Black Widow Optimization-Based Optimal PI-Controlled Wind Turbine Emulator

In this article, the parameters of the proportional-integral (PI) controller of the wind turbine (WT) emulator, i.e., proportional and integral gain of the PI controller, are optimized using a black widow optimization algorithm (BWOA). The proposed system is developed and analyzed using MATLAB/Simulink environment. The performance of the BWOA optimized PI controller is compared with a BAT algorithm, particle swarm optimization, and genetic algorithm optimized PI controller to measure the effectiveness of the proposed control system. The developed system is tested for different operating conditions such as static wind speed settings, static pitch angle conditions, step-change in wind speed settings, and step-change in pitch angle settings. Finally, the proposed system is realized in real-time by hardware experimentations. The results of the experimentation are compared with simulation results as well. The presented simulation and hardware result shows good agreement, which confirms the effectiveness of the proposed method. Thereby, the proposed optimization-based PI-controlled wind emulator can be recommended for emulating the characteristics of any type of WT with a low-cost system.


Introduction
Wind power generation, integration, and control have gained more attention among researchers globally to achieve global energy sustainability [1]. Typically, wind power generation is the second-largest power energy source in the world [2]. More research is ongoing in maximum power extraction of wind power generation and grid integration [3]. In various applications, such as wind-powered battery charging, wind-powered electric vehicle charging stations, and in similar domains, researchers face an uphill task in testing maximum power tracking algorithms in the matching design of the battery charging controller and control of electric vehicle charging in real-time. Due to the exorbitant cost of wind turbines (WT), the stochastic nature of wind, and numerous program of the FPGA control board. The WT emulator for the stand-alone application was developed in [22]. The WT characteristics were emulated using closed-loop control of SEDCM. The simulation study has been implemented for a WT emulator using MATLAB. PI current control logic of the WT emulator was implemented in the FPGA hardware control board, and it has been employed for the DC motor control.
The controller was used for the DC motor control from the above-reported literature, and mostly PI current control has been employed. Moreover, accurate tuning of gain parameters such as the PI control's proportional and integral value is not reported in the literature for useful emulation of WT characteristics in all regions. Invariably the WT emulator control algorithm was implemented using dSPACE, FPGA, and digital signal processor (DSP). These hardware controllers are costlier and also present complexity in the implementation. It is identified that scope is abundant in developing WT emulator considering the following objectives: to emulate the WT emulator in three operating regions and achieve effective emulation of a WT in all regions by using a black widow optimization algorithm optimized PI controller. The black widow optimization algorithm optimized PI controller is compared with the genetic algorithm (GA), BAT algorithm, and particle swarm optimization (PSO) to optimize the PI current controller and realize WT emulator control algorithm using a low-cost microcontroller board.
The main contributions of the article can be given as follows: • Proposed an effective control method to design and analysis of WT emulator.

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The gains of the PI controller were effectively optimized using a black widow optimization algorithm.

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Optimized PI controlled DC-DC buck converter fed permanent magnet direct current motor with a low-cost microcontroller is proposed.

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The prototype of the proposed WT emulator is developed, and obtained results are compared with the results acquired via simulation.

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The proposed emulator's efficiency has been tested for three different cases to assess the developed WT emulator's superiority.
The paper's organization as follows: design and analysis of WT emulator using PI controlled DC-DC converter fed PMDC motor is presented in Section 2. Section 3 presents the black widow optimization algorithm (BWOA), GA, PSO, and BAT algorithm optimization for PI controlled WT emulator. Simulation results and discussions are outlined in Section 4, and in Section 5, explanations about hardware implementation are presented. Concluding remarks are provided in Section 6.

