Optimization of wind turbine energy and power factor with

lable at ScienceDirect

Energy 35 (2010) 1324–1332

Contents lists avai

Energy

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

Optimization of wind turbine energy and power factor with an evolutionarycomputation algorithm

Andrew Kusiak*, Haiyang ZhengDepartment of Mechanical and Industrial Engineering, 3131 Seamans Center, The University of Iowa, Iowa City, IA 52242-1527, USA

a r t i c l e i n f o

Article history:Received 10 August 2009Received in revised form13 November 2009Accepted 17 November 2009Available online 30 November 2009

Keywords:Wind turbinePower factorPower outputPower qualityData miningNeural networkDynamic modelingMulti-objective optimizationEvolutionary computation algorithm

* Corresponding author. Tel.: þ1 319 3355934; fax:E-mail address: [email protected] (A. Ku

0360-5442/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.energy.2009.11.015

a b s t r a c t

An evolutionary computation approach for optimization of power factor and power output of windturbines is discussed. Data-mining algorithms capture the relationships among the power output, powerfactor, and controllable and non-controllable variables of a 1.5 MW wind turbine. An evolutionarystrategy algorithm solves the data-derived optimization model and determines optimal control settings.Computational experience has demonstrated opportunities to improve the power factor and the poweroutput by optimizing set points of blade pitch angle and generator torque. It is shown that the pitch angleand the generator torque can be controlled to maximize the energy capture from the wind and enhancethe quality of the power produced by the wind turbine with a DFIG generator. These improvements are inthe presence of reactive power remedies used in modern wind turbines. The concepts proposed in thispaper are illustrated with the data collected at an industrial wind farm.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Distributed energy generation is becoming prevalent in theenergy market, especially with the rapid expansion of alternativeenergy [1,2]. This newly distributed generation creates challengesrelated to power quality [3–5]. The power quality issue can beaddressed at the wind turbine or the wind farm level. This paperfocuses on a single generator, which is fundamental to powerquality improvement at the aggregate level.

Numerous metrics are used to measure the power quality ofa wind turbine, the most common of which are power factor,reactive power, and harmonic distortion. As the generation of windenergy on an industrial scale is relatively new, the area ofimprovement in power quality remains open. Tapia et al. [3] pre-sented a control strategy for reactive power control of a wind farm,including double-fed induction generators, and thus the voltagelevel control of distribution network was improved. Harmonicsgenerated by the interactive wind and photovoltaic hybrid powersystem were investigated by Giraud and Salameh [6]. Muljadi andMcKenna [7] analyzed the power quality issues in a hybrid power

þ1 319 3355669.siak).

All rights reserved.

system involving wind turbines and diesel generators. Ko and Jat-skevich [8] discussed modeling and control of a wind-hybrid powergeneration system to enhance power quality. In their simulationstudy, a fuzzy-LQR (linear-quadratic regulator) controller wasshown to be effective against disturbances caused by the windspeed and load variations.

Maximizing the power capture from the wind is one of the maindrivers in the design of the wind turbine control system. Boukhezzaret al. [9] proposed a non-linear approach to control a variable-speedturbine to maximize power in the presence of generator torqueconsiderations. Datta and Ranganathan [10] developed a searchalgorithm to track the peak power points for variable-speed windturbines. Munteanu et al. [11] applied a linear-quadratic stochasticapproach to solve the power optimization model, and tested it usingan electromechanical wind turbine simulator. A trade-off betweenthe efficiency of energy conversion and input variability was studiedin the simulation experiments. Muljadi and Butterfield [12] devel-oped a pitch control strategy to maximize power and minimizeturbine loads for different wind speed scenarios.

Data mining is an emerging science that has found successfulapplications in various areas including manufacturing [13,14],marketing [15,16], medical informatics [17], and energy [18–21].Evolutionary computation is a powerful tool for solving complexoptimization models. Successful applications of evolutionary

mailto:[email protected]

www.sciencedirect.com/science/journal/03605442

http://www.elsevier.com/locate/energy

Fig. 1. Active power, power factor, and wind speed plot for a wind turbine: (a) powerfactor, (b) active power, (c) wind speed.

Table 1Variables used for dynamic modeling of wind turbines.

Variables Description Unit

v Wind speed m/sx1 Blade pitch angle �

x2 Generator torque %y1 Active power kW

y2 Power factor No unit

y3 Rotor speed rpm

Table 2Description of the data set.

