A LiDAR-based Yaw Control for Wind Turbines

1. Introduction

The monotonic growth of wind energy has significantly expanded the renewable energy sector, reducing reliance on fossil fuels [1]. Efficient control of wind farms plays a crucial role in optimizing energy output and ensuring their sustainability. By effectively managing the operation, maintenance, and performance of each turbine, we can maximize energy yield, minimize downtime, and prevent component failure. This becomes increasingly important in our current era, where renewable energy is vital for mitigating climate change and ensuring energy security. A notable advancement in this field is the utilization of Light Detection and Ranging (LiDAR) technology. LiDAR enables precise measurement of wind speed and direction at greater distances ahead of the turbines, facilitating the implementation of predictive control strategies. This technology not only optimizes the performance of individual turbines but also enhances the overall efficiency and productivity of the entire wind farm, resulting in improved economic viability and better integration of wind energy into the power grid.

In single wind turbine management for maximizing power production and reducing load variation, it is aligned with the upcoming wind flow [2]. Within wind farm arrays, wind turbines may experience significant underperformance [3] and encounter unsteady loading, leading to increased maintenance costs. Additionally, climate change trends can cause shifts in wind roses, potentially creating unfavorable conditions for wind farms. Therefore, monitoring and control strategies are crucial for achieving optimized operations in an ever-changing environment[4].

Extensive studies have advanced wind turbine control and optimization, resulting in significant performance and load reductions [5]. Coupled control and position optimizations yield the best improvement, increasing power density substantially [6]. Nacelle-mounted forward-looking LiDAR enhances turbine alignment and power performance [7], as well as improves evaluation of flow interaction models within wind farms [8]. Combining LiDAR with strategies like feed-forward collective pitch control shows potential for optimizing wind plant efficiency [7]. LiDAR-based control techniques, including a model predictive controller (MPC), significantly reduce generator speed variation [9]. Nacelle-mounted scanning LiDAR improves energy production and reduces fatigue loads [10]. LiDAR-assisted control reduces rotor speed variation, tower loads, and power fluctuations [11]. Optimizing LiDAR scan patterns and utilizing ground-based LiDAR improve accuracy and enable advanced control capabilities [12,13,14]. Efficient LiDAR-enabled controllers outperform non-LiDAR controllers [15]. High LiDAR data availability and consideration of wind profile and rotor area characteristics are important for effective control of large wind [16]. Comprehensive fatigue analysis identifies efficient yaw ranges and optimal angles for increased power output and extended operational lifetime [17].

The implementation of active yaw control has opened up possibilities for wake management, aiming to optimize the power conversion of wind turbines within wind farms while reducing unsteady loading[18]. Yawed rotors can induce wake deflection [19,20]. Miao et al. [21] conducted a study on the impact of yawing on the performance of two aligned wind turbines, observing an increase in combined power production when the up-wind turbine was yawed at a specific level. Bartl et al. [22] investigated yaw control in two wind turbines under different turbulence intensities and inflow directions through measurements, achieving a 3.5% to 11% increase in total power through cooperative control. Fleming et al. [23] estimated a 14% power increase for a downwind wind turbine under a 10-degree wind inflow angle (angle between wind direction and the row of turbines) and a 4% overall production increase for the wind farm using a wake steering strategy. They utilized FLORIS [24], a model based on the works of Jensen [25] and Jimenez [26], which has since evolved into more complex formulations [27]. Sinner et al. [28] estimated a 4% increase in power production through wake steering at a specific wind inflow angle in a six-turbine wind farm. Bastankhah and Porté-Agel [20] conducted wind tunnel experiments using a five-turbine array, exploring the effect of various yaw angles on the first turbine and reporting a significant power increase.

