Huakun Liu

Investigation of SSR in Practical DFIG-Based Wind Farms Connected to a Series-Compensated Power System

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 ~ 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.

Quantitative SSR Analysis of Series-Compensated DFIG-Based Wind Farms Using Aggregated RLC Circuit Model

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 DFIGs 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.

SEDC's Ability to Stabilize SSR: A Case Study on a Practical Series-Compensated Power System

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 SEDCs 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 SEDCs ability to stabilize SSR.

A small-signal impedance method for analyzing the SSR of series-compensated DFIG-based wind farms

Interaction between fixed series compensation and doubly-fed induction generator (DFIG)-based wind farms can cause a new type of subsynchronous resonance (SSR) problem, which is also named as subsynchronous control interaction (SSCI). To explain its basic mechanism as well as to evaluate the risk, this paper proposes a small-signal impedance method, based on which, a practical series-compensated power system including DFIGs can be simplified into a second-order series RLC circuit around the operating point concerned and then the frequency and stability of SSR can be intuitively represented by the equivalent parameters of the circuit. The derivation of the circuit parameters is given and the asymmetry phenomenon of equivalent impedance matrix in dq0 reference frame is observed. Both Eigenvalue analysis and time-domain simulation have verified the effectiveness of the proposed method and its advantage in accuracy over the existing impedance-based method. The impacts on SSR due to wind speed, number of online DFIGs and their control parameters are also investigated.

Subsynchronous Interaction Between Direct-Drive PMSG Based Wind Farms and Weak AC Networks

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.

Characteristic Analysis of Subsynchronous Resonance in Practical Wind Farms Connected to Series-Compensated Transmissions

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.

Continuous-Mass-Model-Based Mechanical and Electrical Co-Simulation of SSR and Its Application to a Practical Shaft Failure Event

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.

A mechanism study of SSR for multiple DFIG wind generators connected to a series-compensated power system

With the increasing application of series compensation in power systems to transmit power from large wind farms, a new type of subsynchronous resonance (SSR) is emerging as a bottleneck. This paper investigates its mechanism and influential factors by conducting an in-depth analysis on a real SSR event happening on a practical system in North China. The SSR event is reproduced with time-domain simulation. Eigenvalue calculation and circuit analysis reveals that this SSR is a kind of induction generation effect (IGE) with active participation by DFIG controllers. Besides grid parameters, several other factors, including wind speed, number of online wind generators and their grid/rotor-side converter control parameters, affect the damping and thus stability of the SSR Their influence on this DFIG control-participated IGE is examined. Some counter-measures to the problem are also suggested and commented.

Probabilistic Stability Analysis of Subsynchronous Resonance for Series-Compensated DFIG-Based Wind Farms

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.

Stability Analysis of SSR in Multiple Wind Farms Connected to Series-Compensated Systems Using Impedance Network Model

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.