A. Kusiak, H. Zheng / Energy 35 (2010) 1324–1332 1325

computation algorithms have also been reported in a variety ofdomains [22–25].

In this paper, data mining and evolutionary computation areintegrated to optimize the power factor and the amount of powerproduced by a wind turbine. Data-mining algorithms identifydynamic models from a large volume of the SCADA (SupervisoryControl and Data Acquisition) wind farm data collected, and anevolutionary computation algorithm is then applied to solve the bi-objective power optimization model.

As most wind farms are relatively new, it is natural that theirperformance has not been adequately studied. Prediction of thepower produced by a wind farm at different time scales is ofinterest to the electricity grid.

DataSet

Start Time Stamp End Time Stamp Description

1 7/01/08 12:00 AM 7/31/08 11:50 PM Total data set; 4466observations

2 7/01/08 12:00 AM 7/24/08 12:00 PM Training data set; 3457observations

3 7/25/08 12:10 AM 7/31/08 11:50 PM Test data set; 1009observations

2. Problem formulation and methodology

2.1. Power optimization problem formulation

The theoretical wind energy captured by the rotor of a windturbine is computed from Eq. (1) [9,26]:

Pr ¼ 0:5rpR2Cpðl;bÞv3b (1)

where Pr is the wind energy captured by the rotor, r is the airdensity, R is the rotor radius, and vb is the wind speed beforepassing the rotor. The parameter Cp is the power coefficient thatdepends on the blade pitch angle b and the tip-speed ratio l

determined from Eq. (2) [10,27]:

l ¼ urRvb

(2)

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

quite extensive. The values of bopt and lopt maximize the powercoefficient Cp,opt. Since l is a function of ur, it is obvious that thereexists an optimal rotor speed ur,opt.

Maximization of the power extracted from the wind calls foroptimal control settings of the wind turbine parameters. However,optimization of the power alone does not necessarily guarantee thequality of the power generated by the wind turbine. Power qualityis measured by different metrics, e.g., power factor, harmonicdistortion, and transient overvoltage. In this paper, the definition ofthe power factor provided in Eq. (3) [26,27] is used as the primarymetric of power quality.

PF ¼ PS

S2 ¼ P2 þ Q2

P ¼ Sjcosfj(3)

where PF is the power factor, P is the active power measured inWatts (W), S is the apparent power measured in volt-amperes (VA),Q is the reactive power measured in reactive volt-amperes (VAr),and f is the phase angle between the current and the voltage andmeasured in degrees (�).

True power factor measures the efficiency of electric powerutilization, and the goal for wind turbine control is to maintaina power factor of 1. However, the power factor of wind turbines isdifficult to control, and thus its value is frequently lower than 1 forindividual wind turbines and wind farms.

In this paper, optimization of the active power and the powerfactor by supervisory control of a wind turbine is pursued. The plotsof active power, the power factor, and the wind speed of a turbineover a 36-hour time period are shown in Fig. 1(a) through Fig. 1(c).The wind speed during this time period is in the range of 2–7 m/s(considered here as a low wind speed scenario). At times the value ofthe power factor and the active power are low. A well designed

Table 3Performance of the models learned by different algorithms.

Parameter Algorithm MAE Std Maximum Minimum

Active Power (kW) C&R Tree 48.27 60.42 331.13 0.01SVM 84.32 56.15 713.11 0.25NN 2.39 3.53 67.91 0.00

Power Factor C&R Tree 8.92 9.36 70.85 0.01SVM 8.76 9.22 80.91 0.00NN 1.39 2.52 29.00 0.00

Rotor Speed (rpm) C&R Tree 0.54 0.63 6.90 0.00SVM 0.73 0.77 5.22 0.00NN 0.13 0.21 1.03 0.00

Table 4Sensitivity analysis of the MLP NN model for training data set of Table 2.

Active Power Power Factor Rotor Speed

Parameter Sensitivity Parameter Sensitivity Parameter Sensitivity

y1(t�1) 3.72 y2(t�1) 89.77 y3(t�1) 58.31x1(t) 283.46 x1(t) 140.99 x1(t) 194.72x1(t�1) 1.57 x1(t�1) 30.70 x1(t�1) 11.07x2(t) 622.49 x2(t) 127.24 x2(t) 87.57x2(t�1) 219.89 x2(t�1) 25.90 x2(t�1) 20.63v1(t) 3.42 v(t) 45.44 v(t) 30.37v(t�1) 2.97 v(t�1) 10.84 v(t�1) 12.17

A. Kusiak, H. Zheng / Energy 35 (2010) 1324–13321326

turbine controller could boost the active power and at the same timeimprove the power factor.

