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28 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 2, NO. 1, JANUARY 2011 Adaptive Control of a Wind Turbine With Data Mining and Swarm Intelligence Andrew Kusiak, Member, IEEE, and Zijun Zhang, Student Member, IEEE Abstract—The framework of adaptive control applied to a wind [13]. Munteanu et al. [14] designed two control loops to opti- turbine is presented. The wind turbine is adaptively controlled to mize power at low frequency and high frequency scenarios [14]. achieve a balance between two objectives, power maximization and However, in the previous research, the investigation of another minimization of the generator torque ramp rate. An optimization model is developed and solved with a linear weighted objective. The beneﬁcial avenue to reduce the cost of producing wind power, objective weights are autonomously adjusted based on the demand reducing the cost of wind turbine operation and maintenance, is data and the predicted power production. Two simulation models limited relative to power optimization. Senjyu et al. [15] studied are established to generate demand information. The wind power the impact of limited activation of the blade pitch angle on the is predicted by a data-driven time-series model utilizing historical power output [15]. Kusiak et al. [16] developed a framework wind speed and generated power data. The power generated from the wind turbine is estimated by another model. Due to the intrinsic of anticipatory control for optimization of wind turbine perfor- properties of the data-driven model and changing weights of the mance expressed in four different metrics [16]. Although the objective function, a particle swarm fuzzy algorithm is used to solve published literature offers valuable insights into performance it. optimization of wind turbines by considering multiple objec- Index Terms—Adaptive control, blade pitch angle, data mining, tives, determining the importance of each objective in response electricity demand simulation, generator torque, neural networks, to changing wind conditions is an open issue. optimization, particle swarm fuzzy algorithm, power prediction. In this paper, an adaptive approach to wind turbine control is presented. It is designed to achieve a balance between power optimization and smooth drive train control in response to the I. INTRODUCTION changes in wind speed and electricity demand. The smoothing of the drive train is accomplished by minimizing the torque HE growing awareness of climate change, the environ- ramp rate rather than controlling the rotor speed presented in T ment, fuel supply uncertainty, and raising energy costs have elevated interest in renewable energy. As one of the most [16]. The former reduces extreme loads, which translates into a lower maintenance and operation cost. To model the turbine, a viable sources of renewable energy, wind power is undergoing data-driven approach is introduced. To realize the adaptive tur- rapid expansion. bine control, estimates of future electricity demand and wind Although wind energy research has expanded in scope to power to be produced at the same time are desired. A time-se- cover domains such as, for example, wind energy conversion ries model extracted by a data-driven approach predicts the fu- [1], [2], the design of wind turbines [3], [4], the condition mon- ture wind power. A simulation model is used to generate the itoring of wind turbines [5], [6], reliability studies [7]–[9], and future demand due to the lack of demand data in this research. the design of wind farms [10], [11], numerous challenges are Supervisory Control and Data Acquisition (SCADA) data ahead as large-scale wind technology is new and is likely to be from turbines installed at a large wind farm (150 MW) have further developed. The cost of producing electricity from the been used in this research. To develop and validate the models wind is intricately related to the successful development and proposed in this research, 0.1-Hz (10-s) data from three ran- commercialization of wind turbines. One meaningful way to re- domly selected wind turbines are used. duce the cost is to maximize the power generated from a wind turbine. Numerous approaches to increase power output by op- II. PROBLEM FORMULATION timizing the power coefﬁcient have been published in the lit- erature. Boukhezzar et al. [12] designed a nonlinear controller for optimizing the power of the DFIG generator [12]. Wang et A. Adaptive Control al. [13] investigated an intelligent maximum power extraction The framework of adaptive wind turbine control is illustrated algorithm to improve the