Implementation and Validation of Algorithm forEstimating the Possible Power of Curtailed Wind Turbines Exposed to WakeEffects

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IN

DEGREE PROJECT MATHEMATICS, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2017,

Implementation and Validation of Algorithm for Estimating the

Possible Power of Curtailed Wind Turbines Exposed to Wake Effects

LOÏC DEFOUR

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

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Implementation and Validation of Algorithm for Estimating the Possible Power of Curtailed

Wind Turbines Exposed to Wake Effects

LOÏC DEFOUR

Degree Projects in Optimization and Systems Theory (30 ECTS credits) Degree Programme in Applied and Computational Mathematics (120 credits) KTH Royal Institute of Technology year 2017

Supervisor at Vattenfall AB: Nikolaos Styliaras Supervisor at KTH: Xiaoming Hu

Examiner at KTH: Xiaoming Hu

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TRITA-MAT-E 2017:43 ISRN-KTH/MAT/E--17/43--SE

Royal Institute of Technology School of Engineering Sciences KTH SCI

SE-100 44 Stockholm, Sweden URL: www.kth.se/sci

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Abstract

In countries with high wind power penetration such as Denmark and Germany, wind farms are now requested to provide ancillary services. This implies that wind operators like Vattenfall must curtail (down-regulate) their farms from their possible power so that power reserves can be used in case of an outage in the electrical network. However, the estimation of the possible power of a farm is a complex task as it depends on many parameters such as the ambient conditions, the operational status of the turbines and the layout of the farm. The current estimation ignores these and unfortunately, this yields to an overestimation of the possible power when the farm is curtailed.

Tuhfe Göçmen published recently the PossPOW algorithm whose goal was to integrate these parameters in the estimation of the possible power so that the method would still be applicable during curtailments. Here, this algorithm was studied in depth to determine if it could be employed in real cases. In particular, it was tested on different situations than the ones investigated initially. It turned out that the actual algorithm failed to consider correctly the wind direction, a crucial parameter for the quality of the estimate.

Therefore, modifications in the initial algorithm were applied to deal with this issue and these led to significant improvements in its performances.

The PossPOW algorithm even with the proposed corrections was not able to reach the expected accuracy. But several areas of improvement were given to enhance the performances of the algorithm in the future. In parallel, this study raised the question of optimal curtailment strategies that which according to the developed models could increase the production of wind farms. Nevertheless, real experiments on wind farms are needed to try these strategies and assess their potential in practice.

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Abstract

I länder med en stor andel vindkraft, som Danmark och Tyskland, kommer det att krävas att vindkraftverk levererar systemtjänster. Det gör att vindkraftoperatörer som Vattenfall är tvungna att nedreglera sina kraftverk från sin möjliga produktion, så att denna kraft kan användas om det uppstår en brist i elnätet. En uppskattning av ett vindkraftsverks möjliga produktion är emellertid komplex eftersom den beror på många parametrar, som omgivningens förhållanden, turbinernas drifttillstånd och vindkraftverkets layout. Den nuvarande uppskattningen beaktar inte dessa vilket leder till en överskattning av möjlig produktion när vindkraftverk är nedreglerad.

Tuhfe Göçmen publicerade nyligen PossPOW-algoritmen vars mål var att integrera dessa parametrar i uppskattningen av möjlig produktion så att metoden även är giltig vid nedreglering. Här har denna algoritmen studerats för att avgöra om den är tillämpar i praktiken. Speciellt, har algoritmen utvärderats under förhållanden som inte hade testats tidigare. Det visade sig att algoritmen misslyckades att ta hänsyn till vindriktningen på ett korrekt sätt, en väsentlig parameter för uppskattningens kvalitet. Den har därför modifierats för att hantera det problemet, vilket har lett till signifikanta förbättringar av algoritmens noggrannhet.

PossPOW-algoritmen, även med de föreslagna förändringarna, uppnådde dock ej förväntad noggrannhet och ett antal förändringar har därför föreslagits som kan förbättra algoritmens prestanda. Studien har även undersökt möjligheten till optimala strategier för nedreglering för att öka vindkraftverkets produktion. Det krävs dock fältstudier för att verifiera huruvida det finns en signifikant potential för detta.

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Acknowledgements

I would like to thank my parents and my sister for the support they gave me during all my university years, I could not have done it without them. I am deeply grateful to Emilie who has always been patient and lovely with me even when I was not deserving it.

A special mention to my grandfather who will always be a source of inspiration for me.

I would like to express my sincere thanks to Nick, Jonas and Alin from Vattenfall from whom I have learnt so much and who have made my Master thesis so inspiring and pleasant. It was an amazing experience for me to be part of their team. Thanks to Andrew, Vincent, Wiljan, Sotos and my other Vattenfall colleagues for these 20 weeks, I enjoyed a lot spending time with them.

This thesis would not be the same without the kindness Tuhfe Göçmen. She was really open-minded, ready to collaborate, always answering my numerous mails and very friendly during my stay at DTU. A big thank.

Thanks to Professors Xiaoming Hu and Anthony Papavasiliou for being my supervisors at KTH and UCL during this thesis.

Last but not least, thanks to Marco with whom I could free my mind from the thesis during our tennis games and for his culinary talents which are much better than his tennis serve.

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List of Figures

2.1 Representation of wind turbine components . . . 4

2.2 Different curves of the offshore Vestas V90-3MW turbine . . . 6

2.3 Typical power curve and its different regions . . . 7

2.4 1-minute averaged data in normal operation for A01 . . . . 8

2.5 Thanet wind farm . . . 9

2.6 Wake loss profile downstream a wind turbine according to the Larsen model 12 2.7 The revised Larsen model . . . 13

2.8 Wake recovery in Lillgrund . . . 14

3.1 Diagram of the PossPOW algorithm . . . 18

3.2 Calibration of the WindDirection at A03 . . . . 19

3.3 Validation of the REW S estimation . . . 21

3.4 Wake model applied in the PossPOW algorithm . . . 23

3.5 Scatter plot used in the estimation of C_T,us . . . 24

3.6 Comparison between computing T I with U or u . . . . 24

3.7 Comparison of T I between an upstream and a downstream turbine . . . 25

3.8 The re-Larsen model applied on the turbine pair (A03, B03) of Thanet209red 26 3.9 Representation of the wake meandering . . . 27