2.2. Dynamic modeling of wind turbines

The power generation process of a 1.5 MW wind turbine witha DFIG generator can be represented as a triplet (x,v,y), where xeRm

is a vector of m controllable variables, e.g., blade pitch angle and

Fig. 2. The bar chart of performance of models extracted by different data-miningalgorithms: (a) active power, (b) power factor, (c) rotor speed.

generator torque; veRk is a vector of k non-controllable (measur-able) variables, e.g., wind speed and wind direction; yeRl is a vectorof l system response (corresponding) variables, e.g., active power,power factor, and rotor speed. The value of y changes in response tothe controllable and non-controllable variables.

Table 1 lists the variables of the wind turbine considered in thispaper that were computationally selected based on their signifi-cance using the approach presented in [19]. The data used in thisresearch is 10-minute average data collected by SCADA systems of1.5 MW wind turbines. The cut-in, cut-out, and rated wind speed is3.5, 20, and 12.5 m/s, respectively. In the range of wind speedsreflected in the available SCADA data, the blade pitch angle changesin the interval [-2, 85�]. Based on the turbine specifications, thegenerator torque ranges within [0, 100%], and its maximum changerate is 40%, while the active power is in the interval [0, 1600 kW].The power factor changes within [0, 1] (no unit), and the rotorspeed range is [0, 23 rpm].

The energy conversion process of a wind turbine can expressedas y¼ f(x,v), where f(�) is the process function of the controllable (x)

Fig. 3. The low and high wind speed scenarios: (a) Low wind speed scenario in thetime window 7/25/08 12:00 AM to 7/26/08 1:00 AM, (b) High wind speed scenarios inthe time window 7/27/08 4:30 AM to 7/28/08 5:30 AM.

Table 5The optimization results for different weights of a low wind speed scenario.

Weight Active Power (kW) Power Factor

Mean Std Mean Std

w ¼ 1 429.77 149.59 80.19 12.72w¼ 0 387.65 146.12 85.73 8.25w¼ 0.5 391.79 152.12 85.72 8.23


and non-controllable (v) variables. To optimize the power producedand its quality, the functionf(�) needs to capture the dynamicprocess of a wind turbine, which is challenging. Dynamic modelinghas been applied in control and engineering systems, chemistry,economics, and ecology [28,29]. A process, including the windenergy conversion, can be considered as a dynamic Multi-Input-Single-Output (MISO) system. The dynamic models for activepower, power factor, and rotor speed are expressed in Eqs. (4)–(6).

y1ðtÞ¼ f1ðy1ðt�1Þ;x1ðtÞ;x1ðt�1Þ;x2ðtÞ;x2ðt�1Þ;vðtÞ;vðt�1ÞÞ (4)



where y1(t) is the active power at time t, and y1(t�1)is the activepower at time t�1, which is 10 minutes before time t. The functionsf1(�), f2(�) and f3(�) capture the mapping between the variableslisted in Table 1. The three dynamic MISO models (Eqs. (4)–(6)) ofa wind turbine are extracted by a data-mining algorithm from theSCADA data.

The selection of an appropriate data-mining algorithm forbuilding dynamic models (Eqs. (4)–(6)) is critical. Two basic

Fig. 4. The optimization results for different weights of a low wind speed scenario: (a)active power, (b) power factor.

metrics, the MAE (mean absolute error) and Std (standard deviationof absolute error) are used to compare and validate the perfor-mance of various data-mining algorithms and models. The AE(absolute error), MAE, and Std are expressed in Eqs. (7)–(9).

AE ¼��by � y

�� (7)

MAE ¼

XN

i¼1

AEðiÞ

N(8)

Std ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN

i¼1

ðAEðiÞ �MAEÞ2

N � 1

vuuuut(9)

where N is the number of test data points used to validate theperformance of the dynamic MISO model, by is the predicted valueof a variable, andy is the observed value of a variable, e.g., the activepower, the power factor, and the rotor speed listed in Table 1.

The small values of the MAE and Std imply superior perfor-mance of the corresponding model.