Modeling of WT Emulator
The mathematical modeling of WT, DC-DC buck converter, PMDC motor, and PI controller is discussed in the present section. Figure 1 depicts the arrangement of the typical WT emulator. The WT emulator comprises of DC supply, DC-DC buck converter, PMDC motor, WT reference model, permanent magnet synchronous generator (PMSG), current controller, PWM pulse generator, and electrical load. The WT reference model receives three inputs, i.e., wind speed, pitch angle, and speed of the PMDC motor. Based on these inputs, the WT model generates the reference current for the next stage. The reference current from the WT reference model and the armature current of the PMDC motor are compared, and it is processed through a proportional-integral current controller. The PI current controller generates the duty cycle for the next stage based on the error current. The duty cycle is processed through a PWM pulse generator to generate the PWM pulse for the DC-DC buck converter switch. The converter voltage and current vary based on the duty cycle, and it is used to control the PMDC motor characteristics. The PMDC motor emulates the WT reference model characteristics. In this WT emulator control structure, the PI controller parameters, such as proportional (K P ) and integral (K I ) gains, are optimized using a black widow optimization algorithm. The WT reference model receives three inputs, i.e., wind speed, pitch angle, and speed of the PMDC motor. Based on these inputs, the WT model generates the reference current for the next stage. The reference current from the WT reference model and the armature current of the PMDC motor are compared, and it is processed through a proportional-integral current controller. The PI current controller generates the duty cycle for the next stage based on the error current. The duty cycle is processed through a PWM pulse generator to generate the PWM pulse for the DC-DC buck converter switch. The converter voltage and current vary based on the duty cycle, and it is used to control the PMDC motor characteristics. The PMDC motor emulates the WT reference model characteristics. In this WT emulator control structure, the PI controller parameters, such as proportional (KP) and integral (KI) gains, are optimized using a black widow optimization algorithm.

Modeling of WT Reference Model
The mathematical model of WT is the heart of the WT emulator. The WT's mathematical model provides the reference torque or current for the current controller to mimic the characteristics of the WT using a DC-DC buck converter fed PMDC motor. The WT torque is related to the speed of the PMDC motor, pitch angle, and wind velocity, and it is expressed in Equation (1): where Cp(λ,β) is WT power coefficient, VW is the wind velocity or speed (m/s), R is the turbine radius (m), ρ is the air density (kg/m 3 ), β is the pitch angle (deg), and λ is the tip speed ratio. The WT power coefficient is related to pitch angle and tip speed ratio, and it is expressed in Equation (2): where C1, C2, C3, C4, C5, and C6 are the empirical power coefficients, and the values for these coefficients are 0.5176, 116, 0.4, 5, 21, and 0.0068, respectively. λi is the tip speed ratio at i th step time. Figure 2a shows the WT power coefficient's response concerning tip speed with different pitch

Modeling of WT Reference Model
The mathematical model of WT is the heart of the WT emulator. The WT's mathematical model provides the reference torque or current for the current controller to mimic the characteristics of the WT using a DC-DC buck converter fed PMDC motor. The WT torque is related to the speed of the PMDC motor, pitch angle, and wind velocity, and it is expressed in Equation (1): where Cp(λ, β) is WT power coefficient, V W is the wind velocity or speed (m/s), R is the turbine radius (m), ρ is the air density (kg/m 3 ), β is the pitch angle (deg), and λ is the tip speed ratio. The WT power coefficient is related to pitch angle and tip speed ratio, and it is expressed in Equation (2): where C 1 , C 2 , C 3 , C 4 , C 5 , and C 6 are the empirical power coefficients, and the values for these coefficients are 0.5176, 116, 0.4, 5, 21, and 0.0068, respectively. λ i is the tip speed ratio at i th step time. Figure 2a shows the WT power coefficient's response concerning tip speed with different pitch angles. From this figure, the maximum power coefficient C pmax is 0.48 for pitch angle equal to 0 • and normalized tip speed ratio (λ nom ) equal to 8.1 [23].
The tip speed ratio and power of the WT model being expressed in Equations (3) and (4), respectively, where A is the turbine swept area (m 2 ), and N is the speed of the generator (rad/s). In this work, the rated power of the WT is fixed at 500 W; base wind speed is set at 12 m/s. Figure 2b shows the response of WT power concerning the speed of the WT at different wind speed profiles, and Figure 2c shows the response of WT power concerning the speed of the WT at different pitch angles.
The tip speed ratio and power of the WT model being expressed in Equations (3) and (4), respectively, where A is the turbine swept area (m 2 ), and N is the speed of the generator (rad/s). In this work, the rated power of the WT is fixed at 500 W; base wind speed is set at 12 m/s. Figure 2b shows the response of WT power concerning the speed of the WT at different wind speed profiles, and Figure  2c shows the response of WT power concerning the speed of the WT at different pitch angles.

