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

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## Abstract

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## 1. Introduction

- Proposed an effective control method to design and analysis of WT emulator.
- The gains of the PI controller were effectively optimized using a black widow optimization algorithm.
- Optimized PI controlled DC–DC buck converter fed permanent magnet direct current motor with a low-cost microcontroller is proposed.
- The prototype of the proposed WT emulator is developed, and obtained results are compared with the results acquired via simulation.
- The proposed emulator’s efficiency has been tested for three different cases to assess the developed WT emulator’s superiority.

## 2. Modeling of WT Emulator

_{P}) and integral (K

_{I}) gains, are optimized using a black widow optimization algorithm.

#### 2.1. Modeling of WT Reference Model

_{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):

_{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].

^{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.

#### 2.2. Modeling of the DC–DC Buck Converter

_{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.

#### 2.3. Modeling of the PMDC Motor

_{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.

#### 2.4. Modeling of the PI Controller

_{P}, K

_{I}is proportional gain and integral gain of the PI controller, respectively. The error current is denoted by ΔI

_{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.

## 3. Tuning of PI Current Controller of WT Emulator Using BWOA

_{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].

_{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):

_{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.

_{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.

## 4. Simulation Results and Discussions

_{WTE}) and power of the wind turbine reference model (P

_{WTR}), and it is expressed in Equation (15):

## 5. Experimental Verification of BWOA Optimized PI Controlled WT Emulator

_{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.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Wind turbine (WT) Emulator using proportional-integral (PI) controlled DC–DC converter fed permanent magnet direct current motor.

**Figure 2.**Characteristics of WT: (

**a**) Cp-λcharacteristics for different pitch angle, (

**b**) power-speed characteristics at different wind speed profile, and (

**c**) power-speed characteristics at different pitch angle.

**Figure 3.**Block diagram of the PI controlled DC–DC buck converter fed permanent magnet direct current (PMDC) motor-based WT emulator.

**Figure 14.**Experimental results of case 1 conditions: (

**a**) voltage and current of the motor, and (

**b**) L-L voltage and line current of the generator.

**Figure 15.**Experimental results of case 2 conditions: (

**a**) voltage and current of the motor, and (

**b**) L-L voltage and line current of the generator.

**Figure 16.**Experimental results of case3 conditions: (

**a**) voltage and current of the motor, and (

**b**) L-L voltage and line current of the generator.

**Table 1.**Specification of BWOA, genetic algorithm (GA), particle swarm optimization (PSO) and BAT algorithm.

Black Widow Optimization Algorithm | Genetic Algorithm | Particle Swarm Optimization | BAT Optimization | ||||
---|---|---|---|---|---|---|---|

Spider Size | 40 | Population Size | 40 | Swarm Size | 40 | BAT Size | 40 |

Generations | 100 | Generations | 100 | Iterations | 100 | Iterations | 100 |

Reproduction rate | 0.6 | Crossover rate | 0.7 | Cognitive factor (C1) | 1.2 | Lower limit of the frequency (fmin) | 0 |

Cannibalism rate | 0.44 | Social factor (C2) | 1.2 | Upper limit of the frequency (fmax) | 100 | ||

Mutation rate | 0.4 | Mutation Rate | 0.3 | Lower limit of the inertia weight (Wmin) | 0.1 | Loudness factor at starting (R0) | 0.9 |

Upper limit of the inertia weight (Wmax) | 0.9 | Pulse rate at starting (P0) | 0.9 |

Algorithm | K_{P} | K_{I} | Best Fitness | Worst Fitness | Standard Deviation | Mean | Mean Computation Time (s) |
---|---|---|---|---|---|---|---|