2.3. The bi-objective power optimization model

In this paper, two objectives, active power and power factor, areoptimized. Assuming x1ðtÞ and x2ðtÞ are the optimal settings forthe blade pitch angle and the generator torque at time t, theoptimal active power and the power factor are expressed inEqs. (10) and (11).

y�1ðtÞ ¼ f1�

y1ðt� 1Þ;x*1ðtÞ;x1ðt� 1Þ;x*

2ðtÞ;x2ðt� 1Þ; vðtÞ; vðt� 1Þ�

(10)

y�2ðtÞ ¼ f2�

y2ðt� 1Þ;x*1ðtÞ;x1ðt� 1Þ;x*

2ðtÞ;x2ðt� 1Þ; vðtÞ; vðt� 1Þ�

(11)

where y1ðtÞ is the optimal active power at time t, and y2ðtÞ is theoptimal power factor at time t. As the value of the power factorshould be as close as possible to one, jy*

2ðtÞ � 1j is minimized. Tomaximize the power output, jy*

1ðtÞ � 1600j is minimized. The twoobjective functions of the power output and quality are expressedin Eqs. (12) and (13):

Jpower ¼��y*

1ðtÞ � 1600�� (12)

Jpf ¼ jy�2ðtÞ � 1j (13)

where Jpower is the objective function corresponding to the poweroutput, and Jpf is the objective function corresponding to the powerfactor. To balance the two objectives in Eqs. (12) and (13), theweighing scheme of Eq. (14) is used.

J ¼ wJpower

1600þ ð1�wÞJpf (14)

where w is the weight coefficient in the interval [0, 1]. To avoid theweight bias, the two objective functions need to be scaled to theinterval [0, 1]. This is accomplished by dividing the value of Jpower by1600 as shown in Eq. (14). Since the power factor value is in therange [0, 1], Jpf of Eq. (13) does not need to be scaled.


Several constraints need to be taken into account to compute theoptimal control settings of a wind turbine. First, the turbine powershould be within [0, 1600 kW], and thus 0 � y�1ðtÞ � 1600 should besatisfied. Second, Betz’s law [36] needs to be obeyed. Based on theprevious research [30], the turbine power output y1 should besmaller than 2.625v3. Eq. (12) is then transformed into Eq. (15).

Jpower ¼��y�1ðtÞ �min

n1600;2:625vðtÞ3

o�� (15)

There are also several constraints related to the rotor speed, theblade pitch angle, and the generator torque. The maximum rotorspeed is 23 rpm, and thus 0 � y3ðtÞ � 23 has to be satisfied. As thegenerator torque is limited to 100%, and its change rate should bebelow 40%, the following two constraints hold: 0 � x*

2ðtÞ � 100 andx*

2ðtÞ � x2ðtÞ � 40. According to the historical SCADA data, the pitchangle is mostly operated within the range [- 2�, 85�]. Thus anadditional constraint for pitch angle needs to be satisfied:�2 � x*

1ðtÞ � 85.

Fig. 5. The optimization results for low wind speed scenario with the weight w¼ 0.5: (a)original blade pitch angle, (d) Optimal vs original generator torque, (e) Optimal vs original

Based on the above discussion, a bi-objective wind turbinepower optimization strategy at sampling time t can be instantiatedas model (16).

minx*

1ðtÞ;x*2ðtÞ

Jð�Þ

subjectto

y*1ðtÞ¼ f1

�y1ðt�1Þ;x*

1ðtÞ;x1ðt�1Þ;x*2ðtÞ;x2ðt�1Þ;vðtÞ;vðt�1Þ

�y*

2ðtÞ¼ f2�y2ðt�1Þ;x*


�y*



�y*

1ðtÞ�minn

1600;2:625vðtÞ3o

0�y*2ðtÞ�1

0�y*3ðtÞ�23

�2�x*1ðtÞ�85

0�x*2ðtÞ�100;

��x*2ðtÞ�x2ðtÞ

��40 ð16Þ

Optimal vs original active power, (b) Optimal vs original power factor, (c) Optimal vsrotor speed.

Table 6The optimization results for different weights of a high wind speed scenario.

Weight Active Power (kW) Power factor

Mean Std Mean Std

w¼ l 1151.54 123.64 95.58 3.13

w¼ 0 1108.69 123.33 96.36 2.80w¼ 0.5 1121.08 123.26 96.31 2 77

Fig. 6. The optimization results for different weights of a high wind speed scenario: (a)active power, (b) power factor.


Solving optimization model (16) is challenging. The modelsidentified from SCADA data may not have an analytical form, e.g.,f(�) is represented by a set of rules, a tree, or a neural network. Forthis reason, an evolutionary strategy algorithm [1,38,39] has beenselected to search the optimal settings for the pitch angle andgenerator torque of wind turbines.

