LSTM-NN Yaw Control of Wind Turbines Based on Upstream Wind Information

: Based on wind lidar, a novel yaw control scheme was designed that utilizes forecast wind information. The new scheme can reduce the power loss caused by the lag of accurate measurement data in the traditional yaw control strategy. A theoretical analysis of the power loss caused by the traditional wind measurement inherent error and the wind direction based traditional yaw control strategy was conducted. The yaw angle error and yaw stop / start frequency in an actual wind ﬁeld were statistically analyzed, and a novel Long Short Term-Neural Network (LSTM-NN) yaw control strategy based on wind lidar information was proposed. An accurate forecast of the wind direction could reduce the power loss caused by the inherent yaw misalignment, while an accurate forecast of wind speed could increase the stop / start frequency in the medium speed section within the partial load range and reduce the frequency in the low speed section within the partial load range. Thus, the power captured could be increased by 3.5% under certain wind conditions without increasing the yaw duty. Based on a simple wind evolution model and a novel yaw control strategy, the validity of the yaw control strategy was veriﬁed in a FAST / Simulink simulation model.


Introduction
Effective wind energy utilization depends on whether the rotor can accurately track wind and reduce losses in wind energy capture.A yaw system will realize a quick and smooth alignment of the rotor to the wind direction as it changes, enabling the wind turbine to extract the maximum wind energy.Many different kinds of yaw systems have been reviewed [1], and some novel systems have been proposed, e.g, a maglev yaw system (MYS) and its corresponding robust trajectory tracking control in the levitation and landing process based on the nonlinear disturbance observer (NDOB).Davide et al. [2] proved that the yaw control upgrade should consider optimizing the nacelle response when the yaw error exceeds a certain threshold, which was determined to be 1% of annual energy production.Frequent start-up and shutdown will cause damage to the yaw system and its associated components, which will affect the stable operation of the wind turbines and reduce the lifetime of the yaw system.Improving the yaw control strategy is therefore of great significance for improving the power capture of wind turbines, prolonging their overall life, realizing the safe and reliable operation of wind power generation systems, and reducing the cost of wind power generation [3].The yaw control can be used for optimization at the wind farm level [4] and the single wind turbine level [2].
Wind farm yaw control has raised concerns of wake-redirection due to yaw misalignment.Rott et al. [5] studied on the dynamic influence of wind direction on wake by adjusting the yaw error.Cardaun et al. [6] proved that damage equivalent loads are in proportion to yaw misalignment within Energies 2020, 13, 1482 2 of 23 fixed intervals.Damiani et al. [7] also explored the effects of yaw offset operation on the loads of a commercial-grade wind turbine.The rotor aerodynamics were presented under different yaw misalignments to investigate the physics and load predictions.Ke et al. [8] studied the influence of wind-rain loads(loads caused by wind-rain combination action) on the pressure coefficients at the two windward sides of a blade and tower within a yaw angle of 40 • , which were found to be important.For single wind turbine yaw control, current commercial yaw strategies are typically stop-start based, e.g, on hysteresis dead-bands, yaw misalignment counters/timers, etc. [9].Kung et al. [10] compared the effect of PID control and a fuzzy logic controller (FLC) in yaw control and concluded that the FLC had a better robustness.Farret et al. [11] studied a yaw motor motion with a hill climbing control (HCC) algorithm through detecting power, and the results showed that there was a maximum yaw misalignment of 8 • .Zhu et al. [12] established a PID neural network (PIDNN) yaw control strategy based on a cloud model classifier and PIDNN regulator.The simulation results showed that it had improved static and dynamic response characteristics and robustness.The fuzzy-PID synthesis control proposed by Hu et al. [13] can solve three kinds of errors in the yaw process, i.e, large, medium, and small.The simulation results showed that the synthesis control strategy had a better stability and robustness, but it was not tested under turbulent wind conditions.Liu [14] proposed a piecewise composite control strategy based on the yaw system of a hydraulic motor.When the wind direction change was less than 15 • , a pressure difference feedback control was used to control the small angle wind direction deviation.Li [15] proposed a compound control strategy based on the HCC algorithm in the case of a small wind direction deviation, but a simulation analysis under complex wind conditions was not conducted in the study.
To solve the lagging effect of wind vane measurement results, Liu et al. [16,17] proposed a yaw strategy based on wind direction prediction.A Kalman filter algorithm was applied to the wind direction prediction of yaw control, which overcame the weakness of the lag of the wind vane measurement, realized an accurate windward alignment of yaw, and reduced the time required for yaw actions.Zhang [18] proposed a wind direction prediction based on a back propagation (BP) neural network.Hure et al. [19] proposed an optimal yaw controller design method based on wind direction predictions over a short period of time.Song et al. [20] proposed a new yaw control strategy based on model predictive control (MPC), which increased the wind turbine capture power by approximately 1% [21] and proposed a novel data driven yaw control algorithm synthesis method based on reinforcement learning.Song et al. [22] proposed a novel control structure that consisted of a wind direction predictive model (moving average method-based Kalman filter model) and a novel yaw control method (two methods were discussed, one using the predicted wind direction as the tracking reference and the other based on an MPC using a finite control set), which was capable of reducing yaw error.The MPC-based controller also had the advantage of reducing yaw actuator usage.
Lidar wind measurement technology can obtain wind information at a distance ahead of the wind turbine, which would enable yaw control without the need for predictions based on complicated algorithms.However, the application of lidar in yaw control has only focused on yaw error correction [23][24][25][26] and direct measurements [27][28][29].The potential of lidar has therefore not been fully developed.In this study, the lidar speed and direction signals were used together as input signal in a novel LSTM-NN yaw control strategy which used the lidar measurement speed and direction signal and their value after evolution to judge yaw actuation and yaw error to redistribute yaw actuation times within the working range and improve power capture without increasing yaw duty.
The sources of power loss in current yaw technology were analyzed theoretically, and the existing yaw problems in an actual wind field were analyzed statistically.Based on the measurement of wind information by a nacelle-based pulse lidar in advance of the arrival of wind at the turbine and the value in the rotor plane after its evolution, predicted wind direction information was used to obtain yaw error and reduce the power loss caused by yaw lag in traditional measurements.Predicted wind speed information was used to plan yaw actuation, increase the number of yaw actuations in the medium speed section within the partial load range, and reduce the number of yaw actuations in the low speed Energies 2020, 13, 1482 3 of 23 section within the partial load range, to achieve an increase in power capture without increasing the yaw duty.Finally, the effectiveness of the novel yaw control strategy was verified in a FAST (Fatigue, Aerodynamics, Structures, and Turbulences)/Simulink simulation model.
The main contributions and novelties of the paper is a novel LSTM-NN yaw control strategy based on lidar information.The input layer is the lidar measured wind speed and direction information and their corresponding values after evolution.The hidden layer is the strategy that redistribute yaw actuation times and determine the yaw start time.The output layer is the yaw angel and yaw action start time.