Modeling of the DC-DC Buck Converter
The buck converter can convert the fixed DC voltage into a variable DC output voltage based on

Modeling of the DC-DC Buck Converter
The buck converter can convert the fixed DC voltage into a variable DC output voltage based on the buck converter's duty cycle. The relation between duty cycle and an output voltage of the buck converter can be expressed as [12]: where V(s) is the converters output voltage, vs. is the input voltage, D(s) is the duty cycle, and R L is a resistive load of the converter in ohms. The specification of parameters used for the DC-DC buck converter is: inductance (L) is 10 mH, capacitance (C) is 4800 µF, switching frequency is 3 kHz, the voltage rating is 240 V, and the power rating is 750 W.

Modeling of the PMDC Motor
The PMDC motor is used to convert electrical energy into useful mechanical energy based on its input voltage. The transfer functions related to the mechanical and electrical parameters of the motor, such as speed, input voltage, and armature current can be expressed as [12]: where V(s) is the input voltage of the motor, I a (s) is the armature current of the motor, N(s) is the speed of the motor, B is the frictional coefficient of the motor, J is the inertia of the motor, L a is the armature inductance of the motor, R a is the armature resistance of the motor, K t is the torque constant of the motor and K b is the back emf constant of the motor. The specification used for this motor is: J is 0.02215 kg-m 2 , B is 0.002953 N-m/(rad/s), R a is 2.581 ohms, L a is 0.028 H, K b is 0.08 V/rpm, K t is 1 N-m/A, the power rating is 700 W, and voltage rating is 220 V.

Modeling of the PI Controller
The transfer function model of the proportional-integral controller used for the WT emulator can be expressed as: where K P , K I is proportional gain and integral gain of the PI controller, respectively. The error current is denoted by ∆I a (s). Generally, the PI controller's gain parameter is tuned by the trial and error method and the ZN method. However, these methods had some disadvantages, such as the trial and error method, which takes more time to find the PI controller's optimal value; the ZN method only provides the initial guess for the PI controller's gain parameter. To overcome this problem, optimization techniques may be utilized to adjust the parameter of the PI controller. In this work, a new optimization algorithm, i.e., a black widow optimization algorithm, is used to optimize the parameter of the PI current controller of the emulator to emulate the exact characteristics of the reference WT mathematical model. Figure 3 shows the overall block diagram of the PI controlled DC-DC converter fed PMDC motor-based WT emulator.
provides the initial guess for the PI controller's gain parameter. To overcome this problem, optimization techniques may be utilized to adjust the parameter of the PI controller. In this work, a new optimization algorithm, i.e., a black widow optimization algorithm, is used to optimize the parameter of the PI current controller of the emulator to emulate the exact characteristics of the reference WT mathematical model. Figure 3 shows the overall block diagram of the PI controlled DC-DC converter fed PMDC motor-based WT emulator.

Tuning of PI Current Controller of WT Emulator Using BWOA
The proposed near accurate WT emulator using a black widow optimization algorithm optimized PI controlled DC-DC converter fed permanent magnet direct current (PMDC) motor is presented in this section. The PI current controller parameters such as proportional gain (KP) and integral gain (KI) of the WT emulator is optimized using the black widow optimization algorithm (BWOA). The black widow optimization algorithm is imitating the lifestyle of the evolution of the black widow spider. Generally, female black widow spiders make the net during the night and leave some pheromone in some place of her net to attract male black spiders to have matting. Male black widow spiders get attracted by this pheromone and join in the net. The female black widow spider eats the male black widow spider after or during mating. After mating, the female black widow lays egg socks on the net. After 11 days, young spiders come out from the eggs, and these spiders will participate in sibling cannibalism. The young spiders stay in the mother's net for a short period, and interestingly, the mother even eats some young spiders during this brief period sometimes. Other young spiders from the net are considered the fittest young spiders based on this concept; this black widow optimization algorithm is developed [24].