3.10 Representation of a partial wake situation . . . 28

3.11 The re-Larsen model with the corrections applied on (A03, B03) of Thanet209red . . . . 29

3.12 Wake superposition model used in the PossPOW algorithm . . . 30

3.13 Performances of the PossPOW algorithm on Thanet209red . . . . 32

3.14 Statistical representation of the error of the 1-second estimation of the possible power on Thanet209red . . . . 33

3.15 The re-Larsen model applied on the training dataset of the PossPOW algorithm . . . 34

3.16 The re-Larsen model with the partial wake correction . . . 35

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3.17 The re-Larsen model applied on the validation dataset of the PossPOW algorithm . . . 36 3.18 The re-Larsen model with new fitted parameters applied on the validation

dataset of the PossPOW algorithm . . . 37 4.1 Comparison of the weight functions used in the regression . . . 40 4.2 Dataset used to model the wakes in Thanet209red . . . . 41 4.3 The mathematical wake model applied on (A03, B03) of Thanet209red . 42 4.4 The computations of the wake losses in a row of turbine with the mathe-

matical wake model . . . 43 4.5 The mathematical wake model applied on (C02, D02) of Thanet209red . 43 4.6 The mathematical wake model . . . 44 4.7 Sensitivity analysis of the mathematical wake model . . . 46 4.8 The computations of the wake losses in a row of turbine with the hypo-

thetical wake model . . . 47 4.9 The hypothetical wake model applied on several pairs of Thanet209red . 48 4.10 The two submodels in the hypothetical wake model . . . 49 4.11 Power maximization with the hypothetical wake model . . . 51 4.12 Performances of the PossPOW algorithm with the mathematical wake

model on Thanet209red . . . . 52 4.13 Performances of the PossPOW algorithm with the mathematical wake

model on Thanet209 . . . . 53 4.14 Performances of the PossPOW algorithm with the hypothetical wake model 54 4.15 Error propagation along a row of turbine with the two wake engineering

models . . . 55 5.1 Neural network fitting of the power curve of A01 . . . . 57 5.2 Comparison of the two time delay estimation methods . . . 59

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List of Tables

3.1 Fitted parameters of the re-Larsen model and their 95% confidence interval 26 4.1 Fitted parameters of the mathematical wake model and their 95% confi-

dence interval . . . 42 4.2 Performances of the two engineering wake models in parallel with TSO

requirements . . . 54

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Chapter 1 Introduction

1.1 Background

As offshore wind farms are becoming bigger contributors to the overall installed power capacity, more challenges emerge. Wind power has grown in such a scale, that wind power plants are expected to behave like conventional power plants, in the way that they should provide ancillary services to the grid. These services are documented by the grid operators of many countries in a collective way and are known as grid code requirements.

Countries with high wind power penetration such as Denmark or Germany come with stricter requirements.

One of the most common requirement is for the wind farm to be able to contribute to the grid frequency regulation. In case there is a falling grid frequency, wind farms may have to assist in its restoration by releasing some extra power to the grid. Naturally, that implies that a power reserve has to be kept, so turbines in some cases run in an non-optimal operating point in relation to active power production. When this happens, turbines are said to be curtailed or down-regulated.

Another typical case where a power reserve should be kept is for market purposes.

Any deviation in the planned power production from the planned demand can be traded each day in the balancing market. The parties that are involved in this procedure are called balancing responsible parties (BRPs) and are compensated based on the amount of reserves that they maintain, even while they are not using it.

Therefore, it is evident that an accurate estimation of the amount of the reserve power is crucial. In fact, according to the European Network of Transmission Systems Operators for Electricity (ENTSO-E), transmission system operators (TSOs) within continental Europe should be held responsible for the quality of their reserves. For each country, there are guidelines that specify the limits that the error between the estimated and actual reserve should fall in to. The estimation of the reserves is made by estimating the possible power of wind farms. Namely, given the actual wind profile, how much power the wind farm is able to produce. Then by looking what is currently produced, reserves can be estimated.

However, there has been a gap regarding the estimation of the possible power of a wind farm in a specific occasion. In large offshore wind farms, where the wake effects

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are not negligible, the current signal from the supervisory control and data acquisition (SCADA) system that is labelled possible power fails to deliver accurate values when some of the turbines are curtailed. The reason is that when upstream turbines are curtailed, the wake effects at the downstream turbines are reduced, a fact that is not mapped to the SCADA signal.

A PhD study in the Technical University of Denmark (DTU) addressed this issue by developing an algorithm that estimates the possible power of a wind farm by performing a back-calculation from the current power. This study was carried out by Tuhfe Göçmen and published in January 2016 as part of a project called PossPOW. The uncertainties of this algorithm and the related benefits for trading purposes are assessed by the continuation of this project, the CONCERT project.

1.2 Assignments and scope

There are two main purposes for this assignment. The first one is to have the PossPOW algorithm, incorporated to the wind farm control platform that has been developed in Matlab for the internal Vattenfall project, called Wind Farm Controller.

The goal is to provide a better estimation of the possible power of the wind turbines, which in the current version is approximated by simply mapping the input wind speed to the turbine power curve.

The second purpose will be beneficial for market purposes within Vattenfall. There is a big interest in establishing a way to estimate the possible power, i.e. the reserve they currently have, so that all the accuracy requirements are met. They have concluded in four different ways, but they need to evaluate their accuracy and applicability. The PossPOW algorithm is one of them and therefore, its implementation and evaluation will provide an important input to the Business Area Markets. For both of these purposes to be fulfilled, a proper validation of the results is essential. The validation will be performed by comparing the results of the algorithm with actual data from wind farms.

The main activity of this Master Thesis is to implement the algorithm developed in the PossPOW project, in a generic way, so that it can be used in the Wind Farm Controller model. The evaluation of the results is also a core activity of this assignment.

More specifically, the project scope and activities include:

• Studying and understanding in detail the work carried out by Tuhfe Göçmen, Possible Power Estimation of Down-Regulated Offshore Wind Power Plants;

• Implementation of the PossPOW algorithm as a Matlab function, in a generic way so that it can be added to existing Vattenfall Wind Farm Controller platform;

• Determining an effective method to validate the results of the algorithm. Data is available through the Vattenfall Wind Power Data Center and the SCADA system.