Yaw power loss
Consider the power coefficient, which is the extent to which wind turbines absorb energy from natural wind energy: In theory, when there is an angle θ between the wind direction and the normal direction of the rotor, the sha f t power is : Power loss ratio m determines the relationship between the trubine capture energy and the θ.It is common sense that m = 3.However, according to the results of a wind tunnel test conducted at the National Renewable Energy Laboratory (NREL), m = 2 [30].But, there is still evidence that an exponent significantly less than 2 is more accurate for some turbines [31].Power loss ratio decreased with the decrease of m.In this study, we take m = 2.
The percentage power loss with the variation in yaw angle error is shown in Figure 1.Active yaw systems generally use a motor-driven gear reducer fitted to a drive yaw gear ring to complete a yaw action.Due to the real-time variation and uncertainty of natural wind direction and the influence of turbulence generated by the rotor on the wind direction meter, the detection accuracy of the wind direction meter has a large error, which makes it difficult for the active yaw system to work accurately.Therefore, improving the accuracy of wind measurements can effectively improve power capture.

Traditional Yaw Control Strategy
The principle of a typical yaw control system is shown in Figure 2. The wind vane monitors the deviation signal between the wind direction and the rotor axis direction and sends this signal to the controller for processing.The controller outputs the yaw angle and direction command through the control program and drives the yaw mechanism to carry out the corresponding yaw operation.At the same time, the rotor axis changes.When the rotor axis is consistent with the wind direction, the yaw motor stops, and the yaw brake automatically locks up.Then, the yaw process ends.The control accuracy of the traditional control method is mainly determined by the measurement accuracy of the wind vane.Currently, the yaw system of a commercial wind turbine generally performs the yaw strategy when the wind direction and the nacelle angle deviation are greater than a certain degree and does not work when the wind direction and the nacelle angle deviation are less than it.Only the cumulative error of yaw misalignment is calculated, and yaw operation is conducted immediately when the set yaw threshold is reached.The yaw misalignment value will be large, resulting in a partial power loss, and the power gain obtained in the low wind speed segments is much lower than that of the power gain in the moderate wind speed segment with the same yaw action.Therefore, it is not scientifically sound to consider the yaw control only with yaw error and without the segmentation of wind speed.

Traditional Yaw Control Strategy
The principle of a typical yaw control system is shown in Figure 2. The wind vane monitors the deviation signal between the wind direction and the rotor axis direction and sends this signal to the controller for processing.The controller outputs the yaw angle and direction command through the control program and drives the yaw mechanism to carry out the corresponding yaw operation.At the same time, the rotor axis changes.When the rotor axis is consistent with the wind direction, the yaw motor stops, and the yaw brake automatically locks up.Then, the yaw process ends.

Traditional Yaw Control Strategy
The principle of a typical yaw control system is shown in Figure 2. The wind vane monitors the deviation signal between the wind direction and the rotor axis direction and sends this signal to the controller for processing.The controller outputs the yaw angle and direction command through the control program and drives the yaw mechanism to carry out the corresponding yaw operation.At the same time, the rotor axis changes.When the rotor axis is consistent with the wind direction, the yaw motor stops, and the yaw brake automatically locks up.Then, the yaw process ends.The control accuracy of the traditional control method is mainly determined by the measurement accuracy of the wind vane.Currently, the yaw system of a commercial wind turbine generally performs the yaw strategy when the wind direction and the nacelle angle deviation are greater than a certain degree and does not work when the wind direction and the nacelle angle deviation are less than it.Only the cumulative error of yaw misalignment is calculated, and yaw operation is conducted immediately when the set yaw threshold is reached.The yaw misalignment value will be large, resulting in a partial power loss, and the power gain obtained in the low wind speed segments is much lower than that of the power gain in the moderate wind speed segment with the same yaw action.Therefore, it is not scientifically sound to consider the yaw control only with yaw error and without the segmentation of wind speed.The control accuracy of the traditional control method is mainly determined by the measurement accuracy of the wind vane.Currently, the yaw system of a commercial wind turbine generally performs the yaw strategy when the wind direction and the nacelle angle deviation are greater than a certain degree and does not work when the wind direction and the nacelle angle deviation are less than it.Only the cumulative error of yaw misalignment is calculated, and yaw operation is conducted immediately when the set yaw threshold is reached.The yaw misalignment value will be large, resulting in a partial power loss, and the power gain obtained in the low wind speed segments is much lower than that of the power gain in the moderate wind speed segment with the same yaw action.Therefore, it is not scientifically sound to consider the yaw control only with yaw error and without the segmentation of wind speed.

Yaw misalignment
The traditional yaw control is simple stop/start strategy using a yaw error 15 • as threshold and a yaw rate 0.5 • /s.Yaw error comes from the wind vane installed on the nacelle behind the rotor.Hence, the data is lagging and affected by the wake comes from rotor rotation.To calculate the power loss caused by yaw misalignment during the operation of actual wind turbines, 10 days (December 3-12, 2018) of wind turbine data were collected by Zhejiang Windey Co, Ltd. from a WD-147 wind turbine in the Zhangbei Yangji wind farm.The data were processed in the Supervisory Control And Data Acquisition (SCADA) system, sampling time was 10 mins, and invalid data were eliminated.The unit used a wind vane to measure the wind direction signal and the rated power was 2.5 MW.The statistical results showed that the wind turbine yaw misalignment was concentrated between −20 • and 5 • , and the mean error was approximately 9.57 • .A histogram of the results and a Gaussian fitting curve are shown in Figure 3.

Yaw misalignment
The traditional yaw control is simple stop/start strategy using a yaw error 15° as threshold and a yaw rate 0.5 °s ⁄ .Yaw error comes from the wind vane installed on the nacelle behind the rotor.Hence, the data is lagging and affected by the wake comes from rotor rotation.To calculate the power loss caused by yaw misalignment during the operation of actual wind turbines, 10 days (December 3-12, 2018) of wind turbine data were collected by Zhejiang Windey Co, Ltd. from a WD-147 wind turbine in the Zhangbei Yangji wind farm.The data were processed in the Supervisory Control And Data Acquisition (SCADA) system, sampling time was 10 mins, and invalid data were eliminated.The unit used a wind vane to measure the wind direction signal and the rated power was 2.5 MW.The statistical results showed that the wind turbine yaw misalignment was concentrated between −20° and 5°, and the mean error was approximately 9.57°.A histogram of the results and a Gaussian fitting curve are shown in Figure 3.
According to Equation (3), with a mean yaw error of 9.57°, the power loss of the WD-147-2.5MW wind turbine due to yaw misalignment accounted for approximately 2.76 % of the total loss.For a 100 MW wind farm, assuming the average available time to be 6 h per day for 365 days per year, the annual loss of power due to yaw misalignment is 6.03 × 10 6 kWh.The annual economic loss of power due to yaw misalignment is 3.03 million yuan per year, when calculated at a price of 0.5 yuan per kWh.

