Hybrid DSO-GA-based sensorless optimal control strategy for wind ...

Journal of Mechanical Science and Technology 27 (2) (2013) 549~556 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-012-1239-0

Hybrid DSO-GA-based sensorless optimal control strategy for wind turbine generators† Jin-sung Kim, Jong-hyun Jeon and Hoon Heo* Department of Control and Instrumentation Engineering, Korea University, Seoul, 137-701, Korea (Manuscript Received December 26, 2011; Revised August 29, 2012; Accepted October 22, 2012) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract The operation of a wind turbine generator involves natural uncertainty due to aerodynamic characteristics, resulting in a system that performs inefficiently. In general, the conventional controller now in wide use is not suitable for every operating point, because its tuning parameters and set-points do not meet the varying system characteristics. A study into an optimal control technique is conducted to reduce the negative effects of inherent uncertainty in system operation. In order to resolve the uncertainty problem, an optimal control method for an effective wind turbine generator is designed on the basis of a sensorless frame by utilizing a hybrid of the direct search optimization method (DSO) and the genetic algorithm (GA). This method is easy to implement and computation of functional derivatives is not necessary. The conventional GA is well known for its high performance in global optimization and its effectiveness in making ideal choices for control variables. The proposed DSO-GA hybrid differs from the conventional GA in terms of the sampling survey and the crossover operation. Moreover, the proposed multivariable optimal control strategy is a sensorless optimization technique that determines the pitch angle of the blades and the yaw angle of the nacelles to produce stable maximum power from a wind turbine system under steady-state operation. The proposed DSO-GA controller is implemented for a lab-scale wind turbine generator exposed to artificial wind, and the experimental results constitute a 3-D performance surface model of output voltage, which is used as an objective function for simulation. The optimization procedure with the objective function is carried out by means of the conventional and proposed methods, whose results reveal that the proposed DSO-GA optimizer yields far better performance in terms of generation number, convergence rate, and robustness. Both techniques are applied to a wind power generator through simulation and experiments. The performances are compared, and conclusions are drawn for each case. Keywords: Optimization method; Genetic algorithm; Golden section method; Optimal control; Wind turbine generator; Direct search method ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction Wind energy has received wide attention and has become one of the most competitive forms of renewable energy [1, 2]. The control strategies for effective operation of a wind turbine generator are divided into two groups according to the method of speed control for the rotor; namely, constant speed operation or variable speed operation. Operation at constant speed, regardless of wind speed, has been used in the development of a control technology for wind turbines. However, the disadvantage of this method is the inability to produce maximum electricity from varying wind speed. For this reason, variable speed operation of the rotor has been chosen of late [3]. The variable speed modes that are commercially available mainly use an optimal tip-speed ratio in the output control method. The tip-speed ratio is the ratio between the speeds of the blade tip and the wind. This is calculated using the blade radius, the *

Corresponding author. Tel.: +82 2 3290 3995, Fax.: +82 2 929 7808 E-mail address: [email protected] † Recommended by Associate Editor Yang Shi © KSME & Springer 2013

rotational speed, and the wind speed [2]. Further, if the optimal tip-speed ratio and wind speed are given, the rotation speed that provides maximum output can be calculated. This may seem a simple method of calculation, but it requires information on the wind speed and the tip-speed ratio. The average wind speed is often difficult to measure accurately from a wind speed meter located on a nacelle. For that reason, Simoes et al. [4] applied to a wind power system a maximum power point tracking (MPPT) control method that is frequently applied to solar power systems. This method uses fuzzy theory to maintain the tip-speed ratio of the wind turbine as close as possible to the optimal tip-speed ratio. However, the main disadvantage of this method is the need for an exact maximum power point (MPP) curve that comes from a presimulation. Many sensors and estimators are needed to obtain the input parameters of the pre-simulation that yields the precise MPP curve. Further, this method can often track in the wrong direction under rapidly varying wind speeds. Hence, to overcome the disadvantages of the aforementioned method, this paper proposes a DSO-GA hybrid as the

