The need for more sustainable and cost-effective energy generation has increased the interest in offshore wind development in deep-water regions. Floating wind turbines offer a promising solution at water depths where bottom-fixed structures are not feasible. Currently, the implementation of floating wind turbines remains limited due to high costs and complex system dynamics. There is a need for efficient, automated optimisation tools that can efficiently identify cost-effective design spaces early in the development process. While optimisation studies have been conducted for semi-submersible and spar-type platforms, limited optimisation related research exists on tension leg platforms (TLPs). This study addresses that gap by developing an optimisation framework for TLPs supporting 15MW wind turbines, allowing for efficient, accurate and cost-effective design iterations while considering platform specific dynamics,.

To achieve this, a frequency-domain model was developed by extending the open source RAFT software. The extensions incorporate features particularly relevant to TLP modelling, including tower flexibility, a sum-frequency force approximation and an analytical tension leg mooring module. The resulting frequency-domain model achieves an error margin within $\pm16\%$ of non-linear time-domain simulations for TLPs with (near) vertical tendons, while reducing computational time by 98.5\%. This makes the model suitable for dynamic analysis within optimisation studies, while enabling TLP-specific response characteristics to be captured at a fraction of the computational cost.

The developed model was integrated into a multi-step genetic algorithm-based optimisation framework to explore the design space, with the objective to reduce the levelised cost of energy (LCOE). The framework, built around a single-column TLP design with four pontoons with tendons at their ends, took into account six design variables to describe the essential system properties. The resulting six dimensional complex design space considers the main column diameter and draft, pontoon diameter and length, tendon angle and tendon pretension. To enable complete design performance evaluations and potentially provide early-stage insights that support certification preparation, each concept was assessed against an extensive set of load cases according to standards, covering both ultimate and fatigue loads in operational and extreme conditions.

The results of the optimisation study identified draft, tendon pretension, tendon angle and pontoon length as the most influential parameters for dynamic performance due to their strong influence on platform stability and mooring stiffness. The column and pontoon diameter had the most significant influence on platform mass and therefore platform cost, while pretension dominated mooring system cost. Despite the identification of these most influential variables, the highly coupled nature of TLPs requires to take all identified design variables into account.

A detailed cost model was implemented, enabling comparison of design concepts within the study, and comparison with floating wind platform designs in other research. To achieve this, the model combines variable platform and mooring costs with fixed lifecycle costs. Multiple optimisation runs revealed several distinct, cost-efficient design spaces, with convergence toward lower LCOE values with increasing iterations of the optimisation. The most cost-effective designs achieved LCOE values around 65 €/MWh, making them competitive with other floating wind concepts across different studies.

Altogether, this work provides an efficient optimisation framework for TLPs in the context of floating offshore wind. It enables accurate and cost-effective design iterations that account for TLP-specific dynamics while significantly reducing computational time. By considering a wide range of load cases and maintaining a balance between speed, adaptability and physical accuracy within a limited degree of uncertainty, the framework offers a holistic approach. This makes it well suited to support early-stage design decisions and concept selection for future deep-sea wind farms using TLPs.