performance of wind turbine systems in Fig. 1. In this paper, a wind turbine is optimized subject to the following two objectives: power maximization and minimiza- Manuscript received January 09, 2010; revised August 05, 2010; accepted tion of the torque ramp rate. A weighted linear combination August 27, 2010. Date of publication September 02, 2010; date of current ver- sion December 15, 2010. This work was supported by the Iowa Energy Center of the two objectives is used in the bi-objective optimization under Grant 07-01. model. The values of two weights are impacted by the amount The authors are with the Intelligent Systems Laboratory, The University of (excess or deﬁcit) of the generated power and the projected Iowa, Iowa City, IA 52242 USA (e-mail: andrew-kusiak@uiowa.edu). power demand. Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. As illustrated in Fig. 1, three models, the wind turbine power Digital Object Identiﬁer 10.1109/TSTE.2010.2072967 generation model, the wind power prediction model, and the 1949-3029/$26.00 © 2010 IEEE KUSIAK AND ZHANG: ADAPTIVE CONTROL OF A WIND TURBINE WITH DATA MINING AND SWARM INTELLIGENCE 29 TABLE I DATA DESCRIPTION the noncontrollable and controllable parameters, as shown in the following: (1) where is the current time, represents the sampling time of data (10-s data), and is the function describing the wind turbine energy conversion process learned by the data-mining algorithms. Fig. 1. Framework of adaptive wind turbine control. 1) Algorithm Selection: To build the model (1), the following seven data-mining algorithms have been considered: neural network [19]–[21], neural network ensemble [22], -nearest electricity demand model, are established to realize the adap- neighbor [23], support vector machine [24], [25], boosting tree tive control framework. The wind power prediction model and (regression) [26], [27], classiﬁcation and regression tree [28], the electricity demand model are utilized as references in deter- and random forest (regression) [29]. mining values of the weights of the objectives. The wind turbine Table I describes the industrial data selected from three wind power generation model aims to accurately estimate the power turbines to conduct the research discussed in this paper. The data generated from a wind turbine with the control settings. Estab- are partitioned into three datasets: training dataset, test dataset, lishing accurate models of power generation and power predic- and validation dataset. Turbine 1 provides the training and test tion is challenging, and in this paper, it is accomplished with datasets, and the data from Turbines 2 and 3 are used to vali- data-mining algorithms that have been successfully applied in date the models derived by various data-mining algorithms. The other domains, e.g., industry and service [17], [18]. training dataset is used to extract models by the data-mining The energy of the wind and the electricity demand are algorithms. The test dataset is applied to test the accuracy of variable, and therefore, the weights assigned to the two corre- the models and selection of the best-performing data-mining al- sponding objectives need to be adjusted accordingly. A novel gorithm. The validation dataset examines the robustness of the optimization algorithm, the Particle Swarm Fuzzy Algorithm, data-driven model established by the selected algorithm. is developed to determine the weights of the two objectives and The four metrics (2)–(5), the mean absolute error (MAE), the solve the optimization model that is composed of data-driven standard deviation of mean absolute error (SD of MAE), the models developed in this paper. Two controllable parameters, mean absolute percentage error (MAPE), and the standard de- blade pitch angle and generator torque, are the solution to viation of mean absolute percentage error (SD of MAPE), are the optimization problem, and they are considered the recom- applied to evaluate the performance of the data-driven models mended settings for the control system of a wind turbine to manipulate wind turbines. (2) To maintain good quality of data-driven models, a relearning scheme is applied to the models using the continuously collected data. (3) B. Wind Turbine Power Generation Model The power conversion of a wind turbine is represented by the (4) 4-tuplet , where represents the wind speed (non- controllable parameter), is the generator torque (controllable parameter), is the blade pitch angle (controllable parameter), and is the power generated by the wind turbine (response pa- rameter). The value of the response parameter is impacted by (5) 30 