Linear Parameter-Varying Model Predictive Control for Hydraulic Wind Turbine
Abstract
:1. Introduction
2. Mathematical Modeling
2.1. The Nonlinear Model of the Hydraulic Wind Turbine
2.1.1. Wind Turbine Rotor
2.1.2. Variable Displacement Pump
2.1.3. Variable Hydraulic Motor
2.1.4. Hydraulic Transmission Circuit
- The leakage coefficient, density and bulk modulus of the oil were constant, and did not change with temperature or other factors;
- The charge pump, relief valve and hydraulic lines were not considered;
- The pressure loss was neglected in the hydraulic line.
2.1.5. Synchronous Generator
2.2. LPV Model of the Hydraulic Wind Turbine
3. Model Predictive Control Based on LPV
4. Simulation Study and Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Symbol | Parameter | Value | Unit |
---|---|---|---|
R | Rotor radius | 4 | m |
Air density | 1.225 | kg/m3 | |
Jp | The total inertia of the rotor in the wind turbine and pump | 8 | kg·m2 |
Bp | Damping coefficient of the pump | 0.02 | N·m/(rad·s−1) |
DP | Pump displacement | 300 | ml |
Dm | Motor displacement | 35 | ml |
Bm | Damping coefficient of the motor | 0.009 | N·m/(rad·s−1) |
Jm | The total inertia of the rotor in the variable motor and generator | 0.1278 | kg·m2 |
The effective bulk modulus of hydraulic oil | 1.43 × 103 | MPa | |
Cv | Total system leakage coefficient | 8 × 10−12 | m3/(s·Pa) |
V | The total compression volume | 0.05 | m3 |
The time constant of the generator | 0.02 | s | |
The time constant of the pump | 0.1 | s | |
The time constant of the motor | 0.1 | s |
Parameter | Value | Unit |
---|---|---|
Stator resistance | 0.645 | Ω |
Inductance | 3.371 | mH |
Pole pairs | 2 | - |
Synchronous speed | 1500 | r/min |
Rated line voltage | 380 | V |
Rated power | 10 | kW |
ηg | 95% | - |
Scenario | Wind Speed | Turbulence Intensity | RMSE | PID | LPV-MPC | LPV-MPC with KF |
---|---|---|---|---|---|---|
1 | 8.3 m/s | 7.2% | 0.0133 | 0.0115 | 0.0086 | |
1.5556 | 0.9694 | 0.2653 | ||||
0.0107 | 0.0069 | 0.0017 | ||||
2 | 10 m/s | 5% | 0.0078 | 0.0067 | 0.0049 | |
1.2253 | 0.6867 | 0.0558 | ||||
0.0106 | 0.0045 | 0.0005 | ||||
3 | 10 m/s | 10% | 0.0119 | 0.0076 | 0.0061 | |
1.6785 | 1.0188 | 0.3042 | ||||
0.0112 | 0.0066 | 0.0021 |
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Han, B.; Gao, H. Linear Parameter-Varying Model Predictive Control for Hydraulic Wind Turbine. Actuators 2022, 11, 292. https://doi.org/10.3390/act11100292
Han B, Gao H. Linear Parameter-Varying Model Predictive Control for Hydraulic Wind Turbine. Actuators. 2022; 11(10):292. https://doi.org/10.3390/act11100292
Chicago/Turabian StyleHan, Bin, and Hongyan Gao. 2022. "Linear Parameter-Varying Model Predictive Control for Hydraulic Wind Turbine" Actuators 11, no. 10: 292. https://doi.org/10.3390/act11100292