Upwind Horizontal Axis Wind Turbine Output Power Optimization via Artificial Intelligent Control System

Power capturing capacity is one of the key performance indicators of wind turbines. This article presents a study done on the optimization of output power of upwind horizontal axis wind turbine using artificially intelligent control system. The study shows how blade tip speed ratio (λ) and pitch angle (β) are optimized to increase wind turbines power conversion coefficient (Cp) which increases the output power. An artificial intelligence system named Mandani fuzzy inference system (MFIS) was applied to optimize the power conversion coefficient in combination with blade pitch actuator control. To this end, a novel optimization technique is designed that maximizes the power harvesting ability of wind turbines by updating the parameters of the membership functions of fuzzy logic found in the MFIS. With the application of this optimization method, a power conversion coefficient Cp of 0.5608 value is achieved at optimal values of λ and β. As a result, the energy harvesting ability of the wind turbine considered is improved by 16.74%. This study clearly shows that the wind energy harvesting capacity of wind turbines can be enhanced via optimization techniques that could be further implemented in wind turbine blade pitch drive system. Thus, this novel optimization method creates further insights for the wind energy industry in reducing the cost of energy generation.


Introduction
The wind turbine power capturing capacity is one of its main performances. Variable-speed and variable-pitch horizontal axis wind turbines (HAWT) have a good capacity of power capturing from the wind. These types of wind turbines use typically two control strategies; speed control and blade pitch angle control. When the wind speed is between cut-in and rated values, the speed control can repeatedly alter the rotor speed to maintain it at a value around rated speed, and hence, the turbine output power will be optimized. While the wind speed becomes above the rated speed, blade pitch angle adjustment is mandatory to limit rotor output power to the rated value by maintaining the rotor speed constant at the rated value.
In addition to the wind speed, major parameters of the wind turbine to harvest maximum energy from the kinetic energy of the wind are mainly related to blade aerofoil. These are blade length, blade chord length, blade twist angle (sum of pitch angle and attack angle), and turbine's lift coefficient to drag coefficient ratio. To maximize the power output of the wind turbine rotor, research has focused on the blade aerofoil shape known as a lifting surface. Devices that improve blade aerodynamic such as small skewed fins (vortex generators) are inserted into modern wind turbine blades [1,2]. This is to create a thin current of turbulent air on the surface of the blade aerofoil and prevent the aerofoil from stalling at low wind speed. The turbulent air delays airflow separation or mixes the boundary of the air layer (laminar and turbulent flows on the upper surface of blade aerofoil) with faster-moving air from the free stream. This reduces wake on the upper surface of blade aerofoil, enhances lifting force, and reduces the effect of aerodynamic drag force and losses due to it; and hence improves the wind turbine energy capturing capacity.
The wind turbine rotor can harvest only a fraction of power available in the wind due to the airflow requirements. The ratio of harvested power by wind turbine rotor to extractable power over an area swept by the turbine blade in the wind is called a power conversion coefficient (C p ). According to Betz's limit, theoretically, the maximum value of the power conversion coefficient from wind kinetic energy to mechanical energy is 0.593 [3,4].
The objective of this study is to optimize the power harvesting capacity of the upwind HAWT through optimization of C p using an artificial intelligent control system called the Mamdani fuzzy inference system (MFIS). The wind speed is naturally an uncertain meteorological phenomenon. It causes uncertainty in power harvesting. The fuzzy logic is a very suitable tool to handle such uncertain conditions. The MFIS can map a non-linearity between its inputs and outputs. The major contributions of this study are 1. Use of MFIS scheme for C p optimization with the controller of a wind turbine blade pitch actuator. 2. Optimization of wind turbine output power in wind energy conversion systems (WECS) by robust handling of uncertain wind speed. 3. Introduction of advanced and simplified technique to optimally update parameters of the membership function of fuzzy logic in the proposed scheme. 4. Deployment of the proposed optimization tool, an interesting improvement in the output power of the wind turbine is achieved. In the next parts of this paper, the Literature Review, Methodology, the Optimization Technique, Results and Discussion of the research are presented.

