A LiDAR-Based Active Yaw Control Strategy for Optimal Wake Steering in Paired Wind Turbines

Abstract

In this study, we investigate a yaw control strategy in a two-turbine wind farm with 3.5 MW turbines, aiming to optimize power management. The wind farm is equipped with a nacelle-mounted multi-plane LiDAR system for wind speed measurements. Using an analytical model and integrating LiDAR and SCADA data, we estimate wake effects and power output. Our results show a 2% power gain achieved through optimal yaw control over a year-long assessment. The wind predominantly blows from the southwest, perpendicular to the turbine alignment. The optimal yaw and power gain depend on wind conditions, with higher turbulence intensity and wind speed leading to reduced gains. The power gain follows a bell curve across the range of wind inflow angles, peaking at 1.7% with a corresponding optimal yaw of 17 degrees at an inflow angle of 12 degrees. Further experiments are recommended to refine the estimates and enhance the performance of wind farms through optimized yaw control strategies, ultimately contributing to the advancement of sustainable energy generation.

1. Introduction

The monotonic growth of wind energy has significantly expanded the renewable energy sector, reducing reliance on fossil fuels [1]. The 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 the precise measurement of wind speed and direction at greater distances ahead of 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 the improved integration of wind energy into the power grid.

In single wind turbine management for maximizing power production and reducing load variation, the turbine 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 operation in an ever-changing environment [4].

Extensive studies have advanced wind turbine control and optimization, resulting in improved performance and load reductions [5]. Coupled control and position optimizations yield the best improvements, increasing power density substantially [6]. Nacelle-mounted forward-looking LiDAR enhances turbine alignment and power performance [7], as well as improving the evaluation of flow interaction models within wind farms [8]. Combining LiDAR with strategies like feed-forward collective pitch control shows the potential for optimizing wind plant efficiency [7]. LiDAR-based control techniques, including model predictive controllers (MPCs), 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]. Higher level LiDAR data availability and the consideration of wind profile and rotor area characteristics are important for the effective control of large wind turbines [16]. Comprehensive fatigue analysis identifies efficient yaw ranges and optimal angles for increased power output and an 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 the 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 (the angle between the 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 overlaps. 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

In this investigation, we leveraged data from a fixed 4-beam nacelle-mounted LiDAR system (Figure 1a). This system was implemented at a utility-scale wind farm comprising two Siemens SWT-DD-142 wind turbines that are also illustrated in Figure 1a, each with a 3.5 MW capacity. The turbines, located near Rostock City, Germany, are aligned at 297 degrees north and are spaced 328 m apart (Figure 1b).

When the wind direction is either 297 or 117 degrees, the wake effect from one turbine impacts the power output of the other. A fixed 4-beam LiDAR system was mounted on the nacelle of wind turbine number 2 (Figure 1a), enabling the measurement of wind parameters at 10 planes upwind, ranging from 50 to 450 m (0, 75, 100, 150, 200, 250, 300, 350, 400, and 450 m) in front of the turbine that is depicted in Figure 2. This setup allowed for the direct estimation of the upwind velocity deficit and the axial induction using the measurement system.

Figure 3 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. In addition to LiDAR, complementary SCADA data were used to calculate the wind direction, $D_h$, and the horizontal wind 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) to (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 3.

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

(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 are replaced in Equation (9).

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

(7)

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

(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 the following equation:

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

(10)

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

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

(11)

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

(12)

Figure 4 illustrates the basic parameters used to assess the turbine interaction; these include the wake expansion growth rate, K; see [33]. The radial and axial distances between the 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 the wind inflow angle for overlap, $\theta$, is as follows:

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

(13)

Equation (13) is satisfied for $\theta$ between 0° and 30°, so an overlap in this range was 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 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)

Initially, in 1983, Jensen [25] introduced a top-hat shaped wake model, wherein the wake deficit was assumed to remain constant throughout the wake region. This assumption, however, was not strongly corroborated by empirical findings. Subsequently, in 2014, Bastankhah et al. [35] formulated a wake deficit model grounded in a Gaussian distribution. In 2016 [20], they further developed this model to account for the wake deficit due to yaw angles, as delineated in Equation (15). In this equation, $D$ is the rotor diameter, $\delta$ is the wake deflection, and ${\sigma }_y$ and ${\sigma }_z$ are wake width in lateral and vertical directions, respectively.

In this study, the full overlap inflow directions were 117° and 297° north. Then, using the parameters from Equation (16), the performance and power gain of the turbine system were estimated with Equation (17). The value of $V^{*}$ was then calculated using the wind speed at the downwind rotor plane. The magnitude of power gain is dramatically influenced by the $E$ parameter, which has shown variable values across different studies. As stated in reference [36], $E$ ranges from 1.3 to 2.5, with $E$ values of 1.3 and 2.5 representing the lower and upper limits of power gains, respectively.