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basis of a sensorless optimal control strategy for wind turbine generators. This does not need accurate information regarding the wind turbine generator and its environment. The genetic algorithm was first proposed by Holland [5], and further description was provided by Goldberg [6]. A conventional GA is usually started with a population of individuals (actually binary or decimal strings), which evolves into new and better populations (according to a performance index) by means of naturally inspired operators, such as reproduction, crossover, mutation, and inversion [7]. At the same time, real-coded GA methods based on the GA have been introduced to a wide variety of applications (Blanco et al. [8]; Huang and Huang [9]; Leung et al. [10]; Thilagar and Rao [11]; Tsutsui and Goldberg [12]). Recently, Arumugam et al. [13] proposed the hybrid crossover for realcoded genetic algorithms. This hybrid crossover operation is carried out with a combination of three different methods: arithmetic crossover, average convex crossover, and directionbased crossover [13]. Chang [14] proposed genetic algorithms with multi-crossover operations for PID controller tuning. Moreover, following a direct search optimization method (Nelder-Mead simplex search method) has improved the performance of real-coded GAs. A hybrid scheme combining a Nelder-Mead simplex search method and a real-coded GA has been successfully studied by Fan et al. [15]. Application of a real-coded GA to the wind turbine generator system has been carried out. Paraschivoiu et al. [16] studied a computing procedure for the optimum pitch angle variation of blades in a wind turbine system by using a conventional real-coded GA [16]. Further, real-coded GAs have been used in PID gain tuning for wind turbine control systems (Donha et al. [17]; Belghazi and Cherkaoui [18]; Attia et al. [19]). Many studies in a wide range of literature have reported that real-coded GAs play very significant and effective roles in wind turbine control systems (only for pitch control of blades). This paper focuses on a sensorless (without angle sensors or a wind speed meter) multivariable (pitch and yaw angles) optimal control strategy for a lab-scale wind turbine generator by using a proposed real-coded GA. Incidentally, a conventional hybrid method uses a local direct search method (Nelder-Mead simplex search method) combined with a metaheuristic method (e.g., particle swarm optimization or GA method) whose scheme is based upon parallel structures working independently on a segmented population. However, in this study, the concept of a direct search method is directly applied to the genetic operators in the genetic algorithm. In other words, this method differs mainly in two respects from the conventional optimal control algorithm that uses a realcoded GA. First, the sampling survey is carried out using the golden section method for measuring the fitness of genes in each generation, rather than using complete enumeration. Second, an improved crossover operation is used. In the science of genetics, it is well known that heterogeneous breeding is more beneficial than homogenous breeding to select advan-

tages in any breeding population [20]. Therefore, the feature vector of the offspring generation is based on the previous vector (feature vector of parent generation) by using a GramSchmidt orthogonalization scheme to create an offspring generation whose genetic traits have a low similarity index with those of the parent generation. Finally, the developed DSO-GA strategy has been tested through a simulation in a lab-scale wind turbine generator to verify that its search efficiency and convergence rate are greater than those of a conventional GA. The rest of this paper is organized as follows: Section 2 explains the background of the genetic algorithm; Section 3 describes the procedures of the proposed DSO-GA method and the conventional GA; Section 4 presents the simulation results for a lab-scale wind turbine generator; and, finally, Section 5 provides conclusions.

2. Background of genetic algorithm The genetic algorithm technique was inspired by the mechanism of natural selection, a biological process in which stronger individuals are likely to emerge the winners in a competitive environment. The GA uses a direct analogy of such natural evolution to perform global optimization in order to solve highly complex problems [21]. It presumes that the solution of a problem is an individual and can be represented by a set of parameters. These parameters are regarded as the genes of the individual and can be structured as a string of concatenated values. The representation of the variables is defined by the encoding scheme. The variables can be represented by binaries, real numbers, or other forms, depending on the application data. The range, or search space, is usually defined by the problem. The GA has been successfully applied to many different problems, such as travelling salesmen, graph partitioning, filter design, and power electronics. It has also been applied to a machine-learning dynamic control system using learning rules and adaptive control [22]. A combination of the GA with other artificial intelligence techniques, such as fuzzy sets and artificial neural networks, to form a hybrid system has been the solution for a great number of problems. Success with the GA for solving high-dimensional problems has been reported in the literature too. An illustrative flowchart of the implementation of the GA algorithm is presented in Fig. 1 [23-25]. In the genetic algorithm, the genetic operators are applied to selected individuals from the current population to create a new population. In general, the three main genetic operators of reproduction, crossover, and mutation are used. By using different probabilities in applying these operators, the rate of convergence can be changed. Crossover and mutation operators should be carefully designed, since their choices contribute greatly to the performance of the overall genetic algorithm [21, 23].

