This study presents a submodule capacitor voltage self‐balancing method for modular multilevel converters (MMCs) based on switching state matrix construction, which has an advantage over eliminating massive sensor demanding and alleviating computational burden for a large number of submodules. It is mathematically proved that MMC has only one static equilibrium operating point to which the submodule capacitor voltages will converge naturally by the evaluation of capacitor voltage deviation index. A novel switching state matrix of submodules is constructed off‐line according to the mathematical proof, and the switching state vectors are cyclically selected from the matrix and distributed to the switching gate signals among the submodules to realize capacitor voltage self‐balance, avoiding real‐time capacitor voltage sampling and sorting. The proposed method is compatible with the conventional double closed‐loop control of MMCs. Theoretical conclusions are verified by simulations and experiments.

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With the increasing proportion of renewable power generations in the power system, the power grid impedance may fluctuate greatly, and it is difficult for the virtual synchronous generator (VSG) with a single control structure to meet the stability requirements. Thus, the control principles of the two types of VSGs are compared to conclude that there are similarities in the control structure of the two VSGs. And the small signal models of the two types of VSGs are established to analyze the stability boundaries, coming to the conclusion that the stability region is complementary. Based on the conclusions, the paper puts forward the idea of switching operation modes: switch to the U‐VSG mode when the grid strength weakens and switch to the PQ‐VSG mode when greater, so that the inverter can keep stable in a wider range of grid strength. Therefore, the characterization method of the switching boundary with hysteresis properties is proposed. Then the improved recursive least squares (RLS) algorithm is introduced to identify the power grid impedance online without additional injected disturbance, based on which the adaptive multi‐mode smooth switching control strategy is proposed. Finally, the effectiveness of the analysis and the control strategy are verified by simulations.

This study presents global asymptotic stability verification of submodule capacitor voltage self-converging modular multilevel converters (SC-MMCs) according to the characteristic root method, which constructs a submodule switching state matrix for voltage balancing control. The mathematical model of MMC is established in form of the state-space equation. It is proved that SC-MMCs have the characteristic of global asymptotic stability at a certain time from the perspective of switching state matrix characteristic roots, according to the theories of Lyapunov stability and continuous-time piecewise linear system stability. Then, the submodule capacitor voltage self-convergence over a period of time is deduced based on the capacitor voltage deviation vector. Under the constraints of linearly independent switching state matrix row vectors, submodule capacitor voltage self-convergence without real-time voltage calculation and feedback can be achieved. The global asymptotic stability of SC-MMCs and the efficacy of submodule capacitor voltage self-convergence based on switching state matrix are testified by simulations.