Research Article
A wind energy generation replication method with wind shear and tower shadow effects
Advances in Mechanical Engineering 2018, Vol. 10(3) 1–11 Ó The Author(s) 2018 DOI: 10.1177/1687814018759216 journals.sagepub.com/home/ade
Lei Fu1,2, Yan-ding Wei1,2, Sheng Fang2, Geng Tian2 and Xiao-jun Zhou1,2
Abstract Wind energy has become one of the most promising renewable energy in recent decades. However, severe rotor oscillations arose by the wind shear and tower shadow effects were not only harmful to the power quality but also threatening to the stability of the energy system. Meanwhile, it is difficult to simulate the effects under the local condition. Therefore, it is indispensable to develop an immersion environment for the wind energy conversion. To cover these requirements, a novel approach to simulate the process of the wind energy generation with wind shear and tower shadow effects is presented. In particular, the replication method is applicable to both fixed and variable speed turbines, for the rotor oscillations synchronizing with the rotations at a constant angle. The equivalent wind speed of the effects contributes to the aerodynamics model as nonstationary time series. For stationary processing the nonstationary signals in the time domain, the analysis of computer order tracking is imported to solve the spectral leakage in the fast Fourier transform spectrum. Finally, based on this method, an immersion environment is realized through two coupled induction motors in an electric closure test bed. Experimental results demonstrate that the proposed replication method is effective and accurate in terms of both static and dynamic performances. Keywords Wind turbine simulator, wind shear, tower shadow, computer order tracking
Date received: 9 May 2017; accepted: 22 January 2018 Handling Editor: Chun-Liang Yeh
Introduction In response to the global energy crisis and the increasing desire to reduce fossil fuel usage, wind energy has become one of the most promising renewable energy sources due to its environmentally friendly, socially beneficial, and economically competitive characteristics. As a result, many studies have been focused on the development of wind turbines with the aim of making wind turbines more efficient and reliable and less expensive.1–3 Considering the cost and space limitations of a real wind turbine, a test-rig facility is an ideal choice to simulate the static and dynamic characteristic states of real wind energy conversion systems. There have been
several in-depth studies using wind turbine simulators. A DC motor is suitable for assuming the role of the driving source of the wind turbine simulator due its excellent characteristics, including output torque and 1
The State Key Laboratory of Fluid Power and Mechatronic Systems, College of Mechanical Engineering, Zhejiang University, Hangzhou, China 2 Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, College of Mechanical Engineering, Zhejiang University, Hangzhou, China Corresponding author: Yan-ding Wei, The State Key Laboratory of Fluid Power and Mechatronic Systems, College of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China. Email:
[email protected]
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License (http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages (https://us.sagepub.com/en-us/nam/ open-access-at-sage).
2 input current. Previous studies4,5 utilized the DC motor with armature current control as the wind power input. However, this approach requires a large-sized DC motor and is more costly compared to an AC motor. Compared to DC motors, induction motors have the advantages of low cost and compact size. Kojabadi et al.6 developed a wind turbine simulator based on an induction motor to create a controlled environment for a drive train. However, the drive train is neglected in the simulator model, as the drive train affects the dynamic performance of the wind turbine. Mihet-Popa et al.7 and Monfared et al.8 achieved the experiment platforms to reproduce the dynamic characteristics of wind turbines. Nevertheless, those simulators are simplified in aspect of the wind model, which is an important factor in wind energy. Combining the achievements of previous researches, a scaled-down emulator operated on a programmable wind speed model, showing the approximate dynamic characteristics in Sajadi et al.,9 which can conduct various tests by adopting different control strategies. Although those simulators have been investigated in depth, limitations still exist in terms of dynamic performance because of wind shear and tower shadow effects, which influence the power quality of wind turbine systems.10 Many studies have demonstrated that wind shear and tower shadow effects negatively influenced the power quality such as AC tie-line power oscillations of wind turbine systems. For instance, Wan et al.11 established and analyzed the simulation results under the effects of tower shadow and wind shear. The results revealed that the effects would significantly influence the aerodynamic data of wind turbine systems under various wind speeds. Furthermore, Tan et al.12 determined that the oscillations caused by wind shear and tower shadow were harmful to the stability of the wind energy system when the oscillation frequency approached the natural frequency of the wind turbine systems. The aforementioned studies demonstrate that there are five key points in the design of wind turbine simulating environment: (1) the wind profile can be realized on different models; (2) the wind turbine simulating environment should present the static and dynamic characteristics, such as the wind turbine power coefficient at various pitch angles and the power curve at different wind speeds; (3) the transmission system, main shaft, and gearbox can be modeled and virtually simulated according to various parameters; (4) especially, the effects of wind shear and tower shadow should be considered in terms of the dynamic characteristics; and (5) the motion controller must be of high performance. Although various simulating methods have satisfied some of the five requirements mentioned above, there is still considerable potential in developing a highperformance wind turbine simulating approach. In
Advances in Mechanical Engineering other words, it is still essential to design a wind turbine simulating method with real static and dynamic features, especially, with real oscillation effects caused by wind shear and tower shadow. This article proposes a novel approach to simulate the process of the wind energy generation with wind shear and tower shadow effects, with the aim of achieving the aforementioned key points for the promotion of wind energy conversion research. The remainder of this article is organized as follows: section ‘‘Wind turbine modeling’’ introduces the wind speed model and aerodynamics of the wind turbine with wind shear and tower shadow effects. Section ‘‘Simulator implementation’’ focuses on the implementation of the proposed system in the hardware and control strategies. Section ‘‘Experiment’’ presents experimental results demonstrating the effectiveness and accuracy of the simulating platform. Section ‘‘Conclusion’’ provides the conclusions of this article.
