Combining Sliding Mode and Fractional-Order Theory for Maximum Power Point Tracking Enhancement of Variable-Speed Wind Energy Conversion
Abstract
1. Introduction
2. Literature Review
Research Gap
3. Materials and Methods
3.1. Mean Components of Wind Turbine
- Anemometer for measuring wind speed; the data are controlled by the controller;
- Blades to propel movement by harnessing the power of the wind;
- Brake, used on storm days or in case of maintenance (hydraulically, mechanically, or electrically);
- Controller to control the functions of the turbine (to turn on and shut off the turbine);
- Gear box, connecting the lower speed shaft with the higher one, which increases the speed from 60 rpm to more than 1000 rpm; in some cases, it could reach the 1800 rpm required to generate electricity;
- Generators to produce 60-cycle AC electricity;
- Low-speed shaft, which moves 30 to 60 rpm based on the wind speed;
- A nacelle at the top of the tower, which contains most of the turbine parts (generator, brake, speed shafts, and controller);
- High-speed shaft, which drives the generator;
- Pitch, which increases the turbine efficiency in case of low-speed wind, or decreases the efficiency in extreme cases;
- Rotor, which comprises the blades along with a hub;
- A tower made of concrete or steel, which produces electricity based on its height;
- Wind vane, which indicates the wind direction and passes the data to the yaw system to move the nacelle to face the wind direction;
- Yaw drive, which receives the data from the vane and keeps the blades facing the wind;
- Yaw motor, which supplies the yaw drive with power.
3.2. Fractional Order Slide Mode Control FOPI SMC_P
3.3. Controller Optimization for FOPID Using PSO
- Tracking Error: The deviation of the system output from the desired reference trajectory.
- Control Effort: The magnitude of the control signals, to ensure that they are within practical limits.
- Robustness: The ability of the controller to maintain performance in the presence of disturbances and model uncertainties.
- Initialization: An array of particles with random positions and velocities is created.
- Fitness Evaluation: Each particle’s fitness value is evaluated according to the desired optimization function.
- Update Best Positions: The algorithm updates the personal best and global best positions based on the current fitness evaluations.
- Update Velocities and Positions: The velocities and positions of the particles are updated using the iterative equations.
- Iteration: Steps 2–4 are repeated until the stopping criterion is met, typically based on the number of iterations or a convergence threshold.
4. Results
4.1. Maximum Power of Wind Turbine
4.2. Response of Controllers with PSO
4.3. Wind Profile
4.4. Response of Controllers with Disturbance and PSO
4.5. Wind Profile Disturbance and Sensor Noise-FOPID SMC with OPT Optimization
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Description | Parameter | Description |
---|---|---|---|
Pr | Rated power | Jg | Generator inertia (high-speed shaft) |
α | Empirical wind shear exponent | ηg | Efficiency of generator |
H | Hub height | αgc | Generator and converter parameter |
R | Radius of rotor | τr | Aerodynamic torque |
ρ | Air density | Cq | Torque coefficient |
ζ | Damping factor | θ∆ | Drive train torsion angle |
ωn | Natural frequency | τg | Generator torque |
Bdt | Torsion damping coefficient | ωr | Angular speed of the rotor |
Kdt | Torsion stiffness | ωg | Angular speed of the generator |
Jr | Rotor inertia (low-speed shaft) | λ | Tip speed ratio |
Br | Rotor external damping | β | Blade pitch angle |
Bg | Generator external damping | vw | Wind speed |
ηdt | Drive train efficiency | Pg | Generated power |
Ng | Gearbox ratio | vm | Mean wind speed |
Tm | Mechanical torque | Te | Electrical torque |
ω | Angular velocity | Cp | Power coefficient |
θ | Blade angle |
FOPID-Controller | FOPID-SMC | |
---|---|---|
Kp | 0.39138 | 0.83778 |
Ki | 0.73452 | 0.01 |
Lambda | 0.80659 | 0.01 |
Kd | 0.01962 | 0.65638 |
Mu | 0.6882 | 0.9234 |
Time Domain | Without Controller | PID | FOPID | Basic Sliding Mode Control | FOPI–Sliding Mode Control | FOPID–Sliding Mode Control |
---|---|---|---|---|---|---|
Rise Times (s) | 10.1620 | 4.3681 | 3.0966 | 0.2105 | 0.2173 | 0.2262 |
Settling Time (s) | 19.1035 | 28.9442 | 37.39 | 1.3753 | 1.4126 | 1.3468 |
Peak Overshoot (%) | 0 | 7.6399 | 46 | 0.0087 | 0.0442 | 1.7527 |
Steady-State Error | 1.5981 | 0.0361 | 0.0022 | 4.9342 × 10−4 | 0.0029 | 3.5838 × 10−4 |
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Al-Dhaifallah, M.; Saif, A.-W.A.; Elferik, S.; Elkhider, S.M.; Aldean, A.S. Combining Sliding Mode and Fractional-Order Theory for Maximum Power Point Tracking Enhancement of Variable-Speed Wind Energy Conversion. Fractal Fract. 2024, 8, 447. https://doi.org/10.3390/fractalfract8080447
Al-Dhaifallah M, Saif A-WA, Elferik S, Elkhider SM, Aldean AS. Combining Sliding Mode and Fractional-Order Theory for Maximum Power Point Tracking Enhancement of Variable-Speed Wind Energy Conversion. Fractal and Fractional. 2024; 8(8):447. https://doi.org/10.3390/fractalfract8080447
Chicago/Turabian StyleAl-Dhaifallah, Mujahed, Abdul-Wahid A. Saif, Sami Elferik, Siddig M. Elkhider, and Abdalrazak Seaf Aldean. 2024. "Combining Sliding Mode and Fractional-Order Theory for Maximum Power Point Tracking Enhancement of Variable-Speed Wind Energy Conversion" Fractal and Fractional 8, no. 8: 447. https://doi.org/10.3390/fractalfract8080447
APA StyleAl-Dhaifallah, M., Saif, A.-W. A., Elferik, S., Elkhider, S. M., & Aldean, A. S. (2024). Combining Sliding Mode and Fractional-Order Theory for Maximum Power Point Tracking Enhancement of Variable-Speed Wind Energy Conversion. Fractal and Fractional, 8(8), 447. https://doi.org/10.3390/fractalfract8080447