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• This paper proposes a reliability evaluation method considering the static frequency regulation for overcoming the shortcoming of the traditional reliability method. • This paper presents a failure restoration mode integrated into the reliability evaluation through designing system load curtailment, frequency restoration, and load restoration. • This paper establishes a series reliability calculating models which depend on the different failure restoration conditions. The adequacy of power system can be elevated with the increasing grid-connected capacity of wind farm, and meanwhile, the power system reliability is also affected by the intermittent power fluctuation of wind farm. However, the traditional reliability evaluation technique cannot take the power fluctuation into account. Therefore, for considering the positive and negative influence of wind energy on the power system reliability, this paper proposes a reliability evaluation technique through considering static frequency regulation and failure restoration process. A failure restoration strategy which can be integrated into the reliability evaluation model is presented through designing system load curtailment, system frequency restoration, and system load restoration strategies. A series reliability calculating models which depended on the different failure restoration conditions are established. Case studies for different systems are investigated, and the results verify that the proposed method can consider both aspects of the positive and negative influence of wind farm on the power system reliability. [ABSTRACT FROM AUTHOR]

• EMTP-based results clarify that SPCB operation results in WF voltage swell. • The results show that the CSC and DSC controllers with the FRT, are not effective. • To improve the HVRT after the SPCB operation, a dc-link chopper is provided. For transient single phase-to-ground (SPG) faults in transmission lines, single-pole circuit breaker (SPCB) operation can improve system reliability. This issue is more critical in transmission lines emanating from wind farms (WFs). In the large-scale WFs, the grid codes necessitate that wind generation remains in operation during the transmission line faults. For this purpose, the grid codes focus on the development of fault-ride-through (FRT) requirements. In this paper, it is shown that after the SPCB operation, the terminal voltage of the permanent magnet synchronous generator (PMSG)-based wind turbine (WT) rapidly increases and may cross the high-voltage ride-through (HVRT) boundary. Therefore, the WT terminal overvoltage after the SPCB operation may result in undesirable tripping of the WT. The obtained results in this paper show that in most cases both the coupled and decoupled sequence controllers of the WT converter equipped with the FRT requirements are not able to improve the HVRT performance after the SPCB operation. To enhance the HVRT performance of PMSG-based wind turbines after the SPCB operation, a dc-link chopper controller is proposed. EMTP-RV simulation results on the IEEE 118-bus and 5-bus systems show the success and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• Data-driven state space mapping makes the MPC model independent of physical parameters. • Convex optimizaiton model of assessment realizes fast analytical solving. • Coordinated iteration framework exploits the frequency regulation capability. • Partial state space mapping ensures the optimization solvability. With the integration of large-scale wind turbines (WTs) into grids via electronic interfaces, power system operators have necessitated frequency support from wind farms. Due to the large number of WTs and their complex dynamic characteristics, it is necessary to assess the primary frequency regulation (PFR) capability and construct feasible region of wind farms. In order to cope with the problems of incomplete parameters, analytical solving complexity and the coupling influence of power system regulation characteristics, this paper develops a data-driven state space mapping linear model predictive control (MPC) to assess the maximum PFR capability of wind farms and reasonably distribute coefficients to WTs. Besides, a coordinated iteration framework between dispatching center and wind farms is proposed to further optimize the wind farm regulation feasible region. The simulation results verify that the proposed method has the advantages of independence from physical parameters, fast analytical solution, and lower requirements of training samples on limited scenarios. [ABSTRACT FROM AUTHOR]

Grid forming control for modular multilevel converter based high voltage direct current (MMC-HVDC) transmission system is favorable to support the AC systems. This paper presents the hybrid AC-DC impedance model for grid forming based MMC-HVDC with wind farm integration. Comparisons of the hybrid AC-DC impedance with the traditional AC/DC impedance are presented, and the hybrid AC-DC impedance does not contain right half-plane poles caused by DC/AC coupling. Then, the network based impedance analysis is carried out to analyze the stability of grid-forming based MMC-HVDC with wind farm integration. It is found that grid forming based MMC-HVDC may lack damping with two modes of oscillations. Large inertia, DC/AC virtual impedance and wind farm integration can dampen the first mode oscillation, while only AC virtual impedance is effective for the second mode oscillation. The stability comparison of grid forming and grid following based wind farm integration is also presented. Moreover, MMC-HVDC with grid forming control cannot improve the stability of grid following based wind farm integration in weak grid where grid forming based wind farm performs better. Therefore, both wind farm and MMC-HVDC with grid forming control are better in weak grid. Simulation results in PSCAD/EMTDC validate the corresponding analysis. • The hybrid AC-DC impedance based modeling methods for GFM based MMC are presented. • Network based stability analyses are presented with the hybrid AC-DC impedance. • The stability comparison of GFM and GFL based WF integration is presented. [ABSTRACT FROM AUTHOR]

• Proposes a strategy based on the secondary voltage control (SVC) and the use of grid codes recommended by the system operator to determine the reactive power reference value between a wind farm (WF) with doubly-fed induction generator (DFIG) and the electrical grid. The proposed strategy seeks to determine the reactive power reference value required of WF during normal operating and grid faults. • The proposed strategy has been implemented at the central supervision unit level. This strategy can reduce the size of potential compensation devices, such as static synchronous compensators (STATCOM), to be used to improve of the WF response, if needed. • At a level of the local supervision unit, an algorithm is proposed to manage and determine the reference value of the active and reactive power for RSC and GSC for each DFIG WT during normal operating and grid faults. • This algorithm also has multiple goals which are the contribution of both RSC and GSC to optimally control the reactive power of each DFIG WT. It can provide the reactive power via GSC if the rotor currents of the DFIG reach the nominal value, and more is still needed of enhancing the reactive power. Reduce power losses for the entire system when sharing GSC in reactive power control of the DFIG, thus increasing RSC life. This paper proposes a strategy based on the secondary voltage control (SVC) and the use of grid codes recommended by the system operator to determine the reactive power reference value between a wind farm (WF) with doubly-fed induction generator (DFIG) and the electrical grid. The proposed strategy seeks to determine the reactive power reference value required of WF during normal operating and grid faults. When the voltage deviation is within the normal range, the proposed strategy maintains a unity power factor (UPF). If the voltage deviation exceeds the normal range, it provides reactive power compensation to ensure voltage stability. To achieve this objective, the proposed strategy is compared with the SVC. This strategy can reduce the size of potential compensation devices, such as static synchronous compensators, to be used to improve the WF response, if needed. The participation of the grid converter side (GSC) in the reactive power control allows the DFIG to reduce power losses and increases the life of the converters, especially the rotor converter side (RSC). The strategy proposed in this work is implemented on Matlab/Simulink using the S-Function builder to evaluate their performance, which facilitates its integration into real control boards and testing in real experiments in the future. [ABSTRACT FROM AUTHOR]