Yaw actuation analysis
In the wind speed data measured at the meteorological mast at the Zhangbei Yangji wind farm from December 3-12, 2018 (as shown in Figure 4), a low wind speed (3 m/s to 6 m/s) and moderate wind speed (6 m/s to 11.8 m/s) accounted for a large proportion of the wind data, with the high wind speed area accounting for only a small proportion of the total wind.The yaw frequency statistics of the WD-147 unit in the same period are shown in Figure 5.The yaw frequency is mainly concentrated in the middle and low wind speed sections.According to Equation (3), with a mean yaw error of 9.57 • , the power loss of the WD-147-2.5MW wind turbine due to yaw misalignment accounted for approximately 2.76 % of the total loss.For a 100 MW wind farm, assuming the average available time to be 6 h per day for 365 days per year, the annual loss of power due to yaw misalignment is 6.03 × 10 6 kWh.The annual economic loss of power due to yaw misalignment is 3.03 million yuan per year, when calculated at a price of 0.5 yuan per kWh.

Yaw actuation analysis
In the wind speed data measured at the meteorological mast at the Zhangbei Yangji wind farm from December 3-12, 2018 (as shown in Figure 4), a low wind speed (3 m/s to 6 m/s) and moderate wind speed (6 m/s to 11.8 m/s) accounted for a large proportion of the wind data, with the high wind speed area accounting for only a small proportion of the total wind.The yaw frequency statistics of the WD-147 unit in the same period are shown in Figure 5.The yaw frequency is mainly concentrated in the middle and low wind speed sections.
Energies 2020, 13, x FOR PEER REVIEW 6 of 24  The proportion of yaw time in the wind speed range of 3 m/s to 6 m/s was approximately 40%, while in the range of 6 m/s to 11.8 m/s, it was approximately 55%.Statistical data shows that the yaw action is very frequent.The total activity was 1323 times in 10 days, i.e, an average of approximately 132 times per day.The proportion of yaw time in the wind speed range of 3 m/s to 6 m/s was approximately 40%, while in the range of 6 m/s to 11.8 m/s, it was approximately 55%.Statistical data shows that the yaw action is very frequent.The total activity was 1323 times in 10 days, i.e, an average of approximately 132 times per day.The proportion of yaw time in the wind speed range of 3 m/s to 6 m/s was approximately 40%, while in the range of 6 m/s to 11.8 m/s, it was approximately 55%.Statistical data shows that the yaw action is very frequent.The total activity was 1323 times in 10 days, i.e, an average of approximately 132 times per day.

The Novel Yaw Actuation Controller
Based on the lidar wind information prediction, a novel LSTM-NN yaw control strategy was proposed.The yaw angle error was reduced through the using of lidar wind direction data.The predicted wind speed data was used to increase the number of yaws in the mid wind speed section (6 m/s to 10 m/s) and reduce the number of yaws in the low wind speed section (< 6 m/s).The power capture could be increased without increasing the yaw duty.
The yaw control strategy based on lidar is shown in Figure 6.Lidar measured the advance wind information.The wind information from the wind evolution model, which is described in Section 3.3, was also used as an input for the yaw control system to realize the novel LSTM-NN yaw actuation control strategy.The wind evolution model is used here for the reason that commercial nacelle-based lidar can only provide wind information in front the rotor within a certain range, e.g, 50 m to 250 m [32].To get enough wind information to reverse wind speed and wind direction of measuring point, the minimum distance cannot be zero for lidar's "Cyclops" characteristic.Considering the rotor blocking effect (induction zone), the Tylor Frozen hypothesis will bring in large estimation error of wind information of rotor plane.So, it is necessary to consider the wind evolution process from the lidar focus to the rotor plane.

The Novel Yaw Actuation Controller
Based on the lidar wind information prediction, a novel LSTM-NN yaw control strategy was proposed.The yaw angle error was reduced through the using of lidar wind direction data.The predicted wind speed data was used to increase the number of yaws in the mid wind speed section (6 m/s to 10 m/s) and reduce the number of yaws in the low wind speed section (< 6 m/s).The power capture could be increased without increasing the yaw duty.
The yaw control strategy based on lidar is shown in Figure 6.Lidar measured the advance wind information.The wind information from the wind evolution model, which is described in Section 3.3, was also used as an input for the yaw control system to realize the novel LSTM-NN yaw actuation control strategy.The wind evolution model is used here for the reason that commercial nacelle-based lidar can only provide wind information in front the rotor within a certain range, e.g, 50 m to 250 m [32].To get enough wind information to reverse wind speed and wind direction of measuring point, the minimum distance cannot be zero for lidar's "Cyclops" characteristic.Considering the rotor blocking effect (induction zone), the Tylor Frozen hypothesis will bring in large estimation error of wind information of rotor plane.So, it is necessary to consider the wind evolution process from the lidar focus to the rotor plane.

Lidar Model
In the FAST model v8, there is a continuous wave (CW) lidar code embedded.The lidar can measure the wind data (return velocity in the x direction or return radial velocity) precisely [33].However, the code can only measure one point of wind speed and cannot return the wind direction.An improvement has therefore been made according to the Molas-NL nacelle-based short-range pulse lidar [32] inside Simulink to simulate a more realistic lidar.Here, we used the original code to simulate a pulsed lidar, which can return the wind information of a plane up to the rotor at a certain distance.According to the law of time series, a scanning model of pulsed lidar was built in Simulink, as shown in Figure 7a, where [  ] is the inertia reference system of the wind field.The lidar model was mounted on a nacelle and consisted of four laser beams.The angle between the horizontal beams was 30° and the angle between vertical beams was 25°.The scanning time between adjacent beams was 0.25 s and one circular scan was finished within 1 s.The main gate was set to be 100 m, and therefore the four measuring positions of the lidar were established as [−100 26.79 22.17