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Step 2 (Evaluation): For each individual i in the current generation k , evaluate the fitness function using a lot test method. The fitness function for maximization can be expressed in terms of the objective function and penalty function as

( )

Maximize  f xi k + p   

(1)

where i = 1,2,3,…,N and k = 1,2,3,…,M. The penalty function is defined as follows:   k − f xi p =    0 

( )

2

 The individuals ∉ R  The individuals ∈ R

(2)

In Eq. (2), R is the feasible region.

Fig. 1. Flowchart of the conventional genetic algorithm.

Step 3 (Selection): At first, population with N individuals is randomly divided into two groups. In each group, select the best individual xˆ k and xɶk by using the tournament selection method based on the fitness results [28].

3. Conventional GA and proposed DSO-GA hybrid 3.1 Procedure of conventional GA At the beginning, an initial population is randomly generated. The individuals are candidate solutions to the problem. Then, the fitness value of each individual is evaluated by calculating the fitness function in a decoded form. Hence, based on the fitness of each individual, a group of the best individuals is formed through a selection process. The genetic operators of crossover and mutation are applied to this surviving population in order to improve the next generation of the solution [26]. Crossover is a recombination operator that combines parts of two parent individuals to produce offspring. This operator extracts common features from different individuals in order to achieve even better solutions. Mutation is an operator that introduces variations into the individual. This operation is performed occasionally with a regular probability [22]. Through the mutation operator, the search space is explored by looking for better points. However, mutation is a source of variability and too large a mutation rate results in a less efficient evolution, except in the case of a particularly simple problem. In other words, mutation is a random search operator and must therefore be used sparingly; otherwise, the algorithm becomes little more than a random search [23]. The process continues until the population converges to the global maximum or another stopping criterion is met. The steps performed by the conventional GA are detailed below [20-25, 27]. Step 1: Randomly generate the individuals of the initial population.

Step 4 (100% Crossover): In the conventional crossover mechanism, two individuals are used to make a crossover with each other. The conventional crossover operation is represented as follows: [28] If f ( xˆ k ) < f ( xɶk ) , then xi k +1 = xi k + c1r ( xˆ k − xɶk ) If f ( xˆ ) ≥ f ( xɶ ) , then xi k

k

k +1

= xi + c1r ( xɶ − xˆ ) k

k

k

(3) (4)

where i = 1,2,3,…,N and k = 1,2,3,…,M. The random number r ∈ [0,1] determines the crossover grade of xi k +1 , and c1 is a small positive constant of crossover. Step 5 (35% Mutation): The individuals mutate according to the following equation: [28] xi k +1 = xi k + c2Φ

(5)

where i = 1,2,3,…,N and k = 1,2,3,…,M. The random perturbation vector Φ produces small disturbances in xi k +1 , and c2 is a small positive scalar of mutation. Step 6: Update the current population with the new population and increment the generation. Loop to Step 2 until a stopping criterion is met.

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Step 3 (35% Mutation): The mutation operation is defined as

