strengthen power systems and interconnect RES, thereby increasing the share of RES in the global energy mix. In the past decades, the modular multilevel converter (MMC) has become the mainstream VSC topology, and has enabled a wide-scale utilization of VSC- HVdc links at high power ratings. Despite the advantages brought by the MMC, the increasing utilization of MMC-HVdc connections in power systems raises significant concerns regarding small-signal stability analysis. The MMC has a unique internal dynamic behavior characterized by harmonics of multiple frequencies. On the one hand, the small-signal stability of power systems is traditionally studied using linear time-invariant (LTI) component models. On the other hand, in the presence of multiple frequencies at steady state, linearization yields a linear time-periodic (LTP) MMC model, which is hardly compatible with existing power system models. Therefore, the multifrequency- periodicity of the MMC challenges the development of accurate LTI models of the converter to be utilized in small-signal stability studies. Frequency-lifted modeling techniques such as the dynamic phasor (DP) theory or the harmonic state space (HSS) framework are commonly applied to develop LTI state-space models of the MMC. However, the state-of-the-art frequency-lifted models of the MMC are mostly associated with a high number of state variables. The large number of states of the existing frequency-lifted models makes them less convenient for small-signal stability analysis, and simultaneously challenges the available computational resources. Furthermore, the maximum frequency harmonic to be considered in small-signal stability studies involving MMCs, as well as the implications of ignoring harmonics in these studies, are often not addressed. This thesis presents a detailed study on the influence of harmonics on the small-signal stability of the MMC. A generic DP-based state-space model of the MMC and its controllers is developed. The developed DP model of the converter is used to study the properties of harmonics that are observed in the currents and capacitor voltages of the MMC. Different model order reduction techniques are proposed to independently reduce the orders of the converter and controller models. The developed models are used to study the impact of computational time delays on the small-signal stability of the MMC, and to design advanced active harmonic suppression (AHS) controllers giving the converter active filtering functionality. Both the full- and reduced-order DP-MMC models are compared against detailed benchmark models, and the accuracies of the proposed reduced-order models are evaluated. With the help of the comparisons, the maximum frequency to be included in DP models of the MMC is determined. The small-signal stability of the developed models is assessed by means of eigenvalue calculations. The calculations reveal the representativeness of the reduced-order models under varying operating conditions. The results of the stability analyses allow to choose an appropriate reduced-order model depending on the type of study and the steady-state operating point. To sum up, this thesis demonstrates that an accurate representation of the multifrequency-periodic nature of the MMC is crucial in small-signal stability analysis, and provides a wide range of reduced-order LTI state-space models of the converter to study its small-signal stability under various operating conditions. In doing so, this thesis draws the attention to accurate component models representing harmonics, and the necessity of such models in the small-signal stability analysis of future power systems.

Publication year:2022

Accessibility:Open