Optimal Design of a Multibrid Permanent Magnet Generator for a Tidal Stream Turbine
Abstract
:1. Introduction
2. System Modeling
2.1. Renewable Resource and Tidal Turbine Modeling
2.1.1. Power and Energy Calculation
2.1.2. Power Rating Choice
2.2. Gearbox Modeling
2.3. Single Stage Geared PMG Design
2.3.1. Electromagnetic Torque
2.3.2. Air-Gap
2.3.3. Magnet Height
2.3.4. Slot Height
2.3.5. Stator and Rotor Yoke Height
2.3.6. Teeth Pitch Ratio
2.3.7. Maximum Magnetic Field
2.3.8. Iron Losses
2.3.9. Synchronous Inductance
2.4. Power Electronic Converter Design
3. Design Optimization
3.1. Cost-Function
3.2. Optimization Constraints
4. Design Results and Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
TST | Tidal stream turbine |
DD | Direct drive |
2D | Two-dimensional |
PMG | Permanent magnet generator |
3D | Three-dimensional |
AEP | Annual energy production |
PWM | Pulse width modulation |
Nomenclature
Input shaft power | |
Turbine blade swept area | |
Sea water density | |
Power coefficient | |
Tip speed ratio | |
Optimum tip speed ratio | |
Pitch angle | |
Cut-in tidal current speed | |
Cut-out tidal current speed | |
Rated tidal current speed | |
Rated input shaft power | |
Occurrence frequency | |
Gear face width | |
Sun gear diameter | |
Planet gear diameter | |
Ring gear diameter | |
Scaling factor | |
Gearbox output shaft torque | |
Application factor | |
Tooth loads intensity index | |
Gearbox weight constant | |
Gearbox ratio | |
Gear ratio between sun and planet gears | |
Z | Planet gears number |
Gearbox specific cost | |
Gearbox weight | |
Gearbox estimated cost | |
Gearbox losses | |
Speed-dependent losses constant | |
Tidal stream turbine rated power | |
Rotor speed | |
Rated rotor speed | |
Electromagnetic torque | |
Stator current loading | |
Maximum air-gap flux density | |
Air-gap flux density | |
Saturation flux density | |
First harmonic winding factor | |
Phase shift between the electromotive force and the current | |
Stator radius | |
Equivalent core length | |
3D flow leakage corrective coefficient | |
Air-gap coefficient | |
Mechanical air-gap | |
Additional Carter air-gap | |
Carter factor | |
Magnet height | |
Vacuum permeability constant | |
Magnets relative permeability | |
Magnets remanent flux density | |
Maximum air-gap flow density | |
Pole pitch | |
Stator yoke height | |
Rotor yoke height | |
Slot height | |
Fill factor | |
Teeth pitch ratio | |
p | Pole pairs number |
Slots per pole per phase number | |
m | Phases number |
Maximum magnetic field in the magnet | |
Permanent magnet coercive magnetic field | |
Iron losses | |
Magnetic field frequency in the iron | |
Specific hysteresis loss | |
Specific eddy current loss | |
Phase winding number of turns | |
Leakage inductance | |
Power electronics cost | |
Permanent magnet generator cost | |
Tidal stream turbine cost | |
Copper specific costs | |
Iron specific costs | |
Permanent magnet specific costs | |
Copper specific weight | |
Iron specific weight | |
Permanent magnet specific weight | |
Set of possible solutions | |
Maximum electrical frequency |
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Tidal Stream Turbine | |||
Rated power [MW] | 0.5 | 1.5 | 5 |
Rated rotor speed [rpm] | 80.3 | 47.0 | 25.8 |
Rotor diameter D [m] | 6 | 10.3 | 18.8 |
Cut it tidal current speed [m/s] | 1.0 | ||
Cut out tidal current speed [m/s] | 6.2 | ||
Maximum power coefficient | 0.455 | ||
Optimum tip speed ratio | 5.90 | ||
Sea water density [kg/m3] | 995.6 | ||
Single Stage Planetary Gearbox | |||
Gearbox application factor | 1.5 | ||
K-factor [N/mm2] | 2.76 | ||
Gearbox weight constant | 0.6 | ||
Planet gears number Z | 6 | ||
Gearbox specific cost [€/kg] | 6 | ||
Speed dependent losses constant [%] | 1.5 | ||
PMG System | |||
Hysteresis losses at 1.5 T and 50 Hz pFe0h [W/kg] | 2 | ||
Eddy-current losses at 1.5 T and 50 Hz pFe0e [W/kg] | 0.5 | ||
Specific cost of electrical steel cFe [€/mT] | 449.77 | ||
Specific cost of copper cCu [€/mT] | 4259.18 | ||
Specific cost of NdFeB magnet cm [€/mT] | 84,538.60 | ||
Specific cost of power electronics cconv [€/kW] | 40 |
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Touimi, K.; Benbouzid, M.; Chen, Z. Optimal Design of a Multibrid Permanent Magnet Generator for a Tidal Stream Turbine. Energies 2020, 13, 487. https://doi.org/10.3390/en13020487
Touimi K, Benbouzid M, Chen Z. Optimal Design of a Multibrid Permanent Magnet Generator for a Tidal Stream Turbine. Energies. 2020; 13(2):487. https://doi.org/10.3390/en13020487
Chicago/Turabian StyleTouimi, Khalil, Mohamed Benbouzid, and Zhe Chen. 2020. "Optimal Design of a Multibrid Permanent Magnet Generator for a Tidal Stream Turbine" Energies 13, no. 2: 487. https://doi.org/10.3390/en13020487