In conclusion, the control and optimization of wind turbines play a crucial role in maximizing energy output, minimizing maintenance costs, and improving the overall efficiency of wind farms. LiDAR technology has emerged as a valuable tool for accurate wind measurement, enabling the implementation of advanced control strategies[29]. By incorporating LiDAR data into control algorithms, wind turbines can adapt to changing wind conditions, optimize power production, and reduce unsteady loading. Active yaw control and wake management techniques further enhance the performance of wind turbines within wind farm arrays[30]. Ongoing research and advancements in this field continue to contribute to the development of more efficient and sustainable wind energy systems.

However, while many studies have focused on the efficiency of aligned turbines, fewer investigations have examined optimal yawing under partial wake overlap. This study aims to explore the optimized yaw angle of utility-scale wind turbines under different partial wake and overlap scenarios, considering the potential trade-offs between yaw misalignment strategy and power production. Section 2 describes the methods and field setup, Section 3 discusses the results, and Section 4 summarizes the main findings.

2. Materials and Methods

The study is carried out on a two Siemens SG3.4-175, 3.5 MW wind turbine array located in the proximity of Rostock, Germany. The turbines are aligned 297 degrees from the north; see Figure 1. The downwind turbine (hereon No. 2) is equipped with a four-beam LiDAR system that can measure wind parameters at ten distances upwind, namely, $X_d$= 50, 75, 100, 150, 200, 250, 300, 350. 400, 450 m.

Figure 2 illustrates the basic quantities of the LiDAR and measurement planes. As indicated in reference [31], the production of the downwind turbine can be affected by the partial momentum deficit induced by the upwind turbine when the wind is from an angle of approximately 297 or 117 degrees North. In addition to LiDAR, complementary SCADA data is used to calculate absolute wind direction, $D_h$, and speed, ${HWS}_h$, at the hub height. The relative angles $\alpha$ and $\beta$ from the LiDAR sensor, given in Figure 2, are 5 and 15 degrees respectively. The $\vartheta$ and $\phi$ angles are inferred from equations 1 and 2, trigonometrically, as follows.

$$\vartheta ={\cos }^{-1}\left({\displaystyle \frac{\cos \alpha }{\sqrt{1+{\left(\tan \beta \right)}^2{\left(\cos \alpha \right)}^2}}}\right)$$

(1)

$$\phi ={\cos }^{-1}\left({\displaystyle \frac{\sin \beta }{\sqrt{{\left(\tan \alpha \right)}^2{\left(\cos \beta \right)}^2+{\left(\sin \beta \right)}^2}}}\right)$$

(2)

The parameters needed to compute the wind veer are calculated from equations 3-5 and replaced in equation 6. Here, ${RWS}_i$ is the so-called radial wind speed, the projection of the absolute wind speed along the sensor i-beam; see Figure 2.

$$Z\pm =Z_h\pm x_d\tan \vartheta \sin \phi$$

(3)

$${\beta }_{+}={\mathit{tan}}^{-1}( {\displaystyle \frac{{RWS}_0-{RWS}_1}{\mathit{tan}\vartheta \mathit{cos}\phi ({RWS}_0+{RWS}_1)}})$$

(4)

$${\beta }_{-}={\mathit{tan}}^{-1}( {\displaystyle \frac{{RWS}_2-{RWS}_3}{\mathit{tan}\vartheta \mathit{cos}\phi ({RWS}_2+{RWS}_3)}})$$

(5)

$$Veer={\displaystyle \frac{{\beta }_{+}-{\beta }_{-}}{Z_{+}-Z_{-}}}$$

(6)

The parameters needed to calculate the horizontal component of the wind speed from the upper, ${HWS}_{+}$, and lower, ${HWS}_{-}$, beams are calculated from equations 7 and 8 and replaced in equation 9.

$$U_{+}={\displaystyle \frac{{RWS}_0+{RWS}_1}{2\cos \vartheta }} \text{\&} U_{-}={\displaystyle \frac{{RWS}_2+{RWS}_3}{2\cos \vartheta }}$$

(7)

$$V_{+}={\displaystyle \frac{{RWS}_0-{RWS}_1}{2\sin \vartheta \cos \phi }} \text{\&} V_{-}={\displaystyle \frac{{RWS}_2-{RWS}_3}{2\sin \vartheta \cos \phi }}$$

