Power optimization of wind turbines with data mining and evolutionary computation

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Renewable Energy 35 (2010) 695–702

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Renewable Energy

journal homepage: www.elsevier .com/locate/renene

Power optimization of wind turbines with data mining andevolutionary computation

Andrew Kusiak*, Haiyang Zheng, Zhe SongDepartment of Mechanical and Industrial Engineering, The University of Iowa, 3131 Seamans Center, Iowa City, IA 52242-1527, United States

a r t i c l e i n f o

Article history:Received 8 July 2009Accepted 25 August 2009Available online 17 September 2009

Keywords:Wind turbineData miningNeural networksOptimizationEvolutionary computation algorithms

* Corresponding author.E-mail address: [email protected] (A. Ku

0960-1481/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.renene.2009.08.018

a b s t r a c t

A data-driven approach for maximization of the power produced by wind turbines is presented. Thepower optimization objective is accomplished by computing optimal control settings of wind turbinesusing data mining and evolutionary strategy algorithms. Data mining algorithms identify a functionalmapping between the power output and controllable and non-controllable variables of a wind turbine.An evolutionary strategy algorithm is applied to determine control settings maximizing the poweroutput of a turbine based on the identified model. Computational studies have demonstrated meaningfulopportunities to improve the turbine power output by optimizing blade pitch and yaw angle. It is shownthat the pitch angle is an important variable in maximizing energy captured from the wind. Poweroutput can be increased by optimization of the pitch angle. The concepts proposed in this paper areillustrated with industrial wind farm data.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

The U.S. wind power market is rapidly expanding; however,operations and maintenance costs [20,21] may create a barrier to aneven more rapid expansion [23].

The capital and operating investments in wind power can bereduced in various ways. In fact, the wind energy industry islooking for novel ways of reducing costs. Examples of areas wherethe cost could be reduced include: site selection for wind farms,layout design, and predictive maintenance [11,13,14,20,21,24]. Thesite selected and layout design of a wind farm could extend thelifetime of turbines as well as increase wind energy production.The turbine stress level could be reduced, resulting in a lesser loadon mechanical components, including a gearbox, which is expen-sive to maintain and replace.

Another meaningful way to reduce costs is to optimize thecapture of energy from the wind with effective control strategies[1,3,6,15–18,30]. Such an optimization should be performedwithout adverse effect on the lifetime of turbine components, e.g.,the gearbox. Wind turbine technology is relatively new, and there isplenty of room to improve the performance of wind turbines in thepresence of operations and maintenance constraints. Maximizingthe energy captured from the wind makes wind energy morecompetitive in the overall energy portfolio.

siak).

All rights reserved.

The theoretical wind energy captured by the rotor of a windturbine is computed from Eq. (1) [1,3]:

Pr ¼ 0:5rpR2Cpðl;bÞv3 (1)

where Pr is the wind energy captured by the rotor, r is the air density,R is the rotor radius, and n the wind speed. The parameter Cp is calledthe rotor power coefficient, and it depends on the blade pitch angleb and the tip-speed ratio l determined from Eq. (2) [1,3]:

l ¼ urRv

(2)

where ur is the rotational speed of the rotor.The literature on optimization of the power coefficient Cp is

quite extensive. It is widely accepted that Cp has a uniquemaximum Cp,opt with the corresponding values of bopt and lopt.Since l is a function of ur, it is obvious that given the wind speedan optimal rotor speed ur,opt is attained. The most recent researchon optimal control of wind turbines can be found in [1,3,6,15–18,22,30]. Simple maximum power tracking algorithms are dis-cussed in [3,6]. Control models of simultaneous power and torqueoptimization are presented in [1,3,17]. Pitch and yaw angle areimportant in wind turbine control as they impact the efficiency opower generation. Optimal control strategies are needed toincrease the power produced by individual wind turbines and theentire wind farm.

