Power Curve and Design Optimization of Drag Power Kites

Transcription

1 Institute for Electrical Drive Systems and Power Electronics, Department of Electrical Engineering and Information Technology, Technische Universität München Power Curve and Design Optimization of Drag Power Kites Florian Bauer, R. Kennel, C. Hackl, F. Campagnolo, M. Patt, R. Schmehl October 5th, 2017, Airborne Wind Energy Conference 2017, Freiburg, Germany

2 2

3 How does an optimal drag power kite look like? 2

4 How does an optimal drag power kite look like?... and what are the sensitivities of design parameters? 2

5 Outline 1. Model Derivation 2. Power Curve Optimization 3. Design Parameter Optimization 4. Parameter Studies 5. Conclusions 3

6 Kinematics 4

7 Assumption 1: Loyd s model (extended) 5

8 Assumption 1: Loyd s model (extended) v a = cos(ϕ) cos(ϑ)v w C 2 L +(C D,eq + C D,rot ) 2 C D,Σ 5

9 Assumption 1: Loyd s model (extended) v a = cos(ϕ) cos(ϑ)v w C 2 L +(C D,eq + C D,rot ) 2 C D,Σ Assumption 2: azimuth and elevation are constant effective values 5

10 Kinematics Kite Aerodynamics 6

11 cf.: D. Vander Lind. Airfoil for a flying wind turbine. US Patent 9,709,026. July

12 8

13 CFD result 8

14 CFD result Assumption 3: quadratic approximation c D = c D,0 + c D,2 c 2 L 8

15 Assumption 4: thin airfoil C L = c L 1+ 2 A with A = b2 A/n mw C D,k = c D + C2 L πea C D,k,i + C D,k,a + C D,k,o cf.: J. Katz and A. Plotkin. Low-Speed Aerodynamics. Cambridge Aerospace Series. Cambridge University Press, ISBN:

16 Assumption 4: thin airfoil C L = c L 1+ 2 A with A = b2 A/n mw C D,k = c D + C2 L πea C D,k,i + C D,k,a + C D,k,o cf.: J. Katz and A. Plotkin. Low-Speed Aerodynamics. Cambridge Aerospace Series. Cambridge University Press, ISBN:

17 Assumption 4: thin airfoil C L = c L 1+ 2 A with A = b2 A/n mw C D,k = c D + C2 L πea C D,k,i + C D,k,a + C D,k,o Assumption 5: no interaction between wings and rotors cf.: J. Katz and A. Plotkin. Low-Speed Aerodynamics. Cambridge Aerospace Series. Cambridge University Press, ISBN:

18 Kinematics Kite Aerodynamics Tether 10

19 Assumption 6: wind contribution on airspeed negligible along tether length After conversions: C D,te = 1 4 d te L te A c D,te cf. e.g.: B. Houska, M. Diehl, Optimal control for power generating kites, in: Proceedings of the 9th European Control Conference, Kos, Greece, 2007, pp

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21 Mechanical strength: F te,max A te,core Electrical resistance: R te,wire L te A te,wire R te = R te,wire n te,c,+ + R te,wire n te,c, Dielectric strength: Total diameter, mass: Feasibility condition: E te,ins = f(u te,n,r wire,w ins ) [straight-forward summation] [no overlapping electrical cables] 13

22 Kinematics Rotors Kite Aerodynamics Tether 14

23 Aerodynamic power: P a = 1 2 ρav3 ac D,rot 15

24 Aerodynamic power: P a = 1 2 ρav3 ac D,rot Assumption 7: actuator disk Single rotor: F rot,s =2ρA rot,s v 2 aa(1 a) P rot,s =2ρA rot,s v 3 aa(1 a) 2 15

25 Aerodynamic power: P a = 1 2 ρav3 ac D,rot Assumption 7: actuator disk Single rotor: F rot,s =2ρA rot,s v 2 aa(1 a) P rot,s =2ρA rot,s v 3 aa(1 a) 2 After conversions: C D,rot =4 n rota rot,s A a(1 a) and η a,+ =1 a r rot 15

26 Kinematics Rotors Kite Aerodynamics Power Conversions Tether 16

27 17

28 η a,+ =1 a 17

29 η a,+ =1 a via P te-loss = R te I 2 te 17

30 η a,+ =1 a via P te-loss = R te I 2 te Assumption 8: constant efficiency factors for others 17

31 Kinematics Rotors Atmosphere Kite Aerodynamics Power Conversions Tether 18

32 Assumption 9: logarithmic wind shear v w = v w,href ln h z 0 ln href z 0 with h = h to + L te sin(ϑ) Assumption 10: Rayleigh distribution p(v w,href )= v w,h ref ṽ 2 w,h ref exp v2 w,h ref 2ṽ 2 w,h ref 19