Wind turbine modeling Wind speed model Wind speed varies according to the local heating and atmospheric conditions such as the temperature, the horizontal pressure gradient force, the Coriolis force, and the friction force, which influence the generated power quality and dynamic characteristics of the wind turbine. Therefore, the wind speed model plays an important role in determining the dynamic performance of the wind turbine simulator. The Van der Hoven13 spectrum is regarded as one of the best-known references of the wind speed spectrum and has been adopted in other wind turbine simulators.14 The IEC 614001:200515 codes recommend introducing the Kaimal model or Von Karman isotropic model for wind turbine simulation. In this article, the Kaimal model is adopted and expressed in equation (1), where Vh is the average wind speed at the hub of the wind turbine, f is the frequency in Hertz, k is the index referring to the direction of the velocity component, Sk is the component spectrum of the single-side velocity, sk is the standard deviation of the velocity component, and Lk is the integral scale parameter of the velocity component Sk =
4s2k Lk =Vh ð1 + 6fLk =Vh Þ5=3
ð1Þ
Based on the power spectrum density, the harmonic component at each frequency can be estimated by the discrete angular frequency and the corresponding values of the power spectral density in equation (2). The turbulent wind speed consists of a linear superposition of the sine harmonic terms of equation (3)
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Figure 1. The characteristics of the pitch-regulated variable speed turbine: (a) Wind turbine power coefficient vs. tip speed ratio at various pitch angles and (b) Power curve vs. wind speed characteristics at various pitch angles.
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S ðvi ÞDvi Ai = 2p y ðt Þ = y 0 +
N X
Ai cosðvi t + fi Þ
ð2Þ ð3Þ
i=1
where y0 is the average wind speed; Ai and vi denote the magnitude and discrete angular frequency of the ith component of the spectrum, respectively; and fi is a random phase angle in the range [0, p].
A pitch-regulated variable speed turbine is one type of major wind turbine and is the only type that can achieve the theoretical power curve. When a wind turbine is running below the rated wind speed, the control strategy is to use variable speed and fixed pitch to capture the maximum energy. After the rotor reaches the rated wind speed, it runs at the fixed speed and in the variable-pitch mode to guarantee power efficiency at the rated value. The power of the wind energy that passes through the rotor blades is expressed in equation (4) ð4Þ
where r is the air density (kg/m3), y wind is the wind speed (m/s), and Rrotor is the rotor radius (m). As a nonideal rotor can only capture part of the wind power, the rotor power coefficient is a measurement of the rotor efficiency as defined in equation (5) Trotor =
1 Cp ry 3wind pR2rotor vrotor 2
8 21 > 0:4b 5 eli + 0:0068l < Cp = 0:5176 116 li 1 1 0:035 > 3 : = li l + 0:08b b + 1
ð6Þ
The tip speed ratio is defined in equation (7)
Aerodynamics of the wind turbine
Pwind = 0:5ry3wind pR2rotor
The rotor power coefficient is a function of the tip speed ratio l and blade pitch angle b, whose relationship is shown in Figure 1(a). The coefficient Cp can be calculated with the tip speed ratio l and the blade pitch angle b. A simplified equation is represented as follows in equation (6)
ð5Þ
l=
vrotor Rrotor ywind
ð7Þ
Based on the equations (4)–(7), the wind turbine power versus wind speed characteristics at various pitch angles is concluded in Figure 1(b). From Figure 1(a) and (b), it is seen that the control of the pitch-regulated variable speed turbine is complex, where each pitch angle is corresponding to a Cp curve. Figure 2 presents a curve of wind turbine power versus wind speed in different control strategy regions.16 Each turbine has three different important wind speeds: the cut-in wind speed, rate wind speed, and cut-out wind speed. The wind turbine starts to operate when the wind speed is greater than the cut-in speed. This stage is called the maximum Cp tracking stage, defined as control stage A1, when the blade pitch angle keeps a constant value to capture the wind energy as effectively as possible. At the beginning of control stage A1, the rotation speed of the wind turbine rotor remains constant at the minimum value. With increasing wind speed, the rotation speed of the rotor increases, which is aimed at controlling the system running under the optimal tip
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Figure 2. Wind turbine power curve versus wind speed at different control areas.
