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Objectives and Constraints for Wind Turbine Optimization Objectives and Constraints for WindTurbine Optimization S. Andrew Ning National Renewable Energy Laboratory January, 2013 NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC. Overview 1. Introduction 2. Methodology (aerodynamics, structures, cost, reference model, optimization) 3. Maximum Annual Energy Production (AEP) 4. Minimum m/AEP 5. Minimum Cost of Energy (COE) 6. Conclusions NATIONAL RENEWABLE ENERGY LABORATORY 2 Introduction Wind Turbine Design Aerodynamic Performance Capital Structural Costs Design Optimization Maintenance and Uncertainty Control Costs Quantification Strategy Farm Site Layout Selection NATIONAL RENEWABLE ENERGY LABORATORY 4 Wind Turbine Optimization Objectives Design Vars • Max P/min Mb • Blade shape • Max AEP • Rotor/nacelle • Min COE • Turbine Fidelity Optimization • Analytic • Gradient • Aeroelastic • Direct search • 3D CFD • Multi-level NATIONAL RENEWABLE ENERGY LABORATORY 5 Wind Turbine Optimization Objectives Design Vars • Max P/min Mb • Blade shape • Max AEP • Rotor/nacelle • Min COE • Turbine Fidelity Optimization • Analytic • Gradient • Aeroelastic • Direct search • 3D CFD • Multi-level NATIONAL RENEWABLE ENERGY LABORATORY 6 Methodology Model Development 1. Capture fundamental trade-offs (physics-based) 2. Execute rapidly (simple physics) 3. Robust convergence (reliable gradients) NATIONAL RENEWABLE ENERGY LABORATORY 8 Aerodynamics • Blade-element momentum theory ‣ hub and tip losses, high-induction factor correction, inclusion of drag ‣ 2-dimensional cubic splines for lift and drag coefficient (angle of attack, Reynolds number) • Drivetrain losses incorporated in power curve • Region 2.5 when max rotation speed reached • Rayleigh distribution with 10 m/s mean wind speed (Class I turbine) • Availability and array loss factors NATIONAL RENEWABLE ENERGY LABORATORY 9 Blade Element Momentum ⌦r(1 + a 0) plane of rotation φ U (1 a) W 1 - NATIONAL RENEWABLE ENERGY LABORATORY 10 Blade Element Momentum ⌦r(11+ + a0 ) plane of rotation φ U (11 a) W 1 - NATIONAL RENEWABLE ENERGY LABORATORY 11 Blade Element Momentum ⌦r(1 + a 0) plane of rotation φ U (1 a) W 1 - NATIONAL RENEWABLE ENERGY LABORATORY 12 Blade Element Momentum sin ¢ cos ¢ f(¢)= =0 1 a(¢) - A (1 + a (¢)) - r 0 NATIONAL RENEWABLE ENERGY LABORATORY 13 Blade Element Momentum S.Andrew Ning, “A Simple Solution Method for the Blade Element Momentum Equations with Guaranteed Convergence,” Wind Energy, to appear. CCBlade NATIONAL RENEWABLE ENERGY LABORATORY 14 principal material direction n L r D t S ply angle Figure 1: Example of composites layup at a typical blade section. Principal material direction of laminas, shown in brown, is skewed with respect to the blade axis. This causes bend-twist coupling as evident Compositeat the blade tip. Sectional Analysis Sector 2 Sector 3 Sector 1 AA BB Laminas schedule at AA Laminas schedule at BB Figure 2: Example of spar-cap-type layup of composites at a blade section PreComp NATIONAL RENEWABLE ENERGY LABORATORY 15 Beam Finite Element Analysis 1 1 K = [EI](⌘)f 00(⌘)f 00(⌘)d⌘ ij L3 i j Z0 pBEAM NATIONAL RENEWABLE ENERGY LABORATORY 16 Panel Buckling ⇡ 2 E(⌧ )⌧ 2 N =3.6 d⌧ b cr b 1 ⌫(⌧ )2 ⇣ ⌘ Z − NATIONAL RENEWABLE ENERGY LABORATORY 17 Fatigue (gravity-loads) NATIONAL RENEWABLE ENERGY LABORATORY 18 Cost Model • Based on NREL Cost and Scaling Model • Replaced blade mass/cost estimate • Replaced tower mass estimate • New balance-of-station model NATIONAL RENEWABLE ENERGY LABORATORY 19 Reference Geometry • NREL 5-MW reference design • Sandia National Laboratories initial layup • Parameterized for optimization purposes NATIONAL RENEWABLE ENERGY LABORATORY 20 Design Variables Description Name # of Vars chord distribution {c} 5 twist distribution {θ} 4 spar cap thickness distribution {t} 3 tip speed ratio in region 2 λ 1 rotor diameter D 1 machine rating rating 1 NATIONAL RENEWABLE ENERGY LABORATORY 21 Constraints minimize J(x) x subject to (rf rm✏50i)/✏ult < 1,i=1 ,...,N ultimateultimate tensile tensile strain strength (r r ✏ )/✏ > 1,i=1,...,N ultimateultimate compressive compressive strain strength f m 50i ult - (✏50j rf ✏cr)/✏ult > 0,j=1 ,...,M sparspar cap cap buckling buckling - 6/60 < 1.1 tiptip deflectiondeflection at at rated rated speed !1/(3⌦rated) > 1.1 bladeblade natural natural frequency frequency 0 /S < 1 fatigue at blade root due to gravity loads root-gravity f fatigue at blade root (gravity loads) 0 /S > 1 fatigue at blade root due to gravity loads root-gravity f - fatigue at blade root (gravity loads) V <V maximum tip speed (imposed directly in analysis) tip tipmax maximum tip speed cset(x) < 0 NATIONAL RENEWABLE ENERGY LABORATORY 22 Maximum Annual Energy Production Why a single-discipline objective? 