A Magnus Wind Turbine Mathematical Model
Keywords:
Magnus effect, wind turbine, simulation, rate of wind use, wind power
Abstract
Wind power units using the Magnus effect are an alternative to conventional blade units in regions having a too low or a high wind potential. A feature of their design is the use of rotating cylinders for producing torque on the wind wheel shaft. The aim of the study was to develop a mathematical model of such unit. Three models of the wind energy utilization coefficient were considered: analytical, regression and correlation. The models were subjected to an analysis, based on which conclusions about their applicability limits were drawn, and their main advantages and disadvantages were highlighted. An alternative simulation aerodynamic model was synthesized using the computational aerodynamics method. The developed model was verified by comparing the unit power output estimated by the simulation model with experimental data obtained on a real unit in the course of field tests. The study results have shown that the developed model based on computational aerodynamics features high accuracy and can be used to simulate a wind power unit based on the Magnus effect under variable wind conditions. In the future, the presented model can be used in the development of algorithms for detecting the maximum power point for this type of wind power units.
References
1. Lukin G.L. et al. Experimental Prototype of High-Efficiency Wind Turbine Based on Magnus Effect. – 27th International Workshop on Electric Drives, 2020, DOI:10.1109/IWED48848.2020.9069565.
2. Alassaf O. et al. Cylindrical Blades Magnus Wind Turbine Optimization and Control System. – 29th International Workshop on Electric Drives, 2022, 10.1109/IWED54598.2022.9722582.
3. Lukin G. et al. Investigation of FEM Software for Magnus Effect Simulation. – 28th International Workshop on Electric Drives, 2021, DOI:10.1109/IWED52055.2021.9376396.
4. Bychkov N.M., Dovgal A.V., Kozlov V.V. Magnus Wind Turbines as an Alternative to the Blade Ones. – Journal of Physics: Conference Series, 2007, vol. 75(1), 012004, DOI:10.1088/1742-6596/ 75/1/012004.
5. Sedaghat A. Magnus Type Wind Turbines: Prospectus and Challenges in Design and Modelling. – Renewable Energy, 2014, vol. 62, pp. 619–628, DOI: 10.1016/j.renene.2013.08.029.
6. Jinbo M. et al. Fixed and Adaptive Step HCC Algorithms for MPPT of the Cylinders of Magnus Wind Turbines. – 3rd Renewable Power Generation Conference, 2014, DOI: 10.1049/cp.2014.0921.
7. Jinbo M. et al. MPPT of Magnus Wind System with DC Servo Drive for the Cylinders and Boost Converter. – Journal of Wind Energy, 2015, No. 2, DOI:10.1155/2015/148680.
8. Wind is Blowing to a New Direction [Электрон. ресурс], URL: https://challenergy.com/en/ (дата обращения 26.12.2022).
9. Seifert J. A Review of the Magnus Effect in Aeronautics. – Progress in Aerospace Sciences, 2012, vol. 55, pp. 17–45, DOI: 10.1016/ j.paerosci.2012.07.001.
10. Mara K. et al. Development and Validation of a CFD Model Using ANSYS CFX for Aerodynamics Simulation of Magnus Wind Rotor Blades. – International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management, 2014, DOI:10.1109/HNICEM.2014.7016231.
11. ГОСТ Р 54418.1-2012 (МЭК 61400–1:2005). Возобновляемая энергетика. Ветроэнергетика. Установки ветроэнергетические. Ч. 1. Технические требования. М.: Стандартинформ, 2016, 82 c.
12. González-Hernández J.G., Salas-Cabrera R. Representation and Estimation of the Power Coefficient in Wind Energy Conversion Systems. – Revista Facultad de Ingeniería, 2019, vol. 28(50), pp. 77–90, DOI:10.19053/01211129.v28.n50.2019.8816.
