Analysis on Sub-Synchronous Oscillation Associated with Wind Farms Based on Direct-Driven Wind Generators

Large scale wind turbine connected to the power grid is easy to induce subsynchronous oscillation. “Curse of dimensionality” will be encountered when the subsynchronous oscillation mode is analysed and evaluated based on the full-order model of the wind farm. It is urgent to research the fast and effective analysis method of subsynchronous oscillation mode when the wind farm is connected to the power grid. Therefore, a reduced order calculation method of the subsynchronous oscillation mode of PMSG based wind farm connected with a power grid based on the Arnoldi method is proposed. This method can quickly obtain the eigenvalues corresponding to the subsynchronous oscillation mode through iterative approximation when PMSG-based wind farm connected to the power system. This can be used to analyze the subsynchronous oscillation of large-scale wind farms connected to the power grid and provide an effective means for the evaluation of it. By changing system stability, collector network structure, and wind farm interconnection scale, the accuracy of the eigenvalues distribution between the full-order system and the reduced order system are compared. Moreover, the reduced order and computation time are considered. The results present that the proposed method can quickly and accurately obtain the subsynchronous oscillation mode in the system.

With increasing installation capacity and wind farms penetration, wind power plays more important role in power systems, and the modeling of wind farms has become an interesting research topic. In this paper, a coherency-based equivalent model has been discussed for the doubly fed induction generator (DFIG). Firstly, the dynamic models of wind turbines, DFIG and the mechanisms are briefly introduced. Some existing dynamic equivalent methods such as equivalent wind model, variable speed wind turbine model, parameter identification method and modal equivalent method to be used in wind farm aggregation are discussed. Then, considering wind power fluctuations, a new equivalent model of a wind farm equipped with doubly-fed induction generators is proposed to represent the interactions of the wind farm and grid. The method proposed is based on aggregating the coherent group wind turbines into an equivalent one. Finally, the effectiveness of the equivalent model is demonstrated by comparison with the wind farm response obtained from the detailed model. The dynamic simulations show that the present model can greatly reduce the computation time and model complexity.

Subsynchronous oscillations have occurred in wind farms due to the high penetration of converter-based technology in power systems and may potentially lead to grid instability. As an effective solution, synchronous condensers, with their ability to control voltage and inject reactive power in the power system, are increasingly being adopted, as they can lead to the mitigation of such oscillations in weak grid conditions. However, the impact of synchronous condensers’ power ratings on system stability is a topic that requires further investigation. In fact, an improper selection of a synchronous condenser’s rating will not extinguish existing subsynchronous oscillations and may even cause the emergence of new oscillatory phenomena. This paper presents a novel examination of the impact that the synchronous condenser’s power rating has on the small-signal stability of a wind farm with existing subsynchronous oscillations while being connected to a weak grid. The wind farm’s model is developed using state-space modeling, centering on grid interconnection and incorporating the state-space submodel of a synchronous condenser to show its impact on subsynchronous oscillation mitigation. The stability analysis determines the optimal synchronous condenser’s power ratings for suppressing these oscillations in the wind farm model. The findings are corroborated through time domain simulations and fast-Fourier transformation (FFT) analysis, which further validate the stability effects of a synchronous condenser’s rating.

This paper has investigated the sub-synchronous oscillations (SSO) phenomenon in hybrid wind farms with DFIG and PMSG. Firstly, a mathematical model of the hybrid wind farms is established. The model includes four parts: hybrid wind turbine, DFIG rotor machine-side controller (RSC), PMSG stator grid-side controller (GSC) and series compensation line module. Based on this model, the factors affecting the SSO phenomenon in the hybrid wind farms are explored by eigenvalue analysis. It is concluded that the variation of wind speed increases the possibility of SSO generation in DFIG wind farms, but the addition of PMSG wind farms can suppress the effect of wind speed variation. In comparison to single DFIG wind farms or PMSG wind farms, hybrid wind farms are less likely to generates SSO that results from the variation of PLL parameters. In addition, too large series compensation degree can lead to a more severe dynamic response of SSO phenomenon.