1. No structural model 2. No cost model 3. Organizational structure 4. Computational limitations NATIONAL RENEWABLE ENERGY LABORATORY 24 Maximize AEP at Fixed Mass maximize AEP (x) with respect to x = c , ✓ , λ {{ } { } } subject to cset < 0 mblade = mc NATIONAL RENEWABLE ENERGY LABORATORY 25 Maximize AEP at Fixed Mass NATIONAL RENEWABLE ENERGY LABORATORY 26 AEP First maximize AEP (x) with respect to x = c , ✓ , A {{ } { } } subject to Vtip <Vtipmax NATIONAL RENEWABLE ENERGY LABORATORY 27 AEP First maximize AEP (x) with respect to x = c , ✓ , A {{ } { } } subject to V <V subject to Vtip <Vtip max Mb i <i iaero dr aero aero0 ⌘ t ✓ Z ◆ Splan <Splan0 (root < (root0 NATIONAL RENEWABLE ENERGY LABORATORY 28 AEP First maximize AEP (x) with respect to x = c , ✓ , A {{ } { } } subject to Vtip <Vtipmax iaero <iaero0 Splan <Splan0 J(root < J(root0 minimize m(x) with respect to x = t { } subject to cset(x) < 0 NATIONAL RENEWABLE ENERGY LABORATORY 29 Comparison Between Methods AEP mass COE 0.5 0 -0.5 % change -1 -1.5 AEP 1st mass 1st min COE NATIONAL RENEWABLE ENERGY LABORATORY 30 Mass First minimize m(x) with respect to x = c , t {{ } { }} subject to cset(x) < 0 maximize AEP (x) with respect to x = ✓ , λ {{ } } subject to Vtip <Vtipmax minimize m(x) with respect to x = c , t {{ } { }} subject to cset(x) < 0 NATIONAL RENEWABLE ENERGY LABORATORY 31 Comparison Between Methods AEP mass COE 0.5 0 -0.5 % change -1 -1.5 AEP 1st mass 1st min COE NATIONAL RENEWABLE ENERGY LABORATORY 32 Minimize COE minimize COE(x) with respect to x = c , ✓ , t , λ {{ } { } { } } subject to cset(x) < 0 NATIONAL RENEWABLE ENERGY LABORATORY 33 Comparison Between Methods AEP mass COE 0.5 0 -0.5 % change -1 -1.5 AEP first mass first min COE NATIONAL RENEWABLE ENERGY LABORATORY 34 Conclusions 1. Similar aerodynamic performance can be achieved with feasible designs with very different masses. 2. Sequential aero/structural optimization is significantly inferior to metrics that combine aerodynamic and structural performance. NATIONAL RENEWABLE ENERGY LABORATORY 35 Minimum Turbine Mass / AEP Cost of Energy FCR (TCC + BOS) + O&M m COE = turbine AEP ⇡ AEP NATIONAL RENEWABLE ENERGY LABORATORY 37 Vary Rotor Diameter minimize COE(x; D) or m(x; D)/AEP (x; D) with respect to x = c , ✓ , t , λ {{ } { } { } } subject to cset(x) < 0 NATIONAL RENEWABLE ENERGY LABORATORY 38 Maximize AEP at Fixed Mass NATIONAL RENEWABLE ENERGY LABORATORY 39 Tower Contributions to Mass/Cost mass cost 14% 17% 12% 53% 24% 33% 38% 9% rotor nacelle tower rotor nacelle tower bos o&m NATIONAL RENEWABLE ENERGY LABORATORY 40 Maximize AEP at Fixed Mass NATIONAL RENEWABLE ENERGY LABORATORY 41 Maximize AEP at Fixed Mass NATIONAL RENEWABLE ENERGY LABORATORY 42 Fixed Mass mfixed = mblades + mother NATIONAL RENEWABLE ENERGY LABORATORY 43 Fixed Mass NATIONAL RENEWABLE ENERGY LABORATORY 44 Fixed Mass NATIONAL RENEWABLE ENERGY LABORATORY 45 Conclusions 1. m/AEP can work well at a fixed diameter but is often misleading for variable diameter optimization 2. Problem must be constructed carefully to prevent over- incentivizing the optimizer to reduce tower mass NATIONAL RENEWABLE ENERGY LABORATORY 46 Minimum Cost of Energy Robust Optimization Wind Power Class Wind Speed (50m) 3 6.4 4 7.0 5 7.5 6 8.0 7 11.9 NATIONAL RENEWABLE ENERGY LABORATORY 48 Robust Optimization minimize <COE(x; V hub) > where V (6.4, 11.9) hub ⇠ U with respect to x = c , ✓ , t , λ,D,rating {{ } { } { } } subject to cset(x) < 0 NATIONAL RENEWABLE ENERGY LABORATORY 49 Robust Design Vhub NATIONAL RENEWABLE ENERGY LABORATORY 50 Conclusions 1. Optimization under uncertainty is important given the stochastic nature of the problem 2. Fidelity of the cost model can dramatically affect results NATIONAL RENEWABLE ENERGY LABORATORY 51 Conclusions Conclusions 1. Sequential (or single-discipline) optimization is significantly inferior as compared to integrated metrics 2. m/AEP can be a useful metric at a fixed diameter if tower mass is handled carefully 3. High-fidelity cost modeling and inclusion of uncertainty are important considerations NATIONAL RENEWABLE ENERGY LABORATORY 53 Acknowledgements • Rick Damiani • Pat Moriarty • Katherine Dykes • George Scott NATIONAL RENEWABLE ENERGY LABORATORY 54 ThankYou .
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