13. Luo D., Huang D., Wu G. Analytical Solution on Magnus Wind Turbine Power Performance Based on the Blade Element Momentum Theory. – Journal of Renewable and Sustainable Energy, 2011, vol. 3(3), 033104, DOI:10.1063/1.3588039.
14. Richmond-Navarro G. et al. A Magnus Wind Turbine Power Model Based on Direct Solutions Using the Blade Element Momentum Theory and Symbolic Regression. – IEEE Transactions on Sustainable Energy, 2016, vol. 8(1), pp. 425–430, DOI:10.1109/TSTE.2016.2604082.
15. Richmond-Navarro G., Ureña-Sandí N., Rodríguez G. High Correlation Models for Small Scale Magnus Wind Turbines. – 5th International Conference on Renewable Energy: Generation and Applications (ICREGA), 2018, DOI:10.1109/ICREGA.2018.8337574.
#
1. Lukin G.L. et al. Experimental Prototype of High-Efficiency Wind Turbine Based on Magnus Effect. – 27th International Workshop on Electric Drives, 2020, DOI:10.1109/IWED48848.2020.9069565.
2. Alassaf O. et al. Cylindrical Blades Magnus Wind Turbine Optimization and Control System. – 29th International Workshop on Electric Drives, 2022, 10.1109/IWED54598.2022.9722582.
3. Lukin G. et al. Investigation of FEM Software for Magnus Effect Simulation. – 28th International Workshop on Electric Drives, 2021, DOI:10.1109/IWED52055.2021.9376396.
4. Bychkov N.M., Dovgal A.V., Kozlov V.V. Magnus Wind Turbines as an Alternative to the Blade Ones. – Journal of Physics: Conference Series, 2007, vol. 75(1), 012004, DOI: 10.1088/1742-6596/ 75/1/012004.
5. Sedaghat A. Magnus Type Wind Turbines: Prospectus and Challenges in Design and Modelling. – Renewable Energy, 2014, vol. 62, pp. 619–628, DOI: 10.1016/j.renene.2013.08.029.
6. Jinbo M. et al. Fixed and Adaptive Step HCC Algorithms for MPPT of the Cylinders of Magnus Wind Turbines. – 3rd Renewable Power Generation Conference, 2014, DOI: 10.1049/cp.2014.0921.
7. Jinbo M. et al. MPPT of Magnus Wind System with DC Servo Drive for the Cylinders and Boost Converter. – Journal of Wind Energy, 2015, No. 2, DOI:10.1155/2015/148680.
8. Wind is Blowing to a New Direction [Electron. resource], URL: https://challenergy.com/en/ (date of appeal 26.12.2022).
9. Seifert J. A Review of the Magnus Effect in Aeronau-tics. – Progress in Aerospace Sciences, 2012, vol. 55, pp. 17–45, DOI:10.1016/j.paerosci.2012.07.001.
10. Mara K. et al. Development and Validation of a CFD Model Using ANSYS CFX for Aerodynamics Simulation of Magnus Wind Rotor Blades. – International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management, 2014, DOI:10.1109/HNICEM.2014.7016231.
11. GОSТ R 54418.1-2012 (IEC 61400–1: 2005). Vozobnov-lyaemaya energetika. Vetroenergetika. Ustanovki vetroenergeticheskie. Ch. 1. Tekhnicheskie trebovaniya (Renewable Power Engineering. Wind Power Engineering. Wind turbines. Part 1. Technical Requirements). М.: Standartinform, 2016, 82 p.
12. González-Hernández J.G., Salas-Cabrera R. Representation and Estimation of the Power Coefficient in Wind Energy Conversion Systems. – Revista Facultad de Ingeniería, 2019, vol. 28(50), pp. 77–90, DOI:10.19053/01211129.v28.n50.2019.8816.
13. Luo D., Huang D., Wu G. Analytical Solution on Magnus Wind Turbine Power Performance Based on the Blade Element Momentum Theory. – Journal of Renewable and Sustainable Energy, 2011, vol.3(3), 033104, DOI:10.1063/1.3588039.