Multiple wind farms (WFs) model consists of wind speed model and single WF model. In the multiple WFs integrated power system, the wind speeds at different WFs are correlated to some degree if the distance between WFs is not very large. Hence, a novel MC-Nataf-CD method combining partitions Monte Carlo (MC) sampling, Nataf transformation and Cholesky Decomposition (CD) is proposed to simulate correlated wind speeds with desired cross-correlation coefficients. The wind speeds generated by the proposed wind speed model is closer to both the historical data and the Weibull fitting curve. For the single WF model, wake effects, the forced outage rates (FORs) of wind turbine generators (WTGs) and the reliability of the connected grids inside a WF need to be taken into consideration. Four different single WF models are proposed to reveal the impact of these relevant factors. A statistical method based on state-sampling MC simulation is implemented for the reliability estimation of Roy Billinton Test System (RBTS) with multiple WFs, using both historical and simulated wind speed data. The simulation results and the calculated reliability indices demonstrate that the proposed techniques are effective and accurate in the modeling of correlated multiple WFs.

Study of wind farms is an area of active research. Researchers have proposed simplified wind farm models that define the wake structure in a wind farm and how they affect the performance of the wind turbines. Interestingly, these models do not take into account an important aspect of fluid flow, i.e., the fluid–structure interaction (FSI) between the turbines and the wind, which has an important role to play. This motivated researchers to implement numerical analysis tools to model the geometry of the wind turbines in computational fluid dynamics (CFD) based models of a wind farm in order to better understand the wake structure and study the performance of the wind farms. However, modeling the complex geometry of the blades and the turbines makes these models computationally expensive. In this paper, we propose an FSI methodology which can simplify the blade resolving CFD models and eliminate the requirement for modeling these complex geometries during preliminary engineering phase. As an example, we present simulations of up to three back-to-back wind turbines and compare the results with those obtained from wind engineering software, FLORIS. The proposed methodology demonstrates how the approach can be used to develop a relatively less computationally expensive wind farm model. The approach formulated in this paper follows an intermediate way between the analytical wind farm models and CFD models by introducing modifications to one of the most basic wind farm models (Jensen's model) and using it to develop a simplified CFD model using the decomposed immersed interface method strategy.

Large scale wind power penetration has a significant impact on the reliability of the electric generation systems. A wind farm consists of a large number of wind turbine generators (WTGs). A major difficulty in modeling wind farms is that the WTG not have an independent capacity distribution due to the dependence of the individual turbine output on the same energy source, the wind. In this paper, a model of the wind farm output power considering multi-wake effects is established according to the probability distribution of the wind speed and the characteristic of the wind generator output power: based on the simple Jenson wake effect model, the wake effect with wind speed sheer model and the detail wake effect model with the detail shade areas of the upstream wind turbines are discussed respectively. Compared to the individual wake effect model, this model takes the wind farm as a whole and considers the multi-wakes effect on the same unit. As a result the loss of the velocity inside the wind farm is considered more exactly. Furthermore, considering the features of sequentially and self-correlation of wind speed, an auto-regressive and moving average (ARMA) model for wind speed is built up. Also the reliability model of wind farm is built when the output characteristics of wind power generation units, correlation of wind speeds among different wind farms, outage model of wind power generation units, wake effect of wind farm and air temperature are considered. Simulation results validate the effectiveness of the proposed models. These models can be used to research the reliability of power grid containing wind farms, wind farm capacity credit as well as the interconnection among wind farms

The large integration of wind power and the complexity of internal connections of wind farm have increased the difficulty of establishing the equivalent wind power output model of wind farm. Taking into account the geographical distribution of wind turbines and the curtailment of wind power, this paper proposes a novel wind farm equivalent output model considering wind curtailment. First, an improved combination method based on the quartile method and the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) is proposed to eliminate the outliers in operating data. Second, with reference to the layout of wind turbines in the wind farm, four basic wind farm equivalent output models with equivalent transformations between wind speed and wind power relationship are established. At last, a k-means clustering-based wind turbine operating status identification method is proposed, and it is further combined with the outlier elimination model and the basic wind farm equivalence model such as to obtain the wind farm equivalence aggregation model with the consideration of wind curtailment. Case study is carried out based on the actual output data of 15 scattered wind turbines in wind farm from Hebei. The proposed equivalent aggregation model is established and compared with the equivalent model without considering curtailment. Study results show that the proposed the equivalent aggregation model possesses higher accuracy, reliability and versatility.