Model (16) is transformed into the standard bi-objective form(17) with the inequality constraints placed in the objective function.

minx*

1ðtÞ;x*2ðtÞfObj1;Obj2g

subjectto

y*1ðtÞ¼ f1

�y1ðt�1Þ;x*


�y*



�y*



��2�x*

1ðtÞ�85

0�x*2ðtÞ�100;

��x*2ðtÞ�x2ðtÞ

��40 ð17Þ

where

Obj1 ¼ J and Obj2 ¼ maxn

0; y�1ðtÞ �minn

1600;2:625vðtÞ3oo

þmaxf0; y�2ðtÞ � 1g þmaxf0; y�2ðtÞ � 23g

The objectiveObj2 attaining zero implies that all constraints aresatisfied.

To solve the bi-objective optimization model, an evolutionarystrategy algorithm [17,30,31] is used. The stopping criterion used inthis algorithm is the number of generations. To simplify compara-tive analysis, some parameters of the evolutionary strategy algo-rithm are fixed; for example, the number of generations is 50 andthe tournament size is set to 4. Numerous experiments have beenperformed to evaluate the impact of the weight used in theobjective function of model (17) on the quality of the solutions. Theexperiments have confirmed that w¼ 0.5 improves the powerfactor and at the same time maximizes the power output.

3. Wind turbine modeling

3.1. Data description

To test the dynamic modeling methods presented in this paper,data from the Supervisory Control and Data Acquisition (SCADA)system of industrial wind turbines was used. The SCADA systemcollects data on more than 100 parameters and stores it at ten-minute intervals (referred to as the 10-minute average data). As allturbines of the wind farm are identical, one wind turbine wasrandomly selected for in-depth analysis. However, the approachpresented in this paper applies to any turbine.

Table 2 provides a description of the data from a turbine selectedin this research. Data set 1 in Table 2 begins at ‘‘7/01/08 12:00 AM’’and ends at ‘‘7/31/08 11:50 PM.’’ During this time period, theturbine performance was normal. Data set 1 was divided into twosubsets, data set 2 and data set 3. Data set 2 contains 3457 time-consecutive data points and was used to develop models with data-mining algorithms. Data set 3 includes 1009 time-consecutive data

points and was used to test the performance of the models learnedfrom data set 2.

3.2. Dynamic models extracted by the data-mining algorithms

Three different data-mining algorithms were used to extract thewind turbine models (Eqs. (4)–(6)) from the training data set ofTable 2. Each of the three identified models was validated on thetest data set of Table 2. The three data-mining algorithms consistedof the classification and regression tree (C&R Tree) [32,33], supportvector machine regression (SVM) [34,35], and neural network (NN)[15,36]. The C&R tree builds a decision tree to predict classes(classification) or Gaussians (regression). The SVM is a supervisedlearning algorithm used in classification and regression. Itconstructs a linear discriminant function separating instances(examples) as widely as possible. The NN algorithms are usuallyused in non-linear regression and classification due to their abilityto capture complex relationships among parameters. Here, 100 NNmodels with different kernels and structures were built, and themost accurate and robust one was selected to construct f(�). Twotypes of neural networks were used, the radial-basis-function(RBF), and the multi-layer perceptron (MLP) NN. Five differentactivation functions were selected for the hidden and outputneurons, namely, the logistic, identity, tanh, exponential, and sinefunctions. The number of hidden units was set between 5 and 20,and the weight decay for both the hidden and output layer variedfrom 0.0001 to 0.001.

Table 3 summarizes the prediction accuracy of models learnedby three different data-mining algorithms using two metrics, MAE(Eq. (8)) and Std (Eq. (9)). Note that the power factor originally inthe range [0, 1] has been scaled to the range [0, 100] (multiplied by100). The bar charts of Figs. 2(a) through 2(c) illustrate graphicallythe performance of the three data-mining algorithms. The neuralnetwork (NN) algorithm performed best among the three

Fig. 7. The result of bi-objective optimization with w¼ 0.5 weight scheme for a high wind speed scenario: (a) Optimal vs original active power, (b) Optimal vs original power factor,(c) Optimal vs original blade pitch angle, (d) Optimal vs original generator torque, (e) Optimal vs original rotor speed.


algorithms, as it has the smallest MAE and Std for the active power,power factor, and rotor speed models. The NN algorithm capturedthe wind turbine dynamics with high fidelity.