• Fault direction is determined from the equivalent reactance at high frequencies. • The proposed protection scheme relies on voltages and currents at the relay point. • Relays at both sides of the line only share their detected fault direction. • The proposed scheme is suitable for long lines and variable wind farm output power. • The method is suitable for single and simultaneous shunt faults. Penetration of large-scale renewables has changed the fault current characteristics, degrading reliability of the transmission line traditional protection system. This paper presents a high frequency directional-based protection scheme for transmission lines connecting large scale wind farms to the high voltage grid. The proposed protection mitigates the negative influence of the wind farm response to faults on the fundamental frequency phasors by using the high frequency components generated during the fault. The proposed protection scheme is applied to the relays at both sides of the protected transmission line independently. Therefore, each relay utilizes its locally measured voltage and current signals. Then, the relays share their individual decisions to obtain the final decision using the proposed operation logic. In addition, the proposed protection scheme does not require a compensation algorithm for the line capacitive current. An assessment study is conducted on the PSCAD/EMTDC software considering different fault types including cross-country and evolving faults, fault locations, fault resistance values up to 500 Ω, line lengths up to 200 km, and output power of the wind farm. The simulation results emphasize the dependability and security of the proposed protection scheme at different test conditions. [ABSTRACT FROM AUTHOR]

• An analytical sensitivity model of the wind farm power that quantitatively portrays the wake effect. • The wind farm power enhancement mechanism which contributes to accelerating the optimization process. • A wind farm power maximization method with higher optimization speed and better scenario applicability. To reduce the wake effect on wind energy capture, it is necessary to optimize the operating parameters of each wind turbine (WT) in the wind farm (WF) to improve the overall wind power. Considering the complex coupling characteristics of wind energy captured by upstream and downstream WTs caused by the wake effect, existing optimization methods for the WF usually adopt intelligent algorithms or numerical sensitivity-based search algorithms. However, most of the existing studies overlook the exploration of the physical mechanism underlying the wake influence on WF power, and the optimization speed still needs to be improved. To this end, in this paper, the analytical sensitivity model of WF power is formulated with the adjustable parameter - the pitch angle which is a key factor for the wake effect. On this basis, the improvement mechanism of how the WF power can be improved by changing the wake effect through the pitch angle is analyzed using the Blade Element Momentum theory, which can be used to guide and accelerate the optimization process. Furthermore, the WF power maximization method based on the analytical sensitivity model is proposed, and its effectiveness and advancement are verified based on SimWindFarm simulation under different operation scenarios. [ABSTRACT FROM AUTHOR]

• The penetration of DFIG wind farms into the power systems can lead to PSB of the distance protection malfunction. • DFIG wind farms lead to an impedance trajectory increase speed in the R-X plane of distance protection during power swing. • Adaptive adjustment of power swing blocking bands in concentric and blinder schemes improves distance protection security. • Power system dominant modes can be used to adjust the power swing blocking band. This article proposes a new approach to improve the security of transmission line protection by correctly detecting power swing when large-scale doubly-fed induction generator wind farms (DFIGWF) exist in the proximity of the relay. In the presence of large-scale DFIGWFs, following large disturbances, power swing may probably cause the distance protection to malfunction. This issue can also lead to widespread transmission line outage and cause instability in the power system. Therefore, a new approach is proposed to solve the challenge by adapting the power swing blocking (PSB) function in the distance protection relays and utilizing the dominant power system oscillation modes. Thus, related calculations are performed in a central module remotely connected to intelligent electronic devices (IEDs) for distance protection and stabilized against power swing. The calculation to adjust the PSB setting of the IEDs in the central module is based on the oscillation modes of the power system and the rate of change of impedance, which is influenced by the penetration rate of the DFIGWFs. Simulation studies have been done on two test systems and the results reveal that the proposed scheme significantly improves the security of distance protection against power swing under different DFIGWF intrusion conditions. [ABSTRACT FROM AUTHOR]

Highlights • The wind farm active power close-loop control structure is proposed. • A frequency domain aggregation and approximation modeling strategy is proposed. • Disturbance frequency analysis is adopted for controller tuning. • Event-driven integral control is used in favor of wind farm active power response. Abstract To further improve the wind power quality and stability, it is necessary to break the existing open-loop wind farm scheduling method and bring new strategies in both wind farm and wind turbine active power control. In this paper, a closed-loop active power control method is proposed based on the active power tracking dynamic characteristics of wind turbines, where the power fluctuations caused by the modeling errors and wind turbulence are isolated and suppressed by a proportional-integral (PI) controller. The PI controller parameters are obtained through the frequency domain analysis with bode diagrams. Then a frequency-domain aggregation and approximation method is proposed to establish the wind farm active power tracking model, and the wind farm-level controller is obtained similarly with the unit-level one but with an event-driven integral structure. Simulation results show the significant improvement and good robustness of the proposed controller. [ABSTRACT FROM AUTHOR]

• Evaluation of the interconnection of grounding system in a wind farm. • Investigation of different configurations such as linear, delta, circle, and four ways. • Presenting the overvoltage distributions over the wind farm under different grounding configuration. • Indicating that the delta connection can be a better choice from both technical and economical viewpoint. • Finding no linear correlation between the increase in branches in grounding system and the decrease in overvoltage stresses. The penetration of renewable energies especially wind energy, is increasing day by day due to environmental issues and energy conflicts in power networks. Height structures such as wind turbines (WTs) are exposed to lightning due to the installation location on heights, plains, or coastal zones. The grounding system of WTs plays an important role in repelling the energy of lightning waves and reducing the resulting over-voltages. In a sense, the turbine grounding system can be interconnected in wind farms through different configurations. In this regard, this paper aims to evaluate the voltage distribution caused by a lightning strike in different arrangements of grounding structure i.e., linear, circular, delta, and four-way with consideration of the transient model of WT components along with the high-frequency model for the grounding system. A wind farm including twelve turbines has been investigated based on five measuring points including blade tips, tower tops, generator terminals, and control systems. The results indicate a considerable reduction of over-voltages in the application of various grounding systems compared to the independent grounding mode in WTs. In addition, the distribution of over-voltages varies depending on how the connections of the grounding system are. While the most decrease in overvoltage might be related to the four-way connection with a costly implementation, the delta-connection of grounding systems in WTs might be a better choice for reducing over-voltages from both economic and technical viewpoints. The circular connection has no technical justification due to the parabolic distribution of over-voltages in comparison with other cases. [ABSTRACT FROM AUTHOR]

