Fast Power Coefficient vs. Tip–Speed Ratio Curves for Small Wind Turbines with Single-Variable Measurements following a Single Test Run
Small wind turbines (SWTs) face tremendous challenges in being developed into a more reliable and widespread energy solution, with a number of efficiency, reliability, and cost issues that are yet to be resolved. As part of the development stages of an SWT, testing the resulting efficiency and deter...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/17/5/1199 |
| _version_ | 1797264605198680064 |
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| author | Patricio A. Corbalán Luciano E. Chiang |
| author_facet | Patricio A. Corbalán Luciano E. Chiang |
| author_sort | Patricio A. Corbalán |
| collection | DOAJ |
| description | Small wind turbines (SWTs) face tremendous challenges in being developed into a more reliable and widespread energy solution, with a number of efficiency, reliability, and cost issues that are yet to be resolved. As part of the development stages of an SWT, testing the resulting efficiency and determining appropriate working ranges are of high importance. In this paper, a methodology is presented for testing SWTs to obtain characteristic performance curves such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula> (power coefficient) vs. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>S</mi><mi>R</mi></mrow></semantics></math></inline-formula> (tip–speed ratio), and torque vs. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi></mrow></semantics></math></inline-formula>, in a simpler and faster yet accurate manner as an alternative energy solution when a wind tunnel is not available. The performance curves are obtained with the SWT mounted on a platform moving along a runway, requiring only a few minutes of data acquisition. Furthermore, it is only required to measure a single variable, i.e., the generator output voltage. A suitable physics-based mathematical model for the system allows for deriving the desired performance curves from this set of minimal data. The methodology was demonstrated by testing a prototype SWT developed by the authors. The tested prototype had a permanent magnet synchronous generator, but the methodology can be applied to any type of generator with a suitable mathematical model. Given its level of simplicity, accuracy, low cost, and ease of implementation, the proposed testing method has advantages that are helpful in the development process of SWTs, especially if access to a proper wind tunnel is prevented for any reason. To validate the methodology, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula> vs. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>S</mi><mi>R</mi></mrow></semantics></math></inline-formula> curves were obtained for an SWT prototype tested under different test conditions, arriving always at the same curve as would be expected. In this case, the test prototype reached a maximum power coefficient (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula>) of 0.35 for wind velocities from 20 to 50 km/h for a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>S</mi><mi>R</mi></mrow></semantics></math></inline-formula> of 5.5. |
| first_indexed | 2024-04-25T00:31:33Z |
| format | Article |
| id | doaj.art-c9bcd8a73a9847ffab85058f2913c54f |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-04-25T00:31:33Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-c9bcd8a73a9847ffab85058f2913c54f2024-03-12T16:43:42ZengMDPI AGEnergies1996-10732024-03-01175119910.3390/en17051199Fast Power Coefficient vs. Tip–Speed Ratio Curves for Small Wind Turbines with Single-Variable Measurements following a Single Test RunPatricio A. Corbalán0Luciano E. Chiang1Department of Mechanical & Metallurgical Engineering, Pontificia Universidad Católica de Chile, Santiago 7820436, ChileDepartment of Mechanical & Metallurgical Engineering, Pontificia Universidad Católica de Chile, Santiago 7820436, ChileSmall wind turbines (SWTs) face tremendous challenges in being developed into a more reliable and widespread energy solution, with a number of efficiency, reliability, and cost issues that are yet to be resolved. As part of the development stages of an SWT, testing the resulting efficiency and determining appropriate working ranges are of high importance. In this paper, a methodology is presented for testing SWTs to obtain characteristic performance curves such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula> (power coefficient) vs. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>S</mi><mi>R</mi></mrow></semantics></math></inline-formula> (tip–speed ratio), and torque vs. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ω</mi></mrow></semantics></math></inline-formula>, in a simpler and faster yet accurate manner as an alternative energy solution when a wind tunnel is not available. The performance curves are obtained with the SWT mounted on a platform moving along a runway, requiring only a few minutes of data acquisition. Furthermore, it is only required to measure a single variable, i.e., the generator output voltage. A suitable physics-based mathematical model for the system allows for deriving the desired performance curves from this set of minimal data. The methodology was demonstrated by testing a prototype SWT developed by the authors. The tested prototype had a permanent magnet synchronous generator, but the methodology can be applied to any type of generator with a suitable mathematical model. Given its level of simplicity, accuracy, low cost, and ease of implementation, the proposed testing method has advantages that are helpful in the development process of SWTs, especially if access to a proper wind tunnel is prevented for any reason. To validate the methodology, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula> vs. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>S</mi><mi>R</mi></mrow></semantics></math></inline-formula> curves were obtained for an SWT prototype tested under different test conditions, arriving always at the same curve as would be expected. In this case, the test prototype reached a maximum power coefficient (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></semantics></math></inline-formula>) of 0.35 for wind velocities from 20 to 50 km/h for a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>S</mi><mi>R</mi></mrow></semantics></math></inline-formula> of 5.5.https://www.mdpi.com/1996-1073/17/5/1199small wind turbine performance curvessmall wind turbine efficiencysmall wind turbine testing method |
| spellingShingle | Patricio A. Corbalán Luciano E. Chiang Fast Power Coefficient vs. Tip–Speed Ratio Curves for Small Wind Turbines with Single-Variable Measurements following a Single Test Run Energies small wind turbine performance curves small wind turbine efficiency small wind turbine testing method |
| title | Fast Power Coefficient vs. Tip–Speed Ratio Curves for Small Wind Turbines with Single-Variable Measurements following a Single Test Run |
| title_full | Fast Power Coefficient vs. Tip–Speed Ratio Curves for Small Wind Turbines with Single-Variable Measurements following a Single Test Run |
| title_fullStr | Fast Power Coefficient vs. Tip–Speed Ratio Curves for Small Wind Turbines with Single-Variable Measurements following a Single Test Run |
| title_full_unstemmed | Fast Power Coefficient vs. Tip–Speed Ratio Curves for Small Wind Turbines with Single-Variable Measurements following a Single Test Run |
| title_short | Fast Power Coefficient vs. Tip–Speed Ratio Curves for Small Wind Turbines with Single-Variable Measurements following a Single Test Run |
| title_sort | fast power coefficient vs tip speed ratio curves for small wind turbines with single variable measurements following a single test run |
| topic | small wind turbine performance curves small wind turbine efficiency small wind turbine testing method |
| url | https://www.mdpi.com/1996-1073/17/5/1199 |
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