Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm

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Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm Zafer Civelek Faculty of Engineering, Electrical and Electronics Engineering, Çankırı Karatekin University, Çankırı, Turkey

a r t i c l e

i n f o

Article history: Received 29 December 2018 Revised 8 April 2019 Accepted 23 April 2019 Available online xxxx Keywords: Wind turbine Pitch control Fuzzy Takagi-Sugeno Genetic algorithm

a b s t r a c t Wind turbines have become popular with the recent interest in renewable energy sources. At wind speeds above nominal wind speeds, the blade pitch angle is controlled to ensure that the wind turbines operate safely and the output power is stable. Since the wind turbines are nonlinear systems, the blade pitch angle controller must also be suitable for such cases. In this respect, the fuzzy controller can accommodate such nonlinearities, making it a suitable candidate for wind turbine blade controls. In this study, a fuzzy controller designed to control the wind turbine blades is optimized with a genetic algorithm that is improved. New features are added to improve Advanced Intelligent Genetic Algorithm’s (AIGA’s) performance. One of these is the addition of acceptable error concept (AEC). The conversion from binary to decimal and from decimal to binary are performed based on the amount of this acceptable error. Although an approximate value can be obtained, conversion from decimal to binary may not be accurately performed especially for the digits following the decimal. These inaccuracies may lead to small errors especially, during back conversion from binary back into decimal in IGA. This is removed by AEC implemented in AIGA. Furthermore, maximum number of crossover points in AIGA is determined as a function of the length of chromosome. This implementation improved algorithm. Simulation results show that optimization makes the output power even better. Ó 2019 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction With the increase in environmental safety concerns, interest to renewable energy has been rising. This rise gave popularity to wind turbines (WT), a type of renewable energy. WTs convert wind energy to mechanical and then to electric energy. The power produced in WTs is directly proportional to cube of wind speed(WS) [1]. However as wind speed changes continuously, WTs cannot produce ceaseless constant power. Nominal WS (NWS) is the required wind speed for WTs to produce the expected power. Below NWSs WTs produce power less than the nominal power (NP). WSs higher than NWSs lead production above the capacity of WTs which damages WTs. Thus some control mechanisms are needed to reduce the produced power to NP ranges. One of the mechanisms is changing the pitch angles of blades [2]. WTs having this capability are known as variable pitch angle WTs. In these WTs, either output power or rotor speeds are measured and pitch angles are changed for values above nominal. Controllers are needed for changing pitch angles [3,4]. Controllers compare either desired output power or rotor speeds with current values. Based on

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the comparison the pitch angles are adjusted. Modern control approaches enabled design of many controllers for this purpose. Van et al. used fuzzy controllers to stabilize to output power of WT [5]. Lasheen and Elshafei proposed fuzzy predictive algorithm for pitch angle control (PAC) where they reduced the size of rule base by utilizing gap-metric criteria [6]. By using type 2 fuzzy instead of proportional-integral-derivative (PID) as controller, Bahraminejad and Iranpour got better results in PAC [7]. Whereas Chen at. all. employed online training recurrent neural network (RNN) instead of proportional-integral (PI) and obtained better performance [8]. Poultangari et. all. adjusted coefficient of PI controller using radial basis function (RBF) neural network (NN) that is optimized by particle swarm optimization [9]. Gao et. all. calculated PI and PID controller coefficients considering the delays in pitch control mechanisms [10]. Ren et. all. designed a nonlinear pitch controller that compensates unexpected random noises [11]. Saravanakumar et al. manipulated output power of WTs, aiming maximum power point tracking (MPPT) by using integral sliding mode control (ISMC) and aiming limited output power by PI control approach for wind speeds below and above nominal values respectively [12]. Some studies use ANN based pitch control for MPPT in WTs where permanent magnet synchronous generator (PMSG) are implemented [13,14]. For MPPT, Lin and Hong

https://doi.org/10.1016/j.jestch.2019.04.010 2215-0986/Ó 2019 Karabuk University. Publishing services by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article as: Z. Civelek, Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j.jestch.2019.04.010