Related Literature Review
Optimization of the power harvesting ability of the wind turbine was carried by many researchers independently using blade element momentum theory (BEMT). Glauert attained a value of 0.416 and Joukowky got 0.5 values for the power conversion coefficient [5]. Gens N. S applied the modified momentum equation and got a better power conversion coefficient than Glauert's and Joukowky's results in HAWT [5]. The optimal actuator disk theory of HAWT was developed by Glauert in 1935. Theoretically, he claimed 0.416-0.587 value of the power conversion coefficient [1]. Currently, BEMT is an industry-standard used by all producers of the wind turbine and its blade [5]. Typical effects of the number of turbine blades and mechanical design of blades aerofoil drag-to-lift ratio on the optimal power conversion coefficient of a horizontal axis wind turbine (HAWT) were presented by Robert E. Wilson and his colleagues [6]. As per the result of their work, the power conversion coefficient is around 0.5. Also, Ranjan Vepa stated that according to the aerodynamic design of the turbine blade and choice of its profile, three-bladed HAWT can convert 35% to 38% of wind energy to mechanical energy [8]. But, in practice, wind turbine converts only 20% to 40% of the wind energy to mechanical energy [7]. Therefore, to improve the power harvesting capacity of the HAWT, an optimization technique for C p is required.
The enhanced value of C p upsurges the wind turbine productivity and hence reduce the cost of energy production. Different algorithms of maximum power point track (MPPT) for performance improvement of WECS were discussed in the literature [9][10][11]. To mention some, tip speed ratio control, power signal feedback control, perturb and observe, hill climb search, optimal torque control, hybrid of MPPT algorithms, and artificial intelligence were debated. The MPPT-curve of the wind turbine was improved by Lyapunov-function based PI control [12]. Accordingly, the 0.472 value of C p was achieved. In another study of MPPT on the permanent magnet synchronous generator employing conventional optimum torque control with a toque error feed-forward algorithm, a C p value of 0.423 was achieved on WECS [13]. According to the researches indication, the maximum achievable value of C p ranges between 0.2 and 0.4 for wind turbines with three or more blades [14,15]. Neuro-fuzzy methods were applied to estimate the C p of the wind turbine and the maximum estimated value was 0.352 [16]. Radial base function neural network along with optimal torque control was employed for MPPT of double fed induction generator (DFIG) using WECS and 0.52 optimal C p is attained [17]. The simulation result of the study on the optimized pathway, aero-generator modeling, and control upon wind turbine driven by PMSG shows a power conversion coefficient of 0.429 [18]. The optimal value of C p of the three-bladed wind turbines is equal to 0.47 [19]. A value of 2.36% improvement in power is obtained by using the maximum extraction technique with power optimization and control [20]. Tony Hawkins [21] implemented robust estimation and Lyapunov extremum seeking control and extracted 47.25% of power in the wind. As per [22], optimally designed wind turbines with two or three blades can have C p above 0.4.
Based on the above discussions on the mechanical design of the wind turbine blade, the HAWT has a good capacity to harvest power from wind. However, due to the uncertain environment, system operational limitation like different losses in the wind energy conversion system (e.g. turbine blade tip loss, and mechanical loss), and controller inaccuracy, generally, wind turbines convert only about 30% to 35% of the available wind energy into electrical energy [8].