Tuning of PI Current Controller of WT Emulator Using BWOA
The proposed near accurate WT emulator using a black widow optimization algorithm optimized PI controlled DC-DC converter fed permanent magnet direct current (PMDC) motor is presented in this section. The PI current controller parameters such as proportional gain (K P ) and integral gain (K I ) of the WT emulator is optimized using the black widow optimization algorithm (BWOA). The black widow optimization algorithm is imitating the lifestyle of the evolution of the black widow spider. Generally, female black widow spiders make the net during the night and leave some pheromone in some place of her net to attract male black spiders to have matting. Male black widow spiders get attracted by this pheromone and join in the net. The female black widow spider eats the male black widow spider after or during mating. After mating, the female black widow lays egg socks on the net. After 11 days, young spiders come out from the eggs, and these spiders will participate in sibling cannibalism. The young spiders stay in the mother's net for a short period, and interestingly, the mother even eats some young spiders during this brief period sometimes. Other young spiders from the net are considered the fittest young spiders based on this concept; this black widow optimization algorithm is developed [24].
The black widow optimization proceeds with a random initial black widow spider population. This population has male and female black widow spiders for generating offspring for the next generation. The initial population of black widow spiders can be expressed as (11) where X N,d is the population of black widow spiders, d is the number of decision variables, N is the number of population, lb is the lower bound of the population, and ub is the upper bound of the population. The potential solution populations (X N,d ) are used to minimize or maximize the following objective function represented in Equation (12): Sustainability 2020, 12, 10357 The next process in the black widow optimization algorithm is reproducing the young spiders from male and female spiders' mating. During or after mating, male spiders may be eaten by female spiders. The random selection process is used to select the pair of spiders for mating to reproduce young spiders. The reproduction process of the black widow optimization is expressed by the equation given in Equation (13): where Y i,d, and Y j,d are the young spiders from reproduction, i and j are a random number between 1 to N and β is the random number between 0 to 1. To avoid random duplication selection of pairs, the reproduction process is carried out for d/2 times. After reproduction, the mother spider population and young spider population are sorted with their fitness function value and cannibalism rate. During the optimization process, three cannibalism procedures are considered. The first one is sexual cannibalism, where the female spider population eats the male spider population during or after mating. This concept can be applied to the fitness value of the female and male spider populations. The second one is sibling cannibalism, where the healthy young spiders eat the weaker young spiders. This concept is applied using cannibalism rate, and with this rate only, fittest young spiders remain in the population, and others are discarded from the population. In the third type of cannibalism, the young spiders eat their mother. This concept is applied based on the fitness value of the mother spider and young spiders.
The next process in the black widow optimization is mutation. The young spiders are selected based on the mutation rate, and a small random value is added with selected young spiders for mutation; and this process is expressed in Equation (14): where Z k,d is the mutated spider population, Y k,d is the randomly selected young spider, k is the random number, and α is the random mutate value. This black widow optimization algorithm depends on three parameters, namely the reproduction rate (RP), cannibalism rate (CP), and mutation rate (MR). The reproduction rate controls the generation of young spiders and provides opportunities to explore the search space for finding a better solution. The cannibalism rate controls the weaker fittest population in the generation, and only the stronger fittest populations are allowed for the next generation. The mutation rate controls the diversity in the current generation to the next generation. The flowchart for the BWOA is shown in Figure 4.
The optimization of the PI controller using BWOA is shown in Figure 5. The BWOA receives the absolute current error as a fitness value from the WT emulator. BWOA optimizes the proportional gain and integral gain to minimize the absolute error in the system. To verify the black window optimization method's effectiveness, it is compared with the BAT algorithm, particle swarm optimization, and genetic algorithm. The parameter used for the GA, PSO, and BWOA is shown in Table 1.
The GA, PSO, BAT, and BWOA optimization is implemented in the R2017b MATLAB software and tested in an i3-4005U CPU, 1.7 GHz personal computer. These algorithms have been executed for 100 runs and 4040 fitness value evaluated in a single run, i.e., 40 population with 100 generation, which equals 4000 fitness value evaluation plus fitness value evaluation for an initial 40 random population. Optimization algorithm results such as optimal gain parameter, best fitness, worst fitness, standard deviation, mean fitness value, and average computation time are taken for 100 trials with GA, PSO, BAT, and BWOA are presented in Table 2. The convergence plots for these algorithms are provided in Figure 6.  The optimization of the PI controller using BWOA is shown in Figure 5. The BWOA receives the absolute current error as a fitness value from the WT emulator. BWOA optimizes the proportional gain and integral gain to minimize the absolute error in the system. To verify the black window optimization method's effectiveness, it is compared with the BAT algorithm, particle swarm optimization, and genetic algorithm. The parameter used for the GA, PSO, and BWOA is shown in Table 1.   The optimization of the PI controller using BWOA is shown in Figure 5. The BWOA receives the absolute current error as a fitness value from the WT emulator. BWOA optimizes the proportional gain and integral gain to minimize the absolute error in the system. To verify the black window optimization method's effectiveness, it is compared with the BAT algorithm, particle swarm optimization, and genetic algorithm. The parameter used for the GA, PSO, and BWOA is shown in Table 1.    population. Optimization algorithm results such as optimal gain parameter, best fitness, worst fitness, standard deviation, mean fitness value, and average computation time are taken for 100 trials with GA, PSO, BAT, and BWOA are presented in Table 2. The convergence plots for these algorithms are provided in Figure 6.