3.2 Procedure of proposed DSO-GA hybrid The important properties for the optimization algorithm are convergence rate, robustness, and solution quality. In the proposed approach, the GA is combined with the DSO to enhance its performance and guarantee solutions. For actual application, it is difficult to obtain exact information with regard to the shape of the objective function in a variety of environments. Accordingly, it is impossible to use derivative information that comes from the objective function. Therefore, the proposed algorithm is easy to implement and computation of functional derivatives is not necessary. Moreover, the proposed method differs in two respects from the conventional optimal control algorithm that uses the GA. First, the sampling survey is carried out using the golden section method for measuring the fitness values of the population at each generation, rather than using complete enumeration. The golden section method finds the extremum of a function within a range of interest by using the golden ratio. Second, improvement is made in the crossover operation. In the field of genetics, it is well known that heterogeneous breeding is more beneficial to natural selection of a population than homogenous breeding [20]. Hence, the feature vector of the offspring generation is based on the previous vector by using a Gram-Schmidt orthogonalization scheme to create an offspring generation whose genetic traits have a low similarity index with those of the parent generation. The vectors of two feature vectors are linearly independent. The steps performed by the proposed DSO-GA hybrid are detailed below. Step 1: Initialize population with individuals xi , xî and feature vector s k , s k −1 are randomly generated. Step 2 (100% Crossover): In the science of genetics, heterogeneous breeding has the selective advantage over homogenous breeding [20]. Based on this theory, the proposed crossover mechanism is represented as follows: xi k = xî k −1 + α k

sk sk

(6)

sk + Φ

xi k = xî k −1 + α k

(7)

sk + Φ

where Φ ∈ [0,1] is a random perturbation vector to produce small disturbances in xi k . For a highly nonlinear objective function as shown in Fig. 3 in Chapter 4, a mutation probability of 35% has been chosen as the most favorable one after many simulations. Moreover, this high probability is used due to the exceptional complexity of the objective function. Step 4 (Evaluation and Selection): For each individual i in the current generation k , evaluate the fitness function given by Eq. (1) using the golden section method. The golden section search method is used to find the minimum or maximum of a unimodal function. This method derives its name from the fact that the algorithm maintains the function values for traces of points whose distances form a golden ratio τ = −1 + 5 / 2 ≈ 0.618 [29, 30]. Therefore, in regard to the width of the uncertainty range, we conclude that the search by golden section converges linearly to the overall optimum of the function with a convergence ratio of approximately 0.618 [31]. The golden section search algorithm uses only the function, not its derivatives, and is among the most efficient region elimination methods for optimizing functions of a single variable, provided that upper and lower bounds are defined. From Eq. (6) or Eq. (7), each α i k is a step-length parameter found by the golden section method for best individual xî k . The steps of the golden section method are listed below.

(

)

Step 4-1: Start from i = 1 .The termination criterion is b − a < ε or i = N . Step 4-2: Let α i k = b − τ (b − a ) and α i +1k = a + τ (b − a ) , where a and b are provided as upper and lower bounds in the optimization process. Step 4-3: Compute f (α i k ) and f (α i +1k ) .

where i = 1,2,3,…,N and k = 1,2,3,…,M. xî k −1 is best individual of past generation and parent of current generation. And, s k is feature vector and parent of current generation. Also, the inner product < s k , s k −1 > is zero. This means that these feature vectors s k and s k −1 are independent of each other. In the presence of severe nonlinearity, the conventional GA may be terminated without finding the global optimum point, even within the designated number of generations. Hence, to overcome this problem of the conventional method, the proposed crossover operator uses the GramSchmidt orthogonalization procedures in Eq. (6) to generate an exploratory search direction based on the previous moves.

Step 4-4: If f (α i k ) ≤ f (α i +1k ) , then b = α i +1k , α i + 3k = α i k , and α i + 2 k = b − τ (b − a ) . If f (α i k ) > f (α i +1k ) , then a = α i k , α i + 2 k = α i +1k , and α i + 3 k = a + τ (b − a ) . Step 4-5: If b − a > ε , set i = i + 2 and go to step 4-3. Step 4-6: If f (α i + 2k ) < f (α i + 3k ) , then If f (α i + 2k ) > f (α i + 3k ) , then

αˆ k = [a,α i + 3k ] . αˆ k = [α i + 2 k , b] .


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Table 1. Specifications of lab-scale wind turbine generator. Type

3 blades, horizontal axis

Tower height (m)

0.97

Blade diameter (m)

0.74

Total turbine mass (kg)

3.98

Working range of wind speed (m/s)

2.4-16.2

Generator

Gearless, DC motor

Ratio of gear box

1 : 10

Range of output voltage (V)

1.5-20

Range of output current (mA)

10-22

Fig. 3. Output voltage vs. pitch and yaw angles for lab-scale experimental wind turbine generator.

Fig. 2. Experimental setup of 3-blade lab-scale wind turbine generator implementing DSO-GA hybrid.