There are several potential drawbacks in the traditional controlapproaches for maximization of the energy captured from the

A. Kusiak et al. / Renewable Energy 35 (2010) 695–702696

wind. First, Cp is assumed to have a unique maximum and b is fixedat its optimal value bopt. This assumption excludes the opportunityto modify b for power optimization. Second, in Eq. (1), Pr is thepower captured by a rotor, not the power output from the turbine.As the models Pr and Po are derived from different principles,maximizing Pr does not guarantee maximum Po. Third, winddirection is not even considered in the wind energy captureequation (1). It is always assumed that the wind is blowingorthogonally to the rotor. Finally, the wind speed n in Eq. (1) isassumed to be computed as a spatial average in a three-dimen-sional field. In practice n is usually provided by an anemometerinstalled at the nacelle or from a meteorological tower. In addition,various wind turbine measurements are affected by a multitude oferrors.

In this paper, a new data-driven approach for maximization ofenergy produced by a wind turbine is presented. This approach isnot affected by traditionally made assumptions and modelsimplifications. The data-driven method identifies the wind turbinepower generation process from the actual process data. The iden-tified process model is tested with actual data to determine modelaccuracy. Such a model allows optimizing wind turbine perfor-mance. The data-driven approaches usually offer limited insightsinto the modeled phenomena. In many cases it can be integratedwith traditional approaches.

2. Problem formulation and methodology

The power generation process of a wind turbine can be repre-sented as a triplet (x,n,y,), where x ˛Rk is a vector of k controllablevariables, e.g., yaw angle, blade pitch angle; v ˛Rm is a vector of mnon-controllable variables (measurable), e.g., wind speed, winddirection (measured by the anemometer); y ˛R is the power output(electricity produced). The value of the power output changes inresponse to controllable and non-controllable variables. Thecontrollable and non-controllable variables are considered in thisresearch as input variables. The underlying relationship is repre-sented as y¼ f(x,v) where f(�) is a function capturing the process ina steady state that is changing in time. Finding optimal controlsettings is formulated as a constrained single-objective y optimi-zation model shown in Eq. (3).

maxx

y

s:t:x˛Sy ¼ f ðx; vÞ

(3)

In the model (3) S is a feasible search space. In many industrialapplications, the non-controllable variables v, the underlyingfunction f(�), and the search space S are time dependent. Once theoptimal vector xopt is determined, it is applied to the wind turbineto achieve the maximum power output.

Modeling wind turbines offer flexibility in considering variablesas controllable and non-controllable. For example, althougha generator speed is usually controllable, it is conceivable thata system with the fixed generator speed could be analyzed.

Finding optimal control settings maximizing wind turbinepower output poses technical challenges. The first one is to derivean analytical accurate model f(�)mapping the input of controllableand non-controllable variables into the power output. Without anaccurate and robust analytical model f(�), it is difficult to solvemodel (3) with traditional optimization techniques. The secondchallenge is that the function f(�) could be non-stationary, andtherefore it needs to be updated to remain valid.

Data mining is an emerging science that has found successfulapplications in many areas [12,19]. Data mining algorithms providea viable alternative for identifying process models from large

volumes of process data. The function f(�) can be identified withdata mining algorithms. An obvious advantage of the data-drivenapproach is that f(�) can be easily and timely updated with newprocess data. Thus, a more accurate control of the wind turbine forpower maximization is guaranteed. Kelouwani and Agbossou [25]used a neural network to identify a wind turbine system to predictthe power output. In this paper, data mining algorithms other thanneural networks, such as the classification and regression tree [5],boosting tree [8,9], and support vector machine regression [4,26],are used to identify the function f(�). It needs to be stressed that f(�)identified by data mining algorithms usually does not have ananalytical form. To efficiently solve model (3), an evolutionarystrategy algorithm [7] is presented.

Fig. 1 illustrates the basic concept used in this paper. A datamining algorithm is used to identify the power generation modelbased on the process data stored in the database. The model can beupdated to reflect the process change over time. The updatefrequency could be, e.g., 2 weeks. Alternatively, a separate routinecould monitor the model performance and refresh the model onceits performance would degrade. The evolutionary strategy algo-rithm generates optimal control settings based on this model.

3. Evolutionary strategy algorithm

The model f(�) identified from wind turbine data may not havean analytical form. For example, f(�) may be represented by a set ofrules, have a tree structure, or be represented as a neural network.The models considered in this paper are not suitable for optimi-zation by gradient optimization algorithms as no explicit modelexists. For this reason, the evolutionary strategy algorithm has beenselected.