33 Kinematics Rotors Atmosphere Kite Aerodynamics Power Conversions Economics Tether 20

34 Assumption 11: launch & landing energy consumption negligible 21

35 Assumption 11: launch & landing energy consumption negligible Year energy yield: E el,yr [Wh/yr] = 8, 760 h 1yr 0 p(v w,href )P el,+ (v w,href )dv w,href 21

36 Assumption 11: launch & landing energy consumption negligible Year energy yield: E el,yr [Wh/yr] = 8, 760 h 1yr 0 p(v w,href )P el,+ (v w,href )dv w,href LCOE: k LCOE = k E el,yr 21

37 Assumption 11: launch & landing energy consumption negligible Year energy yield: E el,yr [Wh/yr] = 8, 760 h 1yr 0 p(v w,href )P el,+ (v w,href )dv w,href LCOE: k LCOE = k E el,yr Yearly costs: k = k inv + k op k inv = K inv I(1 + I) T/yr (1 + I) T/yr 1 k op = I op K inv 21

38 Assumption 11: launch & landing energy consumption negligible Year energy yield: E el,yr [Wh/yr] = 8, 760 h 1yr 0 p(v w,href )P el,+ (v w,href )dv w,href LCOE: k LCOE = k E el,yr Yearly costs: k = k inv + k op k inv = K inv I(1 + I) T/yr (1 + I) T/yr 1 k op = I op K inv Total capital costs: K inv = k dt P el,n-ins + K inv,o&p 21

39 Kinematics Rotors Atmosphere Kite Aerodynamics Power Conversions Economics Tether 22

40 Outline 1. Model Derivation 2. Power Curve Optimization 3. Design Parameter Optimization 4. Parameter Studies 5. Conclusions 23

41 Assumption 12: v w,href [0,v w,href,cut-out] : arg{max u P a} arg{max u P el} 24

42 Assumption 12: v w,href [0,v w,href,cut-out] : arg{max u P a} arg{max u P el} Assumption 13: C 2 L + C2 D,Σ C L 24

43 power wind speed 25

44 power 0= dp a dc D,rot wind speed 25

45 power 0= dp a dc D,rot C D,rot = C D,eq 2 wind speed 25

46 power 0= dp a dc D,rot C D,rot = C D,eq 2 P a v 3 w wind speed 25

47 power 0= dp a dc D,rot C D,rot = C D,eq 2 P a v 3 w wind speed 25

48 power II 0= dp a dc D,rot C D,rot = C D,eq 2 P a v 3 w wind speed 25

49 power F a = F a,min II 0= dp a dc D,rot C D,rot = C D,eq 2 P a v 3 w wind speed 25

50 power F a = F a,min C D,rot v w const. II 0= dp a dc D,rot C D,rot = C D,eq 2 P a v 3 w wind speed 25

51 power F a = F a,min C D,rot v w const. P a v w const. II 0= dp a dc D,rot C D,rot = C D,eq 2 P a v 3 w wind speed 25

52 power F a = F a,min C D,rot v w const. P a v w const. II 0= dp a dc D,rot C D,rot = C D,eq 2 P a v 3 w wind speed 25

53 power I(a) I(b) II F a = F a,min 0= dp a dc D,rot C D,rot v w const. P a v w const. C D,rot = C D,eq 2 P a v 3 w wind speed 25

54 power I(a) I(b) II F a = F a,min 0= dp a dc D,rot C D,rot v w const. P a v w const. C D,rot = C D,eq 2 P a v 3 w Fa = Fa,max wind speed 25

55 power I(a) I(b) II F a = F a,min 0= dp a dc D,rot C D,rot v w const. P a v w const. C D,rot = C D,eq 2 P a v 3 w Fa = Fa,max wind speed 25

56 power I(a) I(b) II III(a) F a = F a,min 0= dp a dc D,rot C D,rot v w const. P a v w const. C D,rot = C D,eq 2 P a v 3 w Fa = Fa,max wind speed 25

57 power I(a) I(b) II III(a) F a = F a,min 0= dp a dc D,rot P a = const. C D,rot v w const. P a v w const. C D,rot = C D,eq 2 P a v 3 w Fa = Fa,max wind speed 25

58 power I(a) I(b) II III(a) F a = F a,min 0= dp a dc D,rot P a = const. C D,rot v w const. P a v w const. C D,rot = C D,eq 2 P a v 3 w Fa = Fa,max wind speed 25