• The SSTI between torsional modes and HVDC controls is significantly affected by the generator de-rating operations. It may aggravate the negative effect of SSTI, changing the effect from non to negative or changing the effect from positive to negative. In this paper, the influence of generator de-rating operations on the SSTI (Sub-Synchronous Torsional Interactions) between torsional modes and controls of a LCC HVDC (Line-Commutated Converter High-Voltage Direct Current) transmission system is studied. The modified CIGRE HVDC benchmark system is adopted for the studies. The simulation analyses (including modal analysis and transient simulations) are made by using the DIgSILENT PowerFactory software. It is found that the turbine shafts torsional responses will be significantly affected by the generator de-rating operations in a negative way. Following the decrease in generation power, some of the turbine shafts torsional modes might become unstable. Furthermore, the SSTI between torsional modes and HVDC controls is also significantly affected by the generator de-rating operations. It may aggravate the negative effect of SSTI, changing the effect from non to negative or changing the effect from positive to negative. Moreover, the de-rating operations of a generator unit could even exacerbate the SSTI between the torsional modes of the neighboring generator unit and the HVDC controls. Also, the influence is negative. [Display omitted] [ABSTRACT FROM AUTHOR]

• During the transient overvoltage, an adaptive hierarchical transient overvoltage control scheme is developed to regulate the reactive power outputs of DFIGs and SVG considering the difference in overvoltage of each DFIG. • The reactive power output values of DFIGs and SVG can be set before the occurrence of transient overvoltage. It can effectively avoid the control delay and quickly suppress transient overvoltage. • The existence of dominant clustering result is found first. • DFIGs in the wind farm can be clustered in offline state based on the newly proposed clustering index and dominant clustering result, which solves the issue that transient index cannot be applied to DIFGs clustering in real-time. During grid voltage swell events, the transient overvoltage of doubly-fed induction generator (DFIG) terminal and point of common coupling (PCC) will occur, which may lead to cascading DFIG trip and shorten the life of the equipment. This paper proposes an adaptive hierarchical transient overvoltage control strategy for a DFIG-based wind farm (WF) based on overvoltage forecasting. Firstly, the DFIG transient overvoltage threshold and PCC reactive power demand are derived analytically, respectively. Secondly, the existence of dominant clustering result is found by clustering and analyzing a large number of DFIG transient voltage trajectories. It solves the issue of real-time clustering in DFIG-based WF, and lays the foundation for the referred distributed control scheme. Lastly, an adaptive hierarchical transient overvoltage control strategy is designed based on the predicted variables. These variables include the DFIG maximum overvoltage and reactive power demand, which are calculated by the convolutional neural network (CNN) algorithm. Under this strategy, each DFIG can adaptively adjust its absorbed reactive power based on the predicted variables and the derived overvoltage threshold. Meanwhile, the static var generator (SVG) is combined to realize the fast suppression of overvoltage at PCC and DFIG terminals. The simulation results based on MATLAB/Simulink show that the proposed control strategy can effectively and quickly suppress the transient overvoltage at DFIG terminals and PCC during the gird failure, which can significantly improve the stable operation level of wind farms. [ABSTRACT FROM AUTHOR]

Doubly fed induction generator (DFIG) based wind farms offer some distinct advantages, but their vulnerable nature to grid fault is problematic for the stable operation of power systems with higher wind power penetration. Fault ride through (FRT) capability is a requirement imposed through the grid codes to ensure stable power system operation. A fuzzy logic controlled parallel resonance fault current limiter (FLC-PRFCL) is proposed to aid the DFIG based wind farms to achieve improved FRT capability. To check the effectiveness of the proposed FLC-PRFCL, temporary symmetric and asymmetric faults were applied to the multi-machine system, to which a DFIG based wind farm is connected. The performance of the proposed FLC-PRFCL was compared with that of the crowbar, the bridge-type fault current limiter (BFCL) and conventional proportional-integral (PI) control based PRFCL (PI-PRFCL). Simulations were performed using the Matlab/Simulink software. It was found that the proposed FLC-PRFCL is an effective device for FRT capability improvement of the DFIG based wind farm. Moreover, the proposed FLC-PRFCL outperforms the crowbar, the BFCL, and the PI-PRFCL. [ABSTRACT FROM AUTHOR]

In this study, we derive a statistical model of a power grid from the wind farm's standpoint based on dynamic principal component analysis. The main advantages of our model compared to the previously developed models are twofold. Firstly, our proposed model benefits from logged data of an offshore wind farm over several years which results in the development of a useful model for practical purposes. Secondly, the derived model is computationally inexpensive. Considering an arbitrary wind turbine generator, we show that the behavior of the power grid at the connection point can be represented by 4 out of 9 registered variables, i.e. 3-phase voltages, 3-phase currents, frequency, and generated active and reactive powers. We further prove that the dynamic nature of the system can be optimally captured by a time lag shift of two samples. To extend the derived model of a wind turbine generator to a wind farm, we propose an algorithm that optimally combines the principal components and scores. The principal components are estimated by the optimization of a cost function based on the modeling error while the scores are selected corresponding to the worst case scenario among the wind turbine generators. Our results show that the optimized principal components result in the modeling error less than 5% and the selected scores cover the variance of the data with probability higher than 95% among all generators in the wind farm. [ABSTRACT FROM AUTHOR]

This paper introduces a non-communication based protection algorithm for Multi-Terminal High Voltage Direct Current (MTHVDC) transmission lines. The algorithm relies on using electrical current data at one end for identification of the fault zone without communication between relays. The concept is to use the fault generated transients to differentiate between internal and external faults. Shunt capacitors with predetermined values are installed at the boundary between each two HVDC line sections to assist, together with the busbar stray capacitance, in the classification of internal faults. The high frequency transients will reach the relaying point without any attenuation if the fault is internal; nevertheless, the high frequency transients will be highly attenuated if the fault is external due to the stray capacitance and the installed shunt capacitor at the connection busbar. Discrete Wavelet Transform (DWT) is used to analyze the fault current signals. MTHVDC system modeling and relay design are carried out in the MATLAB/SIMULINK environment. The results of the proposed algorithm were highly reliable regarding different types of faults with different fault resistances and at various locations. [ABSTRACT FROM AUTHOR]