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 2, NO. 1, JANUARY 2011 TABLE II TABLE IV TEST RESULTS OF THE MODELS DERIVED BY SEVEN DATA-MINING TEST RESULTS OF POWER PREDICTION BY DATA-DRIVEN MODELS ALGORITHMS accuracy reported in Table II, it is still impressive considering that the model was built from the data generated at Turbine 1 and tested on Turbines 2 and 3. C. Wind Power Prediction Model To determine wind turbine power at time , the time-series prediction model with the structure presented in (6) is utilized (6) where the notation is the same as in model (1). Fig. 2. First 100 points of test results produced by the neural network model. The time-series prediction model employs the past observed events to determine its future values. In the candidate model (6), TABLE III the past states of the generated power itself and wind speed at PREDICTION ACCURACY RESULTS PRODUCED BY THE NEURAL time periods to are considered. A parameter selec- NETWORK MODEL tion strategy, the wrapper with a random search approach [30], [31], is applied to select the most signiﬁcant parameters. The pa- rameters, , , , , and , are selected, and model (6) is instantiated as model (7) (7) Comparative analysis of the test results of the models built where the notation is the same as in model (1). by the data-mining algorithms is shown in Table II. The model 1) Algorithm Selection: The seven data-mining algorithms derived by the neural network algorithm outperforms all models of Section II-B1 are applied to build power prediction models. in estimating the power generated by a wind turbine. The cor- The training dataset of Table I is utilized to extract models, and responding values of MAPE (0.02) and SD of MAPE (0.07) are the test dataset (Table I) is used to test their accuracy at time . the lowest in Table II. Thus, the neural network algorithm will Table IV presents the test results [expressed with the metrics be used to construct the wind turbine power generation model. (2)–(5)] of the power prediction models derived by the seven Fig. 2 illustrates the ﬁrst 100 values of the observed (mea- data-mining algorithms. The neural network and the neural net- sured) power and the power predicted by the neural network work ensemble provided results with an MAPE of 0.06. How- model. ever, since the values of MAE, SD of MAE, and SD of MAPE 2) Model Validation: The validation dataset is used here to of the neural network ensemble are all smaller than those of the assess the robustness of the neural network extracted model in neural network, the neural network ensemble is considered for Section II-B1. Two validation datasets are used: Dataset 1 is col- building the power prediction model. lected from wind turbine 2, and validation dataset 2 is collected Fig. 3 illustrates the results for the ﬁrst 100 points of power from wind turbine 3. The details of the two validation datasets prediction by the neural network ensemble using validation are presented in Table I. The four metrics (2)–(5) are used to as- dataset 1. sess the accuracy of the power model with the results presented 2) Model Validation: The validation dataset used in in Table III. The MAPE for validation dataset 1 is 0.05, and the Section II-B2 is used here to assess the robustness of the neural MAPE for validation dataset 2 is 0.03. Although the accuracy network ensemble model. Table V presents the validation of this model tested on two different turbines is lower than the results of this model. Compare the MAPE listed in Tables IV KUSIAK AND ZHANG: ADAPTIVE CONTROL OF A WIND TURBINE WITH DATA MINING AND SWARM INTELLIGENCE 31 Fig. 3. First 100 test points of the observed power and the power predicted by Fig. 5. Simulated demand data from 7:00 A.M. to 9:00 A.M. the neural network ensemble. TABLE V horizontal axis represents the time measured in 10-s intervals, TEST RESULTS OF POWER PREDICTION BY DATA-DRIVEN MODELS the same as the data frequency used to develop the models in Section II-B. In this model, each demand value is a random number generated from a normal distribution with the mean following the pattern (solid line) in Fig. 4. The standard devi- ation is arbitrarily ﬁxed at 50. As presented in Fig. 4, the mean demand reﬂects a scenario where the mean electricity demand is low (200 kW) in the evening after ofﬁce hours (speciﬁcally, 6:00 P.M.) and in the early morning before ofﬁce hours (speciﬁcally, 8:00 A.M.). After 8:00 A.M., the mean demand increases and reaches a maximum at 9:00 A.M.. Between 9:00 A.M. and 5:00 P.M., the mean demand remains constant, and it begins to decline after 5:00 P.M. because the staff leaves the ofﬁce. This demand model M1 is