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This paper develops a comprehensive dynamic-phasor-based small-signal model for the modular multilevel converter (MMC) system under unbalanced grid conditions, which takes into consideration the dynamics of the MMC system under a balanced grid condition as well as the other emerging internal harmonics produced by the unbalanced grid components and more complex controllers. The small-signal model is validated by comparing the time-domain responses from a detailed electromagnetic transient (EMT) simulation in PSCAD/EMTDC. Based on the eigen-analysis and PSCAD-based time-domain simulation studies, this paper reveals the poorly damped modes that cause unstable oscillations in MMC system under the unbalanced grid conditions. From the results, more poorly damped modes involved in the internal harmonics are emerging under unbalanced grid conditions compared with the modes under the balanced grid conditions, and can highly impact the system dynamic behaviors by the selection of the control parameters. It is also shown that, under the unbalanced grid conditions, the feasible region of the control parameters of the vector current control gets narrowed indicating the reduction of the stability margin, smaller (larger) value of proportional (integral) gain of the circulating current suppressing controller can enhance the system stability, and larger values of the proportional and integral gains of the negative-sequence current suppressing control can result in the harmonic instability of the MMC system. Besides, the parameters of multiple complex-coefficient filters for positive- and negative-sequence components extraction also have a big impact on the small-signal stability of the MMC system and are required to be properly selected. [ABSTRACT FROM AUTHOR]

This paper presents a new approach in adaptive out-of-step (OOS) protection settings in power systems in real time. The proposed method uses extended equal area criterion (EEAC) to determine the critical clearing time and critical clearing angle of the system, which are vital information for the OOS protection setting calculation. The dynamic model parameters and the coherency groups of the system for EEAC analysis are determined in real time to ensure that the newly calculated settings suit with the prevalent system operating condition. The effectiveness of the method is demonstrated in simulated data from a 16-machine 68-bus system model. [ABSTRACT FROM PUBLISHER]