The ith individual in the evolutionary strategy is defined as(xi,si), where xi and si are two vectors with k entries, i.e.,xi ¼ ðxi

1;.; xikÞ

T , si ¼ ðsi1;.; si

kÞT . Here i denotes the individual

number of the candidate solution, and k indicates the dimension-ality of the vectors used to represent the individuals (candidatesolutions). Each element of si is used as a standard deviation ofa normal distribution with zero mean. si is used to mutate thesolution xi.

The basic steps of the evolutionary strategy algorithm are [7]:

1: Initialize mParent individuals (candidate solutions) to form theinitial parent population.

2: Repeat until stopping criteria are satisfied (here the maximumnumber of generations).

2.1 : Select and recombine parents from the parent pop-ulation to generate mChild offspring (children).

2.2 : Mutate the mChild children.2.3 : Select the best mParent individuals from the population

of children and parents based on the values of thefitness function.

2.4 : Use the selected mParent children as parents for the nextgeneration.

Given the current status (x,v) of a wind turbine, the initialpopulation xi (i¼ 1,.,mParent) is generated by uniformly sampling inthe neighborhood of x, i.e., x�Dx, where Dx is the neighborhoodsize set for a particular application. The initial populationsi(i¼ 1,.,mParent) is generated by uniformly sampling from therange [slow, sup], where slow and sup are the lower and upperbounds of the standard deviation vector. The fitness value of eachindividual is calculated by the identified process model f(xi,v). Anindividual with high fitness value (i.e., high power output) isconsidered for the next generation. The controllable variable x maydenote pitch angle, yaw angle, or both. If x is the pitch angle, the

Wind turbine

Data mining algorithms

Identified model

Evolutionary strategy algorithm

Database of process variables

Optimal pitch angle and nacelle direction

10-minute average data, e.g., wind

speed and direction

Update the process model

using new process data

Recommendoptimal settings

10-minuteaverage

turbine data

Fig. 1. Optimization framework.

A. Kusiak et al. / Renewable Energy 35 (2010) 695–702 697

yaw angle becomes a non-controllable variable and it is incorpo-rated in v.

3.1. Mutation

An individual (Si,si) is mutated by the Eqs (4) and (5), with si

mutated first, xi mutated next.

si ¼ si1�

eNð0;s0ÞþN1ð0;sÞ;.; eNð0;s0ÞþNkð0;sÞ�

(4)

where N(0,s’) is a random number drawn from the normal distri-bution with a 0 mean and standard deviation s’;Nj(0,s) (j¼ 1.k) isa random number drawn from the normal distribution with a meanof 0 and standard deviation s;Nj(0,s) is generated specifically for sj

i,while N(0,s’) is for all entries, and ‘‘1’’ denotes the Hadamardmatrix product [29].

The new solution is generated from Eq. (5).

xi ¼ xi þ N�

0;si�

(5)

where N(0,si) is a vector of the same size as xi. Each element ofN(0,si) is generated from a normal distribution with a mean 0 andthe corresponding standard deviation from vector si.

3.2. Selection and recombination of parents

To generate mChild children, two parents are selected from theparent population and recombined l times. Assume each time twoparents are selected randomly to produce an offspring from Eq. (6): P

i˛SeletedParents xi

2;

Pi˛SeletedParents si

2

!(6)

SelectedParents is a set including the two indices of therandomly selected parents.

3.3. Children selection

The selection process in the evolutionary strategy algorithm issimple. Once the mChild children are generated, they join the mParent

parents. Then, the best mParent individuals from the total population(mParent parents and mChild children) are selected based on the fitnessfunction value. This selection process ensures that the best indi-viduals are selected to make solutions of the next generation.

4. Industrial case study

To test the methods presented in this paper, data from theSupervisory Control and Data Acquisition (SCADA) system ofindustrial wind turbines was used. The SCADA system collects dataon more than 120 parameters and stores it at 10-min intervals(referred to as the 10-min average data). As all turbines of the windfarm are identical, three wind turbines were randomly selected forin-depth analysis. However, the approach presented in this paperapplies to any turbine equipped with actuators of any type. Topreserve the wind farm’s anonymity, the power measured at eachturbine was scaled to the interval [0,100], which can be interpretedas the turbine power range, e.g., [0 kW, 1000 kW].