59 power I(a) I(b) II III(a) III(b) F a = F a,min 0= dp a dc D,rot P a = const. C D,rot v w const. P a v w const. C D,rot = C D,eq 2 P a v 3 w Fa = Fa,max wind speed 25

60 power I(a) I(b) II III(a) III(b) F a = F a,min 0= dp a dc D,rot P a = const. IV C D,rot v w const. P a v w const. C D,rot = C D,eq 2 P a v 3 w Fa = Fa,max wind speed 25

61 Outline 1. Model Derivation 2. Power Curve Optimization 3. Design Parameter Optimization 4. Parameter Studies 5. Conclusions 26

62 27

63 Key ideas 27

64 Key ideas serious estimates/better models for investment costs of other parts/profit margin as well as for mass: not possible/too hard 27

65 Key ideas serious estimates/better models for investment costs of other parts/profit margin as well as for mass: not possible/too hard! INSTEAD: compute maximum allowed investment costs and maximum allowed mass as result, which are requirements for detailed design 27

66 Key ideas serious estimates/better models for investment costs of other parts/profit margin as well as for mass: not possible/too hard! INSTEAD: compute maximum allowed investment costs and maximum allowed mass as result, which are requirements for detailed design rearrange equations into sequence of explicit analytical equations 27

67 Key ideas serious estimates/better models for investment costs of other parts/profit margin as well as for mass: not possible/too hard! INSTEAD: compute maximum allowed investment costs and maximum allowed mass as result, which are requirements for detailed design rearrange equations into sequence of explicit analytical equations optimize free design parameters w.r.t. cost function w/ constraints w/ CMA-ES 27

68 Key ideas serious estimates/better models for investment costs of other parts/profit margin as well as for mass: not possible/too hard! INSTEAD: compute maximum allowed investment costs and maximum allowed mass as result, which are requirements for detailed design rearrange equations into sequence of explicit analytical equations optimize free design parameters w.r.t. cost function w/ constraints w/ CMA-ES optimization problem: max y s.t. ˆK inv,o&p A y y y 27

69 Outline 1. Model Derivation 2. Power Curve Optimization 3. Design Parameter Optimization 4. Parameter Studies 5. Conclusions 28

70 29

71 90 kw/m2 29

72 Parameter Value nominal airfoil lift coefficient 4.16 tether length m elevation angle tether voltage maximum allowed investment costs (o&p)/wing area 9.8 kv 56 k$/m2 total maximum allowed investment costs 5.5 Mio. $ energy yield per year tether mass maximum allowed kite mass maximum allowed kite mass/wing area 18.5 Mio. kwh 1.1 t 11.7 t 140 kg/m2 wing loading 1.6 t/m2 30

73 Parameter Value nominal airfoil lift coefficient 4.16 tether length m elevation angle tether voltage maximum allowed investment costs (o&p)/wing area 9.8 kv 56 k$/m2 total maximum allowed investment costs 5.5 Mio. $ energy yield per year tether mass maximum allowed kite mass maximum allowed kite mass/wing area 18.5 Mio. kwh 1.1 t 11.7 t 140 kg/m2 wing loading 1.6 t/m2 30

74 Parameter Value nominal airfoil lift coefficient 4.16 tether length m elevation angle tether voltage maximum allowed investment costs (o&p)/wing area 9.8 kv 56 k$/m2 total maximum allowed investment costs 5.5 Mio. $ energy yield per year tether mass maximum allowed kite mass maximum allowed kite mass/wing area 18.5 Mio. kwh 1.1 t 11.7 t 140 kg/m2 wing loading 1.6 t/m2 30

75 Parameter Value nominal airfoil lift coefficient 4.16 tether length m elevation angle tether voltage maximum allowed investment costs (o&p)/wing area 9.8 kv 56 k$/m2 total maximum allowed investment costs 5.5 Mio. $ energy yield per year tether mass maximum allowed kite mass maximum allowed kite mass/wing area 18.5 Mio. kwh 1.1 t 11.7 t 140 kg/m2 wing loading 1.6 t/m2 30

76 31

77 Summary of key results of further parameter studies: 31

78 Summary of key results of further parameter studies: tether material selection and nominal voltage have almost no effect 31

79 Summary of key results of further parameter studies: tether material selection and nominal voltage have almost no effect high airfoil lift and high wing loading are required for high maximum allowed cost and a high power density 31

80 optimum 32

81 Summary of key results of further parameter studies: tether material selection and nominal voltage have almost no effect high airfoil lift and high wing loading are required for high maximum allowed cost and a high power density 31

82 Summary of key results of further parameter studies: tether material selection and nominal voltage have almost no effect high airfoil lift and high wing loading are required for high maximum allowed cost and a high power density wide Region III(a) enables much lower wing loading and higher maximum allowed cost 31