• Prediction method of ground characteristics of wind turbines based on numerical electromagnetic field analysis method. • From the analysis, highly accurate transient grounding characteristics of wind turbines can be guessed. • It was possible to accurately acquire the characteristics of the lightning current flowing from the wind turbine to another wind turbine during a lightning strike. In recent years, it is becoming more common to replace old wind turbines and build new wind turbines with larger capacities in Japan. In the grounding design when replacing wind turbines, wind-turbine owners often utilize a part of the grounding electrodes of the conventional wind turbines to achieve lower grounding resistance with low cost. In addition, in order to make the grounding resistance value of the wind turbine lower than 10 Ω specified by IEC 61400–24, the grounding systems of multiple wind turbines are often connected. The ratio of the cost of constructing a grounding system of a wind turbine is not low, the cost is increasing year by year. Therefore, many companies involved in the design of grounding systems are beginning to use numerical electromagnetic field analysis methods in their designs in order to reduce costs. In this paper, measured and simulated impulse responses of the grounding systems of two single wind turbines and a pair of wind turbines connected by a buried insulated wire are introduced, and its characteristics are considered. In the analysis using the FDTD method, it is difficult to take into account the frequency-dependent characteristics of the soil because Maxwell's equations are time-differenced to formulate the equations used in the FDTD method. To construct a highly accurate analysis model, it may be necessary to build a model that takes into account the frequency-dependent characteristics of the soil. The method to construct such frequency-dependent model is also introduced in this paper. [ABSTRACT FROM AUTHOR]

• A new kind of active arc extinguishing device installed on the collector line of wind farm was developed in this paper. • Based on the multi fracture model, the formation and extinction process of compression arc are analyzed. • The results of the multi physical field simulation show that the multi-fracture active arc extinguishing device is a new and efficient lightning protection method for the collector line of wind farm. Wind farms are mostly concentrated in complex mountain terrain, and lightning accidents occur frequently. In order to ensure the safe and stable operation of the wind farm, based on the gas arc extinguishing technology and taking the collector line as the research object, this paper proposes a multi-fracture active arc extinguishing device for arc extinguishing protection. Firstly, the arc extinguishing principle of the device is analyzed, and then the physical field simulation of the arc extinguishing process is carried out by COMSOL Multiphysics simulation software. The actual operation results show that the device can effectively extinguish the arc generated on the insulator of the collector line. [ABSTRACT FROM AUTHOR]

With the increased penetration of wind energy in many utility grids throughout the world, transmission system operators (TSO) are facing further difficulties regarding power system control and stability. Therefore, modern wind farms should participate to the primary voltage and frequency control of power systems. This paper presents the design of a supervisory control strategy for grid-connected wind farms. Wind turbines within the investigated wind farm are pitch controlled and use the Direct Drive technology. It has a total installed capacity of 50 MW and it includes 25 PMSG-based wind turbines with a rated power of 2 M each. The proposed supervisor is developed with all features that make the wind farm able to provide active and reactive power control. It includes automatic voltage and frequency control with droop and dead band. Performances of this supervisor are evaluated in terms of compliance with the Danish TSO requirements. [ABSTRACT FROM AUTHOR]

This paper studies centralized and distributed schemes for the coordination of power injection in an HVDC grid connected to large wind generation. This coordination of power injection aims to keep the power balanced within the HVDC grid especially during large wind disturbances. Furthermore, the coordination tries to follow the converters’ schedules set by the connecting AC-TSOs every 15-min. This schedule comes from an overall combined AC/DC economic dispatch calculation with lower resolution compared to this coordination. In this paper, the coordination of power injection has been formulated as a non-linear constrained optimization problem for the centralized architecture. Next, the centralized optimization problem is decomposed to sub-problems using the Auxiliary Problem Principle (APP) method for the distributed architecture. This distributed optimization problem is solved by exchanging the required information between the AC TSOs. These two different approaches have been evaluated for a 5-terminal HVDC grid. Furthermore, a sensitivity analysis has been carried out to find the optimal updating rate of power injection set-points. The result shows that the more frequent updating of power injection coordination in the centralized architecture improves the generation reserves in each AC area. [ABSTRACT FROM AUTHOR]

This paper presents a technique for differential protection of Multi-terminal High Voltage Direct Current (MTHVDC) transmission lines. The proposed technique depends on the electrical current data at both ends of each line section. Discrete Wavelet Transform (DWT) is used to detect DC faults as well as filter out the high frequency transients superimposed on the current signals. An operating signal and a restraining signal are used in this technique to discriminate between internal faults and external faults through their ratio in each section of the MTHVDC. The operating and restraining signals depend on energy contents of the de-noised current signals at both ends of each line section. MTHVDC modeling and relay design are carried out in the MATLAB environment. The results demonstrate the high reliability of the proposed relay in the zonal protection of MTHVDC. [ABSTRACT FROM AUTHOR]

Mechanical health and operational efficiency of a wind turbine (WT) are important to the overall cost effectiveness in a wind farm. This paper presents a unit commitment (UC) model based on fatigue damage modeling of blades and uncertainty estimation of wind power forecasting (WPF). A novel glowworm metaphor algorithm (GMA) is developed to solve the proposed UC problem. During the pheromone updating of GMA, the luminescence carrying by glowworm reflects the net improvement by agent moving. This characteristic supports GMA to find the global optima for optimization of UC problem. The proposed UC objective is minimizing the mechanical damages of WTs in the whole wind farm. Uncertain interval of wind power generation is obtained as constraint function based on relevance vector machine (RVM). Data from a wind farm in China are used to validate the feasibility and effectiveness of the proposed method. Simulation results reveal the capabilities of GMA to efficiently get the better performance than benchmark methods, in terms of minimum mechanical damage, reliability and running efficiency. The benchmark methods are particle swarm optimization (PSO) and genetic algorithm (GA). The comparison between UC with and without consideration of WPF uncertainty exhibits the superiority of the incorporation of WPF uncertainty modeling. [ABSTRACT FROM AUTHOR]