Table 1 characterizes the historical data of the three selectedturbines used in this research. The time stamp is either the starttime or end time of each data subset. Each turbine data set isdivided into two subsets with the time sequence preserved. Thetraining subset is used to identify the quasi-steady state model f($),and then the test subset is used to validate the accuracy of theidentified model. All data points are 10-min average values, and thedata sets have been denoised by removing some abnormal points,e.g., those corresponding to the wind turbine being down or thenegative power output.

In this case study, the wind turbine power output y is modeledas a function of variables (x1,x2,v1,v2,v3,v4)defined in Table 2. Thereare two controllable variables and four non-controllable variablesin this case study. By solving model (3), the optimal control settings

Table 1The data set characterization.

Turbine No. Training data set Test data set

1 12/1/2006 0:00 AM,12/23/2006 3:10 AM,2940 data points

12/23/2006 3:20 AM,12/31/2006 11:50 PM,1200 data points

2 12/1/06 0:00AM,12/23/06 7:40 PM,3000 data points

12/23/06 7:50 PM,12/31/2006 11:50 PM,1102 data points

3 12/1/06 0:00AM,12/23/06 6:30 AM,2939 data points

12/23/06 6:40 AM,12/31/2006 11:50 PM,1176 data points

Table 3Prediction accuracy of different algorithms for the test data set.

Algorithm Mean absoluteerror (kW)

Absolute errorstd (kW)

Mean relativeerror (%)

Relative errorstd (%)

Turbine 1C&R Tree 5.853 8.111 11.137 13.712Boosting Tree 3.615 4.246 8.286 8.714SVM 2.662 1.751 8.541 8.253NN 1.285 1.035 3.495 4.688

Turbine 2C&R Tree 6.662 8.050 12.174 13.226Boosting Tree 3.750 4.595 8.192 8.951SVM 2.452 1.951 7.940 10.970NN 1.292 1.126 3.312 5.852

Turbine 3C&R Tree 5.767 7.867 11.618 13.374Boosting Tree 3.322 4.247 8.229 9.073SVM 2.576 1.603 8.622 8.283NN 1.244 1.004 3.495 4.688

A. Kusiak et al. / Renewable Energy 35 (2010) 695–702698

for blade pitch angle and yaw angle are obtained, and thus thepower output is optimized based on the current wind speed,generator speed, wind direction, and the wind direction difference.As the available SCADA data from the wind farm is 10-min averagedata, the evolutionary strategy algorithm recommends the optimalpitch angle and yaw angle every 10 min. If more frequent data (e.g.,10-s) would be available control setting could be updated accord-ingly. However, the update frequency is determined by the appli-cation at hand and the corresponding data support.

4.1. Data mining algorithms for learning process models

Different data mining algorithms have been used to extract themodel y¼ f(x1,x2,v1,v2,v3,v4) from the training subset in Table 1 foreach turbine. Then data points in the test subset in Table 1 weretested for each turbine’s identified model. In this paper, fourdifferent algorithms were used to learn (identify) the model of eachturbine. They include the classification and regression tree (C&RTree) [5], boosting tree regression [8,9], support vector machineregression (SVM) [4,26], and neural network (NN) [2,10]. Inparticular, 100 NN models with different kernels and structureswere built in this research, and the most accurate and robust modelwas selected to construct f(�). Neural networks are suitable formodeling complex non-linear processes. In this research, two typesof neural networks have been used, the radial-basis-function (RBF),and the multi-layer perceptron (MLP) network. Five different acti-vation functions were selected for the hidden and output neurons,namely, the logistic, identity, tanh, exponential, and sine functions.The number of hidden units was set between 5 and 20 and theweight decay for both hidden and output layer varied from 0.0001to 0.001.

Two main metrics are used to measure performance of themodels learned by data mining algorithms, absolute error andrelative error. The absolute error [kW] reflects the differencebetween the predicted and observed values, while the relative errorshows the percentage change in the performance. Table 3summarizes the prediction performance of process models learnedby different data mining algorithms. The neural network (NN)algorithm performed best among the four data mining algorithms,while the C&R tree performance was the least favorable. The NN

Table 2Process variables used for building wind turbine power optimization model.