If f (α i + 2k ) = f (α i + 3k ) , then αˆ k = [α i + 2k ,α i + 3k ] . Here, αˆ k is the optimum step-length for generation k . From this αˆ k , best individual xî k can be selected as follows: xî k = xî k −1 + αî k

sk sk

.

(8)

Step 5: Update the current population with the new population. Loop to Step 2 until a stopping criterion is met.

4. Simulation results for lab-scale wind turbine generator Experiments are conducted in order to obtain an objective function to use as the optimized performance surface model of output voltage in the optimization procedure. In this section, the efficiency and effectiveness of the proposed DSO-GA hybrid and the conventional GA are evaluated in terms of the fitness function of a lab-scale wind turbine generator. The specifications for the lab-scale wind turbine generator are listed in Table 1. As shown in Fig. 2, the system is composed of three parts: the lab-scale wind turbine (generator, servo motor for pitch control, servo motor for yaw control), the NIDAQ (driven by LabView), and the optimal control algorithm (running in Matlab). The lab-scale experimental setup is con-

structed in order to verify the performance of the developed strategy before its application to a real physical system. In the experiments, each optimization algorithm is developed using Labview 7.1 and Matlab R2010a. As shown in Fig. 3, the output voltage is adopted as the objective function for the proposed DSO-GA hybrid and the conventional GA. The objective function is configured using experimental data on the lab-scale wind turbine generator under a wind speed of 7.2-7.5 m/s. In the search region of interest, there exist many local minima and maxima, as shown in Fig. 3, which naturally reveals the severe nonlinearity of the objective function. For both optimization algorithms, the population size is 10 and the maximum number of generations is set at 100. All of the initial individuals (for yaw and pitch angles) are generated randomly from the defined search space. The lower and upper bounds of the search space allow for pitch and yaw angles in the ranges [0, 80] and [70, 110], respectively. The crossover and mutation probabilities are 100% and 35%, respectively, in both the proposed DSO-GA hybrid and the conventional GA. Figs. 4 and 5 show the search traces of the proposed DSO-GA algorithm and conventional GA algorithm while optimizing the fitness function for the lab-scale wind turbine generator. The unique global maximum occurs at a pitch angle of 30° and a yaw angle of 84° with a response value of 4.5119 V (see the contour plots in Figs. 4 and 5). Fig. 4 shows that the conventional GA method began to approach a local optimum and then was diverted toward the global optimum, explaining why this method needed more generations for convergence. In contrast, Fig. 5 shows that the proposed DSO-GA algorithm was already in the neighborhood of the global optimum early in the search period. Moreover, the DSO-GA algorithm searched more globally than the conventional GA algorithm. This observation, insofar as the fitness function is concerned, may partly explain why the proposed method performs better than the conventional algorithm for the lab-scale wind turbine generator. Fig. 6 illustrates the performances of two methods (i.e.,

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J. Kim et al. / Journal of Mechanical Science and Technology 27 (2) (2013) 549~556 110

Yaw angle (deg.)

70

60

90

80 40

30

0

10

20

30

40

0

10

20

30

40

50

60

70

80

90

100

50

60

70

80

90

100

60

Pitch angle (deg.)

Pitch angle (deg.)

50

DSO-GA Conventional GA

100

20

10

0 70

40

20

0 75

80

85

90

95

100

105

110

Generation

Yaw angle (deg.)

Fig. 7. Convergence performance of proposed DSO-GA hybrid vs. conventional GA for single run.

Fig. 4. Search trace of conventional GA method. 70

4.8

60

4.6

4.4 Fitness function value

Pitch angle (deg.)

50

40

30

4.2

4

3.8

20

3.6

10 3.4 0

70

75

80

85

90

95

100

105

110

50

100

150 Generation

200

250

300

Yaw angle (deg.)

Fig. 8. Best fitness values of conventional GA taken from 100 runs.

Fig. 5. Search trace of proposed DSO-GA method. 4.8 4.6

Fitness function value (v)

4.4 4.2

DSO-GA Conventional GA

4 3.8 3.6 3.4 3.2 3 2.8 0

10

20

30

40

50

60

70

80

90

100

Generation

Fig. 6. Comparison of best fitness values of proposed DSO-GA vs. conventional GA for single run.