(8)

$${HWS}_{\pm }=\sqrt{U_{\pm }^2+V_{\pm }^2}$$

(9)

The direction of the horizontal component of the wind speed at hub height, $D_h$, is given by:

$$Dh={\beta }_{+}-Veer(Z_{+}-Z_h)$$

(10)

the shear ${\alpha }_v$[32] and the horizontal component of the wind speed at hub height, ${HWS}_h$, are given by:

$${\alpha }_v=\ln \left({\displaystyle \frac{{HWS}_{+}}{{HWS}_{-}}}\right)/\ln \left({\displaystyle \frac{Z_{+}}{Z_{-}}}\right)$$

(11)

$${HWS}_h={HWS}_{+}{\left({\displaystyle \frac{Z_h}{Z_{+}}}\right)}^{{\alpha }_v}$$

(12)

Figure 3 illustrates basic parameters used to assess the turbine interaction; these include the wake expansion growth rate, K; see e.g., [33]. The radial and axial distances between rotors are $x=dsin\left(\theta \right)$ and $y=dcos\left(\theta \right)$. Note that for $x-Ky\le 2r_0$, the downwind turbine is affected by the wake. The range of wind inflow angle for overlap, $\theta$, is:

$$\sin \theta -K\cos \theta \le {\displaystyle \frac{2r_0}{d}}$$

(13)

An overlap in the range of $0^{°}$ to about ${30}^{°}$ is expected for the setup under study. Considering all wind directions, the range producing overlap in the two-turbine system is $4\theta$, where each turbine takes $2\theta$. The axial induction factor at the rotor plane, a, is estimated from the far-field incoming wind speed, $U_{inc}$, and the wind speed at the rotor plane, $U_r$ from the LiDAR measurements. The thrust coefficient, $C_T$ , is determined from it (equation 14), for the non-yawed rotor [34]:

$$a=1-\left({\displaystyle \frac{U_r}{U_{\infty }}}\right) , C_T=4a\left(1-a\right)$$

(14)

$${\displaystyle \frac{U_r}{U_{inc}}}=1-\left(\left(1-\sqrt{1-{\displaystyle \frac{C_T\cos \gamma }{8\left({\sigma }_y{\sigma }_z/D^2\right)}}}\right)e^{-0.5{\left(\left(y-\delta \right)/{\sigma }_y\right)}^2}{e}^{-0.5{\left(\left(z-z_h\right)/{\sigma }_z\right)}^2}\right)$$

(15)

A reference wake profile is approximated using the analytical approximation by e.g., Bastankhah and Port´e-Agel [20] (equation 15) considering the full overlap inflow directions (${117}^{°}$and ${297}^{°}$North). Then, using the parameters from Equation 16, the performance and power gain of the turbine system are estimated with Equation 17. The value of $V^{*}$ is then calculated using the wind speed at the downwind rotor plane and $E$, which is between 1.3 and 2.5 [35].

$$P_{\gamma 0}={\displaystyle \frac{1}{2}}\rho A{C}_P{\left(U\right)}^3\hspace{1em}\hspace{1em},\hspace{1em}\hspace{1em}{P}_{\gamma }={\displaystyle \frac{1}{2}}\rho A{C}_P{\left(U_{\infty }\right)}^3{\left(\cos \gamma \right)}^E\hspace{1em}\hspace{1em},\hspace{1em}\hspace{1em}{V}^{*}={\displaystyle \frac{U}{U_{\infty }}}$$

(16)

$${PR}_{\gamma }={\displaystyle \frac{{\left(\cos \gamma \right)}^E+{\left(V^{*}\right)}^3}{2}} , Power gain=\left({PR}_{\gamma }-{PR}_{\gamma 0}\right)\times 100$$

(17)

Effects of turbulent intensity, thrust coefficient, and wind inflow angle on the optimal yaw and the power gain of the wind farm for achieving a yaw control strategy and for a possible wake steering application are discussed in the next section.