expressed as (8) if Fig. 4. Electricity demand pattern of model M1. if if (9) and V. It is obvious that this time-series data-driven model is feasible, and its performance is consistent in power prediction. D. Electricity Demand Simulation Model if if Modeling electricity demand is outside the scope of this re- search. In this paper, the electricity demand data has been sim- where presents the demand data generated from the normal ulated. distribution, is the mean of the normal distribution, One basic demand simulation model is developed to generate , , , (8:00 A.M.), daily power demand at 10-s intervals based on the previous lit- (9:00 A.M.), (5:00 P.M.), (6:00 P.M.), erature [32] and the daily electricity consumption by heating (12:00 P.M.), and . ventilating and air conditioning (HVAC) systems. It is known In this model, the demand data is generated from a normal dis- that modeling customer demand is a challenge, as it depends on tribution (8) and the mean demand computed. For the demand factors such as the type of buildings, the region size, the time data generated from (8), two constraints (10) and (11) are used of day, and so on. The demand considered is the net energy of to prevent the value of demand becoming negative or exceeding other generation resources. the maximum capacity of the ofﬁce space This demand model is established to describe a pattern that simulates the usage of electricity in a micro-grid dominated by (10) business ofﬁces (see Fig. 4). (11) The vertical axis of Fig. 4 represents the electricity demand and its maximum of 1500 kW. This arbitrary value of demand Fig. 5 shows a portion of the demand data generated from should match the generation of a single wind turbine. The model (8), (9) from 7:00 A.M. to 9:00 A.M.. 32 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 2, NO. 1, JANUARY 2011 E. Optimization Model III. PARTICLE SWARM FUZZY ALGORITHM (PSFA) The model considered in this paper maximizes the power gen- In this research, a wind turbine is controlled adaptively erated from a wind turbine and minimizes the generator torque according to the predicted power generation and the power ramp rate. Maximizing the generated power estimated by the demand. The two control strategies impact the values of the model of Section II-B is equivalent to weights associated with the two objective functions of model . Here, the difference between the maximum power that could (14). To produce the control strategy associated with the model be potentially generated by a wind turbine and the power output objectives, a particle swarm fuzzy algorithm is developed. from the model is minimized. Two constraints are considered to The particle swarm fuzzy algorithm involves two phases. In construct this boundary, the maximum turbine capacity of 1500 the ﬁrst phase, the weights of the two objectives are determined kW, and the maximum energy that could be extracted from the by a fuzzy algorithm [33] to ascertain the importance of two ob- wind according to Betz’s law, expressed as [16]. jectives (discussed in Section II-E) in the optimization problem The torque ramp rate is expressed in based on the predicted power and demand information. This al- gorithm is expressed by the following: (12) where is the generator torque at time , is the generator (17) torque at time . if As the scales of the two objectives differ, the generated output if (18) is scaled as presented in the following: if (19) (13) (20) The biobjective optimization model is expressed in where is the predicted power and demand from the power pre- diction model (6) and demand models (9) or (11), respectively; is the membership function; is the weight factor to de- termine the ﬁnal weight; is the ﬁnal weight used in the ob- jective of the optimization model (14). is the maximum wind turbine capacity (here 1500 kW) and is arbi- trarily ﬁxed at 200 kW and expressed in the [0, 1] interval. If the predicted power is less than 200 kW, then indicates that the wind speed is low and the smoothing control of the gen- erator torque is less signiﬁcant than power maximization. Thus, (14) the weight assigned to the torque smoothing objective in (14) where is the model’s overall objective; and are the set- will be close to 0. If customer demand is lower than 200 kW, tings of the blade pitch angle and the generator torque at time this implies low energy demand, and the weight assigned to the ; and and are the weights of the two objectives deter- generated power objective in (14) should be small. The value of mined by the particle swarm fuzzy algorithm (PSFA) (discussed indicates that the turbine’s generation capacity has been in Section