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Identifying sources of subsynchronous resonance (SSR) is crucial for understanding and mitigating incidents. Recent studies have shown that SSR impedance and power are effective indicators that can identify an SSR source. However, the calculation of two indexes requires SSR voltage and current phasors as the inputs, which are not directly available from existing online monitoring systems. To address this issue, this paper presents a novel method to calculate SSR impedance/power based on synchrophasors provided by a wide-area monitoring system. As a result, the online detection of SSR sources is enabled. Through mathematical derivation, it is revealed that a synchrophasor under SSR is dominated by four modes: two from the fundamental frequency and two from the SSR frequency. The problem thus can be transformed to a modal parameter extraction (MPE). Two classic MPE algorithms, Prony analysis and the matrix pencil method, are employed in this paper to extract the SSR parameters and calculate the SSR impedance/power. Their performances are verified using synthetic signals and electromagnetic transient simulations. Furthermore, the method is applied to an actual SSR incident involving 23 wind farms. The findings suggest that 17 of 23 wind farms did not contribute negative damping to the oscillation. [ABSTRACT FROM AUTHOR]

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]

A frequency-dependent network equivalent (FDNE) is essential to capture wide-band frequency dynamics in the hybrid simulation of large-scale modular multi-level converter based ac–dc grids. The FDNE model must be enforced to be passive, ensuring the numerical stability in time-domain simulations. However, existing passive enforcement techniques based on global optimization perturbations cannot guarantee convergence, accuracy, and efficiency simultaneously. To address the issues, a two-layer FDNE (T-FDNE) model is developed for the ac grids. The two layers, namely, detailed layer and equivalent layer, have their admittances derived by perturbation test and analytical approach, respectively. The passivity of the T-FDNE model is guaranteed by the proposed local passivity compensation technique using auxiliary rational functions. Since no optimization is required and the passivity is enhanced locally, the convergence, accuracy, and efficiency can be improved considerably. By incorporating the T-FDNE model into the interface model of transient (TS) and electromagnetic transient hybrid simulations, wide-band frequency interactions, especially those of very high frequency, can be reflected effectively. The performance (efficiency and accuracy) of the T-FDNE model as well as of the hybrid simulation method has been validated on a modified and practical ac–dc system in China. [ABSTRACT FROM AUTHOR]

To accurately capture the dynamics of a large-scale ac/dc system as a whole and the interactions between its individual components, a simulation method with high precision and efficiency is in great demand. For this purpose, we develop a multi-domain co-simulation method, in which the target system is partitioned into multiple dc and ac subsystems, represented by our proposed shifted-frequency phasor (SFP) models and the traditional EMT models, respectively. SFP models can be simulated with a much larger time step, leading to a significant improvement in simulation efficiency under a given requirement of precision. Further, a new interface model, namely, hybrid multi-domain transmission-line model (HMD-TLM), is developed to reflect the interactions between SFP models and EMT models, with the additional benefit of producing instantaneous and phasor waveforms simultaneously. Thus, the multi-domain co-simulation is implemented based on the efficient SFP models, the HMD-TLM, and a designed time sequences of simulation. The performance (efficiency and accuracy) of the proposed method has been validated on the well-known CIGRE ac/dc system as well as a practical system integrating large ac grids and modular-multilevel-converter-based multi-terminal dc grids. [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]

With increasing applications of voltage source converter-based HVDC (VSC-HVDC), the potential risk of subsynchronous torsional interaction (SSTI) between turbogenerator and VSC-HVDC has been extensively studied in previous work. However, contradictory results were reported by different researchers. Unlike previous studies, wherein the oversimplified models of VSC and generator were used, this paper uses the full-scale model of a practical modular multilevel converter (MMC)-based VSC-HVDC and the multi-mass shaft model of a turbogenerator to analyze the characteristics of SSTI. Moreover, a different approach, namely, the modal signal injection test, is proposed to identify the damping of torsional modes and the impact from decisive factors such as the loading levels, control strategies of converters, and the coupling strength between VSC-HVDC and ac networks. Comparative analyses between the full-scale and the equivalent models have revealed how system modeling affects SSTI characteristics and helped to explain the inconsistencies among the results of previous studies. [ABSTRACT FROM AUTHOR]

To accurately evaluate the damage caused by subsynchronous resonance (SSR) to a turbo-generator shaft, we have developed a novel mechanical and electrical co-simulation method, wherein the continuous-mass-model-based mechanical system is simulated in a close-loop or coupled way with the electrical power system so that the detailed torque profile along the shaft can be obtained for further analysis of fatigue loss of life. Nonlinear mechanical damping is also modelled to reflect the torsional inter action more precisely. The co-simulation is implemented using commercial electromagnetic transient program and finite element analysis software. A special dynamic data exchange mechanism is designed to make it proceed very efficiently. As a case study, the proposed method has been applied for the root-cause analysis of a recent shaft failure incident in an India power plant. The extensive simulation results have fully demonstrated its effectiveness in acquiring fine-grained torques and its advantages over previous methods. Finally the direct cause of the shaft failure is identified to be the sustained torsional interaction (one type of SSR) between the turbo-generator and its connected series-compensated power system. [ABSTRACT FROM PUBLISHER]

Stochastic time delay is a new challenge for communication networks in wide-area damping control (WADC) systems. Uncertainties introduced by stochastic time delays increase the difficulty of modeling, analyzing the stability, and designing the controller. In this paper, a new approach for stability analysis and controller design through expectation modeling is proposed to solve for the uncertainty in wide-area controlled power systems introduced by the effect of a stochastic time delay. In the proposed method, the expectation model that considers the detailed stochastic time delay distribution is derived to accurately model the effect of a communication network on the wide-area control performance. Through a matrix transformation of the expectation model, the eigenvalue of the WADC system that considers time delay can then be calculated; this eigenvalue can be used for analyzing the system stability. A novel expectation model-based controller design procedure is established, through which traditional methods can be applied in the controller design of a power system with a stochastic time delay. Finally, the effectiveness of the stability analysis and controller design methods are validated through simulations in a power system of four generators and two areas with an HVDC link, and a power system with eight generators and 36 buses. [ABSTRACT FROM PUBLISHER]