The best performing NN for maximization of the active powerwas the MLP NN with a 7-19-1 structure, with logistic and identityactivation functions for hidden and output neurons, respectively.For the power factor, the MLP NN with a 7-20-1 structure per-formed best. This NN had a tanh activation function for the hiddenneurons and logistic activation function for the output neurons. Forthe rotor speed, the best NN had the 7-20-1 structure with thelogistic activation function for both hidden and output neurons.Large values of MAE and Std for the test data set indicate that thedynamic models may need to be refreshed by the data from themore recent time period, which can be easily accomllished. For theexperiments based on the test data of Table 2, the models turnedout to be accurate for at least one week.

The sensitivity of an output to its input perturbation is animportant issue in neural networks [36]. Table 4 shows the sensi-tivity analysis of the three dynamic models built by the MLP NNalgorithms based on the training data set of Table 2. The parameters

have different sensitivity ranks in the three models; however, thepitch angle x1(t) and the generator torque x2(t) rank as the top twoimportant parameters of the models for active power, the powerfactor, and the rotor speed. The sensitivity analysis shows that theset values of x1(t) and x2(t) significantly impact the correspondingvariables (y1(t),y2(t),y3(t)) of a wind turbine.

4. Bi-objective power optimization

Wind speed is a significant parameter impacting control andperformance of a wind turbine. In the case study reported in thissection, two different wind speed scenarios are considered in thebi-objective power optimization model. The plots of the windspeed for each of the two scenarios (low and high wind speed) areshown in Figs. 3(a) and 3(b), respectively. The test data for each ofthe two wind speed scenarios was selected from Table 2, with eachset containing 150 time-consecutive data points. Three typicalvalues of the weight w of Eq. (14) are considered for both low andhigh wind speed scenarios.


For each data point of the two wind scenarios (see Fig. 3), model(17) is solved to find optimal control settings of pitch angle andgenerator torque. For example, assume that for a data point[y1(t),y1(t�1),y2(t),y2(t�1),y3(t),y3(t�1),x1(t),x1(t�1),x2(t),x2(t�1),v(t),v(t�1)] at sampling time t, pitch angle x*

1ðtÞ and generator torque x*2ðtÞ

are the optimal solutions of model (17).

4.1. Low wind speed scenario

Three schemes of the weight w in the objectiveJ ¼ wJpower

1600 þ ð1�wÞJpf are considered for the low wind speedscenarios. In the first scheme, the weight w is set to 1, which impliesoptimization of the power output without considering the powerfactor. In the second scheme, w¼ 0, the power factor is emphasizedwhile the power output maximization is ignored. The final schemeis one where w¼ 0.5 and both the power output and power factorare considered.

The mean and Std (standard deviation) of the active power andpower factor of the 150 time-consecutive data points in the lowwind speed scenarios have been used as metrics of performance ofdifferent weight schemes. Table 5 compares the active power andthe power factor before and after bi-objective optimization forthree different values of the weight w. Note that the power factorhas been rescaled to the range [0, 100] (multiplied by 100). Themean of active power before optimization was 276.09 kW with theStd of 234.35 kW. The mean power factor before optimization was56.27 with the Std of 22.67.

The results in Figs. 4(a) and 4(b) illustrate the best trade-offbetween the two objectives are accomplished for the weight w¼ .5,with the power output and the power factor improved. The powerfactor produced is almost the same as whenw¼ 0, while the poweroutput is only slightly smaller than whenw¼ 1.

Figs. 5(a) to 5(e) plot five wind turbine parameters before andafter the optimization forw¼ 0.5. It is clearly seen that the opti-mized blade pitch angle and the generator torque have increasedthe original active power (see Fig. 5(a)). In the low wind speedscenario illustrated in Fig. 5(b), the power factor could be enhancedsignificantly, and the optimized power factor is much closer to one.In Fig. 5(c), the original pitch angle seems almost constant in thelow wind speed scenario, while the optimal one trends the windspeed change. The other parameters show different behavior aswell.

4.2. High wind speed scenario

The previously introduced weight schemes are used in a highwind speed scenario. Table 6 compares the active power and powerfactor before and after optimization for the high wind speedscenario. The results depend on the weight scheme. Note that thepower factor originally with range [0, 1] has been scaled to therange [0, 100] (multiplied by 100). The mean of the active powerbefore optimization is 1000.05 kW, and the Std is 126.91 kW. Themean of the power factor before optimization is 92.36, and the Stdis 4.98.