speed ratio. In control stage A2, the rotation speed of the rotor reaches the maximum value, where the wind turbine cannot guarantee the optimal tip speed ratio. Hence, the pitch control system is used to adjust the blade pitch angle to capture the maximum wind energy. When the wind speed is above the rated speed, the wind turbine operates at the rated power stage defined as control stage A3, where the pitch control system continues operating to ensure that the rotor can capture the rated power. The wind turbine stalls when the wind speed is beyond the cut-out speed.
Wind shear and tower shadow The wind speed varies with the tower height, which is defined as the wind shear effect. Thus, the turbine blades experience the maximum wind speed when facing directly upward and the minimum at downward. Since the wind turbine has three blades, the wind shear effect occurred 3 times in one rotation, which is regarded as the 3p frequency. A wind shear model17 is simplified as equation (8) V ðr, uÞ = Vh
r cos u + H a = Vh ½1 + Wshear ðr, uÞ ð8Þ H
where r, u, H, Vh, and a are the radial distance from the rotor axis, the blade azimuthal angle, the hub height, the wind speed at the hub height, and the empirical wind shear exponent, respectively. The values of the empirical exponent depend on the type of terrain, described in Dolan and Lehn.17Wshear(r, u) is the component of the wind shear effect, which can be approximated by a third-order truncated Taylor series expansion, as shown in equation (9) r aða 1Þ a 2 2 cos u + cos u Wshear = a H 2 H ð9Þ aða 1Þða 2Þ a 3 3 + cos u 6 H
Figure 3. Aerodynamic torque factor under the wind shear and tower shadow effects.
The third-order term is necessary for the torque oscillations to ensure that the wind shear model is effective because when summing the three blade contributions, the first term leads to a zero component and the second term results in a DC component. The tower shadow effect is caused by the presence of the tower when the blade is directly in front of the tower, which makes the blade experience the minimum wind. Tower shadow can cause a peak-to-peak torque fluctuation of 8%. Each of the three blades experiences minimum wind when under the shadow of the tower. Therefore, the tower shadow effect also contributes to the 3p frequency. The details of the tower shadow model have been discussed in Dolan and Lehn.17 The tower shadow model is shown in equation (10) a2 r2 sin2 u x2 = Vh Wtower ðr, u, xÞ Vtower ðr, u, xÞ = Vh r2 sin2 u + x2 ð10Þ where Vh, a, r, u, and x are the wind speed at the hub height, the tower radius, the radial distance from the rotor axis, the blade azimuthal angle, and the distance between the blade origin and tower midline, respectively. Based on the equations (9) and (10), the total effect of the three blades of the wind turbine is calculated and represented. Figure 3 shows the rotor torque oscillation caused by the wind shear and tower shadow effect in one rotation period. The relative torque factor caused by the wind shear and tower shadow effects is shown, where the torque values are normalized. The horizontal axis represents the angle of the rotor in one rotation, and the vertical axis represents the relative torque factor. From this figure, both wind shear and tower shadow contribute to the 3p torque oscillation. The tower shadow effect is more significant than the wind shear impact. It is essential to represent the tower
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Figure 4. (a) Experimental hardware setup and (b) schematic frame of the hardware.
shadow and wind shear effects in the wind turbine simulator, as the total 3p oscillation contributes approximately 8% amplitude in the aerodynamic torque.
