Magnus-Based Airborne Wind Energy Systems · Magnus-Based Airborne Wind Energy Systems Yashank...
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Magnus-Based Airborne Wind Energy Systems Yashank Gupta ,Jonathan Dumon, Ahmad Hably [email protected] [email protected] [email protected] Among the Airborne Wind Energy concepts Magnus based airborne wind energy systems uses rotating cylinders as aerostat. The rotating cylinder when exposed to wind flow produces a lift force, described as Magnus effect. The Magnus based aerostat have a high lift coefficient which is supplemented by lighter than air capabilities, and have a naturally robust design. The aerostat following a predefined trajectory leads to the development of high traction force in the tether which in turn is used to drive the generator and produce electricity. Introduction Control Strategy : Coeff. of Lift, : Coeff. of Drag, ∶ = , : Coeff. of Drag- − : = 1 2 2 , : = 1 2 2 , : , − = 1 2 2 The above analysis shows that the assumed polynomial expressions for the Coeff. of Lift ( ) and the Coeff. of Drag ( ) .i.e. the aerodynamic model for Magnus cylinder as proposed by Miltuiovnic [1] agrees with the historical experimental data available on Magnus cylinder. = −0.0211 3 + 0.1873 2 + 0.1183 + 0.5, = 0.0126 4 − 0.2004 3 + 0.7482 2 + 1.3447 Mathematical Model Equation of rate of change of translational velocity [2] = − where, = 1 − 0 − − 0 , and F b represents Body forces acting on the ABM and is given by = + + + + + ∶ Weight in Body Frame, : Bouyant Force, : Rope Force, − − : Body frame of ref. , − − : Inertial frame of ref. p: Roll rate, q: Pitch Rate, r: Yaw Rate, : Elevation angle, : Azimuthal angle Static Model • Theoretical Power produced during production phase ( ) as proposed by [3] Loyd (1980) and refined in [4] Argatov et al. (2009) = 1 2 4 cos 3 3 2 , = cos 3 : Reel–out speed • Theoretical Power consumed during recovery phase ( ) = 1 2 cos + 2 , : Reel–in speed • Estimated Power produced in one complete cycle ( ) = − + Hence, to maximize the power is to maximize the ratio 2 , the maximum 2 for the magnus cylinder is found to be at spin ratio, = 3.6. Control of tether length • A PID controller is used in order to follow the radial position through acting on the winch actuator. • The response time for this control loop is set to be faster than the variations of other forces in order to get an efficient production cycle. : Attitude of Magnus cylinder by ZYZ ,,γ : Winch Tension : Tether length : Yaw angle in ZYZ transformation :Reference radial postion Guidance strategy • We apply the guidance strategy given in [5], and another gain η to obtain a constant width trajectory η = η . Simulation Results Swept area comparison of a Magnus based AWE system (Surface = 500 m² and Span = 20 m) in a crosswind maneuver with a conventional Wind turbine (1.5 MW ). Simulated output power during production and recovery phases with a comparison with a simplified static model . Reference and state variable for tether length ( , ), tether tension , angular speed of the Magnus rotor ( , ) , and yaw angle (, ). Power Curves Phase I: Power extraction is maximized following Loyd cond. Phase II: Maximum traction force is reached, continues to increase. Phase III: Maximum speed of the generator is reached. By modifying Surface ( ), Maximum Tension ( ), and Maximum Power( ), the shape of the power curve can be adapted according to the distribution of the wind speed at the site. Comparision of Power Curve based on static model of a Magnus-based AWE system with that of a conventional Wind turbine (1.5MW). References [1] Milutinovic´, M., Coric´, M., and Deur, J. (2015). Operating cycle optimization for a Magnus effect based airborne wind energy system. Energy Conversion and Management, 90, 154–165. doi: 10.1016/j.enconman.2014.10.066. [2] Y. Gupta, J. Dumon, and A. Hably, “Modeling and control of a Magnus effect-based airborne wind energy system in crosswind maneuvers,” pp. 1–8. [3] M. L. Loyd, “Crosswind kite power,” Journal of Energy, vol. 4,no. 3, pp. 106–111, 1980. [4] I. Argatov, P. Rautakorpi, and R. Silvennoinen, “Estimation of the mechanical energy output of the kite wind generator,” Renewable Energy, vol. 34, pp. 1525–1532, 2009. [5] Fagiano, L., Zgraggen, A.U., Morari, M., and Khammash, M. (2014). Automatic crosswind flight of tethered wings for airborne wind energy: modeling, control design and experimental results. IEEE Transactions on Control System Technology, 22(4), 1433–1447. doi: 10.1109/TCST.2013.2279592. Magnus Effect : = 500 2 , = 85 , = 4 : = 1000 2 , = 85 , = 4 Conventional Wind turbine : 1.5MW
Transcript of Magnus-Based Airborne Wind Energy Systems · Magnus-Based Airborne Wind Energy Systems Yashank...