Monitoring the grounding resistance of wind turbine generators (WTG) over the lifespan of a wind farm is important to ensure the safety of the personnel and equipment on the facilities. Conventional methods used to measure grounding resistance are not feasible in periodic maintenance activities of onshore wind farms due to test setup complexity and associated high costs. The clamp-on meter is an alternative method proposed to measure ground resistance in multi-grounded electrical systems. However, a significant error occurs in clamp-on meters on large grounding systems, such as those found in wind farms. Hence, we propose a solution to minimize methodological errors resulting from applying the clamp-on method in wind farms based on a neural network. Besides presenting lower errors than compared methods for a real Brazilian wind farm complex, it offers even greater practicality and safety to the workers involved in the measurement, as well as less test execution time. • Application of clamp-on ground meters in wind farms to measure grounding resistances. • Artificial neural network to minimize methodological errors of the clamp-on method. • Error comparative analysis between proposed, clamp-on and high-frequency method. • The new approach features shorter test run time compared to state-of-the-art methods. • It offers practicality and safety to the workers involved in the measurement. [ABSTRACT FROM AUTHOR]

A new direct current matching control (DCMC) scheme is proposed in this paper. The scheme is ideally suited for the integration of a large number of wind farms with AC grid systems via a multi-terminal HVDC (MTDC) network incorporating several grid-side converters. The proposed DCMC, which matches, in a near-instantaneous fashion, the cumulative injected DC currents from all wind farms with the total of the output DC currents to the AC grids (via inverters) by communicating real-time data between all terminals, is an improvement upon and potential replacement for conventional DC voltage droop and master–slave control strategies. Through the utilization of a wide-area supervisory control and data acquisition (WA-SCADA) system, the proposed DCMC aims to enhance MTDC network voltage stability and facilitate flexible power dispatch to the supplied AC grids, while maximizing the total amount of generated wind power and offering more flexibility in terms of the ability for wind farms to independently control and maximize their outputs without any requirement for output to be constrained. A six-terminal MTDC system connecting three wind farms to three independent mainland AC grids is used to validate the proposed DCMC and compare its performance with conventional control strategies, three simulation studies are carried out to test and verify the DCMC. [ABSTRACT FROM AUTHOR]

Wind speed correlation and wind turbine generator (WTG) outage are two factors affecting the reliability model of wind farms, but they are not addressed simultaneously in the existing literature. Meanwhile, WTG outage is reported to be dependent with wind speed to some extent. Therefore, the extended reliability models of wind farms incorporating both of these two factors and the dependency between WTG outage and wind speed are proposed in this paper. To consider the uncertainties and dependencies of wind speed and WTG failure, Copula method is applied to simulate correlated random variables representing for wind speed and the number of failed WTG units. Moreover, the linear apportioning technique is used to create multistate reliability models of wind farms from hourly wind power models. A number of sensitivity analyses on the modified IEEE RTS with wind power are conducted to validate the proposed reliability models for generation adequacy assessment. Case studies show that the generation adequacy indices increase with the correlation of wind speed and WTG forced outage rate (FOR). It is meaningful to point out that the effect of dependency between wind speed and WTG FOR on generation adequacy is minimal when WTG outages are independent, but it will be substantially larger when WTG outages are highly dependent. The proposed multistate reliability models of wind farms provide foundation for the reliability assessment of power systems with wind power integrated. [ABSTRACT FROM AUTHOR]

In this paper, security constrained generation scheduling (SCGS) problem for a grid incorporating thermal, wind and photovoltaic (PV) units is formulated. The formulation takes into account the stochastic nature of both wind and PV power output and imbalance charges due to mismatch between the actual and scheduled wind and PV power outputs. A hybrid technique in which the basic elements are a genetic algorithm (GA) with artificial neural network (ANN) and a priority list (PL) is used to minimize the total operating costs while satisfying all operational constraints considering both conventional and renewable energy generators. Numerical results are reported and discussed based on the simulation performed on the IEEE 24-bus reliability test system. The results demonstrate the efficiency of the proposed approach to reduce the total production cost for real time operation. Moreover, the results verified that the proposed approach can be applied to different problem dimensions and can score more favorably compared with analytical techniques. [ABSTRACT FROM AUTHOR]

• The compensated PSM proposed in this paper does not need the zero-sequence current as an angle comparison reference. • The virtual magnitude factor-assisted rezoning principle enables the compensated PSM to successfully identify the faulty phase(s) under different fault conditions. • The compensated PSM does not necessitate a high-bandwidth communication channel and additional improvements in wind generators' control strategies. The current angle-based phase selection method (PSM) determines the specific faulty phase(s) based on the relative angles of the superimposed sequence currents at the fault point under different fault types. However, by contrast with synchronous generators (SGs), the superimposed sequence impedances of wind generators present significantly different fault features, which may deprive the unified phase angle property shown in the fault component network, and consequently accompanied by the angle offset between the respective superimposed sequence currents at the relay location and the fault point. In the meantime, the weak-infeed characteristics of the wind farm may weaken the fault signature of the current quantities. As a result, the performance of current angle-based PSM may deteriorate when applied to lines emanating from wind farms. To address these problems, this paper firstly introduces the voltage information to compensate the superimposed sequence currents such that enabling the current angle relationship to be reflected accurately at the relay location. Furthermore, to eliminate the possibility that the current angle-based PSM may provide misleading indications of faulty phase(s) under particular scenarios as it solely depends on the angle comparison, the virtual magnitude factor is constructed and utilized to optimize the fault type zones in the complex plane. Compared with the existing current angle-based PSM, some salient merits of the compensated PSM based on virtual magnitude rezoning are its immunity to the weak-infeed level, independence from wind farms' operating status, and strong tolerance capability against fault resistance. Extensive simulation results under different fault conditions show the expected performance of the proposed PSM. [ABSTRACT FROM AUTHOR]