Lidar Model
In the FAST model v8, there is a continuous wave (CW) lidar code embedded.The lidar can measure the wind data (return velocity in the x direction or return radial velocity) precisely [33].However, the code can only measure one point of wind speed and cannot return the wind direction.An improvement has therefore been made according to the Molas-NL nacelle-based short-range pulse lidar [32] inside Simulink to simulate a more realistic lidar.Here, we used the original code to simulate a pulsed lidar, which can return the wind information of a plane up to the rotor at a certain distance.According to the law of time series, a scanning model of pulsed lidar was built in Simulink, as shown in Figure 7a, where [u v w] is the inertia reference system of the wind field.The lidar model was mounted on a nacelle and consisted of four laser beams.The angle between the horizontal beams was 30 • and the angle between vertical beams was 25 • .The scanning time between adjacent beams was 0.25 s and one circular scan was finished within 1 s.The main gate was set to be 100 m, and therefore the four measuring positions of the lidar were established as [−100   The following text explains the inversion process for the wind speed and direction [32].The two line of sight wind velocities of the upper plane are  1 and  2 , and the upper plane wind speed  and wind direction  can be obtained from: The two line of sight wind speeds of the bottom plane are  3 and  4 .According to Equation ( 5),(6) the bottom plane wind speed  and wind direction  can be obtained.
Therefore, the vertical wind shear is: The rate of change in the vertical wind direction is: The inversion of wind speed  and wind direction  are: The following text explains the inversion process for the wind speed and direction [32].The two line of sight wind velocities of the upper plane are RWS 1 and RWS 2 , and the upper plane wind speed UWS and wind direction UD can be obtained from: The two line of sight wind speeds of the bottom plane are RWS 3 and RWS 4 .According to Equations ( 5) and ( 6) the bottom plane wind speed DWS and wind direction DD can be obtained.
Therefore, the vertical wind shear is: The rate of change in the vertical wind direction is: Energies 2020, 13, 1482 The inversion of wind speed HWS and wind direction HD are: where H hub = H lidar = 90 m, and X t = 100 m.

Induction Zone Modle [34]
When the wind turbine captures energy from the wind, the downstream wind speed of the rotor is reduced.The rotor can be regarded as a porous disc, forming a tubular model, with reduced speed [35].The wind turbine power coefficient C p is a function of the axial inductive coefficient a in Equation ( 1), where a is defined as follows: When a = 1/3, the power capture efficiency reaches the Betz theoretical limit.
According to Medici's method, the induction zone wind speed normalized evolution model is [36]: 2 ).
Simley et al. [37] used ground-based lidar to measure the actual wind speed evolution in the induction zone of a Vestas V27 horizontal-axis wind turbine.The evolution of the wind speed at the hub was small compared with that calculated by Equation (12), which was consistent with the computational fluid dynamics (CFD) simulation results.The actual measurement results show that the wind v component was attenuated by approximately 3% at height of the hub center [37].
According to the above analysis, it was assumed that the wind followed the same evolution law at the same height, and the wind speed only decayed due to this evolutionary process.The influence of gusts, terrain, and other factors were neglected.Equation (12) was corrected according to the CFD simulation results to define the wind speed [34].The induction zone evolution model was as follows [34] (shown as Figure 8, for κ ≤ −1, the model is proportional (linear), while for −1 < κ ≤ 0, the model is affected by the initial wind speed; the curves in the figure, from the top to bottom, are the wind evolution coefficients, with initial wind speeds of 14, 12, 10, 8, 6, 4, and 2 m/s, respectively.): The research object of this study was an NREL 5 MW wind turbine.According to the CFD simulation results, ξ 1 had a value of 1.015, ξ 2 was the inverse proportional function of wind speed ξ 2 = 16/v u∞ , and â had a value of 0.1.The evolution of wind direction is obtained from the wind vector.Assuming that the wind vector changes only in the normal direction of the rotor and the v component of the wind is unchanged, the wind direction after evolution can be obtained: [34] For the time-shift model in the wind evolution process, the relationship between the lidar measurement distance and the average wind speed can be simplified as follows: [34]  The evolution of wind direction is obtained from the wind vector.Assuming that the wind vector changes only in the normal direction of the rotor and the  component of the wind is unchanged, the wind direction after evolution can be obtained: [34] = arctan 2( ) For the time-shift model in the wind evolution process, the relationship between the lidar measurement distance and the average wind speed can be simplified as follows: [34]

Validation Method
Based on the IEC Kaimal Model (IECKAI) [38] and the IEC Von Karman Isotropic Model (IECVKM) [39], the TurbSim code was used to generate a turbulent wind field, with an average wind speed of 7 m/s.The generation time step was 0.50 s, the generation time was 600 s, the grid width and height of the wind field were 40 m, and the hub center height was 90 m.
TurbSim generated a wind time series that could be used directly in FAST lidar code using the four measurement positions established in Section 3.2.The current wind after evolution from the location of the lidar measurement to the wind turbine rotor plane was as follows: Figure 9 shows the wind speed (average wind speed was 7 m/s) and wind direction simulation results based on lidar measurements and the processing of the induction zone evolution model.The wind direction measured by lidar was regarded as the advance wind direction, and the wind direction simulation result obtained from the wind after induction zone evolution model processing was regarded as the current wind direction.As seen from the Figure 6, part of the yaw control strategy was to advance the start the yaw through an advance in its timing.

Validation Method
Based on the IEC Kaimal Model (IECKAI) [38] and the IEC Von Karman Isotropic Model (IECVKM) [39], the TurbSim code was used to generate a turbulent wind field, with an average wind speed of 7 m/s.The generation time step was 0.50 s, the generation time was 600 s, the grid width and height of the wind field were 40 m, and the hub center height was 90 m.
TurbSim generated a wind time series that could be used directly in FAST lidar code using the four measurement positions established in Section 3.2.The current wind after evolution from the location of the lidar measurement to the wind turbine rotor plane was as follows: Figure 9 shows the wind speed (average wind speed was 7 m/s) and wind direction simulation results based on lidar measurements and the processing of the induction zone evolution model.The wind direction measured by lidar was regarded as the advance wind direction, and the wind direction simulation result obtained from the wind after induction zone evolution model processing was regarded as the current wind direction.As seen from the Figure 6, part of the yaw control strategy was to advance the start the yaw through an advance in its timing.
A simulation of only 600 s, with an average wind speed of 7 m/s, does not fully reflect the distribution of yaw time and 0.5 s step time of wind changed too frequently.Therefore, TurbSim was used to simulate an average wind speed of 4, 5, 6, 7, and 8 m/s for both the traditional strategy and the novel LSTM-NN yaw control strategy proposed in this study.Each simulation process was the same as that used for the 7 m/s simulation; the step time has been changed to 2 s, and the simulation time was 1800 s.A simulation of only 600 s, with an average wind speed of 7 m/s, does not fully reflect the distribution of yaw time and 0.5 s step time of wind changed too frequently.Therefore, TurbSim was used to simulate an average wind speed of 4, 5, 6, 7, and 8 m/s for both the traditional strategy and the novel LSTM-NN yaw control strategy proposed in this study.Each simulation process was the same as that used for the 7 m/s simulation; the step time has been changed to 2 s, and the simulation time was 1800 s.