Magnus-Based Airborne Wind Energy Systems
Yashank Gupta ,Jonathan Dumon, Ahmad [email protected]
Among the Airborne Wind Energy concepts Magnus based airborne wind energy systems uses rotating cylinders as aerostat. The rotating cylinder when exposedto wind flow produces a lift force, described as Magnus effect. The Magnus based aerostat have a high lift coefficient which is supplemented by lighter than aircapabilities, and have a naturally robust design. The aerostat following a predefined trajectory leads to the development of high traction force in the tetherwhich in turn is used to drive the generator and produce electricity.
Introduction
Control Strategy
𝑪𝑳: Coeff. of Lift, 𝑪𝑫: Coeff. of Drag, 𝑿 ∶ 𝑆𝑝𝑖𝑛 𝑟𝑎𝑡𝑖𝑜 =𝜔𝑐𝑦𝑙𝑟𝑐𝑦𝑙
𝑣𝑎𝑥𝑧, 𝑪𝑫𝒚: Coeff. of Drag-𝑦𝑏 − 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛
𝑭𝑳 : 𝐿𝑖𝑓𝑡 𝐹𝑜𝑟𝑐𝑒 =1
2𝜌𝑆𝑐𝑦𝑙𝑣𝑎𝑥𝑧
2 𝐶𝐿, 𝑭𝑫 : 𝐷𝑟𝑎𝑔 𝐹𝑜𝑟𝑐𝑒 =1
2𝜌𝑆𝑐𝑦𝑙𝑣𝑎𝑥𝑧
2 𝐶𝐷,
𝑭𝑫𝒚: 𝐷𝑟𝑎𝑔 𝐹𝑜𝑟𝑐𝑒 , 𝑦𝑏 − 𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛 =
1
2𝜌𝑆𝑐𝑦𝑙𝑣𝑎𝑦
2 𝐶𝐷𝑦
The above analysis shows that the assumed polynomial expressions for the Coeff. of Lift (𝐶𝐿) and the Coeff. of Drag (𝐶𝐷) .i.e. the aerodynamic model for Magnus cylinder as proposed by Miltuiovnic [1] agrees with the historical experimental data available on Magnus cylinder.
𝐶𝐷 = −0.0211𝑋3 + 0.1873𝑋2 + 0.1183𝑋 + 0.5, 𝐶𝐿 = 0.0126𝑋4 − 0.2004𝑋3 + 0.7482𝑋2 + 1.3447𝑋
Mathematical Model
Equation of rate of change of translational velocity [2]
𝐯𝐛 =𝟏
𝐦𝐅𝐛 − 𝛚𝐛 𝐯𝐛
where,
𝜔𝑏=
1 −𝑟 𝑞𝑟 0 −𝑝−𝑞 𝑝 0
, and
Fb represents Body forces acting on the ABM and is given by
𝐅𝐛 = 𝐅𝐋 + 𝐅𝐃 + 𝐅𝐝𝐲 + 𝐖𝐛 + 𝐅𝐛𝐮 + 𝐅𝐫
𝑾𝒃 ∶ Weight in Body Frame,𝐅𝐛𝐮 : Bouyant Force,𝑭𝒓 : Rope Force, 𝒙𝒃 − 𝒚𝒃 − 𝒛𝒃 : Body frame of ref. ,𝒙𝒊 − 𝒚𝒊 − 𝒛𝒊 : Inertial frame of ref.
p: Roll rate, q: Pitch Rate, r: Yaw Rate,𝜷: Elevation angle, 𝜼: Azimuthal angle
Static Model
• Theoretical Power produced during production phase (𝑷𝒑𝒓𝒐𝒅) as proposed by [3] Loyd
(1980) and refined in [4] Argatov et al. (2009)
𝑃𝑝𝑟𝑜𝑑 =1
2𝜌4𝑆𝑐𝑦𝑙
𝑣𝜔 cos 𝛽
3
3
𝐶𝐿𝐶𝐿
𝐶𝐷
2, 𝒓𝒑𝒓𝒐𝒅 =
𝑣𝜔 cos 𝛽
3: Reel–out speed
• Theoretical Power consumed during recovery phase (𝑷𝒓𝒆𝒄)
𝑃𝑟𝑒𝑐 =1
2𝜌𝑆𝑐𝑦𝑙 𝑣𝜔 cos 𝛽 + 𝑟𝑟𝑒𝑐
2𝐶𝐷𝑟𝑒𝑐 𝑟𝑟𝑒𝑐 , 𝒓𝒓𝒆𝒄: Reel–in speed
• Estimated Power produced in one complete cycle (𝑷𝒄𝒚𝒄𝒍𝒆)
𝑃𝑐𝑦𝑐𝑙𝑒 =𝑃𝑝𝑟𝑜𝑑 𝑟𝑟𝑒𝑐 − 𝑃𝑟𝑒𝑐 𝑟𝑝𝑟𝑜𝑑
𝑟𝑟𝑒𝑐 + 𝑟𝑝𝑟𝑜𝑑
Hence, to maximize the power is to maximize the ratio 𝐶𝐿𝐶𝐿
𝐶𝐷
2, the maximum 𝐶𝐿
𝐶𝐿
𝐶𝐷
2for
the magnus cylinder is found to be at spin ratio, 𝑋 = 3.6.