• SynCon and STATCOM are compared for their weak grid stability enhancement at zero reactive power injection condition in electromagnetic transient (EMT) simulation. • SynCon shows a better capability of stability improvement compared to STATCOM. • The dq-frame admittance of the two devices are measured using frequency scans and fitted to the s-domain admittance models which are further used for eigenvalue analysis and stability prediction. • The s-domain admittance-based eigenvalue analysis results corroborate with the EMT simulation results. • Analysis of the dq-frame admittance shows that SynCon contributes shunt reactance at steady-state while STATCOM does not; this difference explains why SynCon has a better capability of stability enhancement. Reactive power compensation is an effective method to enhance stability of a power system. Synchronous condenser (SynCon) and static synchronous compensator (STATCOM) are widely used for reactive power compensation. They have the capability of increasing system stability and efficiency by absorbing or generating reactive power. This paper presents a comparison of SynCon and STATCOM under the condition of zero reactive power injection. The two devices are integrated into a grid-connected type-4 wind farm to examine their effects on system stability. It is found that SynCon is more capable in stability enhancement compared to STATCOM. To explain the difference, we measure the d q -frame admittance frequency-domain responses of the two devices using frequency scans. Vector fitting method is then utilized to convert the admittance frequency-domain measurements to an s -domain model. The s -domain admittance-based eigenvalue analysis further confirms that SynCon is advantageous in stability enhancement. The difference of SynCon and STATCOM can be summarized as SynCon providing a steady-state reactance while STATCOM acting as a current source at steady state. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a dual battery energy storage system (BESS) scheme is adopted to compensate power mismatch between wind power and desired power schedule for dispatching wind power on an hourly basis. The two BESSs are utilized to cope with the positive and negative power mismatch respectively, and the roles of them can be interchanged according to the predefined thresholds on state of charge (SOC). Three hourly indices, entitled as expected wind power curtailment (EWPC), expected wind power deficiency (EWPD) and probability of wind power deficiency (PWPD) respectively, are proposed to evaluate the performance on wind power dispatchability provided by the BESS. Sequential Monte Carlo simulation (SMCS) is utilized to compute the three hourly indices. Finally, simulation results on a real Chinese costal wind farm justify the feasibility of the methodology proposed in this paper. [Copyright &y& Elsevier]

Abstract: This paper investigates the modeling of a submarine cable connected with an offshore wind farm by conducting a transient analysis and comparing fundamental experimental results. This study clarifies the effect of reflection waves at the interface between the aerial part and the underwater part of the cable in an offshore wind farm. It can be expressed as a series connection of cables with different modal components. In Alternative Transients Program (ATP) simulations, an underwater cable can be treated as a cable that is buried in the ground and has equivalent resistivity. Simulation results show significant wave deformation because of the quite slow mode 0 component in water. It is confirmed that special attention should be paid to the resistivity of water and the permittivity of the corrosion-proof layer of the cable in such types of investigations. [Copyright &y& Elsevier]

Abstract: Accurate estimation of long term wind speed probability distribution is a fundamental and challenging task in wind energy planning. This paper proposes a nonparametric kernel density estimation method for wind speed probability distribution. The proposed method is compared with ten conventional parametric distribution models for wind speed that have been presented in literatures so far. The results demonstrate that the proposed non-parametric estimation is more accurate and has better adaptability than any conventional parametric distribution for wind speed. [Copyright &y& Elsevier]

Abstract: This paper proposes a solution approach of the power flow problem to assess the steady-state condition of power systems with wind farms in a single frame of reference, in which the state variables of the wind generators are combined with the nodal voltage magnitudes and angles of the entire network for a unified iterative solution through the Newton–Raphson method. Different wind energy conversion systems (WECS) are mathematically derived from the steady-state representation of the induction generator. Suitable strategies for initializing the state variables of the wind generators are also proposed in this paper. Lastly, three numerical examples are presented to numerically illustrate the applicability of the proposed approach. [Copyright &y& Elsevier]

Abstract: In recent years, the number of small size wind farm made up with doubly fed induction generators (DFIG) located within the distribution system is rapidly increasing. DFIG can be utilized as the continuous reactive power source to support system voltage control by taking advantage of their reactive power control capability. In this paper, considering both reactive power control and distribution network reconfiguration can be used to reduce power losses and improve voltage profile, a joint optimization algorithm of combining reactive power control of wind farm and network reconfiguration is proposed to obtain the optimal reactive power output of wind farm and network structure simultaneously. The proposed algorithm has been successfully implemented on the 16 bus distribution network and the results obtained demonstrate the efficiency of the algorithm. [Copyright &y& Elsevier]

Abstract: This paper reports on design of digital control for wind turbines and its relation to the quality of power fed into the Brazilian grid on connecting to it a 192MW wind farm equipped with doubly fed induction generators. PWM converters are deployed as vector controlled regulated current voltage sources for their rotors, for independent control of both active and reactive power of those generators. Both speed control and active power control strategies are analyzed, in the search for maximum efficiency of conversion of wind kinetic energy into electric power and enhanced quality of delivered power. [Copyright &y& Elsevier]

Abstract: This paper presents a control scheme of a variable-speed wind turbine with a permanent-magnetic synchronous generator (PMSG) and full-scale back-to-back voltage source converter. A comprehensive dynamical model of the PMSG wind turbine and its control scheme is presented. The control scheme comprises both the wind-turbine control itself and the power-converter control. In addition, since the PMSG wind turbine is able to support actively the grid due to its capability to control independently active and reactive power production to the imposed set-values with taking into account its operating state and limits, this paper presents the supervisory reactive power control scheme in order to regulate/contribute the voltage at a remote location. The ability of the control scheme is assessed and discussed by means of simulations, based on a candidate site of the offshore wind farm in Jeju, Korea. [Copyright &y& Elsevier]