III). The remaining notation is the same as in (1) and attained or the demand level is at maximum. If the predicted (12). power is greater or equal to 1500 kW, the control should focus In model (8), two controllable parameters, and , are uti- on minimizing the torque ramp rate to prevent the fatigue of the lized to realize the adaptive control of the wind turbine. As pre- drive train and thus reduce the maintenance cost. The demand, sented in model (14), to control the wind turbine conservatively, which is greater or equal to 1500 kW, implies a high level energy the ranges of the two controllable parameters are expressed in consumption and power maximization needs to be emphasized. the following: The second phase of the proposed algorithm involves the particle swarm optimization (PSO) algorithm [34]. In the PSO, (15) each particle represents the candidate optimal solutions of model (14) and can be expressed as , where is a (16) two-dimensional vector at the th iteration, and The lower bound ( 0.57) and the upper bound (90.61) for the is another two-dimensional vector . The vector blade pitch angle that cannot be exceeded are obtained from the represents the position of each particle at iteration , and industrial data used in this research. In addition, the increment vector represents the velocity associated with each particle at (or decrement) of blade pitch angle is set in the range iteration . The initial value of each dimension of the particle’s . The value of the generator torque is expressed in position is generated from a uniform distribution, where is percentage [0, 100], rather than N/m . The adjustment of the generated from and generator torque is done at increments (or decrements) in the is generated from . range . The initial values of the particle’s velocity are all set at 0 at KUSIAK AND ZHANG: ADAPTIVE CONTROL OF A WIND TURBINE WITH DATA MINING AND SWARM INTELLIGENCE 33 TABLE VI TEST RESULTS OF POWER PREDICTION BY DATA-DRIVEN MODELS the initialization step. The optimization procedure is presented next. Step 1) Determine the weights of ﬁtness function , which is the objective function of model (14) that takes the weights of objectives produced by the Fig. 6. Standardized ﬁtness value. fuzzy algorithm. Step 2) Initialize the particle size , the position of each particle , and its velocity , where pitch angle. The particle swarm fuzzy algorithm determines the , , and . weights of the objective function and the recommended control Step 3) Initialize the local best for each particle by settings optimizing the two control objectives, the maximum , and estimate the initial global best power and the minimum torque ramp rate. by , for and 2) Convergence of the Particle Swarm Fuzzy Algorithm: . In this experiment described next, convergence of the particle Step 4) Repeat until the stopping criterion is satisﬁed swarm fuzzy algorithm (PSFA) based on the data point of . Table VI is examined. Ten particles are created, and the stop- ping criterion is set to 1500 iterations. The convergence of the For each particle PSFA is evaluated based on the ﬁtness value. To simplify the Step 4.1) Create random vectors and evaluation procedure, a ﬁtness value every ﬁve iterations from by generating for . 5–100 and the ﬁtness value at iteration 1500 are examined (see Step 4.2) Update the velocities of particles by Fig. 6). The horizontal axis in Fig. 6 represents the number of and update iterations, and the vertical axis shows the standardized ﬁtness the particle positions by . value expressed as Step 4.3) Update the local best by , if . (21) Step 4.4) Update the global best by , if . according to the notation of Section III. As shown in Fig. 6, the rapid drop of the standardized ﬁt- The above algorithm requires parameter initialization. The ness value for the global best indicates the quick convergence of parameter is an inertial constant [35]. It controls the impact the PSFA. In the 1500 iterations, the standardized ﬁtness value of the previous velocity on the current velocity, and usually it drops to 1 at the 50th iteration (converges from 50th iterations) has a value between 0 and 1. It is ﬁxed arbitrarily at 0.5 in this and constantly keeps this value in the following iteration. research. Parameters and are two constants that reﬂect how 3) Optimization Results: The optimization results based on much the movement of particles is impacted by the local and this single point (Table VI) are illustrated in Table VII. The ﬁrst global best. Both values are arbitrarily ﬁxed at 2 [36]. The PSO column of Table VII presents the recommended control strategy algorithm used in this research performs