An accurate model of large scale wind farm is demanded for researches about the impacts on the power grid. The total number of wind energy generators is so large that the detailed model of wind farm is computationally prohibitive. Dynamic equivalence can significantly reduce system order with the major characteristics retained. So the aggregation of large scale wind farm is inevitable. An overview of dynamic equivalent methods has been made for wind farms consisting of the widely used wind generators such as the doubly fed induction generator (DFIG) or the squirrel-cage induction generator (SCIG). The dynamic models of DFIG and SCIG and the mechanisms are briefly introduced at first. The wind energy generator is compared with induction motor to show the differences and similarities. Next, the possibility of the existing dynamic equivalent methods such as coherency-based method, parameter identification method and modal equivalent method to be used in wind farm aggregation is studied. The clustering criterions and model validation of wind farms are investigated. The feature and shortcoming of the re-scaled power capacities method are also discussed. At last, some suggestions are given for future equivalent researches of wind farms.

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.

With large wind energy integration into power systems, wind farms begin to influence power systems in a much more significant manner. As wind energy systems utilize different generator technologies from the one utilized in the conventional power plants, the steady-state, transient and small-signal dynamics, as well as, power system stability will thus be significantly affected. The impact of wind energy systems on the power system dynamics and stability is thus of practical importance. As there is a significant increase in installation of wind turbines equipped with doubly-fed induction generator (DFIG) in recent years, a dynamic model of the DFIG wind turbine is firstly developed in this thesis. The model is validated against field measurement data, and the validation gives confidence about the accuracy and applicability of the developed model. DFIG wind farms consist of tens to hundreds of identical DFIG wind turbines increasing the complexity of the wind farm model and simulation time. A novel aggregation technique is developed in this thesis that incorporates a multiplication factor, namely mechanical torque compensation factor (MTCF), to the mechanical torque of the full aggregated wind farm model. The MTCF is initially constructed to approximate a Gaussian function by using fuzzy logic method. By optimizing the MTCF on a trial and error basis, less than 10 percent discrepancy is then achieved between the proposed aggregated model and the complete model. The proposed aggregation technique is then applied to a 120 MVA offshore wind farm comprising of 72 DFIG wind turbines and shows higher accuracy in approximating the wind farm dynamics as it appears at the point of common coupling (PCC) as compared to the full aggregated model. The proposed aggregated model computes faster than the complete wind farm model by 90.3 percent during normal operations and 87 percent during grid disturbances. To overcome the adverse effects due to the fluctuating nature of wind, two wind power smoothing methods are proposed using a fuzzy logic pitch angle controller for a smooth performance with a minimum drop in output power. One method performs partial smoothing with only 4.74 percent drop in the output power while the other method offers complete smoothing with a 8.28 percent drop in output power. The impact of wind energy integration on power system transient stability (PSTS) is studied quantitatively with the transient energy margin (TEM), which is calculated through the evaluation of the transient energy function (TEF). This study is carried out in two ways in the thesis. One is to analyse the impact of transient fault on the DFIG wind turbine as compared to SGs for different factors, like the fault clearing time, the grid coupling, the inertia constant and the voltage sag. The study reveals that transient stability of the DFIG wind turbine is hardly affected by the grid coupling, the inertia constant and the generator terminal voltage sag variations indicating its consistent transient performance within a wide range of these factors. The fault clearing time should be almost 11 percent faster for the system with the DFIG than the synchronous generator (SG). The other is to investigate the impact of the DFIG wind farm on the PSTS with the variation of different factors, which are the voltage sag, the fault clearing time, the load and the wind power penetration level. The study reveals that power systems integrated with DFIG wind farms are sensitive to transient events with high voltage sag, high fault clearing time, low load operation and high wind power penetration level. Machines at different locations individually possess distinct fault response and suffer from a large-scale power imbalance. As a result, reliable operation of DFIG wind farm integrated power systems demands upgraded equipment, such as advanced switchgear, fast breakers/isolators, efficient power reserve systems and advanced reactive power compensating device, etc.