Wind turbine drive train The wind turbine drive train consists of the rotor blade, gearbox, and generator, among other components. Santoso and Le18 noted that a two-mass model with mechanical damping is necessary to accurately represent the transmission characteristics of the wind turbine. Additionally, the high-speed shaft is assumed to be completely stiff.19 Aerodynamic torque equations are expressed based on two-mass models with damping to describe the mechanical characteristics in equation (11) d 2 ut dut dug + K ut ug = Tt + D ð11aÞ 2 dt dt dt d 2 ug dug dut Jg 2 + D + K ug ut = Tg ð11bÞ dt dt dt Jt
where Jt and Jg are the instant inertia of the rotor and generator (kg m2), respectively; ut and ug are the angles of the rotor and generator (radians), respectively; D and K are the equivalent factors of damping (N m s/ rad) and stiffness (N m/rad), respectively; and Tt and Tg are the wind turbine aerodynamic torque and generator electrical torque (N m), respectively. As the wind turbine drive train behaves as a low-pass filter turbine, the frequency response magnitude decreases with decreases in the equivalent inertia at the same frequency, which impacts the dynamic characteristics of
the turbine. Additionally, the natural damping frequency, which is the peak value point in the amplitude– frequency response curve, should be considered. The wind shear and tower shadow effects will cause strong flicker emissions because the natural damping frequency is close to the 3p oscillation frequency.20
Simulator implementation Hardware setup The proposed scaled-down wind turbine simulator has been designed in a laboratory environment, as shown in Figure 4(a), where two 550-W induction motors are connected through a diaphragm coupling. A Siemens SINAMICS S120 system is adopted to guarantee the high performance in motion control. In this system, a control unit named CU320PN is embedded to control the closed-loop motion through the DrivCliQ bus. Depending on the power unit, the 510-V DC link is charged from the three-phase supply, offering power to the drive module. Two independent DC/AC drive modules drive each motor in vector functionality without an encoder. The DC/AC driver 1 is inverted from the DC link to the drive motor under torque control mode as a turbine prime source, whereas the DC/AC driver 2 rectifies AC power regenerated from the generator under speed control mode. Electric energy is exchanged between the motoring and generating motor modules via the DC link, and the electric closure test operated as an ecological cycle system. Only the missing energy is drawn from the line supply, which makes this simulator energy efficient in the long term. Additionally, the brake unit is a program-controlled resistor connected to the DC link. The brake unit is necessary during
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Figure 5. Block diagram of the simulator.
simulation when the generating electric energy is larger than the consumed power, which could lead to the DC link becoming overcharged or even damaged. A Siemens S7 PLC, named the CPU 1212C, is connected to the S120 system through an industrial ethernet following Profinet protocol. In this proposed simulator, the Profinet protocol is set as a free telegram configuration with BICO, where the length of each telegram is eight words. Using this telegram, CPU 1212C can transmit control words and set-point values to the CU320PN while receiving status words and real values from CU320PN in periodic time. A computer supervises the CPU 1212C using OPC server technology, which offers the user motion control of the interface. The console application is realized on the LabVIEW with the datalogging and supervisory control (DSC) module, which enables the shared variables of the S120 system to be read or written through OPC connections. Figure 4(b) shows the relationship and the schematic frame of the hardware.
from the captured rotor power and rotor angular speed. According to the analysis in section ‘‘Wind shear and tower shadow,’’ the aerodynamic torque of the rotor includes the wind shear and tower shadow effects and is also related to the rotor angular speed. The feature of the turbine transmission is represented in the model of the wind turbine drive train shown in section ‘‘Wind turbine drive train.’’ The equivalent inertia model is an essential factor in the wind turbine simulator, where the large inertia of the rotor is difficult to simulate in traditional methods, such as the flywheel method. In this simulator, the electric inertia simulation is used to satisfy the different inertia control demands. The aforementioned calculation is performed on a personal computer (PC) workstation to produce two reference curves: the torque profile of the drive motor and the rotation speed of the generator.