LSTM-NN Yaw Control Strategy Based on Lidar Information
As shown in Figure 10, at time   , the lidar measures the wind speed  ̃+ and the yaw angle error  ̃+ between the wind direction and the nacelle axis.The current wind speed   of the rotor plane and the current yaw angle error   evolved from  ̃− and  ̃− .The above data was then subjected to a moving average to obtain  ̃+  ,  ̃+  , and  ̃  .Then, the input layer data have been obtained.The hidden layer is to redistribute the yaw frequency and judge yaw start time.According to the range of current wind speeds    , the yaw amplitude thresholds Ah1, Ah2, and Ah3 were set at   <  1 <  2 <   (  and   are the start-up and shutdown wind speeds for the wind turbine) to determine whether the errors met the yaw requirements.The time thresholds Th1, Th2, and Th3 were set accordingly to determine whether the average yaw error time span met the time requirements.T(•) is the timer, which increased as long as the conditions were fulfilled.If all requirements were met, the control program calculated the yaw angle .

LSTM-NN Yaw Control Strategy Based on Lidar Information
As shown in Figure 10, at time t now , the lidar measures the wind speed v now+pre and the yaw angle error θ now+pre between the wind direction and the nacelle axis.The current wind speed v now of the rotor plane and the current yaw angle error θ now evolved from v now−pre and θ now−pre .The above data was then subjected to a moving average to obtain v ts now+pre , θ ts now+pre , and θ ts now .Then, the input layer data have been obtained.
The hidden layer is to redistribute the yaw frequency and judge yaw start time.According to the range of current wind speeds v ts now , the yaw amplitude thresholds Ah1, Ah2, and Ah3 were set at v s < v 1 < v 2 < v e (v s and v e are the start-up and shutdown wind speeds for the wind turbine) to determine whether the errors met the yaw requirements.The time thresholds Th1, Th2, and Th3 were set accordingly to determine whether the average yaw error time span met the time requirements.T(•) is the timer, which increased as long as the conditions were fulfilled.If all requirements were met, the control program calculated the yaw angle θ.Traditional yaw control uses 15° as a threshold and a yaw rate of 0.5 °/s.In simulations, the parameters were changed to 4° and 0.5 °/s.The parameters used in Figure 10 are shown in Table 1.The time thresholds Th1, Th2, Th3, and Th4 were not used in simulations, and a moving average was also not applied.This processing may change the performance of the yaw control system; however, neither the traditional yaw control nor the novel lidar-based yaw control used these parameters, so it would not affect the results of the comparison.The motor stop/start time delay has not been considered.To transfer the lifetime of the yaw system in the low wind speed section to that of the moderate wind speed section, the yaw times in the low wind speed section were reduced, the yaw times in the moderate wind speed section were increased, and full use was taken of the advantages of lidar.The conditions of the evolving wind and the advance wind information measured by wind lidar were added to the moderate and low wind speed sections.When there was a large change in wind direction, the rotor was aligned with the average evolved wind direction in advance as a correction to the yaw control.A larger yaw error threshold Ah4 and time threshold Th4 were added for the assessment of wind information directly measured by lidar to realize a fast yaw in advance of the arriving wind.
For example, if the current wind speed satisfies the low wind speed range, i.e, v s < v ts now ≤ v 1 , T θ ts now > Ah1 > Th1, the yaw is immediately started.There are another two conditions from wind measurement by lidar at time t now : when the yaw misalignment directly reaches the threshold T θ ts now+pre > Ah1 & v ts now+pre > v 1 > Th2 or when the yaw misalignment changes greatly Energies 2020, 13, 1482 T θ ts now+pre > Ah4 > Th4.In both cases, the yaw will start in advance of the arriving wind.The yaw start time T depends on the average measured wind speed v and estimated time t of yaw completion.
The specific relationship is as follows: When the above processing finished, yaw angle θ and yaw start time T from the LSTM-NN output layer were sent to the yaw actuation mechanism.
Traditional yaw control uses 15 • as a threshold and a yaw rate of 0.5 • /s.In simulations, the parameters were changed to 4 • and 0.5 • /s.The parameters used in Figure 10 are shown in Table 1.The time thresholds Th1, Th2, Th3, and Th4 were not used in simulations, and a moving average was also not applied.This processing may change the performance of the yaw control system; however, neither the traditional yaw control nor the novel lidar-based yaw control used these parameters, so it would not affect the results of the comparison.The motor stop/start time delay has not been considered.
Table 1.The lidar based yaw control parameters used in Fig. 10.

Simulation Model
The research object investigated in this study was an NREL 5 MW horizontal axis onshore wind turbine, with a rotor diameter of 126 m, a hub height of 90 m, and a rated power of 5 MW.Nacelle-yaw spring constant is 9.03•10 9 Nm/rad.Nacelle-yaw damping constant is 1.92•10 7 Nm/(rad/s).
The simulated wind speed time series (binary TurbSim full-field (FF)) was obtained from TurbSim, which reads a text input file to set the parameters required for the program to be executed.The code and program were obtained from the NWTC(National Wind Technology Center) Information Portal [40].The wind turbine models incorporated in FAST were InflowWind, AreoDyn, Elastodyn, and ServoDyn [41], and the yaw control strategy was built in Simulink, as shown in Figure 11.
Energies 2020, 13, x FOR PEER REVIEW 14 of 24 The research object investigated in this study was an NREL 5 MW horizontal axis onshore wind turbine, with a rotor diameter of 126 m, a hub height of 90 m, and a rated power of 5 MW.Nacelleyaw spring constant is

Simulation Result Under Ideal Condition
Without considering the induction zone wind evolution, step wind speed and direction under ideal condition shown in Figure 12 were used for simulation.The solid lines are current wind speed and direction, while the dotted lines are lidar measure advance wind speed and direction.The wind