Simulation Results and Discussions
In this section, the simulation result of GA, PSO, BAT, and BWOA algorithm optimized PI controlled DC-DC buck converter fed PMDC motor based WT emulator is tested with different operating conditions such as WT emulator power-speed characteristics for static wind profile settings, WT emulator power-speed characteristics for static pitch angle settings, step-change in wind profile settings and step-change pitch angle settings.
Wind speed profile set at 12 m/s, 10.8 m/s, 9.6 m/s, 8.4 m/s, 7.2 m/s, and 6 m/s in wind reference models with a pitch angle maintained at 0 • . The corresponding WT emulator power is measured for different speeds of the WT emulator. Figure 7 shows the WT emulator power response with respect speed of the emulator at different wind speed profile settings with GA-PI, PSO-PI, BAT-PI, and BWOA-PI controlled WT emulator.
The emulation efficiency of the WT emulator is related to the power of the wind turbine emulator (P WTE ) and power of the wind turbine reference model (P WTR ), and it is expressed in Equation (15): Table 3 shows the emulation efficiency of the WT emulator for different wind speed profiles. The WT emulator's emulation efficiency range with the GA-PI controller is from 81% to 95.42%, from 88.31% to 97.34% with PSO-PI controller, from 94.85% to 98.21% with BAT-PI controller, and for BWOA-PI controller, it is from 97.63% to 99.32%. It is evident that BWOA-PI controlled WT emulator has provided maximum efficiency than GA, PSO, and BAT PI-controlled WT emulator.
controlled DC-DC buck converter fed PMDC motor based WT emulator is tested with different operating conditions such as WT emulator power-speed characteristics for static wind profile settings, WT emulator power-speed characteristics for static pitch angle settings, step-change in wind profile settings and step-change pitch angle settings.
Wind speed profile set at 12 m/s, 10.8 m/s, 9.6 m/s, 8.4 m/s, 7.2 m/s, and 6 m/s in wind reference models with a pitch angle maintained at 0°. The corresponding WT emulator power is measured for different speeds of the WT emulator. Figure 7 shows the WT emulator power response with respect speed of the emulator at different wind speed profile settings with GA-PI, PSO-PI, BAT-PI, and BWOA-PI controlled WT emulator.    Figure 8 shows the WT emulator power-speed characteristics for different pitch angle settings with GA-PI, PSO-PI, BAT-PI, and BWOA-PI controlled WT emulator. The emulation efficiency of the WT emulator is calculated using Equation (15), and the corresponding details are provided in Table 4.
Pitch angle is set at 0°, 4°, 8°, 12°, 16° and 20° in wind reference model (wind speed fixed at 12 m/s), and corresponding WT emulator power is measured for different speeds of the WT emulator. Figure 8 shows the WT emulator power-speed characteristics for different pitch angle settings with GA-PI, PSO-PI, BAT-PI, and BWOA-PI controlled WT emulator. The emulation efficiency of the WT emulator is calculated using Equation (15), and the corresponding details are provided in Table 4.    The emulation efficiency range of the WT emulator with the GA-PI controller is from 89.2% to 95.4%, from 93.7% to 97.08% with the PSO-PI controller, from 96.74% to 98.44% with BAT-PI controller, and for BWOA-PI controller, it is from 98.48% to 99.36%. It is ascertained that BWOA-PI controlled WT emulator has provided maximum efficiency than GA, PSO, and BAT PI-controlled WT emulator.
WT emulator is tested for a step-change in wind speed profile, i.e., wind speed is varied from 12 m/s to 10.8 m/s, 10.8 m/s to 9.6 m/s for every 2 s, and corresponding results are measured. The WT emulator's current and power response with GA, PSO, BAT, and BWOA optimized PI controller is shown in Figure 9, and the corresponding performance results are presented in Table 5. From this result, the BWOA PI-controlled WT emulator has a less steady-state error, quick settling time, and less rise time. These parameters are not in favor of the other considered algorithms such as GA, PSO, and BAT algorithm optimized PI controlled WT emulator. WT emulator is tested for a step-change in pitch angle, i.e., the pitch angle is varied from 0 • to 4 • , 4 • to 8 • for every 2 s, and corresponding results are measured. The WT emulator's current and power response with GA, PSO, BAT, and BWOA optimized PI controller is shown in Figure 10, and corresponding performance results are presented in Table 6.