Experiment Basic characteristics of the simulator
Control logic strategy To simulate the static and dynamic characteristics of the wind turbine, the wind turbine model is realized in MATLAB Simulink, which provides a reliable reference curve for the control of the wind turbine simulator. Figure 5 shows the control logic of the proposed simulator. The wind speed model is built based on the Kaimal model, which has been discussed in section ‘‘Wind speed model.’’ Based on the wind speed, the pitch angle estimator adopting the proportional– integral (PI) control method operates only in the power regulation, as noted in section ‘‘Aerodynamics of the wind turbine.’’ The relationship between the rotational speed and wind velocity is referred to as the tip speed ratio. The rotor power coefficient estimator is used to calculate the power of the captured wind energy, which is determined by the blade pitch angle and tip speed ratio. As a result, the aerodynamic torque develops
In this research, a variable speed–variable pitch-type wind turbine is selected to present the actual characteristics of the proposed wind turbine simulator. The original model is based on the report: dynamic modeling of GE 1.5 and 3.6 wind turbine generators. The parameters of the selected wind turbine are listed in Table 1. The power characteristic curves of the wind turbine simulator at different wind speeds are shown in Figure 6 to analyze the static behavior of the system. Using a wind speed step change of 1 m/s, each solid line represents the corresponding power-speed curve of the ideal wind turbine, and the same type point denotes the relevant measured data. Given that the turbine operates above the cut-in wind speed, the test begins at 400 r/ min, which is defined as the minimum start-up speed. To show a direct result between the ideal curve and actual measured data, the generator power is normalized in both cases. From the comparison in Figure 6,
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Table 1. Parameters of the selected wind turbine in the simulation. Turbine specifications
Value
Rated output power (MW) Rated wind speed at Cp max (m/s) Wind turbine inertia constant (kg m2) Generator inertia constant (kg m2) Shaft mutual damping (N m s/rad) Shaft stiffness (N m/rad) Air density (kg/m3)
1.5 11 4 0.01 0.1 20 1.12
As an input for the wind turbine model, the wind speed profile in time series is produced based on the Kaimal model shown in Figure 7(a), where the length of time series is 400 s. Based on the wind speed input and the calculation of the turbine model, the aerodynamic features of the wind turbine are obtained shown in Figure 7(b). In Figure 7(b), the left axis shows the generator rotation speed, and the right shows the output torque from the wind turbine simulator. The variation trend is consistent with the wind speed profile in the time domain. Additionally, although the wind speed fluctuates in the time series, the wind turbine transmission operates as a low-pass filter for the large inertia effect, which results in the decrease in the highfrequency exponent.
Wind shear and tower shadow effects
Figure 6. Generator power characteristic curve of the simulator.
the measured points are located near the reference curve, which verifies that the proposed wind turbine simulator can represent the static characteristics.
The wind turbine torque oscillates due to the tower shadow and wind shear effects, which can negatively affect the generated power quality. Thus, the wind shear and tower shadow effects must be considered in the proposed simulator. Figure 8 shows the dynamic performance of the simulator considering the wind shear and tower shadow effects. The solid line represents the reference curve, whereas the dashed line corresponds to the actual measured data. Both torque and speed follow the reference curve, indicating that the S120 system performs well in terms of motion control. Furthermore, the torque oscillation is reflected on the waveform profile in the time domain. To illustrate the dynamic performance of the proposed simulator, the fast Fourier transform (FFT) algorithm is adopted to analyze the actual torque signal.
Figure 7. (a) Input wind speed profile and (b) corresponding generator speed and wind turbine output torque based on the input wind speed profile.
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Figure 8. (a) Wind turbine output torque curve (J = 8 kg m2) and (b) generator rotate speed curve.
Figure 9. (a) Comparison of the output torques for different inertias in the time domain and (b) comparison of the output torques for different inertias in the frequency domain.
Figure 9(b) shows the frequency spectrum induced in the actual torque. The peak point is at approximately 2.13 Hz. Because the gear ratio is 1:40 and the generator speed is approximately 1600 r/min, the oscillation frequency affected by wind shear and tower shadow is calculated using equation (12) f3p =
1600 3 3 = 2 Hz ð60 3 40Þ
ð12Þ
The calculated oscillation frequency, defined as the 3p frequency, is approximated to the peak characteristic frequency in the spectrum. Therefore, it can be supposed that the amplitude component at the peak characteristic frequency is caused by the wind shear and tower shadow effects. However, a spectrum leakage
occurs near the peak characteristic frequency because the oscillation effects are modulated by the variable generator speed. Each oscillation occurs only when the rotor revolves around the main shaft every 120°, which means that the oscillation frequency is relevant to the rotor rotational speed. As the proposed simulator represents the dynamic features of the variable speed– variable pitch-type wind turbine, the rotor rotational speed is in a nonstationary state. Therefore, the phenomenon of spectrum leakage is reasonable.