Simulation Result Under Ideal Condition
Without considering the induction zone wind evolution, step wind speed and direction under ideal condition shown in Figure 12 were used for simulation.The solid lines are current wind speed and direction, while the dotted lines are lidar measure advance wind speed and direction.The wind speed is continuous step from 4 m/s -8 m/s -11 m/s.The wind direction is shown as continuous step change.In ideal conditions, lidar code in FAST cannot be used, so the simulation input was set in constant values and used as the Simulation input.Advance wind speed and direction measured by lidar are uniformly specified as 10 s in advance.(The wind speed and direction come from wind file type "uniform" in FAST).Step wind speed and direction input under ideal conditions.
Under the given input wind information, the system responses with different yaw control strategy are shown in Figure 13,14.Figure 13 is the nacelle position, while the red line is nacelle position with tradition yaw control strategy.The green line is the nacelle position with novel yaw control strategy.Figure 14 is the yaw stop/start signal, the rising edge is the order to start yaw, and the value of vertical axis is the yaw command value which is the yaw travel.Positive value and negative value are two contrary yaw directions.It can be obtained that, under low wind speed 4 m/s, yaw events of novel yaw control strategy are 3 times including 1 time of advance yaw action, while tradition yaw events are 5 times.Under wind speed 8 m/s, yaw events with novel yaw control strategy are 5 times, while the yaw events with tradition control strategy are 3 times.The total number of yaw events are the same 10 times, and the distribution under different wind speed segment are 3 times, 5 times, 2 times and 5 times, 3 times, 2 times.So, the control target of decreased low wind speed yaw number and increased medium wind speed yaw number is realized.Under the given input wind information, the system responses with different yaw control strategy are shown in Figures 13 and 14. Figure 13 is the nacelle position, while the red line is nacelle position with tradition yaw control strategy.The green line is the nacelle position with novel yaw control strategy.Figure 14 is the yaw stop/start signal, the rising edge is the order to start yaw, and the value of vertical axis is the yaw command value which is the yaw travel.Positive value and negative value are two contrary yaw directions.It can be obtained that, under low wind speed 4 m/s, yaw events of novel yaw control strategy are 3 times including 1 time of advance yaw action, while tradition yaw events are 5 times.Under wind speed 8 m/s, yaw events with novel yaw control strategy are 5 times, while the yaw events with tradition control strategy are 3 times.The total number of yaw events are the same 10 times, and the distribution under different wind speed segment are 3 times, 5 times, 2 times and 5 times, 3 times, 2 times.So, the control target of decreased low wind speed yaw number and increased medium wind speed yaw number is realized.
yaw events of novel yaw control strategy are 3 times including 1 time of advance yaw action, while tradition yaw events are 5 times.Under wind speed 8 m/s, yaw events with novel yaw control strategy are 5 times, while the yaw events with tradition control strategy are 3 times.The total number of yaw events are the same 10 times, and the distribution under different wind speed segment are 3 times, 5 times, 2 times and 5 times, 3 times, 2 times.So, the control target of decreased low wind speed yaw number and increased medium wind speed yaw number is realized.To further understand the novel yaw control strategy shown as Figure 10 and Equation ( 18) of when to start yaw with novel yaw control strategy, Figure 15 is given, where a red line is the wind direction; the green line is the novel yaw target; the blue dot dash line is the nacelle direction.It can be obtained that, when the yaw conditions are satisfied, the yaw target and yaw start time are given simultaneously, which ensures that the yaw event starts in advance and ends at the time of wind direction change, when there is enough yaw time.To further understand the novel yaw control strategy shown as Figure 10 and Equation ( 18) of when to start yaw with novel yaw control strategy, Figure 15 is given, where a red line is the wind direction; the green line is the novel yaw target; the blue dot dash line is the nacelle direction.It can be obtained that, when the yaw conditions are satisfied, the yaw target and yaw start time are given simultaneously, which ensures that the yaw event starts in advance and ends at the time of wind direction change, when there is enough yaw time.
Generator power comparison graph is shown in Figure 16.Total power increase is 0.17%, while at wind speed of 8 m/s total increase is 3.50%.Total yaw travels are the same 75 • .At low wind speed, the power decrease is small and limited, while at medium wind speed, the power increase is relatively large.And the greater the wind direction changes, the more power increases.
To further understand the novel yaw control strategy shown as Figure 10 and Equation ( 18) of when to start yaw with novel yaw control strategy, Figure 15 is given, where a red line is the wind direction; the green line is the novel yaw target; the blue dot dash line is the nacelle direction.It can be obtained that, when the yaw conditions are satisfied, the yaw target and yaw start time are given simultaneously, which ensures that the yaw event starts in advance and ends at the time of wind direction change, when there is enough yaw time.Generator power comparison graph is shown in Figure 16.Total power increase is 0.17%, while at wind speed of 8 m/s total increase is 3.50%.Total yaw travels are the same 75°.At low wind speed, the power decrease is small and limited, while at medium wind speed, the power increase is relatively large.And the greater the wind direction changes, the more power increases.

Simulation Result Under Turbulence Condition
The simulation results of the traditional strategy and the yaw control strategy proposed in this study under turbulence wind conditions are shown in Figures 17a and 18a.The yaw control strategy based on applying the advance wind direction/speed information and current wind speed/direction information to determine the yaw start time can advance yaw action, satisfying the threshold setting and the wind speed condition limit at the same time, and the yaw action could be advanced according to the advance wind direction and wind speed determination thresholds, resulting in better following wind characteristics than with the traditional strategy.The yaw action under the traditional strategy was affected by lagging due to the absence of advance wind information.
The turbulent wind was generated by Turbsim.Its average direction of wind propagation is 0°, so the generator power outputs are almost the same under different control strategy.Thus, we changed the average wind direction manually ten times with random degree shown in Figure 17a,18a.A comparison of the energy capture simulation results of the traditional strategy and the yaw control strategy proposed in this study are shown in Figure 17b,18b.The lidar-based yaw control strategy obtained a greater power capture.According to the numerical calculation, with the yaw control strategy proposed in this study compared with traditional strategy, which would increase the wind turbine power capture by an average of 0.29% (7 m/s) and 0.31% (8 m/s).The power increase is not so significant so that the average wind direction changes only 10 times during 1800 s.