Variable Name Unit

x1 Blade pitch angle �

x2 Yaw angle �

v1 Wind speed m/sv2 Wind direction �

v3 Generator speed rpmv4 Wind direction difference �

y Wind turbine power output kW

algorithm provided high quality predictions for the test data setsand captured the system dynamics with high fidelity. The bestperforming NN determined in this research is the MLP NN with 6-16-1 structure, and the logistic activation function for both hiddenand output neurons.

Table 3 show that the model built on historical data has stableperformance for the three turbines of Table 1 and is valid for futuredeployment. However, updating the learned model with the newdata is necessary for a process that is temporal. The temporalprocess modeling task is accomplished by using data miningalgorithms. A large prediction error (absolute and relative error)indicates that the model built on historical data needs to beupdated. It is hard to determine the exact update cycle time as it isimpacted by various factors, e.g., the wind pattern. For the exper-iment based on the test data for the three turbines of Table 1 themodel turn out to be valid for at least one week.

The absolute error in Table 3 is the difference between the valuepredicted by the model and the observed one. The mean absoluteerror is the average absolute error for the data in the test data. Theabsolute error std is the standard deviation of the absolute errorover the test data set. The relative error is the absolute error dividedby the observed value. In the case of power prediction, the observedvalue acts as the weight in the relative error formula, i.e., identicalabsolute errors produced at two different power levels lead to small(large power) and large (small power) relative errors. The absoluteerror is expressed in kW, which is a widely used metric in windindustry. The relative error indicates how good a prediction isrelative to the value of the parameter being predicted, and it isexpressed as %. While the absolute error is more important formodel evaluation, the relative error indicates performance of thetrained model.

4.2. Parameters of the evolutionary strategy algorithm

Once the power generation model of a wind turbine is identi-fied, the evolutionary strategy algorithm is applied to solve theoptimization problem in Eq. (3).

An evolutionary strategy (ES) algorithm involves a set ofparameters requiring tuning, such as population size, selectionpressure (the ratio between the parent population size and thechildren population size), i.e., mParent/mChild. To heuristically deter-mine parameters for the ES algorithm, numerous experiments wereperformed to determine the impact of the population size and theselection pressure. In this paper s’ is set to 0.5, and s is set to 0.59,based on the computational experience reported in [7].

71.5

72

72.5

73

73.5

74

74.5

1 16 31 46 61 76 91 106 121 136 151 166 181 196

Pow

er (

kW)

Generation Number

µ parent / µ children = 15/45

µ parent / µ children = 15/100

µ parent / µ children = 15/300

µ parent / µ children = 15/600

µ parent / µ children = 15/3000

Fig. 2. Solving model (3) at ‘‘12/23/06 11:30’’ for fixed parent population size andvariable selection pressure.

A. Kusiak et al. / Renewable Energy 35 (2010) 695–702 699

Fig. 4 shows the results of model (3) solved by the ES algorithmfor different selection pressures using a test data point at thesampling time ‘‘12/23/06 11:30 AM’’. The maximum turbine poweroutput is plotted for each generation. The power output increasesas the number of generations increases, and it converges toa plateau after dozens of generations. In Fig. 2 it is easy to see thatthe selection pressure mParent/mChild is an important parameter in theconvergence of the ES algorithm to the maximum power output.

To best selection pressure is determined based on the compu-tational time and the convergence speed is largely decided by thenumber of children. Therefore, a tradeoff between the two isusually considered. For any of the selection pressures in Fig. 2, themaximum power is attained; however, the computational effortdiffers. For mParent¼ 15,mChild¼ 600, the ES is most efficient, whileother selection pressures are more time consuming due to either anincrease in the number of offspring mchild or in the number ofgenerations needed to converge. Although the previous research[7] suggests a good selection pressure mParent/mChild¼ 1/7, numerousexperiments were conducted, and it was determined that mParent/mChild¼ 15/600 performs well, and 100 generations are sufficient forthe algorithm to converge to the local optimal.