The summary of review results related to the recent studies of maximization of output power of the wind turbine is

Reference
Objective Method Optimal Cp [17] Maximum power harvesting RBFNN control strategy of MPPT of WECS 0.5200 [23] Search maximum power point (SMPP) of variable-speed WECS SELF-ADAPTIVE perturb and observe algorithm for MPPT 0.4800 [24] Optimize and control the HAWT PSO with a neuro-fuzzy controller 0. 4669 [25] MPPT for wind turbine Optimal torque control 0.4800 [26] Optimize power capture by wind turbine RBFNN technique 0.4800 [27] Wind turbine output power improvement fuzzy inference based Generator torque control 0.4800 [28] Maximize output power of SCIG based WECS Fuzzy Logic Controller 0.4700 [29] Extract maximum power from the wind control via ANN-PSO for MPPT of small wind turbine 0.4750 [30] Extract maximum energy from the wind Fuzzy logic control based on HCSM 0.4550 [31] MPPT for WECS control via GA Optimization 0.4800 [32] WECS output power maximization Direct torque control of WT driven DFIG 0.4900

Methodology
The wind turbine power conversion coefficient (C p (λ,β)) is associated with the tip speed ratio (λ) and the pitch angle (β) of the turbine blade. The optimal power can be captured only under an optimal value of C p (λ,β) at optimal values of λ and β.
The proposed strategy is employed with real-time wind speed data that was collected from the Adama-II wind farm North site, Adama, Ethiopia. The data was collected at 10 meters above ground from January to June 2020. This site is geographically located at the latitude of 8°18'35.5''N, the longitude of 38°53'4.2''E and elevation of 1712 m above sea level in Ethiopia about 95 km far away to the southeast of Addis Ababa. The picture of the site is presented in Figure 1. The data is collected using the METEO-40 data logger and is logged every 10 minutes. Every day, the METEO-40 data logger stores 144 samples. This data is presented in Figure 2 after extrapolated to the hub height of the SANY SE7715 wind turbine. To validate the result of this study, the factory test report data of the SE7715 wind turbine is used. Practically, the generator's output power and corresponding C p , and rotor speed data were recorded from the SCADA system in the control room. The analysis of data and optimization of C p (λ,β) of the wind turbine was done by using MATLAB software. The simulation and experimental results are compared.
The wind turbine rotor output power (P r ) in watt expressed in (1) as a function of wind speed (V a ) in m/s, air density (ρ) in kg/m 3 , and the swept area (A = πR 2 ) in m 2 with a rotor radius R [33,34]. 2 3 r a Equation (1) indicates the rotor output power depends on and reliant on the pitch angle and the tip speed ratio. Minor variations in λ and β can change the turbine rotor output power. As was discussed in the literature review part of this study, many of the parameters of the wind turbine that influence the energy harvesting ability of the turbine are directly or indirectly related to the blade pitch angle (β). The effect of the blade length in combination with rotor speed (ω) in rad/s and the wind speed on the energy harvesting are governed by the blade tip speed ratio as given in (2). For variable speed and variable pitch regulated HAWT, different but equivalent empirical relations for power conversion coefficient ( ( , are presented as a function of and β in [8,22]. One of such empirical relations [35] is: According to the wind speed condition, pitch angle (β) could be adjusted by the pitch actuator controller; β in (3) is approximately set to zero degrees in the case of the wind speed is below the nominal speed and hence C p ( ,β) depends only on the . This is depicted in Figure 3 for different values of β and computed values for the SE7715 wind turbine, which shows a decrease of C p ( ,β) with an increase of β. To capture maximum power, the turbine should operate at its optimal C p ( ,β). To optimize C p ( ,β), a fuzzy logic control technique is employed. The fuzzy logic is the utmost suitable technique for power extraction from the wind. Because the fuzzy logic can handle an uncertain behavior of the wind speed in energy harvesting by the wind turbine. The key pro of a fuzzy logic-based control tool is that it does not need an exact mathematical model of the system. In the next section, the optimization technique for the output power of the wind turbine is presented.

Output Power Optimization Technique
The Mamdani fuzzy inference system (MFIS) is proposed to maximize the power extraction capacity of off-grid HAWT from the wind. The primary objective of using MFIS is to maximize wind power conversion efficiency-C p ( ,β) of a variable speed horizontal axis wind turbine. The MFIS is integrated with the wind turbine blade pitch actuator control system. The MFIS was built by E. Manani in 1974 for the first time [36].