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

(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)

The effects of turbulent intensity, the thrust coefficient, and the 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

In the previous section, using the measured RWS from LiDAR, the ${HWS}_h$ was calculated according to Equations (4)–(12). Here, with extrapolation over the year ${HWS}_h$ data, a bulk wind speed of 5.84 m/s at the rotor plane is indicated (Figure 5). According to Equation (16) and downstream wind speed, the bulk $C_T$ is 0.62, derived from axial induction using SCADA and LiDAR data. The average turbulence intensity measured by LiDAR is 0.7, calculated as $T_i=\sigma /U$, where $U$ is the average wind speed and $\sigma$ is the standard deviation. The SCADA system measured the average annual wind speed on the rotor plane to be 7.23 $\mathrm{m}/\mathrm{s}$ (Figure 5). Compared to the LiDAR measurements, the SCADA data are well calibrated with the far-field upstream wind speed, indicating that SCADA provides accurate far-field wind speeds at a distance of at least 250 m upwind, not at the rotor plane.

The wind direction, wind farm layout, and location can have a significant influence on the yaw control strategy [37]. The associated wind rose in the area of this study is illustrated in Figure 6. The wind rose at the turbine’s location was obtained with the LiDAR and SCADA data. It was obtained for a yearlong period and was divided into 30 equal sections. This 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 highest wind levels. As seen, the wind farm layout appears appropriate; the major winds blow from south–west, i.e., perpendicular to the arrangement of the turbines.

How both wind turbines in the farm layout produce power when exposed to the regional wind rose are illustrated in Figure 7. The figure shows the power rose, with each line indicating the frequency of the average power in each direction measured by SCADA. A significant decrease in generated power in the wake region for both wind turbines is clear, emphasizing the necessity of wake steering methods to mitigate wake effects in this farm.

The wake for the referential average of the year modeled under different yaw angles is shown in Figure 8. The position of the downwind wind turbine is represented by a black dash line.

Figure 9 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 10, the yaw angle producing the maximum performance changes with a change in $T_i$ and $C_T$ values at 10° to 15° yaw angles. In studies employing Large Eddy Simulation (LES), this occurs at 10° to 20° yaw angles, pointing out that this outcome depends on the location of the wind turbine in the wind farm layout [38].

In Figure 11, 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 11a,b), and the optimal yaw angle obtained from the analytical model (Figure 11c,d), is shown. In Figure 11c,d, we see a decrease in areas with a lower wind speed ratio than that in Figure 11a,b. This is 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 year occurs between wind inflow angles of 15 and 20 degrees (Figure 12a), where the corresponding optimal yaw angles are between 3 to 9 degrees. As seen in Figure 12b, 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 wind inflow angle ($\theta$) values. However, by increasing $\theta$ to values of 12 and 14 degrees, the amount of power gain reaches its maximum amount. Then, with a further increase in $\theta$, 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 behaviors of the power gain are similar in both $E$ values, but their maximum values are different.

Finally, according to the frequency of the 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. The amount of power gain for the times of overlap and during one full year.

	Power Gain (Percent)
$\mathrm{E}:\left({\cos \gamma }^E\right)$	Overlap	Full Year
E = 1.3 (Upper range)	0.58	0.21
E = 2.5 (Lower range)	0.23	0.08

.

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 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. [37], power plants with only two turbines, similar to the wind farm studied in this research, typically exhibit lower power gains. Their study on China’s 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 power gain. Rak et al. [39] estimated that yaw control in a wind farm consisting of eight rows of NREL 5-MW turbines could improve the 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. [40] 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. [41] 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. [42] 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 the 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 performance and power gain of a wind farm with two 3.5 MW wind turbines equipped with a nacelle-mounted multi-plane LiDAR sensor were investigated over a full year. First, the LiDAR data were analyzed, and the average $T_i$ and bulk $C_T$ were calculated. Subsequently, the Bastankhah yawed Gaussian model [20] was employed to optimize the yaw angle and maximize the power gain. The results were thoroughly discussed.

In this case, it was found that in 38% 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% 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.

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 [43]. With the 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 (${\cos \gamma }^E$). 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. Thus, at a wind inflow angle of zero, the amount of power gain and the corresponding optimal yaw angle are zero. However, with an increase in the inflow angle, the power gain and the optimum yaw increase, so that the power gain, corresponding to an optimal yaw of 17 degrees, reaches its maximum values of 1.7% 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, the power gain reaches its maximum value of 0.69%, corresponding to an optimal yaw of 7 degrees. Then, with a further increase in 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.

By increasing the number of wind turbines in an array, the magnitude of power gain due to wake steering also increases. For example, Howlan et al. [44] employed wake steering in a six-turbine array and achieved a 7.7% power gain. Similarly, Beek et al. [45] applied wake steering to a wind farm with 48 turbines and achieved a 3.4% power gain. The method considered in this study could be extended to larger wind farms, which are expected to achieve even greater power gains. Designing a wind turbine control algorithm for real-world applications, particularly considering wake deflection, significantly relies on accurate wind flow direction measurements [46], control parameters, and maintenance constraints, which necessitates further investigation in future studies.