Fixing the selection pressure at mParent/mChild¼ 0.025 andincreasing the number of parents mParent allow the impact of thepopulation size on the final solution to be observed. Fig. 3 illustratesthat increasing the population size does not significantly impactthe performance of the ES algorithm once the selection pressure isfixed. However, as the number of parents mParent increases, thechances of having a better initial solution increase, but thecomputational time increases with the population size. Numerous

71.5

72

72.5

73

73.5

74

74.5

1 16 31 46 61 76 91 106 121 136

Pow

er (

kW)

Generation Number

µ parent / µ children = 15/600

µ parent / µ children = 25/1000

µ parent / µ children = 35/1400

µ parent / µ children = 45/1800

Fig. 3. Solving model (3) at ‘‘12/23/06 11:30’’ for fixed value of selection pressure andvariable population size.

experiments have been performed, and it was determined thatsetting the number of parents at mParent¼ 35 is the best tradeoff.With the increase of the initial parent population (greater than 35),no significant improvement in the quality of the solutions isattained despite the increase in the computational time.

4.3. Results and discussion of power optimization

To evaluate the potential for developing a supervisory controlsystem further maximizing the energy captured from the wind,each data point in the test set is optimized. In other words, for eachdata point in the test data set, model (3) is solved to find optimalcontrol settings (i.e., pitch angle, yaw angle) providing maximumpower output without changing the values of non-controllablevariables. For example, assume that for a test data point[y(t),x1(t),x2(t),v1(t),.,v4(t)] at sampling time t, both the yaw angleand pitch angle are to be optimized, x1

*(t) and x2*(t) are the optimal

solutions of model (3), where x1*(t) is the optimal yaw angle and

x2*(t) is the optimal blade pitch angle. If the yaw angle and the blade

pitch angle are simultaneously optimized, then y(t) andy*(t)¼ f(x1

*(t),x2*(t),v1(t),.,v4(t)) are compared to evaluate a power

gain (PG) y*(t)�y(t), where y*(t) is the optimal power output.Based on the comparison of the four data mining algorithms, NN

is selected to construct f(�) using the training data set in Table 1. Asthe three turbines are identical with a similar power generationprocess, turbine 1 was selected as a representative to perform theexperiments discussed in the next sections. Once the function f(�) islearned by the NN algorithm, model (3) can be solved for all 1200data points in the test set of turbine 1 in Table 1. The parameters ofthe ES algorithm are set as mParent/mChildren¼ 35/1400 and thenumber of generations is fixed as 100.

4.3.1. Simultaneous optimization of blade pitch angle and yawangle

To simultaneously optimize blade pitch angle and yaw angle,model (3) is instantiated as model (7). Based on analysis ofhistorical data, the range of controllable variables is limited, i.e.,x1˛[�20�,�16�]and x2˛[100�,220�].

maxx1 ;x2

y

s:t:ðx1; x2Þ˛Sy ¼ f ðx; vÞ

(7)

Fig. 4 shows the results for the first 105 test data points in Table1 optimized with model (7). It is easy to note that with the opti-mized blade pitch angle and yaw angle, a potential for significantpower gains emerges.

0

20

40

60

80

100

1 11 21 31 41 51 61 71 81 91 101

Pow

er (

kW)

Time (10 minute interval)

Optimal power Original power

Fig. 4. Power produced with the optimized blade pitch and yaw angle vs the originalpower.

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16

Pow

er (

kW)

Wind speed (m/s)Optimal power Original power

Fig. 5. Power curve produced with the optimized blade pitch and yaw angle vs theoriginal power curve.

0102030405060708090

100

0 2 4 6 8 10 12 14 16

Pow

er (

kW)

Wind speed (m/s)Optimal power Original power

Fig. 7. Power curve for the optimized blade pitch vs the original power curve.

A. Kusiak et al. / Renewable Energy 35 (2010) 695–702700

Fig. 5 shows the original and optimized power curves plotted forthe entire test data set of Table 1. It is clearly seen that the opti-mized blade pitch angle and yaw angle have lifted up the originalpower curve. This indicates that, for a given wind speed, the windturbine power output can be increased by adjusting the yaw andthe blade pitch to their computed settings. The turbine hardwarereaction time for a pitch angle is definitely faster than that of theyaw angle. In the experiments considered in the paper, computingthe optimal control setting values consumes about 3 s. The dataused for research in this paper is 10-min average SCADA data. Ifmore frequent data (e.g., 10-s) is available, the non-controllableparameters in different time scales could be analyzed. The conceptdemonstrated is the paper is scalable to different frequency data.