14. Richmond-Navarro G. et al. A Magnus Wind Turbine Power Model Based on Direct Solutions Using the Blade Element Momentum Theory and Symbolic Regression. – IEEE Transactions on Sustainable Energy, 2016, vol. 8(1), pp. 425–430, DOI:10.1109/TSTE.2016.2604082.
15. Richmond-Navarro G., Ureña-Sandí N., Rodríguez G. High Correlation Models for Small Scale Magnus Wind Turbines. – 5th International Conference on Renewable Energy: Generation and Applications (ICREGA), 2018, DOI:10.1109/ICREGA.2018.8337574.
2. Alassaf O. et al. Cylindrical Blades Magnus Wind Turbine Optimization and Control System. – 29th International Workshop on Electric Drives, 2022, 10.1109/IWED54598.2022.9722582.
3. Lukin G. et al. Investigation of FEM Software for Magnus Effect Simulation. – 28th International Workshop on Electric Drives, 2021, DOI:10.1109/IWED52055.2021.9376396.
4. Bychkov N.M., Dovgal A.V., Kozlov V.V. Magnus Wind Turbines as an Alternative to the Blade Ones. – Journal of Physics: Conference Series, 2007, vol. 75(1), 012004, DOI:10.1088/1742-6596/ 75/1/012004.
5. Sedaghat A. Magnus Type Wind Turbines: Prospectus and Challenges in Design and Modelling. – Renewable Energy, 2014, vol. 62, pp. 619–628, DOI: 10.1016/j.renene.2013.08.029.
6. Jinbo M. et al. Fixed and Adaptive Step HCC Algorithms for MPPT of the Cylinders of Magnus Wind Turbines. – 3rd Renewable Power Generation Conference, 2014, DOI: 10.1049/cp.2014.0921.
7. Jinbo M. et al. MPPT of Magnus Wind System with DC Servo Drive for the Cylinders and Boost Converter. – Journal of Wind Energy, 2015, No. 2, DOI:10.1155/2015/148680.
8. Wind is Blowing to a New Direction [Электрон. ресурс], URL: https://challenergy.com/en/ (дата обращения 26.12.2022).
9. Seifert J. A Review of the Magnus Effect in Aeronautics. – Progress in Aerospace Sciences, 2012, vol. 55, pp. 17–45, DOI: 10.1016/ j.paerosci.2012.07.001.
10. Mara K. et al. Development and Validation of a CFD Model Using ANSYS CFX for Aerodynamics Simulation of Magnus Wind Rotor Blades. – International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management, 2014, DOI:10.1109/HNICEM.2014.7016231.
11. ГОСТ Р 54418.1-2012 (МЭК 61400–1:2005). Возобновляемая энергетика. Ветроэнергетика. Установки ветроэнергетические. Ч. 1. Технические требования. М.: Стандартинформ, 2016, 82 c.
12. González-Hernández J.G., Salas-Cabrera R. Representation and Estimation of the Power Coefficient in Wind Energy Conversion Systems. – Revista Facultad de Ingeniería, 2019, vol. 28(50), pp. 77–90, DOI:10.19053/01211129.v28.n50.2019.8816.
13. Luo D., Huang D., Wu G. Analytical Solution on Magnus Wind Turbine Power Performance Based on the Blade Element Momentum Theory. – Journal of Renewable and Sustainable Energy, 2011, vol. 3(3), 033104, DOI:10.1063/1.3588039.
14. Richmond-Navarro G. et al. A Magnus Wind Turbine Power Model Based on Direct Solutions Using the Blade Element Momentum Theory and Symbolic Regression. – IEEE Transactions on Sustainable Energy, 2016, vol. 8(1), pp. 425–430, DOI:10.1109/TSTE.2016.2604082.
15. Richmond-Navarro G., Ureña-Sandí N., Rodríguez G. High Correlation Models for Small Scale Magnus Wind Turbines. – 5th International Conference on Renewable Energy: Generation and Applications (ICREGA), 2018, DOI:10.1109/ICREGA.2018.8337574.