Algorithm tr (s) ts (s) Ess (A) tr (s) ts (s) Ess (A) tr (s) ts (s) Ess (A)
GA-PI    Table 5. Performance analysis of developed emulator for step change in wind velocity.

Algorithm tr (s) ts (s) Ess (A) tr (s) ts (s) Ess (A) tr (s) ts (s) Ess (A)
GA-PI    Table 6. Performance results for wind turbine emulator for a step change in pitch angle.

Algorithm tr (s) ts (s) Ess (A) tr (s) ts (s) Ess (A) tr (s) ts (s) Ess (A)
GA-PI From these results, it is observed that the BWOA PI-controlled WT emulator has a less steady-state error, quick settling time, and less rise time. However, these parameters are not in favor of the other considered algorithms such as GA, PSO, and BAT algorithm optimized PI controlled WT emulator. A black widow optimization algorithm optimized PI controlled WT emulator has shown better performance in all operating conditions from these results analyses. In the next section, BWOA optimized PI controlled WT emulator is tested experimentally.

Experimental Verification of BWOA Optimized PI Controlled WT Emulator
In this section, experimental verification of the BWOA algorithm optimized PI controlled WT emulator is presented. Figure 11 shows the hardware block diagram of the proposed WT emulator. Figure 12 shows the snapshot of the hardware setup of the proposed WT emulator. Figure 13 shows the control logic implemented in the ARDUNIO mega board using the MATLAB/Simulink environment.       A total of two potentiometers are used for providing wind speed and pitch angle command for the WT reference model. The proximity sensor used for sensing the PMDC motor's speed is the third input for the WT reference model. ACS 172-30A is used for measuring the current of the PMDC motor. The wind speed command, pitch angle command, and current sensor data being received in the analog channel (A0, A1, and A3 pins) of the ARDUINO mega board. The proximity sensor data are received in the ARDUINO mega board in the digital pin (D9 pin). The wind speed command, Figure 13. BWOA optimized PI controlled WT emulator control logic implementation using MATLAB.
A total of two potentiometers are used for providing wind speed and pitch angle command for the WT reference model. The proximity sensor used for sensing the PMDC motor's speed is the third input for the WT reference model. ACS 172-30A is used for measuring the current of the PMDC motor. The wind speed command, pitch angle command, and current sensor data being received in the analog channel (A 0 , A 1 , and A 3 pins) of the ARDUINO mega board. The proximity sensor data are received in the ARDUINO mega board in the digital pin (D9 pin). The wind speed command, pitch angle command, current sensor data, and speed sensor data are converted into a suitable form using conversion blocks. After conversion, these data are processed via the WT reference model and PI controller to generate the corresponding duty cycle. This duty cycle is processed via the PWM generating unit to generate the DC-DC buck converter's MOSFET pulse. The generated pulse is taken out from the digital pin (D 4 pin) of the ARDUINO mega board and given through the driver board to control the buck converter for emulating the characteristics of the WT reference model.
Three operating conditions are considered for testing the effectiveness of the BWOA optimized PI controlled WT emulator in real-time. In case 1, Wind speed is set at 9.6 m/s. Pitch angle is set at 0 • using potentiometer of the hardware setup and corresponding results such as the voltage of the motor, current of the motor, the line to line voltage of the generator and line current of the generator are measured and shown in Figure 14. The motor's voltage is around 135 V, the current of the motor is around 2 A, and the motor's power is 270 W. The emulation efficiency obtained from the hardware is around 97.5%, and for simulation, it is around 98.95%. In case 2, Wind speed is set at 12 m/s. Pitch angle is set at 0 • using potentiometer of the hardware setup and corresponding results such as the voltage of the motor, current of the motor, the line to line voltage of the generator and line current of the generator are measured and shown in Figure 15. The motor's voltage is around 163 V, the current of the motor is around 3 A, and the power consumed by the motor is 480 W. The emulation efficiency obtained from hardware is around 97.8%, and it is 99.36% for the simulation analysis.