Wind and solar as two renewable energy resources are largely used to generate clean and sustainable energy in the power systems. To integrate these renewable energies in the power system, different aspects of the power system such as reliability and operation are affected that must be investigated. It is due to the variation in the generated power of these resources that are arisen from the variation in the wind speed and solar radiation. To model the uncertainty nature of large-scale wind and photovoltaic farms in the operation studies of the power system, an appropriate multistate reliability model is developed for the wind and photovoltaic farms considering both failure of main components and variation in the wind speed and solar radiation. To determine the optimum number of states in the reliability model of wind and photovoltaic farms, XB index is calculated and based on the fuzzy c-means clustering technique the transition rates among different states are obtained. To calculate the transition rates among different states, the fuzzy numbers are used that results in the accurate and reduced reliability model for wind and photovoltaic farms. To determine the probability of different states in the reliability model of wind and photovoltaic farms in the operation studies, matrix multiplication technique is utilized to determine important indices of the power system such as the unit commitment risk. In this paper, the amount of required spinning reserve of a power system containing wind and solar generation units can be determined based on the reliability criterion. The proposed technique is applied to the two reliability test systems including RBTS and IEEE-RTS and the reliability-based operation indices of these systems are calculated to present the effectiveness of the proposed analytical method.

<strong class="journal-contentHeaderColor">Abstract.</strong> Offshore wind farms are more commonly installed in wind farm clusters, where wind farm interaction can lead to energy losses; hence, there is a need for numerical models that can properly simulate wind farm interaction. This work proposes a Reynolds-averaged Navier-Stokes (RANS) method to efficiently simulate the effect of neighboring wind farms on wind farm power and annual energy production. First, a novel steady-state atmospheric inflow is proposed. This inflow model is well suited for RANS simulations of large wind farms because it does not lead to the development of nonphysical wind farm wakes. Second, a RANS-based wind farm parametrization is introduced, the actuator wind farm (AWF) model, which represents the wind farm as a forest canopy and allows to use of coarser grids compared to modeling all wind turbines as actuator disks (ADs). When the horizontal resolution of the RANS-AWF model is increased, the model results approach the results of the RANS-AD model. A double wind farm case is simulated with RANS to show that replacing an upstream wind farm with an AWF model only causes a deviation less than 1 % in terms of wind farm power of the downstream wind farm. Most importantly, a reduction in CPU hours of 74.4 % is achieved, provided that the AWF inputs are known, namely, wind farm thrust and power coefficients. The reduction in CPU hours is further reduced when all wind farms are represented by AWF models; namely 89.3 % and 99.9 %, for the double wind farm case and for a wind farm cluster case consisting of three wind farms, respectively. For the double wind farm case, the RANS models predict different wind speed flow fields compared to output from simulations performed with the mesoscale Weather Research and Forecasting model (WRF), but the models are in agreement with the inflow wind speed of the downstream wind farm. The double wind farm case is also simulated with the TurbOPark engineering wake model. Similar wake shapes are reproduced by TurbOPark but the model predicts a larger wind farm wake magnitude compared to RANS and WRF. TurbOPark predicts much better results when its ground model is switched off and a wake expansion coefficient of 0.06 is used. The RANS-AD-AWF model is also validated with SCADA measurements in terms of wind farm shape; the model captures the trend of the measurements for a wide range of wind directions, although the SCADA measurements indicate more pronounced wind farm wake shapes for certain wind directions.

Torsional subsynchronous oscillations caused by grid-connected wind farms in a complex multi-machine power system under the condition of near strong modal resonance

With the increasing capacity of grid connected wind farms, the influence of wind power to stable operation of an electric power system is becoming more and more important. In order to analyze the active power output characteristics of wind farm, a multimachine representation dynamic equivalent method based on the fuzzy clustering algorithm is proposed. First, indicators which can characterize the active power output performance of a doubly fed induction wind generator (DFIG) are researched. Second, a fuzzy C-means (FCM) clustering algorithm is first applied to the modeling of wind farm. DFIGs are divided into groups by analyzing the indicator data with FCM. Finally, DFIGs of the same group are equivalent as one DFIG to realize the dynamic equivalent modeling of wind farm with DFIG. Simulation results demonstrated that the established dynamic equivalent model can reflect the active power dynamic response characteristics of wind farm with DFIG effectively; meanwhile, the model of wind farm is simplified and computation complexity is reduced.