Figs. 6(a) and 6(b) depict the performance of the bi-objectivepower optimization for three weights. The two optimizationobjectives, the power output and the power factor, may conflictwith each other. The w¼ 0.5 weight scheme is the best amongthree different weight schemes tested, as its power factor optimi-zation result is almost the same as forw¼ 0, while the maximizedpower output is slightly smaller than forw¼ 1.

To illustrate the bi-objective power optimization results withaw¼ 0.5 weight scheme, the plots in Figs. 7(a) to 7(e) illustrateoriginal and optimized active power, the power factor, the bladepitch angle, the generator torque, and the rotor speed of the wind

turbine for a high wind speed scenario. There is an increase in thepower produced for the high wind speed scenario (see Fig. 7(a)).Though the original power factor in Fig. 7(b) is close to one, it can befurther improved and smoothed. The other parameters, in partic-ular the blade pitch angle, show different behavior as well.

The benefits of the bi-objective optimization for the high andlow wind speed scenarios are clearly visible in the results reportedin this paper. The potential power output and power factor gainsthat can be accomplished with the approach proposed in this papershould be of interest to the wind industry. It has reported that a 1%energy loss for a 400 MW wind farm may be worth, e.g., $1 millionper year [39].

5. Conclusion

An approach for optimization of power factor and the powerproduced by wind turbines was presented. The priority betweenthe two objectives is established by weights. Gains in the powerproduced and its quality measured with the power factor arereported. The proposed approach generated optimized settings ofthe blade pitch angle and the generator torque. The novelty of theproposed approach is in the seamless integration of data miningand evolutionary computation. Data-mining algorithms identifieddynamic process models for power output, the power factor, andthe rotor speed of a wind turbine from the actual wind farm data.Then an evolutionary strategy algorithm solved the bi-objectiveoptimization model with constraints to find the optimal settings ofthe pitch angle and generator torque. The simulation results basedon the historical SCADA data showed significant potential forimprovement of power produced by a wind turbine and the powerfactor in high and low wind speed scenarios.

The optimization approach presented applies to wind turbinesand can be extended to other industrial processes. The power factorimprovement enhances the efficiency of the electricity powerutilization, mitigates the power harmonic distortion and transientovervoltage, and extends the life of the wind turbine electronicsand electrical components. The active power objective maximizesthe power captured from the wind and thus increases theproductivity of the wind farm.

The research reported in this paper can be used as a basis for thedevelopment of predictive control and predictive maintenancemodels for wind turbines. Additional constraints and objectivescould be considered in the optimization model. In future research,an expanded set controllable or non-controllable variables will beconsidered once the relevant data becomes available.

Acknowledgement

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

References

[1] Hvelplund F. Renewable energy and the need for local energy markets. Energy2006;31:2293–302.

[2] Migoya E, Crespo A, Garcıa J, Moreno F, Manuel F, Jimenez A, et al. Comparativestudy of the behavior of wind-turbines in a wind farm. Energy 2007;32:1871–85.

[3] Tapia A, Tapia G, Ostolaza JX. Reactive power control of wind farms for voltagecontrol applications. Renewable Energy 2004;29:377–92.

[4] Dittrich A, Hofmann W, Stoev A, Thieme A. Design and control of a windpower station with double fed generator. 7th European Conference on PowerElectronics and Application 1997;2:723–8.

[5] Jangamshetti SH, Guruprasada Rau V. Normalized power curves as a tool foridentification of optimum wind turbine generator parameters. IEEE Trans-actions on Energy Conversion 2001;16:283–8.


[6] Giraud F, Salameh ZM. Measurement of harmonics generated by an interactivewind/photovoltaic hybrid power system. Electric Power Components andSystems 2007;35:757–68.

[7] Muljadi E, Mckenna HE. Power quality issues in a hybrid power system. IEEETransactions on Industrial Applications 2002;38:803–9.

[8] Ko H, Jatskevich J. Power quality control of wind-hybrid power generationsystem using fuzzy-LQR controller. IEEE Transactions on Energy Conversion2007;22:516–27.

[9] Boukhezzar B, Siguerdidjane H, Maureen Hand M. Nonlinear control of vari-able-speed wind turbines for generator torque limiting and power optimiza-tion. ASME Transactions: Journal of Solar Energy Engineering 2006;128:516–30.

