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Most of the existing stability analysis methods are capable of determining the oscillatory stability of black-box converter interfaced generators (CIGs) under given operating conditions only but can hardly identify the critical operating conditions. In this letter, an oscillatory stability region (OSR) is defined with the short-circuit ratio and output power as variables, and a method to obtain the OSR for the black-box CIG is proposed. First, the CIG is modeled as a variable-operating-point impedance model (VOPIM) through perturbation tests. Then, the critical operating points, for which the CIG system has a zero-damping oscillation mode, are determined by VOPIM-based oscillatory stability analysis so as to obtain the OSR. Finally, the accuracy of the OSR is verified through control hardware-in-the-loop tests. The OSR is of significant meaning for the control strategy and operation plan optimization of the CIGs. [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]

This paper analytically examines how the condition of weak grid connection affects the torsional sub-synchronous oscillations (SSOs) induced by a grid-connected DFIG in a power system. The examination focuses on the SSO mode of grid-connected DFIG, which is dominated by the phase locked loop (PLL) or DC voltage control. Theoretical analysis is carried out to prove that the condition of weak grid connection amplifies the impact of modal resonance between the DFIG and torsional dynamics of synchronous generators. The amplifying effect of weak grid connection exhibits as the decrease of damping of SSO mode of DFIG and increase of the associated residue when the grid connection weakens. Consequently, the DFIG is more likely to induce torsional SSOs under the condition of weak grid connection, leading to system instability in the worst case. Analytical examination presented in the paper reveals the mechanism about how the condition of weak grid connection plays a key role for the DFIG to induce the torsional SSOs. An example multi-machine power system with the grid-connected DFIG is presented. Results of modal analysis and non-linear simulation using detailed model of DFIG validate the analysis and conclusions made in the paper. [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]

Recently, emerging oscillation issues have been caused by subsynchronous interaction (SSI) between voltage source converters (VSCs) based renewable generators and ac/dc grids. To investigate the dynamics of SSI, several impedance models (IMs) of VSC have been developed in previous studies. They are established in different reference frames and consider the entire or just parts of the control systems. However, it is still an unanswered question whether or not the existing IMs are suitable for SSI analysis and to what extent the IMs with different modeling details affect subsynchronous dynamics. To fill in this gap, this paper, first, reviews the existing IMs of VSC and clarifies their relationship. Then, their frequency characteristics are examined so as to select the proper models for the studies of sub-/supersynchronous and high-frequency dynamics. Next, both zero-pole and IM-based SSI analyses are carried out on a simplified system and a real-world wind-farm system that suffered actual SSI incidents. The results indicate that the outer-loop control has a significant impact on the subsynchronous dynamics, and only those IMs taking full-scale controls and frequency-coupling effects into account can reflect SSI accurately. Finally, both modal analysis and electromagnetic transient simulations have been conducted to verify the theoretical results. [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]

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]

A new type of subsynchronous resonance (SSR), namely, subsynchronous control interaction (SSCI), was recently observed in doubly-fed induction generators (DFIGs) interfaced with series-compensated power networks. In this paper, a more accurate method based on aggregated RLC circuit model is proposed to intuitively explain and quantitatively evaluate this type of SSR. For a practical power system containing multiple DFIGs and fixed series compensation, an improved impedance model (IM) is derived, which incorporates DFIG's full-scale control system. Around the series-resonant frequency, IM can be further represented with an aggregated RLC circuit model. Its equivalent parameters are worked out and then used for the quantitative assessment of potential SSR risk. The proposed method is applied for SSR analysis of a practical wind farm system in North China that experienced actual SSR incidents. The consistence between the obtained results and field measured data verifies its effectiveness very well. Further, its advantage in accuracy over existing impedance-based approaches is validated by both eigenvalue analysis and time-domain simulations. The method is also used to quantitatively investigate the impact on SSR stability from the various factors, including wind speed, number of online DFIGs and their control parameters. [ABSTRACT FROM AUTHOR]

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]

Supplementary excitation damping controller (SEDC) has been widely acknowledged as one of the effective measures to stabilize subsynchronous resonance (SSR). However, how to quantify its stabilizing ability is still an open issue raising widespread concerns. There are few in-depth studies or conclusions in this aspect yet. This paper presents a quantitative measure of SEDC's ability to damp SSR, namely stabilizing ability index (SAI). It is defined as the percentage margin of the effective gain relative to the critical stability gain (CSG). The CSG is the minimum gain of SEDC to guarantee SSR stability, while the effective gain is the control gain of SEDC actually functioning following system disturbances. A practical system is used to investigate the various factors determining the effective gain, the CSG and thus the SAI, based on eigenvalue analysis as well as time-domain simulation. The dominant factors identified include: the total equivalent series-compensation degree of system, the parameters and operating status of the generator, the response time and ceiling voltage of the exciter, and the severity of the disturbance. Why and how these factors affect the control capability of SEDC is examined and thus a practical method is offered for the assessment of SEDC's ability to stabilize SSR. [ABSTRACT FROM AUTHOR]

The Shangdu power plant has four 600-MW turbine-generators connected to the North-China Grid through two 500-kV transmissions, which are compensated with 45% fixed series capacitors. Extensive studies conducted on the system model indicate that the system suffers from multimodal subsynchronous resonance (SSR). To solve the problem, a countermeasure is developed by combining the supplementary excitation damping control (SEDC) and the torsional stress relay (TSR). In this paper, the characteristics of the SSR problem are investigated. Then the developed SEDC is presented. To validate the effectiveness of the proposed SEDC as well as the results of model studies, field tests were conducted under various operating conditions. The tests fully exposed the realistic threat of SSR in the system. Meanwhile, it is demonstrated that the developed SEDC can improve torsional damping significantly, and thus solve the multimodal SSR problem effectively. This is the first time in China that practical SEDCs have been developed and their ability to mitigate multimodal SSR has been verified in a real series-compensated system. [ABSTRACT FROM AUTHOR]