3. Results and Discussion

The year-long LiDAR data indicates a 5.84 $m/s$ bulk wind speed in the rotor plane (Figure 4). Bulk $C_T$ is 0.62, obtained from the axial induction using SCADA and LiDAR data. The average annual wind speed measured by the SCADA system is 7.23 $m/s$ on the rotor plane, as shown in Figure 4. Compared with LiDAR, it is well-calibrated with the far-field upstream wind speed. It indicates that the SCADA data provides far-field wind speed at a distance of at least 250 meters upwind, not at the rotor plane.

Wind direction, wind farm layout and location can make a significant influence on yaw control strategy [36]. The associated wind rose in the area of this study is illustrated in Figure 5. The wind rose at the turbines location is obtained with the LiDAR and SCADA data. It is obtained for a yearlong and divided into 30 equal sections. It shows that the turbine pair receives winds from 180 to 270 degrees north at about 40% of the year. It is roughly 15% for the first quarter and 25% for the second and fourth quarters. So, the wind distribution indicates that the third quarter has the major wind. As seen, the wind farm layout appears appropriate; the major winds blow from the South-West, i.e., perpendicular to the arrangement of the turbines.

The wake for the referential average of the year modelled under different yaw angles is shown in Figure 6. The position of the downwind wind turbine is represented by a black dash line.

Figure 7 illustrates the wake of the upwind turbine in the rotor plane of the downwind turbine (black circles). In a yaw optimization approach, the wake deflection has a positive impact on the production of the downstream turbine that must overcome the negative effect of the upstream turbine yaw misalignment on its energy production.

As indicated by Figure 8, the yaw angle producing the maximum performance changes with the change of $T_i$ and $C_T$ values in ${10}^{°}$ to ${15}^{°}$ yaw angles. In studies employing Large Eddy Simulation (LES), this is occurred in ${10}^{°}$ to ${20}^{°}$ yaw angles, pointing that it depends on the location of the wind turbine in the wind farm layout [37].

In Figure 9, the wind speed ratio ($U/U_{\infty }$) in two cases: data without the yaw angle of the upstream turbine obtained from the SCADA and LiDAR systems (Figure 9a,b), and the optimal yaw angle obtained from the analytical model (Figure 9c,d) is shown. In Figure 9c,d, we see a decrease in areas with a lower wind speed ratio than that in Figure 9a,b. Because with more misalignment of the upstream turbine rotor, more intact and high momentum wind flow reaches the downstream turbine.

The maximum amount of power gain in the average annual occurs between wind inflow angles of 15 and 20 degrees (Figure 10a), where the corresponding optimal yaw angles are between 3 to 9 degrees. As seen in Figure 10b, the changes in power gain and the corresponding optimal yaw angle behave like a Bell curve along with the range of the wind inflow angle.

Changes in the power gain at different angles of the upcoming wind indicate that the amount of power gain is very low at small values of wind inflow angle ($\theta$). But by increasing $\theta$ to values of 12 and 14 degrees, the amount of power gain reaches its maximum amount. Then with a further increase of $\theta$, the amount of power gain decreases again until the downstream turbine leaves the wake area of the upstream turbine and then the power gain becomes zero. The appearance behaviours of power gain are similar in both $E$ values, but their maximum values are different.

Finally, according to the frequency of wind speed in different upstream angles, the amount of wind farm power gain increase, both in the overlap range and during one full-year, is calculated according to Table 1.