In addition, there may be data from the DanTysk wind farm, where planned curtailments will be done in order to validate the current estimation methods. The availability of this data depends on whether the curtailments will be done in time to suit the thesis work;

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• After the validation procedure, a conclusion should be made regarding the applicability and the reliability of the current algorithm for the aforementioned purposes.

1.3 Outline

This thesis is divided in six chapters, of which this is the first.

Chapter 2 gives a general overview about wind power. From the main characteristics of a wind turbine to the presentation of a wind farm, passing by an introduction to wakes, this chapter gathers all the necessary background to understand the next chapters. In addition, it is illustrated why the current estimation of the possible power is failing to give accurate values when the wind farm is curtailed.

Chapter 3 explains and analyzes the PossPOW algorithm in detail. In particular, it is applied on actual data coming from the Thanet wind farm. Finally, its validity is discussed in light of the obtained results.

Chapter 4 proposes two new wake models which give alternatives to the one that is developed in the PossPOW algorithm. The modified versions are evaluated against the same data than previously. Moreover, the possibility to design optimal curtailment strategies is raised through one of the models.

Chapter 5 addresses the next challenges in the estimation of the possible power. As the topic is still very young, many improvements can be realized. Some of them are mentioned in this chapter but are left as further works. Nevertheless, useful references are given for future investigations.

Chapter 6 draws the main conclusions of this work.

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Chapter 2 Wind power fundamentals

2.1 General properties of a wind turbine

When seen from outside, a wind turbine has three main components which are its tower, nacelle and rotor. A detailed representation of a turbine is given in Figure 2.1.

The way of generating electrical power from wind is relatively simple. The idea is to capture the kinetic energy of the wind to induce a rotation of the rotor. Then inside the nacelle, the low-speed shaft rotates with the rotor. However, this speed is too low to produce electricity from the generator also housed in the nacelle. Therefore, a gear box is used to speed up the rotation of the high-speed shaft which is connected to the generator which in turn convert this rotational energy into electrical energy.

Figure 2.1: Representation of wind turbine components (Figure courtesy of the U.S.

Department of Energy [15])

To extract the most of the wind power, the rotor has to face perpendicularly the incoming wind flow. Consequently, when the wind direction changes, the nacelle needs to

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adjust its orientation. This is realized by the yaw motor which is controlled such that the nacelle direction also called the yaw angle is in line with the wind direction measured by the wind vane. Another important factor to take into account when extracting power is the aerodynamic profile of the blades. In a variable-pitch wind turbine, the airfoil-shaped rotor blades are able to rotate along their longitudinal axes thanks to the pitch controller.

By changing the angle of attack of the airfoil, one can actually control the production of the wind turbine. In addition, if the turbine is a variable-speed one, meaning that the rotor speed can be controlled, the tip-speed ratio λ influences the extraction of the turbine. This one is defined as the ratio between the speed at the tip of the blade and the wind speed. Namely λ = ωR/U where ω is the rotor speed, R the rotor radius and U the wind speed. The wind speed U is usually referring to the Rotor Effective Wind Speed (REW S) whose value must not be confounded with the Nacelle Wind Speed (N W S) which is measured by the anemometer mounted on top of the nacelle.

Assuming that the nacelle is correctly aligned with the wind direction, one can quantify how much power the turbine will produce. This is given by the wind power equation

P = 1

2ρπR²U³C_P(λ, θ) (2.1)

where P is the electrical power produced in Watt, ρ the air density in kg/m³, θ the pitch angle of the blades in degree and C_P the power coefficient. This last one is giving an indication regarding the efficiency of the wind turbine. It tells how much the turbine is able to extract from the actual wind power whose magnitude is ¹₂ρπR²U³. As explained earlier, the extraction depends on aerodynamic profile of the blades hence on θ but also on λ. That is why C_P is a function of λ and θ. It should be noted that in this case the electrical losses are implicitly taken into account since P refers to the electrical power.

In theory, the maximal value of C_P without the electrical losses is 0.593 and it is known as the Betz limit. Practically, this value decreases to a value around 0.5.

When producing power from wind, it is necessary to consider the forces or more commonly called the loads on the turbine. One way to address this question is to look at the thrust coefficient C_T which also depends on θ and λ. Without entering into the details, this coefficient indicates how much the wind turbine is modifying the wind flow profile when it passes through the rotor. Using this information, one can evaluate the axial static load whose expression is given by

F = 1

2ρπR²U²CT(λ, θ) (2.2)

where F is the axial load in Newton. In opposition with C_P that can be derived from measurements and/or estimations of P and U , CT is traditionally derived from the blade element momentum (BEM) theory equations. This significant difference in methodology must be considered when using both coefficients.

The C_P(λ, θ) and C_T(λ, θ) are 2D-lookup tables rather than analytical expressions.

However, these are sensitive information and are not shared publicly by the turbine manufacturer. Instead, the turbine owner gets values of P (U ) called the power curve and C_T(U ) the thrust curve. Those curves give values when the turbine is in normal operation. More information about this operational mode is given in the next section but basically, it is the one when the turbine is not curtailed. In normal operation, the values

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of λ and θ are depending on U , that is why C_T can be expressed only as function of U . It should be noted that from P (U ) one can easily derive values of C_P(U ) using (2.1).

Those three curves are plotted in Figure 2.2 for the offshore Vestas V90-3MW turbine.

0 5 10 15 20 25

0 0.5 1 1.5 2 2.5 3

0 5 10 15 20 25

0 0.1 0.2 0.3 0.4 0.5

0 0.2 0.4 0.6 0.8 1

Figure 2.2: Different curves of the offshore Vestas V90-3MW turbine. Left plot: Power curve. Right plot: Thrust curve in magenta and power coefficient in black.

2.2 Control strategies of a variable-speed variable- pitch wind turbine in normal operation

To have a good understanding of how wind turbines are extracting power from wind, it is necessary to look at their control strategies. In this thesis, it is considered that the turbines are variable-speed variable-pitch ones. This type of turbine corresponds to the turbines installed in Thanet, a wind farm that is presented in the next section.