better than the SPEA for the wind turbine. Here, the power generated is 1139.55 kW reported in [16]. The computational time advantage can be ten- (slightly higher than original power output of 1112 kW shown fold and more. The computational efﬁciency gain comes from in Table VI). The ramp rate of the generator torque is nearly the ﬂight function of the PSO. The performance of the PSO zero. The two weights indicate the current control preference. algorithm is presented in Section IV-A2. Weight-Torque Ramp is 0.97 and Weight-Power is 0.03. The values of the weights indicate that the control preference focuses IV. INDUSTRIAL CASE STUDY on the smoothness of the drive train rather than the maximiza- tion of the generated power. A. Single-Point Optimization 1) Description of the Data Point: In this section, the particle B. Multipoint Optimization swarm fuzzy algorithm is demonstrated for a single data point To simulate and demonstrate the adaptive control approach that has been randomly selected from the test dataset of Table I. of a wind turbine, the multipoint optimization based on selected This data point is partially illustrated in Table VI. data from the test dataset in Table I is introduced. This dataset The data in Table VI reﬂects a scenario where the current reﬂects a scenario where the predicted power (supply) is higher power generated from a wind turbine is high and the simulated than the demand at the beginning of the period, and then the demand is low. The current settings of two controllable param- power demand gradually exceeds the predicted power. It con- eters are 76.90 for the generator torque and 1.07 for the blade tains 300 data points from 12/30/2008 8:17:20 A.M. to 12/30/ 34 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 2, NO. 1, JANUARY 2011 TABLE VII TEST RESULTS OF POWER PREDICTION BY DATA-DRIVEN MODELS Fig. 7. Convergence speed for six data points. Fig. 9. Comparison of the optimized torque ramp rate and measured torque ramp rate. Fig. 8. Estimated weights for two objectives. Fig. 10. Comparison of the optimized and original power. 2008 9:07:10 A.M.. The demand data is generated from the de- mand model discussed in Section II-D. 1) Stopping Criterion of the PSFA: Before running the mul- The optimized power generated from a wind turbine and the tipoint optimization, an experiment is designed to evaluate the original power it produced is illustrated in Fig. 10. stopping criterion for the PSFA. Six data points, indexed as 20, Figs. 9 and 10 clearly demonstrate the change in the wind 552, 1020, 1500, 1947, and 3155, are randomly selected from turbine control strategies. As initially predicted, the power gen- the test dataset of Table I. The PSFA has run 1500 iterations for erated is higher than the demand; therefore, the wind turbine is each point. Fig. 7 illustrates the convergence of the PSFA for the controlled for torque smoothness. In this case, a higher weight six points. It is obvious that the PSFA converges quickly, most is assigned to minimizing the generator torque ramp rate. How- of the time within 60 iterations. However, to be more conserva- ever, the direction of the weights gets changed over time. After tive, the number of iterations that the PSFA needs to run is set the initial period, the control strategy switches to maximizing to 100. power in response to the electricity demand gradually exceeds 2) Optimization Results: In this section, the test dataset from the predicted power. The weight assigned to the power maxi- 12/30/2008 8:17:20 A.M. to 12/30/2008 9:07:10 A.M. is merged mization overwhelms the weight of minimizing the torque ramp with the demand data generated from demand model. Fig. 8 rate. Due to the trade-off between the two objectives, increase illustrates the weight values assigned to the two objectives of in the torque ramps can be observed. Constraint (14) limits the model (14). As Fig. 8 shows, Weight-Power is initially lower maximum change of torque ramps. It can be adjusted as needed. than Weight-Torque Ramp; however, over time Weight-Power Fig. 11 demonstrates that the measured blade pitch angle re- dominates Weight-Torque Ramp. Since, in the PSFA, Weight- mains essentially constant at 0.53 . Power and Weight-Torque Ramp are associated with the demand To realize the adaptive control in practice, new set points need and predicted power, Fig. 8 characterizes the scenario discussed to be computed within the data sampling frequency (here 10 s). before in Section IV-B. Fig. 9 shows the optimized generator The computational results with the 10-s data demonstrate that and the measured torque ramp rate. the set points of the torque