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employed online trained improved Elman NN (IENN) in PAC [15]. In some studies, coefficients of PI, PD and PID controllers implemented in pitch controls have been adjusted by fuzzy [16–20]. Moreover linear quadratic Gaussian (LQG) [21], adaptive fuzzy sliding mode control (AFSMC) [22], a new self-tuning PID algorithms [23] are some of the approaches exploited in WT pitch controls. One of the main topics in control design is the suitability of the controller to the system that it will be implemented. The pitch angle control system of wind turbines is nonlinear. PID control method, convenient for linear systems, cannot satisfy the requirements in nonlinear pitch angle control. Thus, fuzzy controller which fits better to nonlinear systems is preferred in this study. Sudden unexpected changes in wind speed, necessitate quick compatible responses from the controller. This is the main reason for using Sugeno-Takagi instead of Mamdani. As results are calculated using mathematics, Sugeno-Takagi works faster than Mamdani. This is another reason for selection of Sugeno-Takagi. The coefficients of Sugeno-Takagi controller can be improved using ANFIS when corresponding outputs of inputs are known. However, for cases where outputs are not known beforehand as in wind turbine pitvh angle control, an optimization schema is needed. Using GA in optimization is the capability of GA searching wide solution space with numerous parameters at the same time. Above mentioned papers obtained from literature proposed controllers for PA. However, published literature about the optimization of the controllers based on the system requirements, being the second important item following the controller design, is limited. Within this limited literature, Taher et al. optimized linear quadratic Gaussian (LQG) controller using differential evolution (DE) algorithm [24]. On the other hand, Civelek et al. optimized coefficient of PID controller by genetic algorithms [25]. Lastly, Belghazi and Cherkaoui used genetic algorithms for PI controller coefficients [26]. In this study, implementation of fuzzy (Takagi-Sugeno) controller optimized by genetic algorithms for WT pitch angle control is presented.

Implementation of TS fuzzy logic for a system with two inputs (x1, x2) shown in Fig. 1 leads two results (y1, y2) and one crisp result (y). In Fig. 1 c10, c11, c12, c20, c21, c22 and w1, w2 denotes coefficients and weights respectively. Based on the system requirements and fuzzy logic clusters number of if-then rules can be increased. The crisp result (y) is calculated by the weighted averages of results (y1, y2) as presented in (4).

y¼

w1 y1 þ w2 y2 w1 þ w2

ð4Þ

Fuzzy logic controller controlling the output power of wind turbine have two inputs and one output. Inputs are error, being the difference between expected and existing rotor speeds, and derivative of it, where these are presented in Eqs. (5) and (6). Output is the value of blade pitch angle.

error ¼ wr expected  wr existing

ð5Þ

deriv ativ e of error ¼ error n  errorn1

ð6Þ

where n in Eq. (6) indicates iteration number. Input fuzzy clusters are shown in Figs. 2 and 3. Some fuzzy rules using Figs. 2 and 3 are represented in Table 1. The TS fuzzy controller is composed of five rules. In (7), the fuzzy rules in Table 1 and their coefficients were rewritten for TS.

y1 ¼ c10 þ c11 x1 þ c12 x2 y2 ¼ c20 þ c21 x1 þ c22 x2 y3 ¼ c30 þ c31 x1 þ c32 x2

ð7Þ

y4 ¼ c40 þ c41 x1 þ c42 x2 y5 ¼ c50 þ c51 x1 þ c52 x2 c10 ¼ 1, c11 ¼ 1, c12 ¼ 1, c20 ¼ 0:5, c21 ¼ 0, c22 ¼ 0:5, c30 ¼ 0, c31 ¼ 0, c32 ¼ 0, c40 ¼ 0:5, c41 ¼ 0, c42 ¼ 0:5, c50 ¼ 1, c51 ¼ 1,c52 ¼ 1 Accordingly, the crisp output of the controller is written in (8).

y¼

y1 w1 þ y2 w2 þ y3 w3 þ y4 w4 þ y5 w5 w1 þ w2 þ w3 þ w4 þ w5

ð8Þ

These coefficients are w1 ¼ 1; w2 ¼ 1; w3 ¼ 1; w4 ¼ 1; w5 ¼ 1.

2. Methodology 2.1. Fuzzy logic (Takagi-Sugeno) controller In this study, Takagi-Sugeno type fuzzy controller was used. In Takagi-Sugeno fuzzy controller (TSFC), the results of ‘‘if-then” rules can be expressed as linear equations. A typical rule expression is presented in (1).