Control of tether length
•A PID controller 𝐊𝟏 is used in order to follow the radial position 𝒓𝒕𝒓𝒆𝒇 through 𝑼𝑻 acting on
the winch actuator. •The response time for this control loop is set to
be faster than the variations of other forces in order to get an efficient production cycle.
𝚯: Attitude of Magnus cylinder by ZYZ 𝛼, 𝛿, γ𝐓𝐂 : Winch Tension𝒓𝒕 : Tether length 𝛄𝐫𝐞𝐟 : Yaw angle in ZYZ transformation𝐫𝐭𝐫𝐞𝐟 :Reference radial postion
Guidance strategy
•We apply the guidance strategy given in [5], and another gain 𝑘η to obtain a constant
width trajectory η𝑟𝑒𝑓 =𝑘η
𝑟𝑡.
Simulation Results
Swept area comparison of a Magnus based AWE system (Surface = 500 m² and Span = 20 m) in a crosswind maneuver with a conventional Wind turbine (1.5 MW ).
Simulated output power during production and recovery phases with a comparison with a simplified static model 𝑷𝒔𝒕𝒂𝒕𝒊𝒄 .
Reference and state variable for tether length (𝒓𝒕, 𝒓𝒕𝒓𝒆𝒇), tether tension 𝑻𝒄 , angular speed of the Magnus
rotor (𝝎𝒄𝒚𝒍, 𝝎𝒄𝒚𝒍𝒓𝒆𝒇) , and yaw angle (𝜸, 𝜸𝒓𝒆𝒇 ).
Power Curves
Phase I: Power extraction is maximized following Loyd cond. Phase II: Maximum traction force is reached, 𝑟𝑝𝑟𝑜𝑑continues to increase.Phase III: Maximum speed of the generator is reached.
By modifying Surface (𝑆𝑐𝑦𝑙), Maximum Tension
(𝑻𝒎𝒂𝒙), and Maximum Power(𝑷𝒎𝒂𝒙), the shape of the power curve can be adapted according to the distribution of the wind speed at the site.
Comparision of Power Curve based on static model of a Magnus-based AWE system with that of a conventional Wind turbine (1.5MW).
References
[1] Milutinovic´, M., Coric´, M., and Deur, J. (2015). Operating cycle optimization for a Magnus effect based airborne wind energy system. Energy Conversion and Management, 90, 154–165. doi: 10.1016/j.enconman.2014.10.066.[2] Y. Gupta, J. Dumon, and A. Hably, “Modeling and control of a Magnus effect-based airborne wind energy system in crosswind maneuvers,” pp. 1–8.[3] M. L. Loyd, “Crosswind kite power,” Journal of Energy, vol. 4,no. 3, pp. 106–111, 1980.[4] I. Argatov, P. Rautakorpi, and R. Silvennoinen, “Estimation of the mechanical energy output of the kite wind generator,” Renewable Energy, vol. 34, pp. 1525–1532, 2009.[5] Fagiano, L., Zgraggen, A.U., Morari, M., and Khammash, M. (2014). Automatic crosswind flight of tethered wings for airborne wind energy: modeling, control design and experimental results. IEEE Transactions on Control System Technology, 22(4), 1433–1447. doi: 10.1109/TCST.2013.2279592.
Magnus Effect
𝐀𝐖𝐄𝐒𝟏: 𝑆𝑐𝑦𝑙 = 500 𝑚2, 𝑇𝑚𝑎𝑥 = 8𝑒5 𝑁, 𝑃𝑚𝑎𝑥= 4𝑀𝑊
𝐀𝐖𝐄𝐒𝟐: 𝑆𝑐𝑦𝑙 = 1000 𝑚2, 𝑇𝑚𝑎𝑥= 8𝑒5 𝑁, 𝑃𝑚𝑎𝑥= 4𝑀𝑊
Conventional Wind turbine : 1.5MW
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