#
1. Lukin G.L. et al. Experimental Prototype of High-Efficiency Wind Turbine Based on Magnus Effect. – 27th International Workshop on Electric Drives, 2020, DOI:10.1109/IWED48848.2020.9069565.
2. Alassaf O. et al. Cylindrical Blades Magnus Wind Turbine Optimization and Control System. – 29th International Workshop on Electric Drives, 2022, 10.1109/IWED54598.2022.9722582.
3. Lukin G. et al. Investigation of FEM Software for Magnus Effect Simulation. – 28th International Workshop on Electric Drives, 2021, DOI:10.1109/IWED52055.2021.9376396.
4. Bychkov N.M., Dovgal A.V., Kozlov V.V. Magnus Wind Turbines as an Alternative to the Blade Ones. – Journal of Physics: Conference Series, 2007, vol. 75(1), 012004, DOI: 10.1088/1742-6596/ 75/1/012004.
5. Sedaghat A. Magnus Type Wind Turbines: Prospectus and Challenges in Design and Modelling. – Renewable Energy, 2014, vol. 62, pp. 619–628, DOI: 10.1016/j.renene.2013.08.029.
6. Jinbo M. et al. Fixed and Adaptive Step HCC Algorithms for MPPT of the Cylinders of Magnus Wind Turbines. – 3rd Renewable Power Generation Conference, 2014, DOI: 10.1049/cp.2014.0921.
7. Jinbo M. et al. MPPT of Magnus Wind System with DC Servo Drive for the Cylinders and Boost Converter. – Journal of Wind Energy, 2015, No. 2, DOI:10.1155/2015/148680.
8. Wind is Blowing to a New Direction [Electron. resource], URL: https://challenergy.com/en/ (date of appeal 26.12.2022).
9. Seifert J. A Review of the Magnus Effect in Aeronau-tics. – Progress in Aerospace Sciences, 2012, vol. 55, pp. 17–45, DOI:10.1016/j.paerosci.2012.07.001.
10. Mara K. et al. Development and Validation of a CFD Model Using ANSYS CFX for Aerodynamics Simulation of Magnus Wind Rotor Blades. – International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management, 2014, DOI:10.1109/HNICEM.2014.7016231.
11. GОSТ R 54418.1-2012 (IEC 61400–1: 2005). Vozobnov-lyaemaya energetika. Vetroenergetika. Ustanovki vetroenergeticheskie. Ch. 1. Tekhnicheskie trebovaniya (Renewable Power Engineering. Wind Power Engineering. Wind turbines. Part 1. Technical Requirements). М.: Standartinform, 2016, 82 p.
12. González-Hernández J.G., Salas-Cabrera R. Representation and Estimation of the Power Coefficient in Wind Energy Conversion Systems. – Revista Facultad de Ingeniería, 2019, vol. 28(50), pp. 77–90, DOI:10.19053/01211129.v28.n50.2019.8816.
13. Luo D., Huang D., Wu G. Analytical Solution on Magnus Wind Turbine Power Performance Based on the Blade Element Momentum Theory. – Journal of Renewable and Sustainable Energy, 2011, vol.3(3), 033104, DOI:10.1063/1.3588039.
14. Richmond-Navarro G. et al. A Magnus Wind Turbine Power Model Based on Direct Solutions Using the Blade Element Momentum Theory and Symbolic Regression. – IEEE Transactions on Sustainable Energy, 2016, vol. 8(1), pp. 425–430, DOI:10.1109/TSTE.2016.2604082.
15. Richmond-Navarro G., Ureña-Sandí N., Rodríguez G. High Correlation Models for Small Scale Magnus Wind Turbines. – 5th International Conference on Renewable Energy: Generation and Applications (ICREGA), 2018, DOI:10.1109/ICREGA.2018.8337574.
Published
2023-02-20
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