As revealed in Figure 4 for the proposed optimization scheme, the wind speed data from an anemometer and a power error are the inputs to the pitch angle actuator controller. When the actual wind speed is far from the nominal value, the error between generator output power (P ge = η g η gb P r ; for η g and η gb are the efficiency of generator and gearbox respectively) and generator nominal (P ref ) power will be non-zero. Based on this error and wind speed status, the turbine blade is pitched by the actuator and hence β and rotor speed are optimally regulated. The β and from the wind turbine are inputs to the MFIS model to optimize C p ( ,β). Next, the detail of the MFIS based optimization technique and wind turbine blade pitch actuator control system is presented.

Pitch Angle Control Mechanism
The wind turbine blade pitch actuator control is formulated based on a fuzzy logic controller. It generates a desired command pitch angle (β d ) as seen in Figure 5 and Figure 4. The hydraulic actuator for the wind turbine blade pitch system is modeled using the first-order model as follows [37].
Where τ is the pitch actuator time constant and usually ranges between 0.2 to 0.25 seconds [37]. The specification of the SE7715 wind turbine blade pitch actuator is presented in Table 2.
Considering these specifications, the pitch actuator controller is designed. For normal operation of the wind turbine, with pitch actuator running at 5°/* + with 0.0133% accuracy, the error is , − = 0.0128 * 90°= 1.15°. Hence the time constant is computed as The input of the fuzzy logic controller is the power error (P e ) between the generator's actual output power (P ge ) and the reference power (P ref ), and the real measured wind speed (V a ) at any instant time. P e was calculated as follows.
The ranges of P e and V a are depicted in Table 3. P e is scaled on the base of 1.5 MW, V a is scaled on the base of 25 m/s, and β d is scaled on the base of 90°The fuzzified linguistic variables of the input to the controller of the blade actuator are presented in Table 3 for EVVB, VVB, VB, B, M, S, VS, VVS ZR are fuzzy subsets that represent extreme very very big, very very big, very big, big, medium, small, very small, very very small, and zero respectively. The pitch angle controller was designed to have suitable values for the pitch angle input to the power conversion coefficient optimization scheme. Thus, as shown in Table 3, the most dominant eleven Mandani fuzzy logic rules "IF P e is P Ej AND V a is V Aj THEN β d is β Dj " are used to generate the command input to the blade actuator. P Ej , V Aj , and β Dj represent universes of a discourse of fuzzy subsets of the error, instant wind speed, and the desired pitch angle respectively. The pitch control traces the status of the wind speed and the power error. The power error is zero starting at the wind speed equal to the rated value onward. As the wind speed increases the pitch command too.

MFIS Based Optimization Technique
The degree of the membership functions is the major feature in the computing of the fuzzy logic sets [38]. This study employs fuzzification of inputs (λ and β) crisps to MFIS and output (C p (λ,β) = C p ) crisp of the MFIS. As shown in Figure 4, the MFIS based optimization scheme has four major blocks or stages to process the input-output data pairs.
The first is the fuzzifier of input-output crisp data pairs. As indicated in (7), the triangular-shaped activation function is used to compute membership functions (MFs) of the crisps.
Where ζ stands for the crisps (inputs λ and β) with j ι σ stands for the center and/or width parameters (σ λj ι (k) and σ βj ι (k)) of MFs for ι = 1, 2,…, 25 = L is numbers of fuzzy inference rules, j = 1, 2,… is fuzzy MFs.  The second stage is the fuzzy inference engine that makes decisions using the fuzzy IF-THEN rules with "AND" or "OR" operators. This block contains the rule-base (IF-THEN N rules), database (defines membership functions of fuzzy sets), and decision-making (computes inference operation: max-product or max-min). For instance, the fuzzy rule-ι is Where λ j ι and β j ι , and C pj ι are the fuzzy sets of premises and output consequent at fuzzy rule ι. Based on the knowledge obtained from Figure 3 and model (3a), the fuzzy sets and rules base is presented in Table 4 and Table 5.
