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The interactions between permanent magnet synchronous generators (PMSGs) and weak grids may cause negatively damped or growing subsynchronous oscillation (SSO). The growing-SSO would evolve into a sustained-SSO when it is predominantly governed by the nonlinearities in the PMSG's converter control, such as current limiter. Most of the existing frequency-domain modeling and stability analysis methods are in the small-signal sense and thus unable to consider the impact of such nonlinearities. Besides, these methods can hardly give vital information to characterize the sustained-SSO, for instance, the magnitude. This paper presents a detailed characteristic analysis of the sustained-SSO while accounting for the effect of current limiter nonlinearity. First, a single-input-single-output (SISO) frequency-domain model of the PMSG is developed. This SISO model comprises the transfer functions of outer-/inner-loop controls and phase-locked loop (PLL). The nonlinear part, i.e., current limiter, is incorporated into the model using the describing function (DF) method. Then, the equivalent transformation on the system's closed-loop characteristic equation is used to separate the SISO model into independent linear and nonlinear parts. This separation enables the use of the DF-based Nyquist criterion for evaluating the system stability and determining oscillation attributes, such as the magnitude and frequency. Both the analytic results and time-domain simulations reveal that the current limiter has a significant impact on the characteristics of the sustained-SSO. [ABSTRACT FROM AUTHOR]

Electromagnetic transient (EMT) and transient stability hybrid simulations are predominantly used to analyze the interactions between HVDC systems and the ac grids. However, the dynamics of the converters will be greatly affected by the waveforms of adjacent ac systems. Waveform distortion as well as time delay caused by interfacing can significantly increase interface errors, resulting in the decrease of the overall accuracy of the simulations. To solve such problems, a dynamic phasor based interface model (DPIM) is proposed in this paper to improve the accuracy of interfaces, especially when the fault occurs near the converters. In doing so, the whole system is partitioned into three parts: the transient stability (TS) subsystem, the EMT subsystem, and the DPIM. During each iteration, the interfaces between the TS subsystem and DPIM are represented by their Norton equivalents at the fundamental frequency and Thevenin equivalents in the dynamic phasor form. Similarly, the interfaces between DPIM and EMT subsystems are represented by their three-phase Norton equivalents and Thevenin equivalents in dynamic phasors, respectively. The effectiveness concerning the accuracy and the efficiency of the proposed method is validated by simulating a practical HVDC Project. [ABSTRACT FROM AUTHOR]

When investigating voltage and current stresses in critical main circuit components during faults of the converter, a detailed equivalent model capable of representing the balancing control strategies of the capacitor voltages on the submodule level, along with blocking and delocking, is always necessary. Among previously proposed equivalent models of the modular multilevel converter (MMC), only submodule averaged models (SAMs) can capture interested inner dynamics inside each arm. However, the simulation accuracy of SAMs is not always satisfactory, especially when the time step is larger than 10 $\mu$s. In order to further improve the simulation accuracy with guaranteed simulation efficiency, the shifted frequency modeling of the half- and full-bridge hybrid MMC is proposed in this paper. Therein, each submodule is represented by Thévenin equivalents derived by submodule dynamic phasors. The arm of the MMC is represented by Norton equivalents to guarantee the efficiency, considering both normal and dc-blocking conditions. The effectiveness of the proposed model in terms of accuracy and efficiency is validated by simulating an MMC-based HVdc transmission. [ABSTRACT FROM AUTHOR]

This paper proposes a novel multirate co-simulation method to improve simulation efficiency of large-scale AC plus multiterminal DC (MTDC) grids. In this method, the whole system is partitioned into different AC and MTDC subsystems. They each are simulated with different time steps according to their requirements of accuracy. Unlike the existing methods where simplified models are adopted, the proposed approach fully reserves both the detailed behavior of converters and the nonlinear dynamics of large-scale AC systems. To realize the coordination between different subsystems, updating and discretization of the interface models are significant to guarantee the overall numerical accuracy and stability of the co-simulation method. Accordingly, the interface models of the partitioned AC and DC networks are represented by time-varying Thevenin and Norton equivalents. To eliminate the aliasing or time-delay errors, their parameters are derived using moving-window prediction, stepwise correction, and averaging techniques. A numerical oscillation suppression algorithm is developed for the discretization of the interface model. Thus, numerical stability is well guaranteed. The variables inside each subsystem as well as the interfaces, which are derived by augmented network equations (ANEs), are calculated simultaneously. The rate ratio of large AC and MTDC systems is determined based on our proposed criterion of electromagnetic transient simulation accuracy. The effectiveness of the cosimulation method is validated on a practical system integrating large AC and modular-multilevel-converter-based MTDC grids. [ABSTRACT FROM AUTHOR]

The steady increase of power electronic devices and nonlinear dynamic loads in large-scale ac/dc systems desperately requires an efficient simulation method. However, the traditional hybrid simulation, which incorporates various components into a single electromagnetic-transient (EMT) subsystem, causes great difficulty in network partitioning and significant deterioration in simulation efficiency. To resolve these issues, a distributed hybrid simulation method is proposed in this paper. The key factor leading the success of this method is a distinct interfacing technique, which includes: 1) a new approach based on the two-level Schur complement to update the interfaces by taking full consideration of the couplings between different EMT subsystems; and 2) a combined interaction protocol to further improve the efficiency while guaranteeing the simulation accuracy. The improved performances of the proposed method in terms of efficiency and accuracy have been verified by the simulation studies on the modified IEEE 39 system as well as a practical ac/dc system, both of which consist of a two-terminal voltage-source converter HVdc and nonlinear dynamic loads. [ABSTRACT FROM PUBLISHER]