DSO-GA hybrid and conventional GA) that start from the same initial point and proceed to the best fitness point by using the fitness function for 100 generations during each individual optimization run. It can be clearly seen from Fig. 6 that

the proposed DSO-GA method yielded fitness value increments significantly larger than those of the conventional GA algorithm in generations 3 through 12. Fig. 7 shows the convergence performances of the DSO-GA hybrid and the conventional GA. The best fitness function of each method is taken after 100 generations. The number of generations for convergence to the best fitness value is actually over 100 for the conventional GA. However, only 12 generations are required for the proposed DSO-GA hybrid to reach the best fitness value. Figs. 8 and 9 illustrate the performances of the two methods by plotting the best fitness versus the number of generations for 100 simulation runs to find the global optimum of the objective function. From these tracks, it can be seen that the conventional GA method began to approach a local optimum and then was diverted toward the global optimum, explaining why this method needed more generations for convergence. However, the DSO-GA hybrid was already near the optimum, emphasizing why the DSO-GA method performs better than the conventional method for the objective function of the lab-scale wind turbine generator. Additionally, in terms of average convergence rate, the conventional GA and DSO-GA hybrid re-

J. Kim et al. / Journal of Mechanical Science and Technology 27 (2) (2013) 549~556 4.8

s α

Fitness function value

4.6

References

4.2

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4

3.6

3.4 0

50

100

150 Generation

200

250

300

Fig. 9. Best fitness values of proposed DSO-GA hybrid taken from 100 runs.

quired 273.34 and 29.33 generations per run, respectively. This shows that the DSO-GA hybrid converged to the global optimum much faster than the conventional GA.

5. Conclusions In this paper, a sensorless DSO-GA algorithm has been studied as the optimal controller of a wind turbine generator. The DSO-GA hybrid was developed by adopting a sampling survey and a crossover method in a combined manner. The sampling survey used the golden section method. The crossover method used a Gram-Schmidt orthogonalization scheme based on the science of genetics. The proposed algorithm successfully revealed its efficient role in the optimization procedure, showing better performance in terms of robustness and convergence rate. Moreover, a comparison of simulation results from the two methods revealed that the DSO-GA hybrid exhibits better performance than the conventional GA in terms of output quality and process convergence rate. Currently, a real-time experimental study is under way for the proposed optimal control strategy based on the DSO-GA hybrid.

Nomenclature------------------------------------------------------------------------

xˆ xɶ

i N M c1 c2 Ф

: Feature vector : Step-length parameter

4.4

3.8

k ε τ p R r

555

: Number of generations : Accuracy of solution : Golden ratio : Penalty function : Feasible region : Random number : Best individual : Second best individual : Number of individual : Population size : Generation size : Small positive constant of crossover : Small positive scalar of mutation : Random perturbation vector

556


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Jin-sung Kim received a B.S. degree in control and instrumentation engineering and an M.S. degree in mechatronics engineering from Korea University, Korea, in 2007 and 2009, respectively. He is currently a Ph.D. student in the Department of Control and Instrumentation Engineering at Korea University. His research interests and areas of study include the optimal control and tuning methods of PID controllers for wind turbine generators and reverse osmosis plants. Jong-hyun Jeon received a B.S. degree in mechatronics engineering from Korea University, Korea, in 2010. He is graduated with M.S. Degree from the Department of Control and Instrumentation Engineering at Korea University. His research interests are in theoretical and experimental studies of controls for wind turbine generators. He is currently with LG Electronics as research engineer. Hoon Heo received his B.Sc. in Mechanical Engineering, M.Sc. in Aerospace Engineering, and Ph.D. in Mechanical Engineering from Korea University, University of Texas at Austin, and Texas Tech University, respectively. He worked as a research engineer in LG Electronics from 1975 and as a principal researcher in the Agency for Defense Development from 1985 through 1989. He is now a professor in the Department of Control and Instrumentation Engineering at Korea University. His current interests include stochastic dynamics and control, new and renewable energy, and optimized management of smart grids through intelligent controls.