• Yet there are few studies for the extremely short-term forecasting of wind power. • Since the proposed approach is nonlinear, it provides more accurate modelling than the ARMA approach. • The proposed approach only uses the EKF algorithm to update the parameters which makes it suitable for online implantation. • It is robust against noisy easements and probabilistic behavior of the wind speed profile. • A proper model for the wind farm to simulate and evaluate the performance of the SVC based on real data is proposed. The inherent time-varying nature of the wind farm power causes undesired voltage flicker in the power network. In order to mitigate the flicker to enhance the performance of the wind power system with very fast dynamics, the static VAr compensator (SVC) is utilized. However, the SVC operates with some delays which negatively affects its performance. This persuades us to predict the reactive power of the wind farm to compensate for the real-world delay. The predicted reactive power is then utilized in the SVC. Therefore, this paper develops a novel fuzzy one-step-ahead prediction approach for the wind farm reactive power. The proposed fuzzy prediction uses a Takagi-Sugeno (TS) fuzzy representation whose unknown parameters are tuned online based on an extended Kalman filter (EKF). The wind farm is modeled as a time-varying current source which its amplitude and phase change every 0.01 s. A large set of the actual data of a wind farm in Manjil, Iran is gathered and directly utilized in the simulation process. Several flicker indices are calculated to evaluate the proposed prediction method. The obtained results show the performance enhancement and flicker mitigation of the suggested power scheme. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an innovative voltage control scheme for a grid-connected wind farm. In wind power generation systems, operating conditions are changing continually by wind speed fluctuations and load changes. Therefore, a robust control mechanism is necessary. To enable a linear and robust control framework, the overall system is represented by a set of reduced-order linear systems that cover an operating range of interest determined by variations of the load. A control-design technique known as the linear quadratic regulator (LQR) can be conveniently utilized for multi-input multi-output systems. However, to make this approach applicable simultaneously to several linear systems, the LQR problem needs to be reformulated for finding a common Lyapunov function for the set of considered linear systems. This is accomplished by representing the underlying control optimization problem in terms of a system of linear-matrix-inequality (LMI) constraints and matrix equations that are simultaneously solved. The solution of LMI equations involves a form of quadratic Lyapunov function that not only gives the stability property of the controlled system but can also be used for achieving certain performance specifications. In addition, to make the control design applicable to realistic systems, with noise and disturbances in the measured signals, we consider a state observer. A candidate wind farm site on Vancouver Island, Canada, is conducted for simulation study. The proposed methodology is also flexible and readily applicable to larger wind farms of different configurations. [Copyright &y& Elsevier]

This paper considers the problem of determining the locations of wind generators in a wind farm consisting of many generators. The objective is to find a generator placement that maximizes profit, which is the product of the cost efficiency of the generators and the total power output from the wind farm. Generator placement is significant because if generator A is located close to generator B and is located downwind of generator B then the power output of generator A is reduced by an amount that varies with the distance between the generators. The problem can be formulated using mathematical programming but to solve the problem one cannot employ traditional optimization methods. Therefore, a greedy improvement heuristic methodology is developed and described in detail. The effectiveness of the proposed heuristic is demonstrated on a suite of test problems. These results indicate that the proposed method represents an effective solution strategy for this problem. [Copyright &y& Elsevier]

• Authors propose MILP approach for optimal cable routing in an onshore wind farm. • The novelty in the proposed algorithm is reliability assessment of the proposed network. Based on the suggested outline of the network, the failure rate as well as the cost of lost energy production for every wind turbine within the farm is updated. • The algorithm supports the optimal selection among different cable options, with different features, prices and capacities. The algorithm also takes into account the calculation of steady-state voltage at the point of connection (POC) and thus, accounts effect of power quality in the network. • The proposed algorithm is tested on an actual distribution model including a wind farm. The algorithm gives optimal solution for all 12 case scenarios that have been tested. Designing an onshore wind farm is a complex planning process that requires various stages to be completed. The prime focus of this work is to assist planners and experts in finding the optimal cable layout of the onshore wind farm. The optimization algorithm is designed using mixed integer linear programming (MILP). The MILP algorithm takes into account system reliability, power transfer capacities and power quality issue. The novelty in this optimization algorithm is to simultaneously minimize cable installation cost and the cost of lost energy production and therefore maximize the reliability of the system. Additionally, the algorithm supports the optimal selection among different cable options, with different features, prices and capacities. By calculating voltage increase at the point of connection (POC), power quality issue is considered as well. The designed algorithm provides optimal results for four different wind farm layouts. Every layout is tested for three different case scenarios, where different number and type of cables are considered. The results show that more cable options contribute in lowering the total costs. Moreover, cables with higher capacity can help in improving the power quality issue. [ABSTRACT FROM AUTHOR]

• The mathematical models for power equipment in wind farm have been developed. • The transients under lightning strike on overhead lines in wind farm are obtained. • The capacitance between windings of step up transformer plays a key role. • The protection area and absorbed energy of surge arrester in wind farm are studied. The overhead line in wind farm is vulnerable to lightning strikes at a high risk. The lightning surge would propagate along the line and damage the equipment in substation. In this work, the mathematical models for transmission tower, overhead lines, power transformer and wind farm substation have been developed in the environment of EMTP, especially the wind turbine converter and step up transformer models. The transients in the case of back flashover and shielding failure are analysed. The influences of radial and cross-shaped connections of wind turbine topology on the wave reflection and refraction have been investigated. The performance of surge arrester, not only the protection area but also the absorbed energy under lightning overvoltage is also computed. The wind farm substation is divided into multi zones and the transient response at different nodes is obtained. It indicates that the characteristics and propagation for surge under lightning strike on overhead line are completely different from direct lightning strike on wind turbine receptor. The capacitance between the high and low voltage side of step up transformer plays a key role in system transients. Compared with back flashover, the overvoltage caused by shielding failure is relatively small; the cross-shaped scheme is preferred and would benefit the lightning protection; the absorbed energy of arresters under a high lightning current is a major consideration. [ABSTRACT FROM AUTHOR]

• A mode switch control and reactive power support strategy are proposed. • Voltage sags are mitigated or eliminated with proposed control. • The real-time local control enables inverters to respond to voltage drops swiftly. • The probability of AC voltage sag impact on windfarm is reduced with proposed control. In recent years, VSC-HVDC has been widely used in windfarm integration owing to its ability of connecting the weak AC system. And the hybrid modular multilevel converter based HVDC(MMC-HVDC) has attracted more attention because of its DC fault blocking capability. However, most of the researches about MMC-HVDC connected to windfarm are focused on frequency response and wind farm fault ride through, without assisting AC system to maintain the voltage via the converter's reactive power control capacity. Based on this, this paper proposes a mode switch control and reactive power support control scheme for the grid connected inverter connected to windfarms. The switch mode control scheme provides three operation modes for MMC to adapt to different operation situations. The reactive power support coordination control scheme is an advanced control scheme for cooperating converter, unloading resistor and wind farm. With the cooperating control, the PCC voltage sag due to the fault is alleviated while reducing the impact of grid failures on the wind farm. Finally, the presented control strategy is simulated in PSCAD/ EMTDC, which verifies the effectiveness of the scheme proposed. [ABSTRACT FROM AUTHOR]