In case 3, Wind speed is set at 12 m/s, and the pitch angle is set at 4 • using potentiometer of the hardware setup. The corresponding results, such as voltage and current of the motor, line-to-line voltage of the generator, and line current of the generator, are measured and shown in Figure 16. The motor's voltage is around 204 V, the current of the motor is around 2.4 A, and the motor's power is 489.6 W. The emulation efficiency obtained from the hardware is around 97.92%, and for simulation, it is around 99.05%. Comparisons of the emulation efficiency from simulation and experimentation for the three cases are shown in Table 7. From the results, it is observed that experimentation results deviate minimally from the simulation results. is around 97.5%, and for simulation, it is around 98.95%. In case 2, Wind speed is set at 12 m/s. Pitch angle is set at 0° using potentiometer of the hardware setup and corresponding results such as the voltage of the motor, current of the motor, the line to line voltage of the generator and line current of the generator are measured and shown in Figure 15. The motor's voltage is around 163 V, the current of the motor is around 3 A, and the power consumed by the motor is 480 W. The emulation efficiency obtained from hardware is around 97.8%, and it is 99.36% for the simulation analysis. angle is set at 0° using potentiometer of the hardware setup and corresponding results such as the voltage of the motor, current of the motor, the line to line voltage of the generator and line current of the generator are measured and shown in Figure 15. The motor's voltage is around 163 V, the current of the motor is around 3 A, and the power consumed by the motor is 480 W. The emulation efficiency obtained from hardware is around 97.8%, and it is 99.36% for the simulation analysis. In case 3, Wind speed is set at 12 m/s, and the pitch angle is set at 4° using potentiometer of the hardware setup. The corresponding results, such as voltage and current of the motor, line-to-line voltage of the generator, and line current of the generator, are measured and shown in Figure 16. The motor's voltage is around 204 V, the current of the motor is around 2.4 A, and the motor's power is 489.6 W. The emulation efficiency obtained from the hardware is around 97.92%, and for simulation, it is around 99.05%. Comparisons of the emulation efficiency from simulation and experimentation for the three cases are shown in Table 7. From the results, it is observed that experimentation results deviate minimally from the simulation results. voltage of the generator, and line current of the generator, are measured and shown in Figure 16. The motor's voltage is around 204 V, the current of the motor is around 2.4 A, and the motor's power is 489.6 W. The emulation efficiency obtained from the hardware is around 97.92%, and for simulation, it is around 99.05%. Comparisons of the emulation efficiency from simulation and experimentation for the three cases are shown in Table 7. From the results, it is observed that experimentation results deviate minimally from the simulation results.

Conclusions
This paper presents the black widow optimization algorithm based on an optimized PI controlled WT emulator. The overall Simulink model of the proposed system was designed and tested in a MATLAB/Simulink environment. BWOA optimized PI controlled WT emulator performances were compared with GA, PSO, and BAT algorithm optimized PI controlled WT emulator. The BWOA optimized PI controlled WT emulator's emulation efficiency range was from 97.63 to 99.36% in simulation. The tracking of the proposed BWOA optimized PI controller's reference command had comparatively less rise time, quick settling time, and less steady-state error than BAT, GA, and PSO algorithm optimized PI controllers. The experimental verification of the proposed BWOA optimized PI controlled WT emulator was carried out in real-time to check the proposed controller's suitability. The emulation efficiency range obtained from experimentation was from 97.5 to 97.92%. Therefore, the proposed black widow optimization algorithm optimized PI controller may be considered suitable for the WT emulator system.

Conflicts of Interest:
The authors declare no conflict of interest.