Simulation Result Under Turbulence Condition
The simulation results of the traditional strategy and the yaw control strategy proposed in this study under turbulence wind conditions are shown in Figures 17a and 18a.The yaw control strategy based on applying the advance wind direction/speed information and current wind speed/direction information to determine the yaw start time can advance yaw action, satisfying the threshold setting and the wind speed condition limit at the same time, and the yaw action could be advanced according to the advance wind direction and wind speed determination thresholds, resulting in better following wind characteristics than with the traditional strategy.The yaw action under the traditional strategy was affected by lagging due to the absence of advance wind information.To evaluate this control method comprehensive, take the average wind speed of 4, 5, 6, 7, and 8 m/s wind speed as simulation input, each case was simulated 1800 s, the total simulation times were 9000 s.Taking the start-up time of the yaw motor as the yaw start point, the results of the statistical analysis of the lidar-based yaw control simulation were obtained.The yaw number distribution results are shown in Figure 19.And the trade-off between energy capture and yaw duty is shown in Table 2. Figure 19 shows that, the yaw number under low wind speed decrease, and the decreasing yaw number is transferred to medium and high wind speed section.With a simulation time of 9000 s, the traditional strategy yawed 285 times, and the yaw control strategy proposed in this study yawed 274 times.For the traditional strategy, the proportion of yaws in the low wind speed section (< 6 m/s), the moderate-wind speed section (6 m/s to 10 m/s), and the high wind speed section was 51.6, 48.4, and 0%, respectively.For the yaw control strategy proposed in this study, the proportion of yaws in the low, moderate, and high wind speed sections was 29.6, 70.0, and 0.4%, respectively.It can be obtained that the LSTM-NN novel yaw control strategy proposed in this study could effectively transfer the lifetime of the yaw system from that of a low wind speed segment to that of a moderate wind speed segment.The turbulent wind was generated by Turbsim.Its average direction of wind propagation is 0 • , so the generator power outputs are almost the same under different control strategy.Thus, we changed the average wind direction manually ten times with random degree shown in Figures 17a  and 18a.A comparison of the energy capture simulation results of the traditional strategy and the yaw control strategy proposed in this study are shown in Figures 17b and 18b.The lidar-based yaw control strategy obtained a greater power capture.According to the numerical calculation, with the yaw control strategy proposed in this study compared with traditional strategy, which would increase the wind turbine power capture by an average of 0.29% (7 m/s) and 0.31% (8 m/s).The power increase is not so significant so that the average wind direction changes only 10 times during 1800 s.
To evaluate this control method comprehensive, take the average wind speed of 4, 5, 6, 7, and 8 m/s wind speed as simulation input, each case was simulated 1800 s, the total simulation times were 9000 s.Taking the start-up time of the yaw motor as the yaw start point, the results of the statistical analysis of the lidar-based yaw control simulation were obtained.The yaw number distribution results are shown in Figure 19.And the trade-off between energy capture and yaw duty is shown in Table 2. Figure 19 shows that, the yaw number under low wind speed decrease, and the decreasing yaw number is transferred to medium and high wind speed section.With a simulation time of 9000 s, the traditional strategy yawed 285 times, and the yaw control strategy proposed in this study yawed 274 times.For the traditional strategy, the proportion of yaws in the low wind speed section (< 6 m/s), the moderate-wind speed section (6 m/s to 10 m/s), and the high wind speed section was 51.6, 48.4, and 0%, respectively.For the yaw control strategy proposed in this study, the proportion of yaws in the low, moderate, and high wind speed sections was 29.6, 70.0, and 0.4%, respectively.It can be obtained that the LSTM-NN novel yaw control strategy proposed in this study could effectively transfer the lifetime of the yaw system from that of a low wind speed segment to that of a moderate wind speed segment.
(< 6 m/s), the moderate-wind speed section (6 m/s to 10 m/s), and the high wind speed section was 51.6, 48.4, and 0%, respectively.For the yaw control strategy proposed in this study, the proportion of yaws in the low, moderate, and high wind speed sections was 29.6, 70.0, and 0.4%, respectively.It can be obtained that the LSTM-NN novel yaw control strategy proposed in this study could effectively transfer the lifetime of the yaw system from that of a low wind speed segment to that of a moderate wind speed segment.Table 2 is the 5 times simulation results summary.The results came from the following processing: (1) In each Simulation, generator power data file (.mat) had been obtained from FAST output list, and the data were summed manually to obtained the total power output; yaw travel was obtained from the integration of the absolute value of the yaw rate in Simulink; yaw number was obtained from the counter model in Simulink, in which the rising edge of the absolute value of yaw rate was the trigger; (2) the above results were then classified as two cases (traditional yaw control and novel yaw control); (3) within each case, the power data were averaged, and the yaw travel and yaw number data were summed.It can be obtained that under the condition of average wind direction is nearly zero, the mean power increased 7.49 kW (increasing by 0.3%), total yaw travel decreased 66 • (decreasing by 5.3%), and total yaw number decreased 11 times (decreasing by 3.9%).The power increase is not so significant so that the average wind direction changes only 10 times during 1800 s, so there were only 50 times average wind direction change during 9000 s Simulation.Considering the ideal condition simulation results shown in Section 5.1 that under medium wind speed power increase is relatively large (wind speed 8 m/s, wind direction changed 4 times within 200 s, power increasing by 3.5%), it can be obtained that this kind of LSTM-NN novel yaw control strategy has great potential in increasing the power output.So, the LSTM-NN novel yaw control strategy can both increase the generator power output and reduce the yaw duty.

Discussion
Commercial field test results (10 days) showed that using wind vane as wind direction sensor with typical traditional stop/start yaw control strategy (using a yaw error 15 • as threshold and a yaw rate 0.5 • /s), the mean yaw error is 9.57 • , and yaw frequency is mainly concentrated in the middle and low wind speed sections (40 and 55%).Thus, the lidar based LSTM-NN novel yaw control strategy was proposed.Limited by the simulation wind condition (turbulence wind average direction is 0 • , the power increase is mainly proved under ideal wind condition (step wind speed and wind direction) when wind speed is 8 m/s, wind direction changes 3 times within 200 s, and the power increases by 3.5%.Yaw travel, yaw number, and their distribution are testified under turbulence wind condition.With a total simulation time of 9000 s, yaw travel decreases from 1249 • to 1183 • , and yaw number decreases from 285 times to 274 times.Yaw distribution under traditional yaw control is 51.6, 48.4, and 0%, while under LSTM-NN, novel yaw control strategy is 29.6, 70.0, and 0.4%.It shows that the lidar has potential application field in yaw control.Future work would focus on load analysis, yaw motor energy consuming, and the field test results comparison.Besides, other potential novel lidar application fields should be explored to improve lidar commercial cost performance.

Conclusions
Using lidar as a pre-measure for the wind information at the turbine enables yaw actuation according to the lidar-measured wind information and its value after evolution.This can improve the lifetime of a yaw system from that of a low wind speed section to that of a moderate wind speed section, reduce the yaw frequency in the low wind speed section (reduce from 51.6 to 29.6%), and increase the yaw frequency in the optimum wind speed section (increase from 48.4 to 70.0%).Adding an assessment of the advancing wind can enable yaw action in advance when there are large changes in wind direction and can advance the yaw process so that, when the yaw action is complete, the rotor is directly facing the incoming wind.Compared with the traditional lagging yaw control strategy, this approach can increase the turbine power by 3.5%, reduce the yaw travel by 5.3%, and reduce yaw number by 3.9% in specific calculation conditions.