• Quantification and comparison of cloud to ground lightning characteristics in the locality of coastal wind farm in Southeast China. • Providing potential evidence of the shielding effect between wind turbines in offshore wind farm. • Pointing out the threat of spring lightning to wind turbines in Southwest China. The effects of wind turbines (WTs) on cloud-to-ground (CG) lightning activities have not been fully understood. Based on the CG lightning data obtained from lightning location system (LLS), this paper quantified and compared the characteristics of CG lightning activities, including lightning density, multiplicity, polarity, peak current, and seasonal distribution, before and after the erection of the wind farms (WFs) in China. The shielding effect of offshore WTs was also analyzed. The results showed that, since the WF located in the southeast China was constructed, the return stroke density, flash density and multiplicity within a radius of approximately 0.5 km around the WTs increased by 27.9%, 7.3% and 10.9% in terms of change rate, respectively; within the same distance, the negative median peak current was -23.9 kA, and the positive median peak current was 12.3 kA. WTs located at the edge of the offshore WF had a shielding effect on the internal WTs. The proportion of spring lightning was up to 41.4% in southwest China. Winter lightning was rare in southern China. The results suggest more detailed factors, such as the local terrain, climate and the layout of WFs, are needed when assessing the lightning risk to WTs. [ABSTRACT FROM AUTHOR]

• Reactive power control in DFIG-based wind turbine to provide ancillary services. • Use EGRPS-based wireless communication to DFIG reactive power management. • Constant monitoring of busbar voltages in electrical systems. • Co-simulation of telecommunications and Power Systems. • Solution for operation planning of modern power systems in smart grid environments. This paper presents an alternative topology analysis for reactive power control in wind farms with wireless communication link integration. The co-simulation environment with telecommunication, machine control, and power system demonstrate in this analysis, that it can be an useful solution for planning the operation of modern power systems and their ancillary services in a smart grid scenario. A low cost and easy implementation EGPRS standard wireless link was adopted to perform the communication from the smart grid operator and the wind farm with the objective of maintain the voltage levels under established limits. The wireless communication was used to send the value of measured voltage of one critical bar to the operator and to return the reactive power reference to the wind farm. The studied scenario is represented by a seven bar power system model connected to a DFIG wind farm. The results obtained by this co-simulation endorse this original proposal and show its operability. [ABSTRACT FROM AUTHOR]

• In this paper, an adaptive differential protection scheme is proposed for wind farm integrated power network. • A particle swarm optimization (PSO) based differential relay algorithm is proposed in this paper. • The positive sequence current differential principle is used. • For different operating conditions, fault conditions and configurations of the system, the threshold value can be calculated online. • The threshold setting is designed considering the fault location and fault inception angle. • The method is tested using a standard power system model integrated with wind farm and simulated using MATLAB R2016a software. In this paper, an adaptive differential protection scheme is proposed for wind farm integrated power network. Any fixed threshold setting based protection scheme is not always suitable for the different operating conditions of power system. Considering the possible modulations in the fault signal, a particle swarm optimization (PSO) based differential relay algorithm is proposed in this paper. The positive sequence current differential principle is used. For different operating conditions, fault conditions and configurations of the system, the threshold value can be calculated online. So, practically the method can be applied to any power system model and the impact of dynamic operation of wind farm on the protection function is negligible. The threshold setting is designed considering the fault location and fault inception angle. Initially, the most effective faults among all the possible faults are identified with a single variable (fault location) objective function. Later, only single-phase-to-ground fault is considered for threshold setting with all possible parameters. The method is tested using a standard power system model integrated with wind farm and simulated using MATLAB R2016a software. Results prove the efficacy of the method. [ABSTRACT FROM AUTHOR]

• This paper proposes two novel probabilistic load flow methods based on holomorphic embedding method. • Holomorphic method is used to solve the power flow in a faster and robust way. • Kernel Density Estimator (KDE) and Saddle Point Approximation (SPA) methods are used to efficiently estimate probabilistic characteristics of load flow outputs. • The correlations between random input variables with non-normal/normal probability distributions have been considered. • Several numerical tests are carried out to assess the robustness and performance. Probabilistic Load Flow (PLF) methods have been extensively regarded due to the growth of uncertainty and renewable energies penetration in power systems. Given that, the current study aims to propose two novel probabilistic load flow methods based on holomorphic embedding method. Holomorphic method, unlike other iterative methods, introduces a nonlinear equation solver in an independent class, recursively. To that end, Kernel Density Estimator (KDE) and Saddle Point Approximation (SPA) methods are used to efficiently estimate probabilistic characteristics of load flow outputs. The correlations between random input variables with non-normal/normal probability distributions have been considered. The proposed algorithms have been examined on the modified IEEE 14- and 118-bus systems. Finally, to consider the uncorrelated and correlated conditions, the researcher compared the simulation results of the two proposed methods with some well-known and published probabilistic iterative load flow methods such as Monte Carlo Simulation (MCS), Parzen Window (PW), Diffusion method, and 2n+1 Point Estimate Method (PEM). MCS is always a dependable solution but time-consuming that make it useless for large power systems. In the present study, the accurate results obtained from MCS are regarded as a reference. The comparison of results shows high efficiency and low computational burden of proposed methods, and also the accuracy of these methods in density function estimation of output random variables. [ABSTRACT FROM AUTHOR]

• The proposed aggregation model of the wind farm shows a high precision in frequency domain. • The proposed aggregation model is convenient for the stability analysis of large-scale grid-connected wind farms. • Wind speed distribution will influence wind farm impedance characteristics greatly. • The inertial controller has negative impacts on the stability of the wind farm system. With the wind power penetration rate continuously rising, a suitable wind farm model considering both accuracy and simplicity is required for power system stability analysis. To accomplish this goal, an accurate aggregated modified sequence impedance model of the wind farm is established in this paper. The modified sequence impedance model of wind turbine generator is established, which considers the coupling between the positive- and negative-sequence impedances. The modified sequence impedances of the ac collection system, transformers, and ac grid are also derived. In this way, the impedance network of the entire wind farm system can be formed and simplified to acquire the accurate aggregated modified sequence impedance. Furthermore, the proposed model is compared with the traditional single-machine aggregated model which shows the necessity of establishing the accurate aggregated model. It is worth noting that the differences among each wind turbine generator's operation points can be included in the proposed model. Compared with the results of impedance measurements of a target wind farm, the accuracy of the proposed aggregated sequence impedance model of the wind farm is verified in frequency domain. The application of the proposed model in the stability analysis of a grid-connected wind farm is also presented with consideration of the ac grid strength. What is more, the effect of the inertial controller on the wind farm system stability is also analyzed to make the impact of this study much more appealing and up to date. [ABSTRACT FROM AUTHOR]