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In this paper, an approximate aggregated impedance model (AAIM) of a grid-connected wind farm with multiple wind turbine generators (WTGs) for the small-signal stability study is derived. The derivation is conducted under the condition that the WTGs inside the wind farm are of the same type and from the same manufacturer. The AAIM derived can be seen as the impedance model (IM) of a grid-connected aggregated WTG. The IM of the aggregated WTG is the weighted average of the IMs of the individual WTGs in the wind farm and hence is simple to be built. The reactance of the line connecting the aggregated WTG to the external AC grid is the maximum eigenvalue of the network reactance matrix of the grid-connected wind farm. In addition, the derivation justifies the representation of a wind farm by an aggregated WTG in the IM-based small-signal stability analysis. Finally, two example grid-connected wind farms are used to evaluate and demonstrate the effectiveness of the AAIM proposed in the small-signal stability analysis. It is also shown that the computational burden of the stability analysis of a large-scale wind farm could be effectively reduced when the AAIM is used. [ABSTRACT FROM AUTHOR]

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]

Recently, high-frequency resonance (HFR) incidents have occurred in several MMC-HVDC projects. The resonance frequency highly depends on system conditions, making mitigation methods designed for specific scenarios ineffective once the grid condition changes. To address the issue, this paper proposes a novel HFR mitigation method based on adaptive notch filters (ANFs). The embedding positions of ANFs in the MMC control are optimally determined through impedance-based analysis. With the HFR frequency estimated by the interpolated discrete Fourier transform, the parameters of ANFs are adaptively tuned. The ANFs improve the damping performance of the captured HFR mode without affecting the dynamic characteristics at other frequencies. As a result, the HFR under varying grid conditions can be mitigated effectively. The effectiveness of the proposed method is verified through electromagnetic transient (EMT) simulations of an actual MMC-HVDC system. [ABSTRACT FROM AUTHOR]

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 complex interactions between renewables and AC/DC networks have brought new oscillation issues. To effectively monitor and suppress these oscillations, the observability and controllability of the oscillatory modes at different locations of the system must be investigated. To achieve this, the paper first defines the concept of modal observability and controllability using the responses of unit-pulse perturbations. Then an eigenvalue-decomposition based method is proposed to calculate these two indexes with the impedance network model (INM) as the input. The obtained modal observability(controllability) has many important applications and one of them is to facilitate the aggregation of the INM. The paper investigates this application by selecting an optimal aggregation port to ensure that the aggregated impedance can reflect the complete system dynamics. Finally, the proposed method is verified on a simple passive circuit and a practical wind power system that experienced actual subsynchronous resonance incidents. Theoretical results as well as EMT simulations demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In the past decade, several subsynchronous control interaction (SSCI) incidents have been reported in various large-scale grid-interfaced doubly-fed induction generator (DFIG) based wind farms. The subsynchronous oscillation caused by the SSCI endangers the safe and reliable operation of wind power systems. The DFIG's converter controls play a crucial role in such interactions; therefore, several SSCI mitigation schemes have been reported, which modify the DFIG's converter controls to stabilize the subsynchronous oscillation caused by the SSCI. However, the effectiveness of such converter control modifications has not been verified through laboratory or field experiments. This paper considers a practical rotor-side subsynchronous damping controller (RSDC) and fills the gap by first validating the RSDC's performance through controller hardware-in-the-loop (CHIL) simulations, and then implementing it in a real-world DFIG connected to a series compensated line. The RSDC fundamentally reshapes the effective impedance of the DFIG to stabilize the subsynchronous oscillation. The CHIL simulations, as well as the field tests, successfully validated the RSDC's ability to suppress the SSCI. The results enhanced the practical confidence of the SSCI mitigation strategy based on RSC's converter control modification. [ABSTRACT FROM AUTHOR]

Recently, a high-frequency resonance (HFR) incident has been captured in an actual HVDC project of China Southern Power Grid, which is regarded as a new stability issue caused by the interaction between the modular multilevel converter (MMC) and the weak ac grid. To investigate this event, this paper proposes a stability analysis method based on the frequency-coupling impedance model (FCIM). First, the FCIMs of the MMC and the ac grid are established in abc-frame individually with the frequency coupling effect of the MMC taken into account. Next, they are aggregated into a two-by-two impedance matrix by numerical calculation. Then, based on the aggregated FCIM, a criterion is developed to locate the HFR modes and to evaluate their stability. Finally, the results obtained from FCIM-based analysis are verified by electromagnetic transient (EMT) simulations as well as the field measurements. [ABSTRACT FROM AUTHOR]

Recently, sub- and super-synchronous oscillation (SSO) associated with converter-based wind turbine generators (WTGs) has been attracting wide attentions. To investigate such SSO incidents, impedance or admittance-based modeling and analysis were widely used. It was discovered that coupling effects exist between impedances or admittances at complementary (i.e., sub and super-synchronous) frequencies. However, there is a lack of experimental validation on the coupling effects of different WTGs. In this paper, the frequency-coupling admittance models (FCAMs) of two types of widely adopted WTGs, i.e., direct-drive and doubly-fed WTGs, are presented at first. Secondly, a perturbation based identification method is proposed to obtain the FCAMs. Next, the method is implemented in a control-hardware-in-the-loop (CHIL) platform based on RTDS. Then with extensive CHIL tests, the FCAMs of both types of WTGs are obtained, and the impacts of frequency-coupling effects on SSO are validated. Finally, the characteristics of frequency-coupling effects and the root causes are further examined. This study is of important reference value to select appropriate models for oscillatory stability analysis. [ABSTRACT FROM AUTHOR]