Control strategies of wind turbine are not exclusively aiming at extracting the maximum power from the wind. If this was the case the power curves provided by the manufacturers would be cubic w.r.t. the wind speed. However, one can easily remark that this is not the case in Figure 2.2 and distinguish three different regions in the power curve. These regions are represented again in Figure 2.3 with two additional regions usually not visible on the manufacturer power curve. This figure is an illustration of a generic power curve of variable-speed variable-pitch turbine. In the following, a short description of the control strategies in the five regions during normal operation is given.

Region 1 is defined by U ≤ U_cut,in, typical values of U_cut,in are 3-4 m/s. Low wind speed value keeps the turbines off as the wind kinematic energy is too low to think producing energy.

Region 2 takes wind speed values between U_cut,in and U₂₋₃. Mathematically, U₂₋₃ can be seen as the value where the power curve changes of concavity. In practice, it is the wind speed value at which the rotor speed is the maximum. During Region 2, the

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U P

U_cut,in U₂₋₃ U_rated U_cut−out

P_rated

1 2 3 4 5

Figure 2.3: Typical power curve and its different regions

goal is to produce at maximum capacity. Looking at (2.1), the maximum production is attained whenever C_P(λ, θ) is equal to C_P,opt, the maximal power coefficient. This value is reached for a unique pair (λ_opt, θ_opt). Consequently, in Region 2, the pitch angle is held constant to θ_opt while ω is controlled such that the tip-speed ratio stays closed to λ_opt. In the case of a fixed-speed wind turbine, ω cannot be changed hence the turbine is producing optimally only for a specific wind speed. In this region, controlling the rotor speed is made by varying the generator electrical torque τ_g. Indeed, the electrical power can be expressed as P = ωτ_g and thus it follows that

1

2ρπR²CP,optU³ = ωτg.

Replacing U by (ωR/λ_opt) from the tip-speed ratio definition and isolating τ_g, this gives τ_g = ρπR⁵C_P,opt

2λ³_opt

!

ω² = Kω². (2.3)

Region 3 starts at U₂₋₃ and ends at U_rated. As explained in [6], over this region the rotor speed cannot be increased and so τ_g is increased until the turbine reaches its rated power P_rated.

Region 4 is characterized by a constant production of P_rated. This region extends up to Ucut,out. The main objective is to reduce the loads on the turbine that is exposed to high wind speeds. This ensures a longer lifetime and reduced maintenance costs on the turbine. Here, the pitch is controlled in order to control the rotor speed by reducing

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the aerodynamic torque on the blade. The power is kept constant by controlling the generator electrical torque.

Region 5 concerns high wind speed values, i.e. higher than U_cut,out. For security reasons and in order to not damage the turbine, this one is stopped.

These five regions describe the normal operation of a wind turbine. Figure 2.4 shows data in normal operation for turbine A01 in Thanet. Only regions 2 , 3 , 4 are represented since in these ones, the turbine is producing power. One can recognize the control strategies for the different regions except near U_cut,in where the turbine seems to have a particular strategy in order to maximize the power production. In the case of the Vestas V90-3MW, one has U_cut,in= 3.5m/s, U_rated= 15m/s and U_cut,out = 25m/s and U₂₋₃ which is not given directly by the manufacturer, looks to be around 12m/s.

Moreover has indicated in its name, P_rated = 3MW.

Figure 2.4: 1-minute averaged data in normal operation for turbine A01

As it was explained previously, sometimes turbines are required to not operate normally. In this situation, it is said that the turbines are down-regulated or curtailed where now the goal is to produce less than in normal operation. That way some reserves are put aside by the farm operator. Curtailment is usually performed by controlling the pitch angle to reduce C_P(λ, θ) and C_T(λ, θ) so that the power produced and the loads on the turbine are decreased. For instance, if curtailment occurs in Region 2, the value of C_P(λ, θ) would not be equal to C_P,opt and the operating point would be set to a non-optimal point.

2.3 Presentation of a wind farm

Wind turbines are usually grouped to form a wind farm. A wind farm is a collection of turbines located in the same area and connected electrically to a Point of Connection

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(PoC) which makes the bridge between the wind farm and the grid.

There exist two types of wind farms, onshore and offshore ones. As its name suggests it, an offshore wind farm is situated at some distance from the shore, in this case in the sea. Ambient conditions can be significantly different between the two types of farms. For instance, the air is often more turbulent on the shore due to the relief and the convection cycles that are more important than in the sea. As it will be explained further in the thesis, the turbulence intensity (T I) is a critical factor when assessing the possible power of a wind farm.

A wind farm is characterized by its layout and its type of turbines. When designing the layout, the goal is to minimize the power losses between the turbines as well as the loads on each turbine given a wind profile distribution. If these were the only aspects to consider, the turbine spacing would be such that two neighboring wind turbines do not affect each other. But in addition, one must think about infrastructure costs and energy losses in the wind farm electrical network. Therefore, the layout of a wind farm results in a trade-off of several parties. Most of the wind farms, especially offshore ones, present a structured layout. Nevertheless, as reported in [2], structured layouts might not be the optimal solution. But solving this kind of problem is a challenging task, especially when it comes to decide for a model of the power losses and the loads on the turbines.

A01

A12 B01

B14 C01

C15 D01

D17 E01

E17 F01

F14 G01

G11 5.34D

7.96D 7.95D 319^◦

0^◦

209^◦

Figure 2.5: Thanet wind farm

This thesis focuses on offshore wind farms. This is justified by the fact that the original PossPOW algorithm was designed for offshore wind farms and moreover, it simplifies several models since there is no influence of the relief for instance. One particular wind farm will be studied here, the Thanet wind farm. This choice is motivated by its structured layout and its large number of turbines which makes it a good representation of actual and future offshore wind farms. Furthermore, the quality of the data turns out to be better compared to other farms, e.g. DanTysk or HornsRev I. A representation

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of the Thanet wind farm is given in Figure 2.5. It is located near the Kent district’s shore and it covers an area of 35km². It is composed of 100 offshore Vestas V90-3MW turbines and thus it has a possible production of 300MW. When officially operating in 2010, it was the largest offshore wind farm in the world. The Thanet wind farm has a row spacing of 5.34D and a column spacing of 7.96D where D is the rotor diameter of a turbine which in this case is 90m.

