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Advanced Control Methods for Power Converters: Focusing on Modular Multilevel Converters
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Development of powerful processors along with the complex structure of modern multilevel converters necessitate the utilization of advanced control methods for power converters. This necessity speciffcally arises in the case of modular multilevel converters (MMCs). Although the unique structure of MMCs establish them as one of the most promising candidates for medium- /high- voltage applications, the complexity in the control of their internal dynamics appears as one of the main technical challenges. It is shown in this work that the dynamics of the MMC can be represented by a bilinear multi-input multi-output discrete-time model, where the bilinearity consists of products between the states and inputs. Therefore, the main goal of this thesis is to propose new control methods applicable to discrete-time bilinear systems, with special attention to MMCs. After discussing the state of the art in the control methods of MMCs and presenting the applications of MMCs in HVDC systems, in the first step, application of predictive-based control strategies for MMCs are considered. A well-known predictive-based strategy for power converters is finite control set model predictive control (FCS-MPC), however, its application for MMCs becomes ineffcient as the computational load of selecting the best switching sequence is cumbersome due to the high number of switching state options. This thesis proposes a new structure for FCS-MPC application of MMCs which reduces the computational burden drastically, reduce the communication between submodules and central controller, reduce the switching frequency and power losses, and provides a trade-off between control of acside currents, differential currents, and submodule capacitor voltages. Afterwards, an stabilizing controller design method is proposed for discretetime bilinear systems by using sum of squares (SOS) programming. It is proved that a polynomial controller in the states cannot verify the global asymptotic quadratic stability of the bilinear systems (under specifisystem structure conditions), therefore, rational polynomial controllers are considered. A scalarized version of Schur complement is proposed. Next, the Lyapunov difference inequality is converted to an SOS problem, and the region of quadratic stability of the bilinear system is maximized by an optimization problem. Handling of input constraints, improving the rate of convergence, and optimization of shape of the Lyapunov function are also considered. Next, the proposed SOS-based control design method for discrete-time bilinear systems is applied to a 20-level MMC. The mathematical bilinear model of the MMC is derived by accounting for ac-side currents, differential currents, dc-side current, and stored energy of the converter. A coordinate transformation to the origin is applied and the steady-state operating point of the MMC is calculated based on the desired reference values. In this work, the Lyapunov based control design strategy, using the SOS programming, guarantees the quadratic stability of the MMC in the calculated region of convergence. This region is maximized to ensure the stability of the MMC for all the possible operating points. The external and internal dynamics of the MMC are controlled by only one designed controller, instead of several PI controllers. The performance of the proposed strategy is evaluated based on the time-domain simulation studies. In the last step, some robustness issues arising in the design of SOS-based controllers for discrete-time bilinear systems are investigated and examined for the dc/dc buck/boost converters. It is shown that the averaged dynamic model of a class of power converters can be represented by discrete-time bilinear models and controlled by proposed SOS-based controller. Thereafter, the behavior of the system for a new operating point is analyzed. It is shown that new dynamics is observed when applying the same controller at a new operating point, even after using the shift of the origin method. Therefore, new criteria is introduced to verify the stability of designed controller for other desired operating points. Another related topic that is covered is the introduction of integral action in the bilinear controller design, providing offset-free control for persistent disturbances.