The next two sections report results of sensitivity analysis. InSection 4.3.2, it is assumed that a yaw angle is not controllable andonly the blade pitch is optimized. In Section 4.3.3, the blade pitch isassumed to be non-controllable and the yaw angle is optimized.

4.3.2. Optimization of blade pitch angleTo find an optimal blade pitch angle, model (3) is instantiated as

model (8) with x1˛[�20�,�16�]. Variable x2 is incorporated into vand it does not change during the optimization process.

maxx1

y

s:t:x1˛Sy ¼ f ðx; vÞ

(8)

Fig. 6 shows the power optimized with model (8) for the first105 test data points of Table 1. When only the blade pitch angle isoptimized, the potential for power gain is significant. Fig. 7 illus-trates the original and the optimized power curves for the total testdata set of Table 1 when only the blade pitch angle is optimized.The original power curve can be shifted upwards.

0102030405060708090

100

1 11 21 31 41 51 61 71 81 91 101

Pow

er (

kW)

Time (10 minute intervals)Optimal power Original power

Fig. 6. Power produced with the optimized blade pitch vs the original power.

4.3.3. Optimization of yaw angleTo find an optimal yaw angle, model (3) is instantiated as model

(8) for x2˛[100�,220�]. The yaw angle is the nacelle directionmeasured by a sensor, usually a vane. Variable x1 is incorporatedinto v and it does not change during the optimization process.

maxx2

y

s:t: x2˛Sy¼ f ðx; vÞ

(9)

Fig. 8 shows the power optimized with model (9) for the first105 test data points of Table 1. Optimizing the yaw angle does notproduce significant power gains. Fig. 9 shows the original and theoptimized power curves generated from the entire test data set ofTable 1 when only the yaw angle is optimized. Only limited powergains can be observed in Fig. 9.

To summarize, the power gains achieved by the three differentoptimization models, (7), (8), and (9), and six metrics, (10) though(15), are defined. The following parameters are used by thesemetrics:

� NTest is the number of test data points� Test is the set containing all time stamps of the test data points� y(t) is the original (measured) power output of a wind turbine� y*(t) is the wind turbine power output optimized with either

optimal blade pitch angle, yaw angle, or both. Note that theoptimal power output is obtained from the data-driven model.

Mean PG ¼ 1NTest

Xt˛Test

�y*ðtÞ � yðtÞ

�(10)

0

20

40

60

80

100

1 11 21 31 41 51 61 71 81 91 101

Pow

er (

kW)

Time (10 minute interval)

Optimal power Original power

Fig. 8. Power produced with the optimized yaw angle vs the original power.

Table 4Power gains summary for different optimization models.

ModelNo.

Mean PG(kW)

Std PG(kW)

Mean relativePG (%)

RelativeStd (%)

Total PG(kW)

Total relativePG (%)

7 7.519 9.231 22.698 37.654 8279.214 14.6548 6.212 7.821 17.414 25.527 6826.481 12.0839 1.329 6.397 2.608 15.687 1463.817 2.591

A. Kusiak et al. / Renewable Energy 35 (2010) 695–702 701

Std PG ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1NTest � 1

Xt˛Test

�y*ðtÞ � yðtÞ �MeanPG

�2s

(11)

Mean relative PG ¼ 1NTest

Xt˛Test

y*ðtÞ � yðtÞyðtÞ � 100% (12)

Wind speed.

7

8

9

10

11

12

13

14

Win

d sp

eed

(m/s

)

Time (10-minute interval)

Original and optimal pitch angle.