Rule ðiÞ : if x1 is Ai1 ;    ; xn is Ain then yi ¼ ci0 þ ci1 xi þ    þ cin xn ð1Þ Pl Pl wi yi i¼1 wi ðci0 þ c i1 xi þ . . . þ c in xn Þ ¼ y ¼ Pi¼1 Pl l i¼1 wi i¼1 wi n X l l X X ¼ð wi cik xk Þ= wi k¼0 i¼1

ð2Þ

i¼1

where, i ¼ 1; 2;    l. l is number of ‘‘if-then” rules. cik (k ¼ 0; 1; 2;    ; n), is coefficients of result of ‘‘if-then” rules. yi is result of i’th ” if-then” rules. Aik is fuzzy cluster. Where x0 ¼ 1, wi is the weight of the ith ‘‘if-then” rule and calculated by (3).

wi ¼

n Y

Aik ðxk Þ

ð3Þ

k¼1

where Aik ðxk Þ, indicates membership degree of xk in Aik [27].

Fig. 1. Takagi-Sugeno inference system.

Please cite this article as: Z. Civelek, Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j.jestch.2019.04.010

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Fig. 2. Error fuzzy clusters. Fig. 4. Advanced Intelligent Genetic Algorithm flow chart.

the relative value of the target function. The higher the fitness value of person, the greater the likelihood of being a nextgeneration parent. The appropriate individuals within the created population are selected by various methods sucah as; roulette wheel, tournament and ranking. In AIGA, roulette wheel selection is preferred.

Fig. 3. Derivative of error fuzzy clusters.

Table 1 Fuzzy Rules. Fuzzy Rules 1. 2. 3. 4. 5.

If If If If If

error error error error error

p and derivative of error p then output nb p and derivative of error n then output ns z and derivative of error z then output z n and derivative of error p then output ps n and derivative of error n then output pb

2.2. Genetic algorithm structure and advanced Intelligent genetic algorithm (AIGA) Although, some genetic algorithms use the decimal system mostly binary coding is implemented in GA. In this study, although the decimal numbers are used in the control system to be optimized, binary system numbers are utilizied in the genetic algorithm coding. The AIGA flow chart is shown in Fig. 4. A follow-up and control algorithm is embedded in AIGA. This algorithm follows the best individuals in the population. It calculates the recurrence numbers of the best individuals and checks whether AIGA has entered any local minima or maxima. If the algorithm decides that AIGA has entered a local minima or maxima, it changes the crossover and mutation rates. So it tries to save AIGA from falling in a local minima or maxima. 2.2.1. Selection Genetic algorithm has a population-based algorithm structure. Each person in the population has a fitness value that indicates

2.2.2. Crossover The crossover is the heart of the genetic algorithm. It enables the production of new individuals from two individuals with high fitness values. The selected crossover method affects the time that GA reaches the goal. A good crossover allows GA to reach the goal in a short time. In the crossover process, there is a concept called crossover ratio. The crossover rate determines the amount of individuals to be crossed. Altough value of this ratio depends on the person designing GA, it is generally kept between 70 and 90% for GA and set as 90% for AIGA. In addition, the number of points used in the crossover is variable. AIGA starts from the single point of crossover. Another algorithm within AIGA follows the best individuals of the population. If a certain number of these individuals are repeated the same, the algorithm increases the number of crossover. This adds diversity to the crossover process. The upper limit of the crossover point is determined as a function of the chromosome length. 2.2.3. Fitness function In the genetic algorithm, a fitness function is used to indicate the proximity of each individual within the population to the solution. The fitness function is set as in (9).

F ðt Þ ¼ c1 :F 1 ðt Þ þ c2 :F 2 ðtÞ

ð9Þ

where FðtÞ, the fitness function sum and c1 and c2 are constant coefficients. The fitness function FðtÞ is consisting of two parts. First part is F1 ðtÞ, measures the stability and smoothness of the output power and the second part, F2 ðtÞ, protects the output power from impulse changes. Calculation of F1 ðtÞ and F2 ðtÞ are given in (10) and (11).

F 1 ðt Þ ¼ 105ðem spÞ=sp

ð10Þ

where em is the mean of error rate, and sp is the setpoint or desired value.