[10] Datta R, Ranganathan VT. A method of tracking the peak power points fora variable speed wind energy conversion system. IEEE Transactions on EnergyConversion 2003;18:163–8.

[11] Munteanu I, Cutululis NA, Bratcu AI, Ceanga E. Optimization of variable speedwind power systems based on a LQG approach. Control Engineering Practice2005;13:903–12.

[12] Muljadi E, Butterfield CP. Pitch-controlled variable-speed wind turbinegeneration. IEEE Transactions on Industry Applications 2003;37:240–6.

[13] Backus P, Janakiram M, Mowzoon S, Runger GC, Bhargava A. Factory cycle-timeprediction with data-mining approach. IEEE Transactions on SemiconductorManufacturing 2006;19:252–8.

[14] Kusiak A, Zheng HY, Song Z. On-line monitoring of power curves. RenewableEnergy 2009;34:1487–93.

[15] Tan PN, Steinbach M, Kumar V. Introduction to data mining. Boston, MA:Pearson Education/Addison Wesley; 2006.

[16] Berry MJA, Linoff GS. Data mining techniques: for marketing, sales, andcustomer relationship management. 2nd ed. , New York: Wiley; 2004.

[17] Seidel P, Seidel A, Herbarth O. Multilayer perceptron tumor diagnosis based onchromatography analysis of urinary nucleoside. Neural Networks2007;20:646–51.

[18] Kusiak A, Zheng HY, Song Z. Models for monitoring of wind farm power.Renewable Energy 2009;34:583–90.

[19] Kusiak A, Song Z, Zheng H-Y. Anticipatory control of wind turbines with data-driven predictive models. IEEE Transactions on Energy Conversion2009;24:766–74.

[20] Hoogwijk M, van Vuuren D, de Vries B, Turkenburg W. Exploring the impacton cost and electricity production of high penetration levels of intermittentelectricity in OECD Europe and USA. Energy 2007;32:1381–402.

[21] Yurdusev MA, Ata R, Çetin NS. Assessment of optimum tip speed ratio in windturbines using artificial neural networks. Energy 2006;31:2153–61.

[22] Eiben AE, Smith JE. Introduction to evolutionary computation. New York:Springer-Verlag; 2003.

[23] Benini E, Toffolo A. Optimal design of horizontal-axis wind turbines usingblade-element theory and evolutionary computation. Journal of Solar EnergyEngineering 2002;124:357–63.

[24] Grady SA, Hussaini MY, Abdullah MM. Placement of wind turbines usinggenetic algorithm. Renewable Energy 2005;30:259–70.

[25] Thilagar SH, Rao GS. Parameter estimation of three-winding transformersusing genetic algorithm. Engineering Applications of Artificial Intelligence2002;15:429–37.

[26] Bianchi FD, De Battista H, Mantz RJ. Wind turbine control systems: principles,modeling and gain scheduling design. 1st ed. London, UK: Springer; 2006.

[27] http://en.wikipedia.org/wiki/Power_gain.[28] Hannon B, Ruth M. Dynamic modeling. 2nd ed. New York: Springer-Verlag; 2000.[29] Kulalowski BT, Gardner JF, Shearer JL. Dynamic modeling and control of

engineering systems. 1st ed. New York: Cambridge University Press; 2007.[30] Zitzler E, Thiele L. Multi-objective evolutionary algorithms: a comparative

case study and the strength Pareto approach. IEEE Transactions on Evolu-tionary Computation 1999;3:257–71.

[31] Bell B. Individual wind turbine and overall power plant performance verifi-cation, San Diego, CA; 2008.

[32] Witten IH, Frank E. Data mining: practical machine learning tools and tech-niques. 2nd ed. San Francisco, CA: Morgan Kaufmann; 2005.

[33] Breiman L, Friedman J, Olshen RA, Stone CJ. Classification and regression trees.Monterey, CA: Wadsworth International; 1984.

[34] Smola AJ, Schoelkopf B. A tutorial on support vector regression. Statistics andComputing 2004;vol. 14:199–222.

[35] Shevade SK, Keerthi SS, Bhattacharyya C, Murthy KRK. Improvements to theSMO algorithm for SVM regression. IEEE Transactions on Neural Networks2000;11:1188–93.

[36] Bishop CM. Neural networks for pattern recognition. New York: OxfordUniversity Press; 1995.

http://en.wikipedia.org/wiki/Power_gain

Documents

Optimization of wind turbine energy and power factor with