Where Z= Zero, S = Small, M = Mean, L = Large, and VL = Very Large is the fuzzy sets of the crisp inputs and output variables. The pitch angle input to MFIS is adjusted by the pitch actuator controller that is presented in section 4.1.
Employing the Mandani max-product inference (obtaining new knowledge or rule from the available knowledge or rule) operation on Eq. (9) is Where the product implication is The third stage is the aggregation of all rules to produce a single output of the fuzzy system as expressed below.
The last stage is the defuzzification. The fuzzy numbers are mapped into a crisp number using the fuzzy max-product combination and centroid of area (COA) defuzzification method. .593] where λ FS, β FS and C p-FS respectively represent the subsets of crisps λ, β and C p . These are the aerodynamic limits of a typical horizontal axis wind turbine with three blades to harvest better energy from the wind. At any iteration number k = 1, 2,..., K, substituting (11) into (13), the crisp output is expressed as in (14).     Graphical demonstration of triangular MFs of λ, β, and C p of a wind turbine are presented in Figure 6. These are plotted for the triangular relations represented in Table 6. As indicated in this figure, the tip speed ratio of value between 0-12, the pitch angle of value between 0-30 degrees and the power conversion coefficient ranges between 0 to 0.593 are used.
They are optimally updated by employing the gradient descent method [39,40] through minimization of the square of the norm of error ( d ε ) between the expected crisp output ( 2 , of fuzzy logic and the desired value ( , , which is expressed as The parameters of MF are updated as Where η is the learning rate and at an initial iteration η ≤ 1 and becomes 0 at the end of iteration for fast convergence of training [41]. To simplify the computation of training, the numerator and denominator of fuzzy logic output crisp equation (14) is separately expressed as Using the chain differential rule, the change in any premise parameter is carried as follows.  (16) is rewritten as in equation (22) considering σ λj ι (k) ≠ 0, σ βj ι (k) ≠ 0 and j ≠ 0. The parameters of the first MF (j = 0) of each crisps input and output of fuzzy are based on the center parameters of the second MFs (j = 1) as depicted in Table 6. To compute parameters of the second MFs using Eq. (22), first, inputs and corresponding expected output data in the fuzzy set, the number of MFs of each input and output and initial value of parameters of MFs is correctly specified as indicated in Table  7. For better accuracy, 50% overlap of MFs at an initial iteration of parameters of the second MF with  Table 7, optimal 1 ( ) k ι Φ is computed at k-iteration. For instance, the first iteration σ λ1 ι (1) is computed using (23). In the same way, σ β1 ι (1) and C p1 ι (1) are computed. At k = 2, the parameters of the second MF of each crisp are Ф 1  As seen in Figure 7, the convergence is reached within the first two iterations under the application of the mentioned learning technique for MFs parameters optimization. The validation of the training result is evaluated by using the root mean squared error of the output in (13); in which the minimum training error of the membership function by the aforementioned method is 0.001485 as in Figure 7.

MF Characteristic Value
At any k-iteration, the parameters of the next MFs (j = 2, 3, 4) are procedurally computed as

Computational Implementation of C p Optimization
There are a total of fifteen (i.e. 3x5) discrete fuzzy sets of the tip speed ratio, the pitch angle, and the power conversion coefficient which are analytically computed from the optimally generated MFs in Table 6. Using these MFs the discrete fuzzy sets of the inputs-output relations are made ready to employ MFIS as depicted in equations (25) - (27). The discrete fuzzy sets defined over the universe of discourse of the blade tip speed ratio ( ) are The discrete fuzzy sets defined over the universe of discourse of the blade pitch angle (β) are ( The discrete fuzzy sets defined over the universe of discourse of the power conversion coefficient (C p ) are Using the discrete fuzzy sets, computation of the optimum power conversion coefficient (C p ) for any size of a wind turbine is carried here. The fuzzy logic crisp output C p should be optimal; hence the power capturing by wind turbine from the wind would be optimal even for lower wind speed. As depicted by (2), the tip speed ratio is related to both the wind speed and turbine rotor speed. As wind speed increases the rotor speed too. The rotor speed can be maintained constant by pitch regulator and hence tip speed ratio too. To implement the MFIS optimization tool for C p , three samples are considered. These are in a lower wind speed region (partial load operation), around the rated wind speed, and in a higher wind speed region (full load operation) cases. For the first case, the rotor speed could be controlled to maintain at the optimal value of 6.268 and the β is maintained at 0 0 .