and the blade pitch angle are usually KUSIAK AND ZHANG: ADAPTIVE CONTROL OF A WIND TURBINE WITH DATA MINING AND SWARM INTELLIGENCE 35 [8] R. Karki, P. Hu, and R. Billinton, “A simpliﬁed wind power generation model for reliability evaluation,” IEEE Trans. Energy Convers., vol. 21, no. 2, pp. 533–540, Jun. 2006. [9] P. J. Tavner, J. Xiang, and F. Spinato, “Reliability analysis for wind turbines,” Wind Energy, vol. 10, no. 1, pp. 1–18, 2006. [10] R. Barthelmie, S. Frandsen, M. Nielsen, S. Pryor, P. Rethore, and H. Jørgensen, “Modelling and measurements of power losses and turbu- lence intensity in wind turbine wakes at Middelgrunden offshore wind farm,” Wind Energy, vol. 10, no. 6, pp. 517–528, 2007. [11] J. Mora, J. Barón, J. Santos, and M. Payán, “An evolutive algorithm for wind farm optimal design,” Neurocomputing, vol. 70, no. 16, pp. 2651–2658, 2007. [12] B. Boukhezzar and H. Siguerdidjane, “Nonlinear control with wind estimation of a DFIG variable speed wind turbine for power capture optimization,” Energy Convers. Manage., vol. 50, no. 4, pp. 885–892, 2009. Fig. 11. Comparison of the optimized and measured blade pitch angle. [13] Q. Wang and L. Chang, “An intelligent maximum power extraction algorithm for inverter-based variable speed wind turbine systems,” IEEE Trans. Power Electron., vol. 19, no. 5, pp. 1242–1249, Sep. computed within 3 s, which is acceptable. The computational ef- 2004. ﬁciency could be further improved by applying different search [14] I. Munteanu, N. Cutululis, A. Bratcu, and E. Ceanga, “Optimization of variable speed wind power systems based on a LQG approach,” Control strategies and code development techniques. Eng. Practice, vol. 13, no. 7, pp. 903–912, 2005. [15] T. Senjyu, R. Sakamoto, N. Urasaki, T. Funabashi, H. Fujita, and H. V. CONCLUSION Sekine, “Output power leveling of wind turbine generator for all op- erating regions by pitch angle control,” IEEE Trans. Energy Convers., Adaptive control of a wind turbine maximizing power gen- vol. 21, no. 2, pp. 467–475, Jun. 2006. eration and minimizing the torque ramp rate was presented. [16] A. Kusiak, Z. Song, and H. Zheng, “Anticipatory control of wind tur- Data-mining algorithms were utilized to generate nonpara- bines with data-driven predictive models,” IEEE Trans. Energy Con- vers., vol. 24, no. 3, pp. 766–774, Sep. 2009. metric models of wind turbine power generation and the wind [17] M. J. A. Berry and G. Linoff, Data Mining Techniques: For Marketing, power prediction model. An integrated model with a linear Sales, and Customer Relationship Management, 2nd ed. New York: combination of weighted objectives was created. The weights Wiley, 2004. [18] S. K. Shevade, S. S. Keerthi, C. Bhattacharyya, and K. R. K. Murthy, associated with the objectives were estimated based on the “Improvements to the SMO algorithm for SVM regression,” IEEE predicted power and demand. The demand was generated from Trans. Neural Netw., vol. 11, no. 5, pp. 1188–1193, Sep. 2000. two simulation models. A novel optimization approach, the [19] H. Siegelmann and E. Sontag, “Analog computation via neural net- works,” Theor. Comput. Sci., vol. 131, no. 2, pp. 331–360, 1994. particle swarm fuzzy algorithm (PSFA), was developed to solve [20] G. P. Liu, Nonlinear Identiﬁcation and Control: A Neural Network Ap- the model developed in this paper. proach. London: Springer, 2001. Industrial data from three wind turbines of the same type [21] M. Smith, Neural Networks for Statistical Modeling. New York: Van Nostrand, 1993. was utilized in this study. The data sampling frequency was [22] L. K. Hansen and P. Salamon, “Neural network ensembles,” IEEE 0.1 Hz. The data from one turbine was used to develop and test Trans. Pattern Anal. Mach. Intell., vol. 12, no. 10, pp. 993–1001, Oct. data-driven models, and the data of two other turbines was em- 1990. [23] Shakhnarovish, Darrell, and Indyk, Nearest-Neighbor Methods in ployed to validate these models. Comparative analysis of var- Learning and Vision. Cambridge, MA: MIT Press, 2005. ious data-mining algorithms was performed. The convergence [24] B. Schölkopf, C. J. C. Burges, and A. J. Smola, Advances in Kernel and the stopping criterion of the PSFA were investigated. Methods: Support Vector Learning. Cambridge, MA: MIT Press, 1999. The feasibility of adaptive control of wind turbines was [25] I. Steinwart and A. Christmann, Support Vector Machines. New demonstrated. In addition to the two objectives applied in this York: Springer-Verlag, 2008. paper, additional objectives, for example, mitigation of wind [26] J. H. Friedman, “Stochastic gradient boosting,” Comput. Statist. Data Anal., vol. 38, no. 4, pp. 367–378, 2002. turbine vibrations, could be considered. [27] J. H. Friedman, “Greedy function approximation: A gradient boosting machine,” Ann. Statist., vol. 29, no. 5, pp. 1189–1232, 2001. REFERENCES [28] L. Breiman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classiﬁca- [1] M. Arifujjaman, M. Iqbal, and J. Quaicoe, “Performance comparison tion and Regression Trees. Monterey, CA: Wadsworth, Inc., 1984. of grid connected small wind energy conversion systems,” Wind Eng., [29] L. Breiman, “Random forests,” Mach. Learning, vol. 45, no. 1, pp. vol. 33, no. 1, pp. 1–18, 2009. 