-26

-24

-22

-20

-18

-16

Pitc

h an

gle

(°)

Time (10 minute interval)Original pitch angle Optimal pitch angle

1 9 17 25 33 41 49 57 65 73 81 89 97

1 9 17 25 33 41 49 57 65 73 81 89 97

a

b

Relative Std ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

NTest � 1

Xt˛Test

�y*ðtÞ � yðtÞ

yðtÞ � 100%�Mean relative PG�2

vuut (13)

Total PG ¼X

t˛Test

�y*ðtÞ � yðtÞ

�(14)

Total Relative PG ¼ Total PGPt˛Test

yðtÞ � 100%

The simulation results presented in Table 4 demonstrate that thethree optimization models perform well and offer the potential toimprove the wind energy capture. Optimizing two turbineparameters (yaw direction and blade pitch) simultaneouslyproduces the largest power gains. On average 7.519 kW (out ofthe max of 100 kW) additional power can be produced based on thetest data set of turbine 1 in Table 1 (see Model 7 in Table 4). Theblade pitch angle (see Model 8 in Table 4) is an important param-eter of optimization. In the case of Model 9 in Table 4, when onlythe yaw angle is optimized, model (9) only achieves a mean relativepower gain of 2.608%. Note all the PG metrics in Table 4 arecalculated based on the power scaled into the range [0 kW,100 kW]. Considering the NN prediction error, the power gain couldbe smaller than reported in Table 4. For example, Model 9, opti-mizing the yaw angle results in the power gain of 2.591% which iswithin the uncertainty interval of the NN prediction error (i.e.,4.688%).

Fig. 10(a) illustrates the first 100 values of the wind speed fromthe test data set for Turbine 1 of Table 1.Fig. 10(b) to 10(c) show theoptimal and original pitch angle, and the yaw angle, respectively forModel 7. The original settings are from the historical data, and theoptimal settings are computed by the evolutionary strategy algo-rithm. As the torque and other factors are not considered, it ispossible that not all gains from the optimized pitch and yaw angle

0

20

40

60

80

100

0 2 4 6 8 10 12 14 16

Pow

er (

kW)

Wind speed (m/s)

Optimal power Original power

Fig. 9. Power curve for the optimized yaw angle vs the original power curve.

could not be realized or some significant gains could be missed dueto low (10 min) frequency data. However, demonstrating thatimpact of the two parameters on the power output is of importanceto performance studies.

Original and optimal yaw angle.

-145

-140

-135

-130

-125

-120

-115

1 9 17 25 33 41 49 57 65 73 81 8 9 97

Yaw

ang

le (

°)

Time (10 minute interval)Original yaw angle Optimal yaw angle

c

Fig. 10. Optimal and original control settings of Model 7; (a) Wind speed; (b) Originaland optimal pitch angle; (c) Original and optimal yaw angle.

A. Kusiak et al. / Renewable Energy 35 (2010) 695–702702

The potential power gain that can be accomplished with theapproach proposed in this paper should be of great interest to thewind industry. It is reported that at least 1% energy loss fora 400 MW wind farm is worth $1 million [27,28]. The benefits of thepotential gain (up to a 14.7% power increase) reported in this paperwould be enormous. Even a portion of these gains would translateinto increased profitability of wind energy, thus making it a morecompetitive alternative to combustion energy.

5. Conclusion

In this paper, a framework for optimization of the powerproduced by wind turbines was presented. The proposed controlapproach generated optimized settings of the blade pitch and yawangle. The novelty of the proposed approach is in the seamlessintegration of data mining and evolutionary computation. Datamining algorithms identified a power generation model from theactual turbine data. Then an evolutionary strategy algorithm solvedthe optimization model to find the optimal settings of the controlparameters. The simulation results based on the historical SCADAdata showed a significant potential for improvement of the windturbine power output across the entire operational range of windspeeds. Since the data used was averaged over 10-min intervals,there was no need to consider operational constraints typicallyassociated with higher frequency data.

The optimization approach presented applies to all turbines ofa wind farm, and can be extended to other industrial processes. Theresearch reported in this paper can also be used as a basis for thedevelopment of predictive control and predictive maintenancemodels for wind turbines. The business impact of the approachdeveloped in this research on the wind industry could be significant.

Other data mining algorithms and computational intelligenceconcepts could be used to enhance the accuracy and robustness ofthe power enhancement model. In future research, additionalcontrol or non-controllable variables will be considered. Once therelevant data becomes available, additional insights could begained.

Acknowledgement

The research reported in this paper has been supported byfunding from the Iowa Energy Center, Grant No. 07-01.

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