F 2 ðt Þ ¼ 105ðemax omax Þ=omax

ð11Þ

Here, omax is the acceptable overshoot value. emax is the highest overshoot value in the running system.

Please cite this article as: Z. Civelek, Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j.jestch.2019.04.010

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2.2.4. Performance analysis of AIGA For performance analysis of AIGA, Benchmark functions, frequently used in IGA’s performance analysis in the literature are utilized. The graphs of these Benchmark functions are presented in Fig. 5 and their formulas are provided in Table 2. In this study, controller was optimized by genetic algorithm. This requires the conversion of decimals (information coming from controller) to binary (required for optimization by genetic). During the test runs, it is realized that the values of the numbers may change arising from conversion from decimal to binary and vice versa. It is further seen that this value change degrades the performance of the GA. To overcome this error, in this study, number of significant digits after the decimal point is asked from user and binary encoding is based on this number. Furthermore, the maximum number of crossover points that was fixed in IGA [25] is set as variable depending on the number of genes in the chromosome

in AIGA in here. Moreover, mutation rate and number of crossover points are determined as a function of the repeated best individual In the tests performed, for all three algorithms, population number and the crossover rate were set as 15 and 90% respectively. The standard GA’s mutation rate was 8% and the crossover method was single point crossover. Mutation rates of IGA and AIGA are set between 8%  200% and 8%  500% by the code implemented in the study. The maximal variable multi-point crossover number in IGA, was constant (n) however in the code implemented it is determined as a function of chromosome length in AIGA. The results of Benchmark functions for all the three algorithms are summarized in table 3. The expected results column of Table 3 shows the functions’ minimum values. The standard GA and IGA columns show closeness to the expected result at the end of 1000 iterations. Since the encoding of the algorithms was done in Matlab / Script envi-

Fig. 5. Graphs of some Benchmark functions used in IGA’s performance analysis in the literature.

Please cite this article as: Z. Civelek, Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j.jestch.2019.04.010

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Z. Civelek / Engineering Science and Technology, an International Journal xxx (xxxx) xxx Table 2 Equations of some Benchmark functions used in IGA’s performance analysis in the literature. Function name

Function P f ðxÞ ¼ ni¼1 x2i

Sphere function

Limits f ðx1 ;    ; xn Þ ¼ f ð0;    ; 0Þ ¼ 0

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2

f ð1; 1Þ ¼ 0

 e0;5ðcos ð2pxÞþcos ð2pyÞÞ þ e þ 20   f ðx; yÞ ¼ sin2 ð3pxÞ þ ðx  1Þ2 1 þ sin2 ð3pyÞ þ ðy  1Þ2 ð1 þ sin2 ð2pyÞÞ

Ackley’s function

f ðx; yÞ ¼ 20e0;2

Lévi function

0;5ðx þy Þ

f ð1; 1Þ ¼ 0

Beale’s function

f ðx; yÞ ¼ ð1; 5  x þ xyÞ þ ð2; 25  x þ xy Þ þ ð2; 625  x þ xy Þ

f ð3; 0; 5Þ ¼ 0

Goldstein–Price function

f ðx; yÞ ¼ ð1 þ ðx þ y þ 1Þ2 ð19  14x þ 3x2  14y þ 6xy þ 3y2 ÞÞð30 þ ð2x  3yÞ2 ð18  32x þ 12x2 þ 48y  36xy þ 27y2 ÞÞ

f ð0; 1Þ ¼ 3

Booth’s function

f ðx; yÞ ¼ ðx þ 2y  7Þ2 þ ð2x þ y  5Þ2

f ð1; 3Þ ¼ 0

2 2

2

3 2

Table 3 Benchmark function results of Standart GA, IGA and AIGA. Standard GA

IGA

AIGA

Function name

expected results

results

Iteration number

results

Iteration number

results

Iteration number

Sphere function Ackley’s function Lévi function Beale’s function Goldstein–Price function Booth’s function