2.4 The wake effects

When a turbine is extracting power from the incoming wind, the dynamic characteristics of the incoming flow are modified behind this turbine. The downstream flow, i.e the flow behind the rotor of the turbine, presents a lower wind speed as well as a higher T I which is computed as

T I = σ_u

¯

u (2.4)

where σ_u and ¯u are respectively the standard deviation and the mean of the wind speed u over a 10-minutes period. As a consequence, downstream turbines extract less power and are exposed to highest loads compared to upstream turbines. This downstream flow is called a wake while the higher loads and the lower production downstream are called the wake effects. This section aims at giving an overview of the physics behind the wakes.

This downstream flow can be divided in two regions: the near and far wake regions.

The near wake region is highly dependent on the blade geometry and extends approxi- mately to 1D to 3D behind the turbine [26]. This region is characterized by the formation of blade tip vortices. Behind that region starts the far wake region whose characteristics are mainly driven by the surrounding ambient conditions and general properties of the turbine such as the ambient turbulence intensity T I_amb, the rotor radius R or the thrust coefficient C_T.

At this stage, it is important to define some adjectives used in the wind power literature. Upstream turbine denotes a turbine that is not affected by wakes. Namely, it is not in the downstream flow of another turbine. Conversely, a downstream turbine is in the downstream flow of another turbine. Then, in this thesis, the word artificial-upstream is employed to denote a turbine which is not necessarily an upstream turbine but whose downstream flow affects another turbine. As an example, if the wind direction is 209^◦ in Thanet, turbine A03 is an upstream turbine and, turbines B03 and C02 are downstream ones. But, B03 is also an artificial-upstream turbine of C02 and by definition, so is A03.

As mentioned above, wind farm layouts are designed in order to minimize wakes and loads inside the wind farm but also, infrastructure costs such as cables. The wake effects are still visible up to 10D and even further in low turbulent conditions [14]. Therefore, the wind farm layout is the result of a trade-off between power losses and maintenance costs because it would be too expensive to have a turbine spacing such that the wake effects are negligible. For instance, Thanet wind farm has a row spacing of 5.34D and a column spacing of 7.96D. From a wake perspective, it can be assumed that if a turbine is affected by wakes, it will be wakes in the far wake region. Therefore, all the wake models presented in this thesis aim at modeling this far wake region. In the following, whenever

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the word wake is mentioned it is referring to a far wake, namely the flow behind a turbine with the characteristics of the far wake region.

A wake can be characterized by two main properties, a radius r_w and a wind speed deficit dU . This flow is often represented as a volume whose section is circular, of radius r_w and the center is aligned with the center of the rotor from which it is originating.

Geometrically, it looks like a cone. If we consider x as the longitudinal coordinate and r as the radial coordinate, a section at x has a radius of r_w(x) and wind speed deficit profile dU (r, x). The expression of dU (r, x) is supposed to be axis-symmetric, this explains why the angular coordinate is discarded in wake formulas.

The next paragraph focuses on the Larsen wake model. This model gives a general understanding of the dynamics of a wake and in particular, formulas for r_w(x) and dU (r, x). Moreover, this model has been chosen as a basis to model the wakes in the PossPOW algorithm.

The revised Larsen wake model (2009) This model is based on the Reynolds Average Navier Stokes (RANS) equations with the thin shear layer approximation.

Larsen defines this model as a simple semi-analytical wake model [11]. Semi-analytical because some constants from the solutions of the RANS equations result of the analysis of full scale experiments. The Larsen model is defined by the two following equations

r_w(x) = (35/2π)^1/5(3c²₁)^1/5(C_TA(x + x₀))^1/3, (2.5)

dU (x, r) = −U∞

9 (C_TA(x+x₀)⁻²)^1/3ⁿr^3/2(3c²₁C_TA(x + x₀))^−1/2− (35/2π)^3/10(3c²₁)^−1/5^o², (2.6) where U∞ is the inflow speed, A is the swept area by the rotor, x₀ denotes the distance between the turbine and the origin of the wake which is located in front of the rotor and c₁ being a mathematical term without particular physical interpretation. The expression of x₀ is depending on C_T and T I and c₁ varies with x₀. The full expressions of c₁ and x₀ can be found in [11].

Figure 2.6 draws the wake losses, i.e. η_U(x, r) = 1 − (U∞+ dU (x, r))/U∞ in terms of x and r. In this case, C_T = 0.8 and T I = 0.05, these are typical values for an inflow speed of 7m/s in an offshore wind farm. It should be noted that Figure 2.6 is only a section of the wake in the longitudinal distance. The dark blue regions, i.e where the wake losses are zero, must be seen as the boundaries of the wake. One can actually get the conic form of the wake and observe that the radius expands with x while the wake losses in the middle of the wake decreases with x. Actually, given (2.5), the wake width, i.e. 2r_w(x), is expanding with a x^1/3 rate.

Figure 2.7 represents how the wake losses are varying over a section in the radial direction of Figure 2.6. In each plot some of the parameters are fixed. The fixed values are x = 5.34D, r = 0, T I = 0.05 and C_T = 0.8. The C_T values are derived from the thrust curve of the offshore Vestas V90-3MW turbine. From the left plots of Figure 2.7, it can be concluded that the wake width is increasing with T I, C_T and x. However, T I has more influence than the two others variables. From the right plots of the same figure,

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Figure 2.6: Wake loss profile downstream a wind turbine according to the Larsen model.

The colors are representing the magnitude of the wake losses η_U whose scale is given in the colorbar.

it looks like that the center line wake loss which is defined as η_U(x, 0) and corresponds to the maximal wake loss over the section, is decreasing hyperbolically with T I and x while it is varying parabolically with C_T. The center line wake loss is also referred as the wake depth. The observations made about the influence of x are in agreement that the ones made with Figure 2.6. The effects of the other variables are analyzed in the next paragraphs.

The reason why the wake depth is decreasing with T I is explained by the fact that when the atmosphere is very turbulent, i.e. T I is high, the atmospheric turbulences tend to cancel the turbulences created by the blade tip vortices. Nevertheless, even if a high turbulent atmosphere means lower wake losses and thus lower power losses downstream, it must be kept in mind that in this situation the loads on the downstream turbine will be higher and this will potentially affect its lifetime. Further downstream, this turbulent mixing is responsible of what is called a wake recovery. Since the flow gets very turbulent downstream, the wake losses between each turbine become close to zero or even negative meaning that the flow accelerates. This phenomenon has been studied by Göçmen in the Lillgrund farm. Figure 2.8 exposes the results of this analysis for a row of turbine where each point corresponds to the power losses at a specific turbine. One could actually observe that the power losses between the first and the second turbine is significant, and that there is a wake recovery between the second and the third one. The same study showed that the evolution of T I along a row of turbine is following the same trend than the one of the power losses.