These have fuzzy rules in their domains [3 9] and [0 0 7.5 0 ] respectively. That is, from Table 5 and Table 6, the membership functions, and the fuzzy rules that have the crisp in the specified domain are defined by R11 and R12 of the MFIS rules. The computation of C p is depicted in the following steps.
Step 1. The individual rule-based implication that is the Mamdani fuzzy min implication yields a resultant output fuzzy set for each activated rules are The activation degrees of membership of the antecedent parts of these rules at the given input crisps are computed using the fuzzy sets depicted in (25) and (26).
Step 3. Aggregation of the two fuzzy sets in (30) is computed to produce single output fuzzy set by Max-operator of fuzzy logic and the result is Step 4. The crisp output value of C p is computed from (31) using the center of the area (COA) defuzzification type as in (32).
The second case is when the wind speed is around the rated value (13 m/s), the blade pitch angle should be increased by a small value to regulate rotor output power to the rated value and secures the wind turbine. Consider for β = 8 0 and = 6 the C p can be computed by MFIS as follows. These crisp inputs have common fuzzy rules in their [3 9] and [7.5 0 22.5 0 ] respective domains. From Table 5 and Table  6, the membership functions and the fuzzy rules that have the crisp in the specified domain are defined by R12 and R13 of the MFIS rules. By repeating the procedure in the first case, the computed C p is 0.4360.
The third case is when the wind speed is greater than the rated value, the blade pitch angle should be increased by moderate value and the tip speed ratio could be smaller to regulate the rotor output power to the rated value.  Table 5 and Table 6, the membership functions and fuzzy rules for these crisp inputs in the specified domain are defined by R4 and R5 of the MFIS rules. Following the steps as in the first case, the computed C p is 0.0329. This study showed 0.5608 is the optimal C p and is greater than the values which are presented under the literature review section. The power conversion coefficient was computed repeatedly at different values of the tip speed ratio and blade pitch angle. The result of C P is plotted in comparison with SE7715 wind turbine factory experimental test results as seen in Figure 8 (a). This result indicated the optimized C p is equal to 0.5608 at 8 m/s, but the maximum C p from the factory experimental test result of the SE7715 wind turbine is 0.4804 at the same wind speed. This is a 16.74% improvement in the power conversion coefficient of the SE7715 wind turbine. Also, the MFIS optimized C p is 0.4360 at 13 m/s wind speed.

Results and Discussion
The corresponding C p from the factory test result of the SE7715 turbine is 0.2537. Figure 8 (a) also showed, at a high wind speed of 22.5 m/s for instance, C p is reduced to 0.0329 to secure the turbine. These results are used to compute the corresponding output power of the SANY SE7715 wind turbine. Using the specifications of this wind turbine in Table  2 and employing (1), the output power is 175.24 kW at 5 m/s wind speed and computed C p of 0.5101. However, from the experimental data in Figure 8 (b) for the same wind turbine, the output is 151.67 kW at 5 m/s wind speed. The improvement in the output power is 23.57 kW. It is equal to a 15.54% improvement in output power. When the wind speed is near the rated value, for instance, the optimal computed C p is 0.542 at 10.5 m/s and hence the rotor output power of the same turbine is 1.725 MW. But the rated power is obtained at 12 m/s as in Figure 8 (b). This shows the developed optimization method provide rated power before the rated wind speed was reached, indicating that more power can be harvested at a lower wind speed. For some wind speeds below the rated value, the result for power harvesting is present in Table 8 for comparison. Figure 8 (b) shows the simulation of output power as a function of wind speed that was computed using the MFIS in comparison with the factory experimental test data.