The increasing penetration of renewables into modern power systems is bringing new oscillatory stability concerns. It is of significance to find all oscillatory modes concerned and evaluate components’ participation into each mode, especially the dominant one. To address this issue, a frequency-domain modal analysis method is developed in this paper. It represents the target system with a networked impedance model and works out the oscillatory modes by locating the zeros of the determinant of the loop impedance matrix or nodal admittance matrix. Loop/nodal participation factors, branch observability, and component sensitivity are derived to give insight into the oscillation, including its origin, oscillation path, and contributive components. The proposed method has been conducted on a simple passive circuit and a practical wind power system that experienced actual subsynchronous resonance incidents. Theoretical results as well as electromagnetic transient simulations have verified its effectiveness. The proposed method has the potential to analyze very large power systems with high penetration of renewables. [ABSTRACT FROM AUTHOR]

Unstable subsynchronous control interaction (SSCI) between wind farms (WFs) and series-compensated grid has posed a big threat to the safety of equipment and the stability of system. Many studies have been conducted on its analysis and control. However, very little research has been done on the protection. To fill the gap, this paper proposes a system-wide protection against unstable SSCI in wind power systems with fixed series compensations. The protection is composed of a centralized protection coordinator (CPC) and several distributed protection relays (DPRs). Local DPRs measure the subsynchronous impedances of WFs in real time. These impedances are next collected by the CPC to calculate the sensitivities of tripping for each WF. The sensitivities are then used to determine the candidate WFs and the number of WTGs to trip at those WFs, so as to stabilize the SSCI. The effectiveness of the proposed protection is verified with detailed electromagnetic simulations on a wind power system that had experienced actual SSCI incidents. [ABSTRACT FROM AUTHOR]

Recent years have witnessed emerging oscillatory stability issues in power systems with high-penetration renewables. These issues are generally caused by the dynamic interaction between the AC/DC grid and power electronic converters used for the integration of renewables. Some previous studies have explored the issues with simplified system models containing only a few converters and idealized networks. However, the interactions between many converters and traditional generators/HVDCs have not been fully considered. To fill this gap, this paper first presents the concept of a unified dq frame impedance network model (INM), with which different converters as well as traditional generators/HVDCs can be incorporated to form an integrated s-domain model of a practical system. As the INM is aggregated into a lumped impedance matrix, a new criterion is then proposed to quantify the oscillatory stability, just by analyzing the frequency characteristics of the determinant of the matrix. Finally, the modeling method and the stability criterion are applied to a real-world system with a very high share of renewables and a realistic risk of oscillatory instability. Their effectiveness has been validated by both field measurements and electromagnetic transient simulations. [ABSTRACT FROM PUBLISHER]

Recently, an emerging subsynchronous resonance (SSR) issue was observed in series-compensated systems comprising multiple wind farms. However, only simplified single-machine-infinite-bus system models were adopted to investigate the characteristics of this issue in the previous work. As a result, it is unable to reflect the impact on SSR from some critical factors, such as the network topology, the spatial distribution of wind farms, the diversity of wind turbine generators, and the distributed wind speed. To fill in this gap, this paper proposes an impedance network model (INM) based SSR stability analysis method. The impedance models of each wind farm and transmission line are established, and then interconnected according to system topology to form the whole INM. Such INM is further aggregated into lumped impedance. By analyzing the impedance-frequency features of the latter, a new stability criterion is developed to quantify the stability of SSR. The application of the criterion is demonstrated on a practical power system containing multiple wind farms. Both field measurements and time-domain simulations have been presented to validate its effectiveness and accuracy. The proposed method is of great potential in analyzing the SSR issue for very large-scale wind power systems. [ABSTRACT FROM PUBLISHER]

Recently, sustained power oscillation at subsynchronous frequency was captured in direct-drive permanent magnetic synchronous generator (PMSG) based wind farms in Xinjiang Uygur Autonomous Region, China. This new type of subsynchronous interaction (SSI) detected in practical systems has never been reported and analyzed before. Therefore, its mechanism and characteristics are not yet clearly clarified. In this paper, a simplified but representative system model with multiple PMSGs interfaced with AC networks is established first based on the actual system and the PMSG model provided by the manufacturer. Then, small-signal eigenanalysis, time-domain simulation, and impedance model analysis are carried out to investigate the interactive dynamics between them. The results show that such interaction between direct-drive PMSG wind farms and weak ac grids characterized by low short-circuit ratio would cause negative-resistance effect for the SSI mode, leading to unstable oscillation. In such cases, the controller of PMSG would saturate soon, resulting in sustained power oscillation in the system. If unfortunately the oscillation frequency matches the torsional mode of any nearby turbogenerator, severe torsional vibration would be excited on the shaft of the latter. The analysis results are finally validated with field measurements of an actual SSI event. To address the problem, a supplementary subsynchronous damping control loop is attached to the controllers of PMSGs to reshape the impedance and thus to stabilize the SSI. [ABSTRACT FROM PUBLISHER]

Given large-scale power networks with series compensation, the study of subsynchronous resonance (SSR) is a significant challenge, in practice, due to the model complexity and computation burden. To tackle these difficulties, this paper proposes a method to reduce a large-scale system to an equivalent model using a metric called damping sensitivity index. The proposed metric can quantitatively identify the boundaries of the equivalent model that ensure the accurate studies of SSR and reduce the computation burdens greatly. The effectiveness of the method is verified by its application to the SSR investigation of the modified IEEE New England 10-machine 39-bus system and 16-machine 68-bus system. The equivalent models obtained by the proposed method are compared with the original systems in terms of driving point impedances, electrical damping, and transient torques. These results obtained show that the equivalent models from the proposed method can reproduce the SSR dynamics of the original systems with a much shorter computation time. [ABSTRACT FROM PUBLISHER]

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]