Finally, to understand why the wake depth is varying parabolically with C_T, one has to go back to the meaning of CT. When CT is low, it means that the downstream flow is not diverging too much from the incoming inflow supposed uniform. This means that the rotative motion of the upstream turbine is not producing turbulences that could

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-300 -200 -100 0 100 200 300 0

0.2 0.4 0.6

0.2 0.4 0.6 0.8

0 0.2 0.4 0.6

-300 -200 -100 0 100 200 300

0 0.2 0.4 0.6

0.05 0.1 0.15 0.2

0 0.2 0.4 0.6

-300 -200 -100 0 100 200 300

0 0.2 0.4 0.6

1000 1500 2000 2500

0 0.2 0.4 0.6

Figure 2.7: The revised Larsen model (2009). Upper left plot: η_U(5.34D, r) in terms of T I. Upper right plot: η_U(5.34D, 0) in terms of T I. Middle left plot: η_U(5.34D, r) in terms of C_T. Middle right plot: η_U(5.34D, 0) in terms of C_T. Lower left plot: η_U(x, r).

Lower right plot: ηU(x, 0).

have modify the profile of the incoming flow. Therefore, the incoming flow downstream is close to the one that is felt upstream and consequently, the wake losses are small between the two turbines. In the opposite case where C_T is very high, the upstream turbine gives the downstream flow a profile that is deviating a lot from the one perceived in front of the rotor. This is resulting from the formation of the blade tip vortices that induce turbulences downstream. Hence a high C_T upstream can be associated to high T I downstream which tends to break the wake hence reducing the losses. However, there is a point at which the C_T is sufficiently high to modify significantly the flow downstream but not high enough such that turbulences dissipate the wake when hitting the downstream turbine. This explains why in the Larsen model, the wake depth is varying parabolically

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with C_T.

4.2. BENCHMARKING STUDY 44

0 5 10 15 20 25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Power Deficit = 1−Pwake/Pfree

Lillgrund Power Deficit in a Row, Spacing=3.3D, wdir=120°±2.5°, ws=9±0.5 m/s, TI=6 %

N.O. Jensen (BinAve) N.O. Jensen (GauAve) G.C. Larsen (BinAve) G.C. Larsen (GauAve) Fuga EllipSys3D RANS k−ε−f_p SCADA

0 5 10 15 20 25 30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Downstream Distance (D)

Lillgrund Power Deficit in a Row, Spacing=4.3D, wdir=222°±2.5°, ws=9±0.5 m/s, TI=6 %

(b) (a)

Figure 4.7: Lillgrund power deficit in a row with (a) 3.3D spacing and 120 ± 2.5 and (b) 4.3D spacing and 222 ± 2.5

are however designed to simulate the flow behaviour at much larger downstream dis- tances. On the other hand, as shown in Figure4.7(a), the wake deficit under-prediction is compensated with a good prediction for the following rows, especially for the Larsen model.

The models are shown to perform better for wider wind direction sectors in Lill- grund by Gaumond et al. [31]. In our case, the EllipSys3D RANS k e fP model over-performs to estimate the power deficit at the second wind turbine, because the fP

function delays the wake recovery compared to the standard k e model.

B2 - Speed Recovery In Figure 4.8, the recovery point is clearly seen at 16.5D for 120 ± 2.5 and 17.2D for 222 ± 2.5 . All the models capture the recovery and for this particular case the Larsen and the k e fP model seem to estimate the power production reasonably well, especially after the second turbine. Both the Jensen and the Larsen models produce better results with the post processing of the wind direction uncertainty using a Gaussian distribution, which was also the case in previous benchmark, B1. Fuga seems to over-predict the power production for the first downstream turbine and then

Figure 2.8: Wake recovery in Lillgrund (Figure courtesy of Tuhfe Göçmen [7])

2.5 Motivation for a revised possible power signal

Now that all the necessary scientific background has been presented, one can grasp why the current possible power signal in SCADA is failing to give accurate estimations when the wind farm is down-regulated.

First, it is important to give an accurate definition of the possible power of a wind farm. The possible power is the amount of power that can be produced by a wind farm given a wind profile and the fact that all the turbines are running in normal operation.

It means that if turbine is feeling a wind of U m/s at its location, the power produced by this turbine must be P (U ). In fact, P (U ) can be understood as the possible power of a turbine. Given that definition, the current way of calculating the possible power of the wind farm is simply to measure U at each turbine, get the turbine possible power with P (U ) and then sum all these to get the possible power of the farm. From its definition, it should be noted that in normal operation, the possible power is equal to the actual production of the wind farm. This means that during the normal operation, the wind farm does not have any power reserves.

But as explained earlier, wind farms can be asked to provide ancillary services. This consists in having some power reserves that are put aside so that if there is an outage from one of the generators in the electrical network, the TSO can use those reserves to compensate this abrupt decrease in power production and still meet the demand. In

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order to have some reserves from the wind farms, the operators are requested to perform a curtailment, also called a down-regulation. Nowadays, the usual practice to realize a curtailment is to decrease by a certain amount the power setpoint of all the turbines composing the farm. This amount is determined by the number of megawatts that the TSO wants to keep as a reserve.

When an artificial-upstream turbine is curtailed, it is not following the normal operation because the turbine is producing less than P (U ), namely what could have been possible to produce in normal operation. This operational change is responsible of a modification of the wake effects downstream that turbine. The reason for this is that in curtailment the pair (λ, θ) is set such that the aerodynamic torque is reduced leading to a drop in the power production, therefore the value of C_T(λ, θ) is modified and this affects the characteristics of the wake. Experiments in HornsRev I conducted by Göçmen showed that when an upstream turbine is curtailed, the wake losses downstream are reduced hence the wind speed increased and this results in an overestimation of the possible power downstream [7]. It should be noted that theoretically it is possible to diminish the wind speed downstream by curtailing the upstream turbine and thus having an underestimation in this case. Indeed, since the wake losses are varying parabolically with C_T, it might be that the value of C_T(λ, θ) in curtailment increases the wake losses.