83 Summary of key results of further parameter studies: tether material selection and nominal voltage have almost no effect high airfoil lift and high wing loading are required for high maximum allowed cost and a high power density wide Region III(a) enables much lower wing loading and higher maximum allowed cost a (low) tower might cover more than its own cost 31

84 Summary of key results of further parameter studies: tether material selection and nominal voltage have almost no effect high airfoil lift and high wing loading are required for high maximum allowed cost and a high power density wide Region III(a) enables much lower wing loading and higher maximum allowed cost a (low) tower might cover more than its own cost for offshore, the maximum allowed cost is more than the double 31

85 Summary of key results of further parameter studies: tether material selection and nominal voltage have almost no effect high airfoil lift and high wing loading are required for high maximum allowed cost and a high power density wide Region III(a) enables much lower wing loading and higher maximum allowed cost a (low) tower might cover more than its own cost for offshore, the maximum allowed cost is more than the double the technology is scalable: the larger the system, the higher the power density and maximum allowed cost 31

86 Summary of key results of further parameter studies: tether material selection and nominal voltage have almost no effect high airfoil lift and high wing loading are required for high maximum allowed cost and a high power density wide Region III(a) enables much lower wing loading and higher maximum allowed cost a (low) tower might cover more than its own cost for offshore, the maximum allowed cost is more than the double the technology is scalable: the larger the system, the higher the power density and maximum allowed cost the model can reproduce measured data by Makani (model verfication, at least in part) 31

87 Source of left (bottom) figure: Damon Vander Lind. Analysis and Flight Test Validation of High Performance Airborne Wind Turbines. In: Airborne Wind Energy. Ed. by Uwe Ahrens, Moritz Diehl, and Roland Schmehl. Berlin, Heidelberg: Springer Berlin Heidelberg, Fig

88 Source of left (bottom) figure: Damon Vander Lind. Analysis and Flight Test Validation of High Performance Airborne Wind Turbines. In: Airborne Wind Energy. Ed. by Uwe Ahrens, Moritz Diehl, and Roland Schmehl. Berlin, Heidelberg: Springer Berlin Heidelberg, Fig

89 Outline 1. Model Derivation 2. Power Curve Optimization 3. Design Parameter Optimization 4. Parameter Studies 5. Conclusions 34

90 35

91 Achievements: 35

92 Achievements: multidisciplinary steady drag power kite model 35

93 Achievements: multidisciplinary steady drag power kite model covers dominant effects of all involved disciplines 35

94 Achievements: multidisciplinary steady drag power kite model covers dominant effects of all involved disciplines explicit, mostly analytical (white-box), based on first principles 35

95 Achievements: multidisciplinary steady drag power kite model covers dominant effects of all involved disciplines explicit, mostly analytical (white-box), based on first principles can reproduce measurements by Makani 35

96 Achievements: multidisciplinary steady drag power kite model covers dominant effects of all involved disciplines explicit, mostly analytical (white-box), based on first principles can reproduce measurements by Makani numerous parameter studies 35

97 Achievements: multidisciplinary steady drag power kite model covers dominant effects of all involved disciplines explicit, mostly analytical (white-box), based on first principles can reproduce measurements by Makani numerous parameter studies Outlook: 35

98 Achievements: multidisciplinary steady drag power kite model covers dominant effects of all involved disciplines explicit, mostly analytical (white-box), based on first principles can reproduce measurements by Makani numerous parameter studies Outlook: my dissertation/our papers: all details and additional enhancements 35

99 Achievements: multidisciplinary steady drag power kite model covers dominant effects of all involved disciplines explicit, mostly analytical (white-box), based on first principles can reproduce measurements by Makani numerous parameter studies Outlook: my dissertation/our papers: all details and additional enhancements airfoil optimizations 35

100 Achievements: multidisciplinary steady drag power kite model covers dominant effects of all involved disciplines explicit, mostly analytical (white-box), based on first principles can reproduce measurements by Makani numerous parameter studies Outlook: my dissertation/our papers: all details and additional enhancements airfoil optimizations verifications: wind tunnel, higher fidelity models, tiny-scale (1 kw) kite on the way, small-scale (20 kw) kite planned 35

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104 Institute for Electrical Drive Systems and Power Electronics, Department of Electrical Engineering and Information Technology, Technische Universität München Power Curve and Design Optimization of Drag Power Kites Florian Bauer, R. Kennel, C. Hackl, F. Campagnolo, M. Patt, R. Schmehl October 5th, 2017, Airborne Wind Energy Conference 2017, Freiburg, Germany 39