Variable Speed Control of Wind Turbines Based on the Quasi-Continuous High-Order Sliding Mode Method
Abstract
:1. Introduction
2. Introduction to High-Order Sliding Mode Control
2.1. Conventional Sliding Mode Control
2.1.1. Chattering
2.1.2. Limited Relative Order
2.1.3. Low Control Accuracy
2.2. High-Order Sliding Model Control
3. Models of Variable Speed Controller
3.1. Wind Turbine Model
3.2. Generator Model
3.3. Nonlinear-Controlled Object Model
4. The Controller Design and Stability Analysis
4.1. Second Order Quasi-Continuous Sliding Mode Controller Derivation
4.2. Stability
5. Simulation
5.1. Simulation Scenario 1: Wind Speed Is below the Rated Speed
5.2. Simulation Scenario 2: Wind Speed Is below and above the Rated Speed
5.3. Simulation Scenario 3: Wind Speed Is above the Rated Speed but Less Than the Cut-Out Speed
6. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Acronyms and Nomenclature
MPPT | Maximum power point tracking | Jg | Generator inertia (kg·m2) |
TSR | Blade tip speed ratio | ng | Gearbox ratio |
Pa | Mechanical power (W) | Tls | The low speed shaft torque (N·m) |
v | Wind speed (m/s) | Ueq | Equivalent control quantity |
ρ | Air density (kg/m3) | US | Switching control quantity |
R | Wind turbine rotor radius (m) | Jr | Rotor moment of inertia (kg·m2) |
λ | Tip speed ratio | Generator speed (rad/s) | |
β | The actual output pitch angle (°) | Kr | The damping coefficient of turbine |
Cp(λ, β) | Turbine power conversion efficiency | rotor (N·m/rad/s) | |
g | The number of pairs of poles | Kg | Generator external damping coefficient |
Ta | Aerodynamic torque (N·m) | (N·m/rad/s) | |
Te | Generator torque (N·m) | Kls | The low speed shaft damping (N·m/rad/s) |
Ths | Input torque to generator (N·m) | Bls | The low speed shaft stiffness (N·m/rad) |
Turbine rotor speed (rad/s) | The reference value of the pitch angle (°) | ||
The low speed shaft speed (rad/s) | C1 | Correction factor | |
Generator synchronous speed (rad/s) | m1 | Relative number | |
Stator winding resistance (Ω) | U1 | Network voltage (V) | |
x1 | Stator winding leakage reactance (Ω) | vcut-in | Cut-in wind speed (m/s) |
Rotor winding resistance (Ω) | vrmax | The wind speed where reaches the | |
Rotor winding leakage reactance (Ω) | rated rotational speed (m/s) | ||
Time constant | vrated | The rated wind speed (m/s) | |
vcut-off | Cut-off wind speed (m/s) |
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Parameter Name | Symbol | Numerical | Unit |
---|---|---|---|
Turbine rotor radius | 38.5 | m | |
Air density | 1.225 | ||
Rated wind speed | 10.6 | ||
Rated turbine rotor speed | 1.6755 | ||
Rated power | 1.5 | MW | |
Rated torque of generator | 8.74 | ||
Time constant of variable pitch actuator | 0.15 | ||
Velocity actuator time constant | 0.05 | ||
Rotational inertia of rotor | |||
Rotational inertia of generator | 123 | ||
Gearbox gear ratio | 104 | ||
Damping coefficient of turbine rotor | 45.52 | ||
Generator damping coefficient | 0.4 |
Abbreviation | Parameter Name |
---|---|
NEXPRR(rad/s) | The expected rotor speed |
NRR(rad/s) | Rotor speed using second order sliding mode controller |
NRRPID(rad/s) | Rotor speed using the PID controller |
NRRTRA(rad/s) | Rotor speed using the conventional sliding mode controller |
NEEerror(rad/s) | Rotor speed error using second order sliding mode controller to the expectation |
NEEerrorPID(rad/s) | Rotor speed error using the PID controller to the expectation |
NEEerrorTRA(rad/s) | Rotor speed error using the conventional mode controller to the expectation |
NPP(W) | Output power using second order sliding mode controller |
NPPPID(W) | Output power using the PID controller |
NPPTRA(W) | Output power using the conventional sliding mode controller |
NEXPPP(W) | Output power calculated by the theoretical power curve |
Simulation Output | PID | Conventional Sliding Mode | Second Order Sliding Mode |
---|---|---|---|
Rotor speed average (rad/s) | 0.9481 | 0.9325 | 0.9479 |
Rotor speed std. (rad/s) | 0.2346 | 0.2285 | 0.2327 |
Mean absolute error of rotor speed (rad/s) | 0.0275 | 0.0136 | 0.0043 |
Std. of absolute error of rotor speed (rad/s) | 0.0214 | 0.0269 | 0.0214 |
Sum of square error of rotor speed (rad/s) | 1.3255 | 0.5224 | 0.3436 |
Output power average (kw) | 241.70 | 241.53 | 242.72 |
Output power std. (kw) | 155.36 | 154.77 | 155.57 |
Simulation Output | PID | Conventional Sliding Mode | Second Order Sliding Mode |
---|---|---|---|
Rotor speed average (rad/s) | 1.5113 | 1.4930 | 1.5097 |
Rotor speed std. (rad/s) | 0.1513 | 0.1634 | 0.1410 |
Mean absolute error of rotor speed (rad/s) | 0.0668 | 0.0603 | 0.0066 |
Std. of absolute error of rotor speed (rad/s) | 0.0987 | 0.0852 | 0.0508 |
Sum of square error of rotor speed (rad/s) | 7.0027 | 5.2260 | 1.1854 |
Output power average (kw) | 840.20 | 840.35 | 846.24 |
Output power std. (kw) | 216.44 | 223.89 | 219.56 |
Simulation Output | PID | Conventional Sliding Mode | Second Order Sliding Mode |
---|---|---|---|
Rotor speed average (rad/s) | 1.7593 | 1.7216 | 1.7467 |
Rotor speed std. (rad/s) | 0.1044 | 0.0975 | 0.0778 |
Mean absolute error of rotor speed (rad/s) | 0.0406 | 0.0647 | 0.0189 |
Std. of absolute error of rotor speed (rad/s) | 0.1044 | 0.0975 | 0.0778 |
Sum of square error of rotor speed (rad/s) | 7.9120 | 7.3733 | 4.3565 |
Output power average (kw) | 144.84 | 143.79 | 147.79 |
Output power std. (kw) | 165.73 | 156.03 | 79.150 |
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Jing, Y.; Sun, H.; Zhang, L.; Zhang, T. Variable Speed Control of Wind Turbines Based on the Quasi-Continuous High-Order Sliding Mode Method. Energies 2017, 10, 1626. https://doi.org/10.3390/en10101626
Jing Y, Sun H, Zhang L, Zhang T. Variable Speed Control of Wind Turbines Based on the Quasi-Continuous High-Order Sliding Mode Method. Energies. 2017; 10(10):1626. https://doi.org/10.3390/en10101626
Chicago/Turabian StyleJing, Yanwei, Hexu Sun, Lei Zhang, and Tieling Zhang. 2017. "Variable Speed Control of Wind Turbines Based on the Quasi-Continuous High-Order Sliding Mode Method" Energies 10, no. 10: 1626. https://doi.org/10.3390/en10101626
APA StyleJing, Y., Sun, H., Zhang, L., & Zhang, T. (2017). Variable Speed Control of Wind Turbines Based on the Quasi-Continuous High-Order Sliding Mode Method. Energies, 10(10), 1626. https://doi.org/10.3390/en10101626