0 0 0 0 3 0

4.6087e-06 0.1086 0.0687 0.3602 1.0902e + 07 0.7363

1000 1000 1000 1000 1000 1000

6.0725e-10 1.1990e-04 4.7990e-06 0.0502 3.0000 0.0145

1000 1000 1000 1000 1000 1000

1.0026e-15 0.0000 1.0000e-15 0.9978e-15 3.0000 1.0000e-15

75 192 107 331 104 290

Table 4 Some test functions. Function 1 Function 2 Function 3 Function 4

pffiffiffiffiffiffiffiffiffiffi sin 6 x2 þy2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi f 1 : maxf ðx; yÞ ¼ 1 þ x: sin ð4pxÞ  y: sin ð4py þ pÞ þ p 6 2 x þy2 þ1015 x  2 y2 2 ½x2 ðyþ1Þ2  x Þ  1 :e½ðxþ1Þ2 y2   10:  x3  y5 :eð f 2 ¼ maxf ðx; yÞ ¼ 3:ð1  xÞ :e 3 4:lg2ðx0;0667Þ2  5 4:lg2ðx0;0667  Þ2 0;64 0;64 f 3 ¼ maxf ðx; yÞ ¼ sinð5; 1:p:xÞ30 :e :sinð5; 1:p:yÞ30 :e f 4 ¼ maxf ðx; yÞ ¼ ½20 þ x2  10: cos ð2pxÞ þ y2  10: cos ð2pyÞ

x; y 2 ½1; 1 x; y 2 ½3; 3 x; y 2 ½0; 1 x; y 2 ½5; 5

Table 5 Algorithm implementation results of test functions. NFO: Number of finding the optimum

f1 f2 f3 f4 Mean

SGA

BSGA

DMGA

AGA

SOGA

IGA

AIGA

53 38 0 0 22,75

1000 1000 998 11 752,25

997 969 861 150 744,25

1000 998 905 10 728,25

1000 998 997 1000 998,75

1000 1000 1000 996 999

1000 1000 1000 1000 1000

ronment, 1:1015 was used instead of absolute zero. Thus the value,1:1015 allowed by Matlab, was used as the desired sensitivity. In Table 3, the iteration number column indicates the number of iterations performed for each algorithm to reach the desired results. For example, while Standard GA in the Sphere function reaches 4; 6:106 , IGA reaches 6; 76:1010 at the end of 1000 itera15

tions. Since, AIGA reached 1; 00:10 at the 75th iteration, superiority of AIGA to both Standard GA and IGA in terms of the number of iterations and the obtained result can easily be seen. This, better performance of IAGA, can also be seen in table 3 for other Benchmark functions. In addition to the performance analysis of the benchmark functions, IAGA was subjected to the test functions given in [28] and shown in table 4. The results of IAGA from this study and of IGA from [25] are summarized in Table 5. Moreover Table 5 shows the number of optimum solutions obtained at the end of 1000 iterations obtained by test functions given in Table 4. Table 5 shows that, AIGA has the advantages of the Standard GA, the Adaptive GA, the Abbreviated BSGA, the Adaptive Mutation Rate GA(the Abbreviated DMGA), the Self Organizing GA (SOGA)

mentioned in [Zhang et al 2009] and the Intelligent GA [25]. It is seen in Table 5 that, AIGA achieved 1000 optimum results for all of the four functions presented in Table 4.

3. Implementation 3.1. Wind turbine Combining fuzzy controllers with modern optimization techniques enabled better and faster control systems. Thus, in this study, AIGA is implemented in adjusting the coefficients of normalization, denormalization and fuzzy controller. Wind power (P); is proportional to the cube of the wind velocity and is given in (12).

P ¼ 0:5qAv 3

ð12Þ

Here; q = air density (kg/m ), A = area swept by the blades (m2 ), v = wind speed (m/s). Fig. 6 shows the change in wind power with respect to wind speed for an uncontrolled system. 3

Please cite this article as: Z. Civelek, Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j.jestch.2019.04.010

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Fig. 6. Wind speed-output power curve without control.

Fig. 8. The {p -TSR curve for different b-angle values.

Fig. 7. Power factor ({p )-TSR (k) curve.

The wind turbine can’t transfer all of the wind power into energy. This rate, which is limited by the Betz limit, can not exceed 59%. The amount of power that can be derived from the wind turbine is determined by the power coefficient ({p ) of the wind turbine, which is a function of the blade pitch angle (b) and the blade tip speed ratio (k). Fig. 7 shows the variation of the power coefficient (Cp) according to the blade tip speed ratio. The mechanical power that the wind turbine can obtain from the wind is given in (13) and (14).

