Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'How does the wind blow behind wind turbines and in wind farms?' taking place on Tuesday, 11 March 2014 at 16:30-18:00. The meet-the-authors will take place in the poster area.

**Berit Floor Lund**Kongsberg Maritime, Norway

Co-authors:

Berit Floor Lund (1)

^{F}

^{P}Per Norman Oma (1) Tommy Jakobsen (1)

(1) Kongsberg Maritime, Trondheim, Norway

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## Presenter's biography

*Biographies are supplied directly by presenters at EWEA 2014 and are published here unedited*

Berit Floor Lund has a a masters in control engineering from NTH in Norway in 1987. In 1987 she joined Sintef Automatic Control in Trondheim. In Sintef she has held positions as researcher, senior researcher in process control and also as research manager/director. In november 2012 she joined Kongsberg Maritime to work with windfarm control. In 2003 she was a visiting researcher at Carnegie Mellon University. She did her doctor's degree in control engineering at NTNU in Norway in 2005. She has several publications within control, estimation and on-line simulation.

## Abstract

**WIND FARM PRODUCTION MAXIMIZATION THROUGH JOINT OPTIMIZATION OF TURBINE INDUCTION FACTORS AND YAW. SIMULATED CASE STUDIES.****Introduction**

In wind farms, a turbine reduces the wind speed and power production for turbines standing in its wake. The severity of the wake loss depends on wind direction, speed and farm layout. Due to the nonlinear relationship between power production and wind speed, the total production of a farm can be increased by reducing the efficiency of the wake causing turbines. Yawing will change the wake direction, potentially reducing the wake impact on downwind turbines. This has been solved as a nonlinear optimization problem, used to investigate for which wind directions yawing pays off compared to just optimizing turbine efficiency.

**Approach**

The wind farm power maximization problem has been formulated as a constrained, nonlinear optimization problem. The algorithm can be run using only the induction factor, or the induction factor in combination with yawing as optimization variables. The constraints are the power limit on each turbine, and in addition upper and lower bounds on the optimization variables see figure . A similar approach is used in [2], however with a cooperative game approach for the optimization, and other approaches in the modeling.

A homogenuous wind field has been used, meaning that the free speed and direction wind is the same throughout the farm. The algorithm could however take individual free winds and wind directions to each turbine accounting for e.g. terrain effects, if needed. Steady state models are used.

The algorithm can take different wake models. However, when using yaw as an optimization variable, some radial variation is needed, here approximated Gaussian distribution is used. As opposed to a true Gaussian distribution, the approximated distribution goes to zero at some point radially, and is scaled in such a way that the integrated decay at any plane downwind is the same as the Jensen wake model at that downwind distance. Also, the distribution has “tails” outside the box defined by the Jensen wake, see figure 2. Larger tails, gives a lower peak in the middle in order for the total area to match the Jensen wake. Referring to the Jensen model, a large value, k=0.1, has been used thus assuming a faster decay, and faster widening of the wake, in order to make conservative assumptions regarding wake propagation, to reduce the overprediction of wake deep in the farm.

A yawed turbine will alter the direction of the wake. A commonly used model for the change in wake direction based is given in [1] and [4]. In theory, a yawed turbine will have a loss in its own production proportional to the third power of the cosine of the yaw angle. However, experiments have shown that the loss smaller, 1.8 in [3]. Here a squared cosine loss term has been used.

**Main body of abstract**

The algorithms used in this paper has been made as a step in the development of Kongsberg Maritime’s wind farm management system. Optimization of the farm power production can in these algorithms be made using only turbine efficiencies alone, or in combination with yawing.

The power maximization problem in figure 1 can be solved using different methods, here using an SQP (sequential quadratic programming) algorithm. Two different farm layouts are considered. One 40 turbine farm has 5 straight rows containing 8 turbines with 7D distance, and 4D distance in between the rows, see figure . The other wind farm is a more typical on shore farm with a less regular layout of the turbines. Here only a few turbines have been considered. For both farms it has been investigated if there is anything to gain by using yawing in addition to the turbine efficiency (induction factor).

