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Abstract
The main purpose of a wind turbine is to create electrical energy for the electrical grid. When extracting energy from the wind, loads are exerted on the turbine blades, which carry through to the drivetrain, nacelle, tower, foundation, and at last to the ground. The main purpose of the structure is to carry these loads and ensure that the structure does not fail for any load case. Building a stronger turbine is often associated with a higher cost and building the cheapest turbine that produces the most power is what makes a turbine successful in the global market. Understanding the tradeoff between the power vs. loads vs. cost is, therefore, crucial to create the turbines with the lowest cost of energy.
This is the motivation behind the present thesis, which investigates the tradeoff between the power that the turbine produces, the loads that are exerted on the structure, and the cost of the turbine. This is achieved through the creation of an optimization framework. It is capable of finding the optimal rotor radius increase for a given set of load constraints and aerodynamic input and costfunction inputs. The optimization framework consists of an aerodynamic solver and an optimization methodology.
The aerodynamic solver is named the Radially Independent Actuator Disc model (RIAD), and it is essentially a different parametrization of the commonly used Blade Element Momentum (BEM) theory equations. RIAD is found to perform better for load constrained power optimization as it directly relates the loads and power. Furthermore, the model provides an intuitive interpretation of aerodynamic losses, allowing for the magnitude of each type of losses to be quantified with ease. As a result, RIAD can help assess the preferred technological improvements to pursue in order to most efficiently lower aerodynamic losses.
The optimization methodology is named Wind Turbine Rotor Optimization with Radial Independence (WOwRI). WOwRI uses the key assumption of radially independent concentric stream tubes to easily determine the optimal power, given load constraints. The result is the Pareto optimal relationship between the power coefficient (CP ) and load coefficients such as thrust (CT ) and bladerootflapbending moment (CFM ). The initial optimization problem is power maximization with load constraints and a fixed radius increase, by optimizing for the loading along the span. Using this solution for the Pareto optimal relationship, the initial optimization problem reduces to a simple problem of optimizing for a set of scalar values  one for each constraint, which is a significant simplification. Extending the optimization with a cost function results in an optimization framework that can optimize for the optimal rotor radius increase, for the best tradeoff between power, loads, and cost.
The optimization framework can be used for parametrically investigating the impact of the aerodynamic loss (power), the constraints (loads), and the costfunction (cost). It is hereby possible to investigate the tradeoff between the power, loads, and cost which forms a guide for wind turbine rotor design. In particular, this applies to the initial design where quantities such as rotor size, power rating, and design concept need to be decided upon. The framework may also guide the development of new technologies by charting out the areas of turbine design which will benefit the most from them.
This is the motivation behind the present thesis, which investigates the tradeoff between the power that the turbine produces, the loads that are exerted on the structure, and the cost of the turbine. This is achieved through the creation of an optimization framework. It is capable of finding the optimal rotor radius increase for a given set of load constraints and aerodynamic input and costfunction inputs. The optimization framework consists of an aerodynamic solver and an optimization methodology.
The aerodynamic solver is named the Radially Independent Actuator Disc model (RIAD), and it is essentially a different parametrization of the commonly used Blade Element Momentum (BEM) theory equations. RIAD is found to perform better for load constrained power optimization as it directly relates the loads and power. Furthermore, the model provides an intuitive interpretation of aerodynamic losses, allowing for the magnitude of each type of losses to be quantified with ease. As a result, RIAD can help assess the preferred technological improvements to pursue in order to most efficiently lower aerodynamic losses.
The optimization methodology is named Wind Turbine Rotor Optimization with Radial Independence (WOwRI). WOwRI uses the key assumption of radially independent concentric stream tubes to easily determine the optimal power, given load constraints. The result is the Pareto optimal relationship between the power coefficient (CP ) and load coefficients such as thrust (CT ) and bladerootflapbending moment (CFM ). The initial optimization problem is power maximization with load constraints and a fixed radius increase, by optimizing for the loading along the span. Using this solution for the Pareto optimal relationship, the initial optimization problem reduces to a simple problem of optimizing for a set of scalar values  one for each constraint, which is a significant simplification. Extending the optimization with a cost function results in an optimization framework that can optimize for the optimal rotor radius increase, for the best tradeoff between power, loads, and cost.
The optimization framework can be used for parametrically investigating the impact of the aerodynamic loss (power), the constraints (loads), and the costfunction (cost). It is hereby possible to investigate the tradeoff between the power, loads, and cost which forms a guide for wind turbine rotor design. In particular, this applies to the initial design where quantities such as rotor size, power rating, and design concept need to be decided upon. The framework may also guide the development of new technologies by charting out the areas of turbine design which will benefit the most from them.
Original language  English 

Place of Publication  Risø, Roskilde, Denmark 

Publisher  DTU Wind Energy 
Number of pages  133 
Publication status  Published  2020 
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 1 Finished

New industrial paradigm for design of wind turbine blades  tip and root optimization for increasing power performance
Lønbæk, K., Jamieson, P., Gaunaa, M., Bak, D. C., Zahle, F., Madsen, J. I. & Hjort, S.
15/09/2017 → 11/02/2021
Project: PhD