Pxt ¼ P{p ðb; kÞ

ð13Þ

Pxt ¼ 0:5qAv 3 {p ðb; kÞ

ð14Þ

Here; {p ðb; kÞ is the power coefficient of the turbine, b is the wing pitch angle, k is the blade tip speed ratio (TSR). The power coefficient, {_p, which is nonlinear in high order and varies with the speed of the wind, is given in (15).



21 116 {p ¼ 0:5176  0:4b  5 e ki þ 0:0068k ki

ð15Þ

The value of ki in (16) is substituted in (15) and the value of {p is calculated. ki is an intermediate variable used to facilitate calculations.

1 1 0:035 ¼  ki k þ 0:08b 3b þ 1

ð16Þ

Blade tip speed ratio-TSR is blade angular velocity and wind velocity ratio and is given in (17).

Fig. 9. Wind Turbine operation regions.

k¼

xxt R

v

ð17Þ

Here; xxt is the turbine rotor’s angular velocity (rad/s). R is the wind turbine’s blade radius (m). Fig. 8 shows the relationship between the blade tip speed ratio and the power coefficient, with the blade angle. Any change in the wind turbine, rotor speed, or wind speed changes the blade tip speed ratio which eventually changes the power coefficient. Thus, the power coefficient will change the amount of power obtained from the wind. According to (9) and (10), by changing b angle, {p , the power coefficient is changed. Wind turbine power control is based on this principle. The mechanical output power of a variable-speed wind turbine is also variable. As can be seen in Fig. 9, there are four working zones in the wind speed - output power curve of variable speed, variable pitch angle wind turbines. Region I, is where the wind speed is less than the cut-in value, where the output power is zero. At this region, turbine does not work. Region II, is the area between the cut-in and the nominal speed. Region III, is the zone between nominal speed and cut-out. Region IV, on the other hand, is the wind speeds above the cut-out value at where, the wind turbine is stopped due to safety reasons. Getting the maximum power is especially important for Region II. At the start of Region III, the tur-

Please cite this article as: Z. Civelek, Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j.jestch.2019.04.010

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bine will reach the nominal gust at nominal wind speed. However, as the wind speed increases, the output power will also increase. Thus, a control system is needed to keep the output power constant within the design limits. This is achieved by changing blade angle which eventually changes the power coefficient and consequently modifies the output power. By increasing the blade pitch angle b, the output force P is tried to be kept constant.

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Sugeno Control block as well as the 15 coefficients shown in (7). Thus, the genetic algorithm optimizes 15 + 3 = 18 variables. To implement genetic algorithm in the fitness functions, error values are needed. These error values are transferred to Matlab / Workspace using the Simulink/error block. The wind speed used in simulation is shown in Fig. 11. The wind system parameters are summarized in Table 6.

4. Simulation The simulation was performed in Matlab / Simulink environment. The Simulink / Wind System Turbine + Generator block shown in Fig. 10 is designed using (12)-(17) of the wind energy system shown in Section 3.1. This block accepts wind speed and pitch angle values as inputs and outputs the output power generated. The Takagi-Sugeno type fuzzy controller described in Section 2.1 is used to control the output power. The controller shown in Fig. 10 accepts the derivation of the error and error shown in Figs. 2 and 3 as an inputs. For this reason, the required power level (set point) and output power for the Simulink / Fuzzy Sugeno Control block are given as inputs. The values obtained from these entries are used to calculate the error and error derivative within the block. The Takagi-Sugeno fuzzy controller takes the coefficients shown in (7) from the genetic algorithm. To achieve this, the coefficient entries from Matlab / Workspace are applied to the Simulink / Fuzzy Sugeno Control block. The genetic algorithm optimizes the normalization and denormalization coefficients of the inputs and outputs used in the Simulink / Fuzzy

Fig. 11. Wind Speed fed to the system.

Fig. 10. Simulink / Wind System Turbine + Generator block implemented in the study.