For the 40 turbine farm, different wind directions relative to the row directions have been investigated. Due to the symmetry of the farm, a 90 degree sector of wind directions have been analysed. At 90 degrees, the wind direction aligns with the 4D rows. At 180 degrees the wind blows along the 7D rows. The chosen wind speed is 10m/s. The production increase using only efficiency as optimization parameter (asterisk), compared to traditional selfish control (i.e. each turbine produces as much as it can), and correspondingly, efficiency combined with yawing (crosses) are plotted for different wind speeds, is shown in figure 4. Compared to selfish production, the production increase is not surprisingly the highest when the wind blows along the 4D row, and less blowing along the 7D row. The magnitude of the answers depend heavily on the wake model and wake model parameters used. Here a Jensen model with k=0.1 (higher than normal) as in combination with a Gaussian distribution radially should give a relatively quick wake decay. This may be the reason for the relatively low numbers (around 2% gain) when the wind blows diagonally. Another important factor here is how decays are added along the row. Here the square root of the sum squared decays are taken.

The difference between the two curves in figure 4 are plotted in figure 5 in order to easier see how the difference between optimizing only with efficiency or in combination with yaw depends on wind direction. As can be seen, there is nothing extra to gain using yaw when the wind direction aligns exactly with the wind farm rows. With a wind direction slightly off the row directions, a large increase in production can be obtained by optimizing with both efficiency and yawing compared to just yawing.

Figure 6 shows a few of the turbines, and how they are yawed at 95 degrees wind direction. Compared to figure 3 which shows selfish control, the speed decay shown on the rotor area is significantly lower.

Also, the optimization algorithms have been applied to a group of turbines which have a less regular layout. Here the free wind conditions are also assumed homogenuous although the row is part of an actual farm where some terrain effects on the wind field could be expected. Figure 7 shows the wind speed decay on the rotor areas using selfish control, Figure 8 shows the corresponding decay and also yawing of some of the turbines.

Analysing the results of the optimization shows that turbines 1 (numbering from the bottom up in the figure), 4, 5 and 6 are rated down with regards to efficiency. Turbine 3 is yawed -23 degrees, an turbine 7 is +16 degrees, turbine 1 is -12 degrees. Turbines 2,4,6,9 are yawed with an absolute value less than 10 degrees. Turbines 5, 7, and 10 are not yawed. The total increase in power production is 6% using only efficiency, and 7.5% using both efficiency and yawing. In this case relatively hard yawing of some turbines did gave only 1.5% theoretical increase in the production.

Even if numbers like 7% production increase would be unrealistic in a real, dynamic situation, a fraction of this would still be a significant production gain.

A turbine tilt of 4 degrees is included when calculating the wake direction in both cases.

**Conclusion**

For most wind directions, the largest increase in farm production comes through reduction of the induction factor (power efficiency) of the wake generating turbines. It is shown that when the wind direction aligns exactly along the rows, the optimization algorithm choses only efficiency with no yawing to maximize production. However the wind direction is slightly off (5-10 degrees) the main row directions of the farm, yawing to steer the direction of the wake may add significantly to the total production.

The difference in increased power, relative to traditional “selfish” control is the largest when the wind direction is within 10 degrees off the direction of a row. In this situation, the wake center hits the downwind turbine area, but off the vertical middle axis.

The quantitative answers in such an optimization depend heavily on especially the used wake model. Here the wake model has an approximated Gaussian distribution radially, however going to zero at the “edges”.

The quantitative answers of such a study depend both on the models chosen, their parameters, assumptions and simplifications made. However, the flexibility in the implementation makes it easy to replace with e.g. other decay models for the wake, other parameters in the wake models in order to adjust to actual cases. The criterion can also be expanded to optimize with regards to additional parameters. The setup can also use other solution methods than SQP.

Even if the optimization is made using steady state models and very idealized wind conditions, and there still is quite a way to go implementing such mechanisms on-line against a highly dynamic reality, the study still illustrates that there is a potential in applying such techniques for increasing the power production in wind farms.

**Learning objectives**

A wind farm power maximization algorithm has been developed which is capable of comparing selfish control, with optimization of power efficiency or joint optimization of efficiency and yawing.

For a farm with a layout in a regular grid, there is most to gain by using optimizing of yaw in addition to efficiency when the wind direction is around 10 degrees off one of the row directions.

**References**

[1] Burton, T. and N. Jenkins, D. Sharpe, E. Bossyani, Wind Energy Handbook 2nd ed., Wiley, 2011.

[2] Park, Jinkyoo and Soonduck Kwon and Kincho H. Law “Wind Farm Power Maximization Based On A Cooperative Static Game Approach”, SPIE, San Diego, March, 2013

[3] Dahlberg, J. and Medici D., “Potential improvement of wind turbine array efficiency by active wake control”, Proceedings of Eur. Wind Energy Conference, 2003.

[4] Wagenaar, J.W. and L.A.H. Machielse, J.G. Schepers, "Controlling Wind in ECN’s Scaled Wind Farm", EWEA, Copenhagen, 2012

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