However in practice, when curtailing a turbine, one tries to reduce the production while minimizing the loads and thus C_T(λ, θ) is moved to a small value for which the wake losses are reduced. Nevertheless, in both cases the current method of the estimation of the possible power would be wrong for the simple reason that the wind speed felt by a turbine in a curtailed wind farm is likely to be different if this same wind farm was in normal operation.

Recently, TSOs have expressed their willingness to harden the requirements regarding the quality of the possible power estimation as it impacts the quality of the estimation of the reserves. In Germany, a pilot phase will be launched in October 2017. During this phase, it will be asked to wind operators like Vattenfall to compare the actual production of the wind farm with the possible power estimation when the farm is operating normally. As expected in normal operation, the possible power must be equal to the actual production because the reserves are zero. But the TSO is asking that the estimation method of the possible power is taking wakes into account. Therefore, the current method cannot be used as it is for the moment. This pilot phase will last one month and the TSO will analyze the distribution of the 1-minute averaged estimation error.

In order to succeed the pilot phase, the requirements P (error_1min≤ 5%) ≥ 68.27% and P (error_1min ≤ 10%) ≥ 95.45% have to be fulfilled. After the pilot phase, these ones will be even stricter since it is assumed that operators will gain knowledge from each other and will be able to improve their method. They will become P (error_1min≤ 3.3%) ≥ 68.27%

and P (error_1min ≤ 10%) ≥ 99.73%. In Denmark, similar requirements are already effective. Danish TSO is asking for a possible power estimation whose the 15-minutes averaged estimation error must be in a 5% error band. Operators that do not meet this, can be penalized financially by paying fees to the TSO.

Apart from the fact that the current method fails to give proper estimates of the possible power, the experiments conducted in HornsRev I raised another interesting subject. According to these, reducing the power extraction at the upstream turbine

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increases the wind speed downstream. Therefore, one can legitimately wonder whether is it possible to increase the whole wind farm production by curtailing upstream turbines.

In the experiments, the curtailment strategy did not lead to an augmentation of the power produced but current researches like [10] are investigating more closely the question.

This topic will be briefly discussed in this thesis as it is not part of the assignment specifications.

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Chapter 3 The PossPOW algorithm

The PossPOW algorithm was developed at DTU between 2012 and 2015 by Tuhfe Göçmen during her PhD thesis. It was developed to give second-wise estimation of the possible power of down-regulated offshore wind farms. The general idea behind this algorithm is to estimate the wind speed at any location in the wind farm given an incoming wind profile as input and if all the turbines are in normal operation. The incoming wind profile is described by the estimated wind speed and wind direction at upstream turbines. Both estimations use operational data given by the SCADA system.

Using this wind profile, the wind speed in the whole farm is estimated using a wake model that returns the wake losses in normal operation. Then, a possible power estimation is eventually obtained with a wind-speed-to-power relationship, e.g a power curve or wind power equation (2.1). The PossPOW algorithm can be seen as an engineering wind farm wake model where operational data are used to estimate the wind speed in the whole wind farm during normal operation. It should be noted that the algorithm is working even if the farm is curtailed.

Figure 3.1 summarizes the workflow of the PossPOW algorithm. In the left block, the REW S which is the wind speed at the rotor scale is estimated using SCADA signals presented in Section 3.1. This block is described in Section 3.2. On the right, the W D estimation block refers to the method employed in Section 3.1 to correct the wind direction signals received from the SCADA system. The last two blocks of the diagram are detailed in Section 3.3 and 3.4 respectively. The algorithm is tested on real data and its performances are presented in Section 3.5. Finally, the validity of the algorithm is discussed in Section 3.6.

3.1 Data in wind power applications

The SCADA system installed inside the wind turbines allows to collect real time data.

A lot of signals that are employed for the control and the analysis of the turbine are recorded. In addition, it is also possible to gather information from the met(eorological) mast installed near the wind farm. Nevertheless, the PossPOW algorithm is not requiring to know the temperature inside the nacelle for instance. In reality, only the following available signals are of interest to estimate the possible power:

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SCADA

REW S estimation at upstream turbines

W D estimation at upstream turbines

Wind farm wake model

Wind speed to power

Possible power

Figure 3.1: Diagram of the PossPOW algorithm (adapted from [7])

• ActivePower, the electrical power in kW produced by the generator;

• ActivePowerSP, the electrical power setpoint in kW whose value is equal to P_rated in normal operation;

• AirDensity, the air density in kg/m³ measured at the met mast;

• BladePitchAngle, the pitch angle in degree of the rotor blades;

• NacelleDirection, the yaw angle in degree;

• RotorRPM, the rotational speed of the rotor in revolutions per minute;

• WindDirection, the wind direction in degree measured by the wind vane;

• WindSpeed, the wind speed in m/s measured by the anemometer, denoted N W S in this thesis.

Even though the PossPOW algorithm is meant to be used for 1-second data, the aforementioned signals are typically not recorded every second. In fact, for each signal, a new recording is done when the measured value changes by a magnitude superior than a given threshold which is specific to the nature of the signal. The advantage of this method is that it reduces considerably the number of data to store. But the drawbacks are that these signals are recorded at different times and the period during two measurements may be long. When retrieving data from the SCADA system, one can actually get values of a signal at each second but these are interpolated values, i.e if a signal was not recorded at specific time a linear interpolation between the two closest measurements is realized.

In this thesis, the PossPOW algorithm is tested on past data of Thanet. The recorded period starts at 22:00 on the 28^th January 2017 and ends at 12:00 the next day. Each

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signal is retrieved with a 1-second time period. This dataset presents the advantage to have a wind direction varying around the 209^◦ direction and a wind speed below U_rated. Therefore, it is convenient to study the wake effects with it. In the following, this dataset is referred as Thanet209. A reduction of this dataset to selected turbines is called Thanet209red. It includes data from turbines A01, A02, A03, B01, B02, B03, C01, C02,

D01, D02, E01 thus 11 turbines on the 100 installed.

