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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]

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 occurrence of unstable subsynchronous control interaction (SSCI) between wind farms and series‐compensated networks poses a considerable threat to the safety of power system. Different from the conventional eigenvalue analysis and Nyquist method, the black‐box‐model based RLC fitting technique becomes more attractive for the assessment of the SSCI risk. However, the method has merely been verified by radial networks whose SSCI mode can be well explained by an RLC circuit. A practical wind power system, however, can be meshed networks comprising multiple geographically distributed wind farms and series capacitors. Thus, it is questionable whether the application of the RLC fitting technique to such systems can still yield a sufficient accuracy. To clarify this aspect, in this work, the performance of RLC fitting in various test systems was examined. The results indicated that the aggregation technique considerably influences the accuracy of the assessment, and the RLC fitting cannot be applied when multiple series capacitors are involved in the SSCI mode. To address this problem, a more advanced frequency‐domain fitting technique known as vector fitting was adopted, and its robustness and effectiveness were verified considering a modified The Electric Reliability Council of Texas (ERCOT) system. [ABSTRACT FROM AUTHOR]

Recently, emerging sub‐synchronous oscillation (SSO) issues caused by the interaction between power electronic converters and weak AC grids have provoked serious stability concerns. Impedance‐based modelling approaches have been widely employed for stability analysis of such interactions. In this study, a sequence‐domain frequency‐coupled impedance model (FCIM) and the corresponding stability criterion are proposed. First, a fast identification method of the FCIM is proposed, in which the impedance‐frequency curves of the FCIMs at multiple frequencies are measured, followed by identification of their transfer function models. Next, the proposed method is applied to model a practical system, where a SSO event once occurred due to the interactions between direct‐drive wind turbines and a weak AC grid. The individual FCIMs of wind turbine generators, steam turbine generators and static var generator in this system are derived. After that, an aggregated FCIM is formed by combining the FCIMs without extra coordinate transformation. Then, the aggregated FCIM‐based stability analysis is carried out to investigate the interaction between the wind farms and weak AC grids. In the end, the results of FCIM‐based stability analysis are verified by time‐domain simulations. [ABSTRACT FROM AUTHOR]

Abstract Emerging subsynchronous oscillation (SSO) issues in grid-connected wind farms have gained serious attention after several incidents occurred in the US and China. The temporal and spatial variation of wind speed, the diversified converter control structures, and the continuously varying number of in-service wind turbine generators (WTGs) greatly affect the equivalent impedance reflected by the wind farms. Such frequency-dependent equivalent impedance, as indicated by both theoretical analyses and practical experiences, has a huge impact on the mechanism and characteristics of SSO. In this regard, WTGs contribute to a more complicated type of SSO than those in conventional turbo-generators (CTGs). For instance, SSO in practical wind power systems can be triggered without the participation of series compensation in the transmission network. The emerging SSO phenomena observed in practical WTGs are relatively new, and cannot be properly interpreted by existing literature. This work will first review the historical development of SSO definitions and classification by IEEE, followed by discussions on recent incidents in practical wind farms due to the emerging SSO. Subsequently, new terminologies and classification of SSO are proposed with the aim to better understand SSO in large-scale wind integrated power systems. This paper offers a practical insight and a future perspective for the reader to properly deal with SSO associated with wind power systems. Highlights • WTGs associated SSO is different from that of conventional CTGs. • The frequency of WTG-associated SSO is greatly influenced by wind speed, series compensation, WTC controls and parameters. • The SSO mechanism in wind farms is difficult to explain with existing IEEE classification. • New classification of SSO is proposed in which it's classified into torsional, L-C and converter-grid oscillation. [ABSTRACT FROM AUTHOR]

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]

The wind speed of high uncertainty has an important impact on the emerging subsynchronous resonance (SSR) caused by the interaction between doubly-fed induction generator (DFIG)-based wind farms and series-compensated transmissions. This paper proposes a piecewise probabilistic collocation method (PPCM) for assessing the probabilistic stability of SSR in terms of the random wind speed. The PPCM can tackle the inherent nonlinearity resulting from the switching among different operational modes of DFIG. Using the proposed PPCM, the more accurate probability density function (PDF) of the damping can be obtained with a small computation burden. Furthermore, for the probabilistic stability assessment of SSR, this paper also develops the Weibull probabilistic model of the wind speed using the two-year statistical data. The results obtained with the proposed method show consistence with those of the Monte Carlo method (MCM). Finally, field data of SSR events in the practical wind farms are also presented to validate the effectiveness of the proposed method and its produced results. [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]

The emerging subsynchronous resonance (SSR) caused by the interaction of wind turbine generators (WTGs) with series compensation has aroused great concerns. For this particular issue, this paper is aimed to fill the gap between theoretical studies and actual observations. By analyzing the field data of 58 SSR events captured in a practical wind power system and examining the observed dynamics with previous theoretical results, the mechanism and characteristics of SSR are revealed in a more explicit and substantial way. The necessary conditions and dominant influential factors are identified and the underlying reasons are discovered. Theoretically derived as well as practically measured impedance models have demonstrated that the converter control of doubly fed induction generator (DFIG) produces negative resistance at the slip frequency and thus causes unstable SSR; while permanent magnet synchronous generators and self-excited induction generators are just passively engaged in those SSR incidents. The distribution of the oscillation frequency has also been examined with field measurements. It is discovered that WTGs at different locations participate into the same SSR mode and their frequencies are not fixed but keep changing with the time, the variation of grid topology, and the number of online generators. [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]

Practical subsynchronous instability events have been observed in doubly fed induction generator‐based wind farms, which are radially connected to fixed series compensated transmission lines. As a special type of subsynchronous resonance, this phenomenon is described here as subsynchronous control interaction (SSCI). This study proposes a centralised SSCI mitigation scheme named as subsynchronous damper (SSD). In this scheme, an additional high‐power electronic voltage‐sourced converter is added to the collection bus of wind farms. It is designed to dissipate the electrical resonance power of SSCI. Thus, SSD provides positive damping for SSCI. Its basic principle is explained with equivalent electric circuit and the sufficient conditions for stabilisation are obtained mathematically. Controller design guidelines are given and have been verified first by eigenvalue analysis. Then a method to choose the capacity of power electronic converter is proposed. The effectiveness of SSD is finally demonstrated by extensive time‐domain simulations on a target system. [ABSTRACT FROM AUTHOR]

Subsynchronous resonance (SSR) was observed in wind farms located in North China. These wind farms prevailingly consist of doubly-fed induction generators (DFIGs) and are connected to series-compensated transmission lines. The observed resonant frequency is about 6 \sim 8 Hz, which is much lower than that of the reported SSR occurred in Texas. The frequency varies during the occurrence and this phenomenon is observed for the first time. The output power is usually within a certain range, when SSR occurs. Based on the practical system, an equivalent simulation system has been established, in which wind farms are modeled as many identical low rating DFIGs. Then, the SSR event is reproduced by simulations. Analysis results indicate that SSR happens even when the equivalent transmission system compensation level seen from wind farms is only 6.67%. Eigenvalue analysis shows that this phenomenon is an electrical resonance, and could be affected considerably by wind speed, number and control of DFIGs. The number of in-service DFIGs has a nonlinear impact on the damping of SSR. An equivalent electric circuit is deduced to intuitively explain why SSR happens and how the above factors affect it. Considering its features, this phenomenon is recognized as DFIG control participated induction generator effect. [ABSTRACT FROM AUTHOR]