Inertia effect A higher inertia (J = 8 kg m2) is selected to represent the same process of the experiment. The dynamic
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Figure 10. Comparison of the results under different inertia effects: (a) J = 4 kg m2 and (b) J = 8 kg m2.
performance of the simulator is shown in Figure 9(a) and (b). The phenomenon of spectrum leakage is also observed for the variable rotation speed of the shaft. Figure 9 presents the comparison in both the time and frequency domains for a more detailed and direct display of the different inertia effects. From Figure 9(a), the inertia effect alters the oscillation amplitude in the time domain. Meanwhile, the component at each corresponding frequency decreases under the larger inertia effect in terms of the spectrum domain as well in Figure 9(b). Moreover, different inertia effects can affect not only the amplitude–frequency response in terms of dynamic performance but also the phase– frequency characteristic. The transient response of the simulator demonstrates that the significant variation of the torque can be simulated under different inertias.
other words, the time axis is stretched where the speed is high. Similarly, the time axis is compressed where the speed is low. Because the torque signal is synchronously sampled to correspond with the rotation speed, the resample torque signal at a constant can be calculated by interpolating between the sampled data using cubic spline interpolation. The short-time Fourier transform is adopted to show the spectrogram of the resampled torque signal in Figure 10(a) and (b), where the left figure corresponds to the low inertia (J = 4 kg m2) and the right figure corresponds to the high inertia (J = 8 kg m2). Because the gear ratio is 1:40 and the oscillation frequency affected by wind shear and tower shadow triples compared to the rotor revolving speed, the oscillation order can be calculated using equation (13) Order3p =
Order tracking analysis A method to identify speed-related signals must be established because of the phenomenon of amplitude leakage in the FFT spectrum caused by the variable generator speed. Order tracking analysis is an optimized analysis method that uses multiples of the referred shaft rotation (orders) as a sample base instead of conventional frequencies (Hz). Traditional order tracking21 requires special analogue hardware to acquire the data at a constant angle, which makes it difficult to improve sampling precision due to the angle limitation of the analogue resolution. Computational order tracking analysis22 acquires data at a constant rate in a time series and then uses software to resample the data at constant angular increments. Computational order tracking analysis is adopted in this article to process the torque data. By assuming a constant angular speed over a short time, a cumulative rotation angle can be calculated and then the resample axis of the rotation angle is determined. In
1 3 3 = 0:075 40
ð13Þ
The spectrogram illustrates that a significant spectral line exists at 0.075 and a relatively weak harmonic component exists at 0.15, which confirms that the simulator does represent the dynamic performance with the wind shear and tower shadow. Furthermore, the spectrum leakage inferred in section ‘‘Wind shear and tower shadow effects’’ is indeed due to the variation of the rotation speed. Moreover, comparing the two figures under different levels of inertia, the observed spectral lines at 0.075 features different intensities, where the spectral line for the low inertia (J = 4 kg m2) is more distinct than the spectral line of the high inertia (J = 8 kg m2).
Conclusion In this article, a novel method to simulate the wind turbine generation process with the wind shear and tower shadow effects is presented. By referring the Kaimal model, the real-wind characteristics are represented.
10 Based on the referring wind model input, the aerodynamics model of the wind turbine is built up with the wind shear and tower shadow effects. In particular, the oscillations of the wind shear and tower shadow effects are synchronizing with the rotor rotations at a constant angle, which make the replication method applicable to both fixed and variable speed turbines. Therefore, the equivalent wind speed with the effects of the wind shear and tower shadow contributes to the aerodynamics model as nonstationary series in the time domain. For stationary processing the nonstationary oscillating signals caused by the 3p effects, the analysis of computer order tracking is adopted, transforming the rotationrelated oscillation signals from time domain to angular domain. To verify the replication method, the emersion environment was realized through a simulating facility platform. A high-performance motion control system is adopted, driving two coupled induction motors in an electric closure test bed. One motor in the torque mode is used as the prime mover, and the other one in the speed mode is presented as an electrical generator. The experimental results indicate that the emersion environment can satisfactorily produce the same performance as simulated results, particularly in terms of the wind shear and tower shadow effects. Furthermore, the transmission characteristics of the wind turbine, as the inertia effect, are presented in the time domain and frequency domain. Moreover, comparing with the spectral leakage in the traditional FFT spectrum, the analysis of computer order tracking shows the advantages in processing the rotation-related signals. This study has proposed a simulating approach for the wind turbine that can simulate not only the basic characteristics, as in previous research, but also the wind shear and tower shadow effects. The proposed simulating method offers an experimental platform for wind energy conversion research, particularly concerning the wind shear and tower shadow effects.
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Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
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Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (project name: Research on fault recognition and diagnosis technology of wind turbine gearboxes based on product test data; no. 51275453).
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