5–32, 2001. [2] Ö. Mutlu, E. Akpınar, and A. Balıkcı, “Power quality analysis of wind [30] I. H. Witten and E. Frank, Data Mining: Practical Machine Learning farm connected to Alaçatı substation in Turkey,” Renewable Energy, Tools and Techniques, 2nd ed. San Francisco, CA: Morgan Kauf- vol. 34, no. 5, pp. 1312–1318, 2009. mann, 2005. [3] D. Laino, C. Butterﬁeld, R. Thresher, and D. Dodge, “Evaluation of [31] R. Kohavi and G. H. John, “Wrapper for feature subset selection,” Artif. select IEC standard wind turbine design cases on the combined experi- Intell., vol. 97, no. 1–2, pp. 273–324, 1997. ment wind turbine model,” Wind Energy, Amer. Soc. Mech. Engineers, [32] D. J. Swider, “Compressed air energy storage in an electricity system Solar Energy Division (Publication) SED, vol. 14, pp. 47–48, 1993. with signiﬁcant wind power generation,” IEEE Trans. Energy Convers., [4] K. Saranyasoontorn and L. Manuel, “A comparison of wind turbine vol. 22, no. 1, pp. 95–102, Mar. 2007. design loads in different environments using inverse reliability tech- [33] B. Mirzaeian, M. Moallem, V. Tahani, and C. Lucas, “Multiobjective niques,” Wind Energy, vol. 126, no. 4, pp. 1060–1068, 2004. optimization method based on a genetic algorithm for switched reluc- [5] A. Kusiak, H. Zheng, and Z. Song, “On-line monitoring of power tance motor design,” IEEE Trans. Magn., vol. 38, no. 3, pp. 1524–1527, curves,” Renewable Energy, vol. 34, no. 6, pp. 1487–1493, 2009. May 2002. [6] A. Kusiak, H. Zheng, and Z. Song, “Models for monitoring wind farm [34] J. Kennedy and R. C. Eberhart, “Particle swarm optimization,” in IEEE power,” Renewable Energy, vol. 34, no. 3, pp. 583–590, 2009. Int. Conf. Neural Networks, 1995, pp. 1942–1948. [7] A. Leite, C. Borges, and D. Falcão, “Probabilistic wind farms gen- [35] Y. Shi and R. Eberhart, “Parameter selection in particle swarm opti- eration model for reliability studies applied to Brazilian sites,” IEEE mization,” in Proc. 7th Annu. Conf. Evolutionary Programming, 1998, Trans. Power Syst., vol. 21, no. 4, pp. 1493–1501, Nov. 2006. pp. 591–600. 36 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 2, NO. 1, JANUARY 2011 [36] M. A. Abido, “Optimal design of power-system stabilizers using par- Engineers, etc. His current research interests include applications of computa- ticle swarm optimization,” IEEE Trans. Energy Convers., vol. 17, no. tional intelligence in automation, wind and combustion energy, manufacturing, 3, pp. 406–413, Sep. 2002. product development, and healthcare. Prof. Kusiak is an Institute of Industrial Engineers Fellow and the Editor-in- Chief of the Journal of Intelligent Manufacturing. Andrew Kusiak (M’89) received the B.S. and M.S. degrees in engineering from the Warsaw University of Technology, Warsaw, Poland, in 1972 and 1974, respectively, and the Ph.D. degree in operations Zijun Zhang (S’10) received the B.S. degree (2008) research from the Polish Academy of Sciences, from the Chinese University of Hong Kong, Hong Warsaw, in 1979. Kong, China, in 2008, the M.S. degree from the Uni- He is currently a Professor at the Intelligent Sys- versity of Iowa, Iowa City, in 2009, and is currently tems Laboratory, Department of Mechanical and In- working toward the Ph.D. degree in the Department dustrial Engineering, The University of Iowa, Iowa of Mechanical and Industrial Engineering, The Uni- City. He speaks frequently at international meetings, versity of Iowa, Iowa City. conducts professional seminars, and does consulta- His research concentrates on data mining and tion for industrial corporations. He has served on the editorial boards of over computational intelligence applied to systems 40 journals. He is the author or coauthor of numerous books and technical pa- modeling, monitoring, and optimization in wind pers in journals sponsored by professional societies, such as the Association for energy and HVAC domains. He is a member of the the Advancement of Artiﬁcial Intelligence, the American Society of Mechanical Intelligent Systems Laboratory at The University of Iowa.