At first glance, the power gain values obtained in this study, ranging from 0.23 to 0.58 in the overlap region and 0.08 to 0.21 in the full year, are relatively lower compared to some other research findings. One of the key factors contributing to this difference is the number of turbines in a row, as it has been observed that the power gain tends to increase with an increase in the number of turbines [31]. As highlighted by Song et al. [36], power plants with only two turbines, similar to the wind farm studied in this research, typically exhibit lower power gains. Their study on China Ming Yang 1.5 MW wind turbines reported a power gain of 0.32% to 0.8% through yaw control, which falls within the range of our results. This similarity suggests that the power gain achieved with two turbines may be more consistent across different studies. However, it is important to consider that other factors such as wind directions and wind farm layouts can also influence the power gain. Rak et al. [38] estimated that yaw control in a wind farm consisting of eight rows of NREL 5-MW turbines could improve total power production by approximately 3.59% to 14.66%. This significant power gain can be attributed to the larger number of turbines and the resulting enhanced wake interactions. Similarly, Li et al. [39] reported a power gain of 2.1% in the major wind direction for a realistic offshore wind farm. These findings highlight the significance of considering specific wind conditions and farm configurations when assessing the potential for power gain through yaw control. Furthermore, Puech et al. [40] conducted a simulation-based investigation using real-world MM82 2-MW logs and reported a power gain of about 0.31% to 0.33%. These results align more closely with our findings, suggesting that variations in turbine design and operational conditions can contribute to differences in power gain values. Additionally, Howland et al. [41] developed a collective control approach using a predictive physics-based, data-assisted wind farm flow control model. In their experiment with four utility-scale wind turbines, they achieved a power gain between 0.3% and 1.0%. This demonstrates the potential for further enhancing power gain through advanced control strategies, even with a limited number of turbines.

Overall, the comparison with other research emphasizes the complex nature of power gain through yaw control, influenced by factors such as the number of turbines, wind directions, wind farm layouts and locations, and control strategies employed. While the power gain values obtained in this study may be relatively lower, they still demonstrate the potential for improving power production through yaw control. Further studies focusing on optimizing control strategies and considering specific wind farm configurations are necessary to enhance power gain and maximize energy production.

4. Conclusions

In this study, using both measurement methods and mathematical models for the wake region, the amount of performance and power gain of a wind farm consisting of two 3.5 MW wind turbines equipped with a nacelle-mounted multi-plane LiDAR sensor was studied for a full year. First, the LiDAR data were analyzed along with SCADA data, and then a data-assisted mathematical model was customized to optimize the yaw angle and thus maximize the power gain, and then the results were deeply discussed.

In this case, it was found that in 38 percent of the year, the wind blows from the third quarter (southwest), which was called the major wind direction in the wind rose. It was 23 percent for the second quarter as well as the fourth quarter. This indicates that the major wind blows perpendicular to the line connecting the two turbines, according to the wind farm layout.

It was also found that the amount of optimal yaw of the upstream turbine and the amount of power gain of the wind farm depend on the values of $C_T$ and $T_i$. These values depend on the wind conditions of the atmospheric boundary layer. With increasing $T_i$, the amount of power gain and the optimal yaw decreases [42]. With increasing wind speed, the value of $C_T$ decreases and therefore the power gain and the optimal yaw of the upstream turbine decrease.

Another factor that affects the calculations of both the optimal yaw and the power gain is the reduction factor of the upstream turbine production due to the yaw misalignment (${\cos \gamma }^E$). So that by reducing the value of $E$ here, the calculated optimal yaw and power gain increases and vice versa. These values create a range for the estimated parameters in this research. In order to reach the right values and achieve more accurate estimations, more experiments should be performed for more accurate corrections and evaluations.

It was also found that the amount of power gain at the corresponding optimal yaw changes as a Bell curve along the overlap range. So that in the wind inflow angle of zero, the amount of power gain and the corresponding optimal yaw angle are zero. But with increasing the inflow angle, the power gain and the optimum yaw increase, so that the power gain, corresponding optimal yaw of 17 degrees, reach its maximum values of 1.7 percent at an inflow angle of 12 degrees, as an optimistic (maximum) estimate ($E=1.3$). At a minimum estimate ($E=2.5$) and an inflow angle of 14 degrees, power gain reaches its maximum value of 0.69 percent, corresponding optimal yaw of 7 degrees. Then, with a further increase of the wind inflow angle, the downstream turbine exits the wake region of the upstream turbine, and then the power gain and the corresponding optimal yaw angle become zero.