Patents
China patent for invention, Wenting Chen, Di Zhang, Hang Liu, et al.A yaw control method of wind turbine, Patent No. ZL 201910383503.4.

Symbol
Quantity Unit

DWS DD
The bottom plane wind speed and wind direction m/s, degree (

Figure 1 .
Figure 1.Relationship between the percentage wind turbine power loss and the variation in yaw angle error   .

Figure 2 .
Figure 2. Typical traditional yaw control system schematic diagram based solely on wind direction information from an upstream wind vane monitor.

Figure 1 .
Figure 1.Relationship between the percentage wind turbine power loss and the variation in yaw angle error θ ε .

Figure 1 .
Figure 1.Relationship between the percentage wind turbine power loss and the variation in yaw angle error   .

Figure 2 .
Figure 2. Typical traditional yaw control system schematic diagram based solely on wind direction information from an upstream wind vane monitor.

Figure 2 .
Figure 2. Typical traditional yaw control system schematic diagram based solely on wind direction information from an upstream wind vane monitor.

Figure 3 .
Figure 3. Statistics of yaw misalignment from 10 days (December 3-12, 2018) of data collected by Zhejiang Windey Co, Ltd. from a WD-147 wind turbine in the Zhangbei Yangji wind farm.

Figure 3 .
Figure 3. Statistics of yaw misalignment from 10 days (December 3-12, 2018) of data collected by Zhejiang Windey Co, Ltd. from a WD-147 wind turbine in the Zhangbei Yangji wind farm.

Figure 4 .
Figure 4. Wind speed distribution measured at the meteorological mast at the Zhangbei Yangji wind farm from December 3-12, 2018.

Figure 5 .
Figure 5. Yaw frequency statistics of the WD-147 unit at the Zhangbei Yangji wind farm from December 3-12, 2018, Yaw number is the number of yaw events.

Figure 4 .
Figure 4. Wind speed distribution measured at the meteorological mast at the Zhangbei Yangji wind farm from December 3-12, 2018.

Figure 4 .
Figure 4. Wind speed distribution measured at the meteorological mast at the Zhangbei Yangji wind farm from December 3-12, 2018.

Figure 5 .
Figure 5. Yaw frequency statistics of the WD-147 unit at the Zhangbei Yangji wind farm from December 3-12, 2018, Yaw number is the number of yaw events.

Figure 5 .
Figure 5. Yaw frequency statistics of the WD-147 unit at the Zhangbei Yangji wind farm from December 3-12, 2018, Yaw number is the number of yaw events.

Figure 6 .
Figure 6.Yaw control scheme based on upstream lidar wind information.
], [−100 −26.79 22.17], [−100 −26.79 −22.17], and [−100 26.79 −22.17].The MATLAB function was used to determine which line of sight wind velocity belonged to which beam according to the scanning time, which solved the time series problem in the scanning period of lidar.The lidar beams and the lidar scanning simulation model in Simulink are shown in Figure 7b.

Figure 6 .
Figure 6.Yaw control scheme based on upstream lidar wind information.
].The MATLAB function was used to determine which line of sight wind velocity belonged to which beam according to the scanning time, which solved the time series problem in the scanning period of lidar.The lidar beams and the lidar scanning simulation model in Simulink are shown in Figure7b.

Figure 7 .
Figure 7. (a) Simulation lidar mounted on a nacelle and consisting of four laser beams.;(b) the lidar beams and the lidar scanning simulation model.

Figure 7 .
Figure 7. (a) Simulation lidar mounted on a nacelle and consisting of four laser beams.;(b) the lidar beams and the lidar scanning simulation model.

Figure 9 .
Figure 9. Wind speed (average wind speed was 7 m/s) and wind direction results from the lidar measurement and processing of the wind evolution model.(a) Wind speed; (b)wind direction.

Figure 9 .
Figure 9. Wind speed (average wind speed was 7 m/s) and wind direction results from the lidar measurement and processing of the wind evolution model.(a) Wind speed; (b)wind direction.

Figure 10 .
Figure 10.Flow chart of the yaw control strategy.

Figure 10 .
Figure 10.Flow chart of the yaw control strategy.

9 9 .Figure 11 .
Figure 11.Structure of the simulation of a 5 MW wind turbine used for verifying the yaw control strategy.

Figure 11 .
Figure 11.Structure of the simulation of a 5 MW wind turbine used for verifying the yaw control strategy.

Energies 2020 , 24 Figure 12 .
Figure 12.Step wind speed and direction input under ideal conditions.

Figure 12 .
Figure 12.Step wind speed and direction input under ideal conditions.

Figure 13 .
Figure 13.System response with different yaw control strategy under the same wind condition.Figure 13.System response with different yaw control strategy under the same wind condition.

Figure 13 . 24 Figure 14 .
Figure 13.System response with different yaw control strategy under the same wind condition.Figure 13.System response with different yaw control strategy under the same wind condition.Energies 2020, 13, x FOR PEER REVIEW 16 of 24

Figure 14 .
Figure 14.Simulation results under given step wind speed and direction.

Figure 15 .
Figure 15.Wind turbine response under novel yaw strategy.

Figure 16 .
Figure 16.Generator power comparison with novel yaw control strategy and tradition yaw control strategy.

Figure 17 .Figure 17 .Figure 17 .Figure 17 .Figure 18 .Figure 18 .
Figure 17.Comparison of the simulation results between the traditional strategy and lidar-based yaw control strategy in turbulent wind (average wind speed was 7 m/s).(a) The effect of wind rotor following the wind direction; (b) power capture comparison.

Figure 18 .
Figure 18.Comparison of the simulation results between the traditional strategy and lidar-based yaw control strategy in turbulent wind (average wind speed was 8 m/s).(a) The effect of wind rotor following the wind direction; (b) power capture comparison.

Figure 19 .
Figure 19.Yaw frequency statistics for the traditional and novel yaw control strategies in simulations with an average wind speed of 4, 5, 6, 7, and 8 m/s.

Table 1 .
The lidar based yaw control parameters used in Fig.10.
• ) VS VDVertical wind speed and wind direction m/s degree ( • ) HWS HDThe inversion of wind speed and wind direction m/s and degree ( • ) The distance to the rotor.x < 0 represents the upstream of the rotor; x > 0 represents the downstream of the rotor m