Before exploiting those data, it is necessary to preprocess them. This mainly consists in converting the data in the units of interest and removing wrong measurements tagged by an error code. Nevertheless, the NacelleDirection and WindDirection signals demand more attention. Indeed, those signals can present a significant bias in their values. This originates from the fact that both measurements are defined according to a 0^◦ direction like the one represented in 2.5. Nowadays, the current practice is to define this one as the direction from north to south. Therefore, the measurement tool in the turbines needs to track the north. However, this is made complicated by the magnetic interactions coming from the large generators of the neighboring turbines [13]. To remove this bias, it is proposed to analyze the wake losses between an upstream and a downstream turbine [21].

Indeed, it is known that the wake losses are maximal when the two turbines are aligned and the direction that aligns the turbines is given by the farm layout. For instance, if one wants to calibrate the WindDirection signal of turbine A03, one can look at the wake losses between A03 and B03 which are known to be maximal for a direction of 209^◦. Then by observing for which wind direction the maximal wake losses are currently happening, one can estimate the bias in the signal. It may be easier to determine this last direction by looking at a filtered version of the signal. In the following, whenever a signal is mentioned as filtered, the considered filter is a Savitsky-Golay filter with a window length of 61 seconds and an order 3, unless stated otherwise. As it will be demonstrated later, this calibration is applicable only for upstream turbines. This procedure is summarized in Figure 3.2 where a bias of 3.5^◦ is discovered.

200 205 210 215 220 225

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

Raw data SG-3 data (60sec)

3.5 degrees

Figure 3.2: Calibration of the WindDirection at turbine A03

Once the bias has been identified, it can be removed from the WindDirection signal as well as the NacelleDirection signal since the yaw angle is supposed to follow the wind

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direction. Nevertheless as it will be mentioned further in the thesis, the uncertainty in the WindDirection values can go up to 5^◦ that which makes its use not cautious. On the other hand, the recording frequency of the NacelleDirection signal is relatively high and the time between two measurements can extend to 30 minutes. Hence a compromise has to be found to determine the wind direction. Here, it is proposed to define the wind direction (W D) as the filtered and unbiased version of the original WindDirection signal.

3.2 Estimation of the rotor effective wind speed

The estimation of the wind speed is an essential step in the calculation of the possible power as it is placed at the top of the algorithm diagram. Therefore, important efforts have to be done to get an accurate estimation of the wind speed.

As indicated in Section 2.1, wind turbines are equipped with an anemometer. This anemometer measures the wind speed at a specific location of the rotor area. However, using this measurement has to be avoided for several reasons. First of all, the anemometer is subjected to a lot of turbulences. Indeed, in many wind turbines such as the Vestas V90-3MW, the anemometer is placed on the top of the nacelle that is located downstream the rotor. This means that the anemometer is located in the near wake region and thus exposed to high turbulences. The consequence is that the N W S signal is highly volatile and therefore, uncertain. Second, this signal refers to a point-wise measurement but the wind speed field at the rotor surface is far from being uniform as stated in [16]. It follows that when one wants to compute the possible power of a wind turbine, it is not cautious to use the N W S because of its uncertainty and its misrepresentation of the wind speed at the rotor scale. This explains why manufacturers are using 10-minutes averaged N W S data to estimate the power curves.

This calls for a method to estimate the wind speed. This method must return an estimation that could be used as an input of a power formula. This supposes that the estimation must be closed to the averaged wind speed profile hitting the rotor surface.

As mentioned before when using (2.1) or the power curve, it is implicitly assumed that U is the REW S. Namely, the averaged wind speed profile on the whole rotor area. In the following, for aesthetic reasons, U denotes the REW S and u, the N W S.

This assumption has lead Göçmen to use P , ρ, θ, ω signals to compute U as the solution of (2.1). Using the definition of the tip-speed ratio λ = ωR/U , one can rewrite (2.1) as

P −1 2ρ C_P

ωR U , θ

πR²U³ = 0 (3.1)

and find U with a root-finding algorithm. The value of the corresponding u available from the SCADA system can be used as an initial guess for the algorithm. However, as mentioned earlier, the table C_P(λ, θ) is not available. To solve this issue, the table is

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approximated by the analytical function C_P(λ, θ) = c₁

c₂ λi

− c₃θ − c₄θ^c⁵ − c₆

exp

−c₇ λi

, and

λ_i =

1 λ + c₈θ

−

c9

θ³+ 1

⁻¹ (3.2)

where the values of the coefficients c₁ to c₉ are given in [7]. The advantage of this method is that it can be used either for down-regulated or normal operation. Obviously, this method is not applicable when the turbine is not producing. In that case, one can estimate the wind speed with u.

It is worth mentioning that U cannot be computed with P (U ). Similarly to the previous method, it cannot estimate the wind speed when the turbine is not running but most important, when the wind speed is above the rated speed, the method fails to estimate correctly the wind speed. This is explained by the fact that above the rated wind speed, the power is maintained constant, making the power curve not invertible in this wind speed range. Furthermore, this method cannot be applied to curtailed turbines since in this case the turbine are following a non-optimal power curve.

Figure 3.3: Validation of the REW S estimation of turbine A01 on October 16^th 2016.

Upper plot: Comparison of two estimation and one measurement methods of the wind speed. P CW S refers to the power curve method. Lower plot: Operational state of the turbine.

The quality of the estimation by (3.1) together with (3.2) has already been demonstrated in [7] and it is confirmed again with the results in Figure 3.3. Indeed, it shows the

Implementation and Validation of Algorithm forEstimating the Possible Power of Curtailed Wind Turbines Exposed to WakeEffects

Implementation and Validation of Algorithm for Estimating the

Possible Power of Curtailed Wind Turbines Exposed to Wake Effects

LOÏC DEFOUR

Implementation and Validation of Algorithm for Estimating the Possible Power of Curtailed

Wind Turbines Exposed to Wake Effects

LOÏC DEFOUR

Abstract

Abstract

Acknowledgements

Table of Contents

List of Figures

List of Tables

Chapter 1 Introduction

1.1 Background

1.2 Assignments and scope

1.3 Outline

Chapter 2

Wind power fundamentals

2.1 General properties of a wind turbine

2.2 Control strategies of a variable-speed variable- pitch wind turbine in normal operation

2.3 Presentation of a wind farm

2.4 The wake effects

2.5 Motivation for a revised possible power signal

Chapter 3

The PossPOW algorithm

3.1 Data in wind power applications

3.2 Estimation of the rotor effective wind speed