Small-Signal Stability Modelling and Analysis of Modular Multilevel Converter and its Closed-Loop Controllers

As the transformation of the electricity generation progresses, the number of power electronic-based devices connected to the electricity grid is expected to grow. To ensure the stability of the power system in a scenario with high penetration of power electronic converters, the dynamics and stability characteristics of these devices have to be comprehensively studied. This is especially important for bulk converters — with capacities in the hundreds of megawatts range — such as high-voltage direct current (HVDC) systems.Small-signal analysis is extensively used in power system stability studies. The calculation of the system eigenvalues provides insights regarding the dynamic behavior and the nature of the interactions within the system. However, generating a small-signal representation of power electronic converters is known to be problematic, due to the switched operation of such converters and their complex control structures. Nevertheless, usage of modular multilevel converters (MMC) in HVDC systems is rapidly increasing. This creates the need for extensive studies regarding its dynamic behavior. Due to the MMC unique submodule-based topology, special actions have to be taken if the stability of the converter is to be analyzed.In this thesis, a small-signal model of a generic MMC was developed by linearizing all the converter plant and control equations, to analyze the converter stability. Averaging was used to eliminate nonlinearities brought forth by the converter switching actions.The main contributions of this thesis are the application of classic linear-time invariant theory to a time-varying system by linearizing the full converter model at different points in time, and the application of modal analysis methods to the MMC.The small-signal model was verified against a large-signal one, both developed in Matlab/Simulink. Additionally, the system eigenvalues obtained analytically and numerically —using Matlab/MuPaD and Simulink Control Design Toolbox, respectively — were benchmarked. After obtaining the system state-space matrix, its transfer functions were used to estimate the input impedance of the MMC in the frequency domain. Using the linearized system matrix and an optimization algorithm, namely MVMO, the locations of the converter eigenvalues were optimized by finding a new set of controller gains. Finally, calculating the converter eigenvalues, understanding the effects of these eigenvalues on the system variables and applying advanced tools to tune the controllers of the MMC, and possibly also its main circuit parameters, may aid system designers in controller design and parametrization studies.Electrical Engineerin