At higher wind speed, the simulation result of optimized power by MFIS is beyond the turbine rating. Therefore, the output power regulation to the rated value is a must. This is achieved by the pitch actuator control system that was presented in section 4. For higher wind speed, the pitch controller generates large pitch command (β d ), and hereafter the pitch actuator acted on the blade to regulate rotor output power to the rated value. The regulated output power at the corresponding pitch angle and the control variables (power error and wind speed) are presented in Figure 9. Figure 9 portrays the simulation result of (a) the wind speed in the range of cut-in and cut-out speeds of the SE7715 wind turbine, (b) the optimized and regulated output power of the SE7715 wind turbine, (c) the power error between the SE7715 wind turbine output power and the reference power, and (d) blade pitch angle. Figure 9 (a) and (c) are the inputs to the fuzzy logic-based controller of the blade pitch actuator. As indicated in the figure at 18 sec the wind speed is 10.5 m/s, the output power is 1.5 MW that is attained before the rated wind speed is reached showing improvement in harvested power. The power error is 98 W and the pitch angle is 0 0 . When the wind speed is increased beyond 10.5 m/s, the blade pitch angle regulates the turbine rotor output power to the rated value. For instance, at 22.5 m/s wind speed, the computed C p is 0.0479 and at 23.5 m/s wind speed C p is 0.0421 and hence the output power is 1.5 MW and 1.501 MW respectively.  The MFIS optimized power conversion coefficient wind turbine is presented in Figure 10 (a). The MFIS optimized C p is maintained constant over the wind speed range of 5-10 m/s and hence turbine can have better-regulated rotor speed, whereas the experimental result is constant for the wind speed in the ranges of 5-9 m/s. The MFIS optimized and pitch regulated rotor output power in Figure 9 (b) is replotted in Figure 10 (b) for comparison with the factory experimental result. Figure 10 (b) confirmed that the MFIS optimized power is better than the factory experimental result of the SE7715 wind turbine. For instance, at 3.5 m/s wind speed, the MFIS optimized power is 50.8 kW whereas the experimental result is 40.18 kW. That is, with optimized C p , the turbine can harvest power at a wind speed lower than the cut-in speed (3.5 m/s). This showed the proposed MFIS optimization technique is well suitable for wind turbine energy harvesting capacity improvement, and it provided new and interesting results. In summary, the result of the proposed MFIS technique is compared to the results of the most recent researches as shown in Table 8. The proposed MFIS technique for the optimization of wind turbine output power is superior.

Conclusion
The method used for the optimization of the energy harvesting ability of wind turbines is developed by using the MFIS fuzzy logic method. Only one parameter (either center or width of MF of fuzzy logic) is optimally updated and optimization of C p of a wind turbine is carried out to maximize energy harvesting from the wind. C p is enhanced by employing the MFIS. The MFIS optimization technique in combination with the fuzzy logic-based controller of the wind turbine blade pitch drive system achieved C p to improve significantly compared to results of recent researches. Comparing the proposed optimization method result with the factory experimental test result of the SE7715 wind turbine, a 16.74% improvement in the energy harvesting capacity is attained. These are the novel elements of the proposed scheme. The wind turbine that operates with optimal power conversion coefficient can get increased turbine's speed regulation range, achieves optimal C p before it attains rated power, offers improved power curve, and hence increased power generation capacity, and reduces the range of cut-in and rated wind speeds. Practically, a programmable logic-based proportional integral derivative controller is employed in the SE7715 wind turbine. A comparative study between the proposed MFIS optimization method with related recent researches indicates the MFIS optimization improved the energy harvesting capacity of the wind turbine. Practical implementation of MFIS strategy with the developed membership functions tuning optimization method is recommended to enhance the performance of wind turbines.