Please cite this article as: Z. Civelek, Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j.jestch.2019.04.010

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Z. Civelek / Engineering Science and Technology, an International Journal xxx (xxxx) xxx Table 6 Wind system parameters. Simulated System Parameters Nominal output power Working mode Cut in wind speed Nominal wind speed Cut out wind speed Rotor diameter Sweep area Blade number Nominal rotor speed Rotor speed range Gear box rate Generator number Generator type Generator nominal output Generator nominal cycle Generator voltage

500 kw Network connection 3 m/s 12 m/s 25 m/s 48 m 1810 m2 3 30 rpm 10–30 rpm 01:50 1 PMSG 500 kw 1500 rpm 690 v Fig. 13. Variation of Pitch angles.

5. Simulation results Simulated wind energy system was run for 300 s. The genetic algorithm was run on 200 iterations. The population of the genetic algorithm was chosen as 15. So for each iteration model was run 15 times. Fig. 12 shows the outputs of optimized and nonoptimized systems. As can be seen clearly in Fig. 12, the genetic algorithm has successfully optimized the coefficients and the 18 variables. The optimized system output is quite good and smooth compared to the nonoptimized system. The fuzzy controller produces pitch angle value according to the wind data applied to the input of the wind turbine. The pitch angle values produced are shown in Fig. 13. With these pitch angle values, the output power is kept stable. The fitness function graph showing that the genetic algorithm finds appropriate values is shown in Fig. 14. AIGA changed the mutation rate as shown in Fig. 15 when it decided that the system trapped into a local minima or maxima. Thus, localities can easily

Fig. 14. Variation of fitness values.

Fig. 15. Mutation rates.

be escaped. The multi-point crossover graph, adding richness to the generated population, is shown in Fig. 16. The y-axis in Fig. 16 shows the number of crossing points applied at each iteration. 6. Conclusion

Fig. 12. Outputs of optimized and nonoptimized systems.

AIGA has been developed by making improvements on the previously designed IGA. The superiority of AIGA has been proven by

Please cite this article as: Z. Civelek, Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j.jestch.2019.04.010

Z. Civelek / Engineering Science and Technology, an International Journal xxx (xxxx) xxx

Fig. 16. Crossover point changes.

its test functions. The AIGA was then used to optimize a fuzzy controller designed to control the blade angle of wind turbines. The coefficients of the Takagi-Sugeno type fuzzy controller and the normalization and denormalization values were successfully optimized with a total of 18 variable AIGAs. Better wind turbine pitch angle control achieved by SugenoTakagi controller optimized by AIGA will improve the stability of wind turbine’s output power, providing a much more stabilized power supply to the energy network. With better control of the pitch angle, the wind turbine will be protected from damaging wind speeds in a faster and a better manner. This will eventually increase the life time of wind turbine and reduce the energy production costs. References [1] T. Senjyu, R. Sakamoto, N. Urasaki, H. Higa, K. Uezato, T. Funabashi, Output power control of wind turbine generator by pitch angle control using minimum variance control, Electr. Eng. Jpn. 154 (2) (2006) 10–18. [2] T. Burton, N. Jenkins, D. Sharpe, E. Bossanyi, Wind energy handbook, John Wiley & Sons, 2011. [3] M. Jelavic´, V. Petrovic´, N. Peric´, Estimation based individual pitch control of wind turbine, Automatika 51 (2) (2010) 181–192. [4] J. Qi, Liu Y. In, PID control in adjustable-pitch wind turbine system based on fuzzy control, in: Industrial Mechatronics and Automation (ICIMA), 2010 2nd International Conference on, IEEE, 2010, pp. 341–344. [5] T.L. Van, T.H. Nguyen, D.-C. Lee, Advanced pitch angle control based on fuzzy logic for variable-speed wind turbine systems, IEEE Trans. Energy Convers. 30 (2) (2015) 578–587. [6] A. Lasheen, A.L. Elshafei, Wind-turbine collective-pitch control via a fuzzy predictive algorithm, Renew. Energy 87 (2016) 298–306. [7] B. Bahraminejad, M.R. Iranpour, Comparison of Interval Type-2 Fuzzy Logic Controller with PI Controller in Pitch Control of Wind Turbines, Int. J. Renew. Energy Res. (IJRER) 5 (3) (2015) 836–846.

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Please cite this article as: Z. Civelek, Optimization of fuzzy logic (Takagi-Sugeno) blade pitch angle controller in wind turbines by genetic algorithm, Engineering Science and Technology, an International Journal, https://doi.org/10.1016/j.jestch.2019.04.010