This paper aims to establish the wideband model of a sub-module in a modular multilevel converter (MMC) and analyze the switch transients of the sub-module. The paper builds an MMC sub-module test circuit and conducts dynamic tests both with and without the bypass thyristor. Then, it builds the wideband model of the MMC sub-module and extracts the model parameters. Finally, based on the wideband model, it simulates the switch transients and analyzes the oscillation mechanism. The dynamic testing shows the bypass thyristor will add oscillations during switch transients, especially during the turn-on process. The thyristor acts like a small capacitor and reduces the total capacitor in the turn-on circuit loop, thus causing under-damped oscillations. This paper found that the bypass thyristor will influence the MMC sub-module switch transients under certain circumstances. This paper proposes a partial inductance extraction procedure for the MMC sub-module and builds a wideband model of the sub-module. The wideband model is used to analyze and explain the switch transients, and can be further used for insulated gate bipolar transistor switch oscillation inhibition and sub-module design optimization.

The increasing penetration of renewable generations (RGs) poses significant challenges to the operation of transmission power systems, especially for not only steady-stage uncertainties but also dynamic-state stability. Hence, the symmetry of RGs and synchronous generations (SGs) should be improved by a proper planning strategy. For this purpose, a multi-stage stochastic planning method is proposed for transmission power systems (TPSs) considering dynamic frequency stability. Specifically, the progressive uncertainties of RGs over stages are addressed with a multi-stage stochastic method with nonanticipativity constraints. In this scheme, the uncertainty is represented by probability-weighted scenarios, and the planning decisions are only dependent on current realizations of RG uncertainties according to nonanticipativity constraints to improve planning efficiency. Moreover, the dynamic frequency stability constraints are derived considering the frequency regulation strategy of RGs, and these nonconvex constraints are further linearized with high accuracy by a maximal affine function-based method to improve the compatibility with the planning model. Subsequently, a progressive hedging algorithm (PHA) is designed to reduce the computational burden by decomposing the multi-scenario high-dimensional model into multiple small-scale models. Finally, the effectiveness of the proposed method, as well as its superiority over existing approaches, are validated through numerical experiments.

To address the stability problem related to grid-connected modular multilevel converter high voltage direct current (MMC HVDC) connected to weak alternative current (AC) systems, the short-circuit ratio (SCR) that affects the stability of the system was analyzed first. Short-circuit ratios with SCR values greater than 1.3 were obtained, and the system could still operate stably. By applying the theoretical equations of classical circuits, it has been theoretically proven that for the constant active power and constant AC voltage control modes on the weak system side, after the flexible direct current enters the weak system mode, the power must be reduced to ensure the stable operation of the system. Combined with the actual situation of the north channel of the Chongqing–Hubei back-to-back MMC HVDC project, which is connected to the weak system mode, measures such as the optimization of the control mode and the improvement of control functions in the weak system mode were proposed, and simulation calculations and real time digital simulator (RTDS) simulation verifications were carried out. These control strategies have been applied to the Chongqing–Hubei MMC HVDC project, and on-site verification tests have been conducted to ensure stable operation in the weak system mode.