GA | 0.0230 | 0.0663 | 0.0250 | 0.47356 | 0.0160 | 0.0299 | 339 |

PSO | 0.0243 | 0.0510 | 0.0243 | 0.45799 | 0.0036 | 0.0259 | 371 |

BAT | 0.0271 | 0.0525 | 0.0241 | 0.43471 | 0.0059 | 0.0266 | 439 |

BWOA | 0.0271 | 0.0522 | 0.0235 | 0.34280 | 0.0086 | 0.0245 | 332 |

Algorithm | Wind Speed Profile | |||||
---|---|---|---|---|---|---|

12 m/s | 10.8 m/s | 9.6 m/s | 8.4 m/s | 7.2 m/s | 6 m/s | |

GA-PI | 95.42 | 94.24 | 92.5 | 89.07 | 86.21 | 81.15 |

PSO-PI | 97.34 | 96.24 | 95.25 | 93.37 | 92.15 | 88.31 |

BAT-PI | 98.21 | 98.16 | 97.50 | 96.40 | 96.20 | 94.85 |

BWOA-PI | 99.32 | 99.07 | 98.95 | 98.37 | 98.06 | 97.63 |

Algorithm | Pitch Angle | |||||
---|---|---|---|---|---|---|

0° | 4° | 8° | 12° | 16° | 20° | |

GA-PI | 95.40 | 92.62 | 92.07 | 91.07 | 90.06 | 89.20 |

PSO-PI | 97.08 | 95.66 | 95.25 | 94.83 | 94.00 | 93.70 |

BAT-PI | 98.44 | 97.92 | 97.67 | 97.05 | 96.94 | 96.74 |

BWOA-PI | 99.36 | 99.05 | 99.05 | 98.50 | 98.22 | 98.48 |

Time (s) | 0–2 | 2–4 | 4–6 | ||||||
---|---|---|---|---|---|---|---|---|---|

Algorithm | tr (s) | ts (s) | Ess (A) | tr (s) | ts (s) | Ess (A) | tr (s) | ts (s) | Ess (A) |

GA-PI | 0.663 | 1.383 | 0.0230 | 2.677 | 3.185 | 0.0274 | 4.294 | 5.112 | 0.0264 |

PSO-PI | 0.317 | 0.520 | 0.0258 | 2.215 | 2.467 | 0.0224 | 4.214 | 4.396 | 0.0244 |

BAT-PI | 0.204 | 0.343 | 0.0121 | 2.111 | 2.386 | 0.0181 | 4.101 | 4.324 | 0.0151 |

BWOA-PI | 0.058 | 0.178 | 0.005 | 2.054 | 2.273 | 0.0065 | 4.056 | 4.258 | 0.0058 |

Time (s) | 0–2 | 2–4 | 4–6 | ||||||
---|---|---|---|---|---|---|---|---|---|

Algorithm | tr (s) | ts (s) | Ess (A) | tr (s) | ts (s) | Ess (A) | tr (s) | ts (s) | Ess (A) |

GA-PI | 0.695 | 1.54 | 0.0240 | 2.677 | 3.415 | 0.0290 | 5.454 | 5.112 | 0.0275 |

PSO-PI | 0.262 | 1.021 | 0.0158 | 2.215 | 3.107 | 0.0178 | 5.102 | 4.396 | 0.0185 |

BAT-PI | 0.165 | 0.854 | 0.0142 | 2.111 | 2.564 | 0.0162 | 4.524 | 4.324 | 0.0151 |

BWOA-PI | 0.067 | 0.231 | 0.0061 | 2.054 | 2.247 | 0.0084 | 4.187 | 4.258 | 0.0072 |

Conditions | Emulation Efficiency in Simulation (%) | Emulation Efficiency in Hardware (%) | Deviation of the Efficiency (%) |
---|---|---|---|

Case 1 | 98.95 | 97.50 | 1.45 |

Case 2 | 99.36 | 97.80 | 1.56 |

Case 3 | 99.05 | 97.92 | 1.13 |

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**MDPI and ACS Style**

Premkumar, K.; Vishnupriya, M.; Sudhakar Babu, T.; Manikandan, B.V.; Thamizhselvan, T.; Nazar Ali, A.; Rabiul Islam, M.; Kouzani, A.Z.; Parvez Mahmud, M.A. Black Widow Optimization-Based Optimal PI-Controlled Wind Turbine Emulator. *Sustainability* **2020**, *12*, 10357.
https://doi.org/10.3390/su122410357

**AMA Style**

Premkumar K, Vishnupriya M, Sudhakar Babu T, Manikandan BV, Thamizhselvan T, Nazar Ali A, Rabiul Islam M, Kouzani AZ, Parvez Mahmud MA. Black Widow Optimization-Based Optimal PI-Controlled Wind Turbine Emulator. *Sustainability*. 2020; 12(24):10357.
https://doi.org/10.3390/su122410357

**Chicago/Turabian Style**

Premkumar, K., M. Vishnupriya, Thanikanti Sudhakar Babu, B. V. Manikandan, T. Thamizhselvan, A. Nazar Ali, Md. Rabiul Islam, Abbas Z. Kouzani, and M. A. Parvez Mahmud. 2020. "Black Widow Optimization-Based Optimal PI-Controlled Wind Turbine Emulator" *Sustainability* 12, no. 24: 10357.
https://doi.org/10.3390/su122410357