###### Abstract
For HTS cable technology to gain extensive acceptance in national and international grids, it is necessary to determine the possible conditions for technological and economic advantages over conventional solutions. However, the literature presents few comparisons between superconducting and conventional lines. These are limited to specific case studies [21; 22; 23; 24; 25], with cable design optimizations not following cost-effectiveness criteria [26; 27; 28] and focusing on single aspects like losses [29; 30; 31; 32], fluid dynamics [33], or phase balance [34], frequently neglecting some elements of a cable system. On the other hand, cable manufacturers, researchers, and grid operator would all benefit from a comprehensive methodology for designing conductors, even if only at a conceptual level. This procedure should optimize the device design from both technical and economic points of view while considering all cable system components across various operating conditions, line characteristics, and specific constraints. A possible approach is to use the _Optimization Tool for Superconducting Cable Research_ (OSCaR) [35]. This tool allows performing techno-economic analyses of superconducting transmission lines while considering a wide range of operating conditions, facilitating extensive parametric studies, and enabling the identification of cost-effective conductor designs. The tool was originally proposed in [36] for medium-voltage AC HTS coaxial cables cooled with liquid nitrogen (LN\({}_{2}\)), but this method can be easily adapted to other configurations, such as MgB\({}_{2}\) DC cables cooled with helium gas [37]. Focusing on a single cable design at a time simplifies both the exposure of the methodology and the resulting output, enhancing their clarity and accessibility for readers. This work investigates the applicability of the OSCaR approach to HVAC coaxial cables wound using HTS-coated conductors. Conventionally, the coaxial configuration is limited to medium-voltage applications due to the need to incorporate thick concentric insulating layers, but the authors considered it worth exploring its use for HVAC lines, as the design can still be quite compact compared with conventional solutions. Indeed, this configuration offers several advantages compared with other CD layout alternatives. Notably, the concentric design practically cancels the external magnetic field outside of the conductor without requiring a superconducting shield layer or the purchase of additional land near the installation site to mitigate magnetic field limitations imposed by regulations. Regarding the voltage level, power grids are increasingly adopting high-voltage or extra high-voltage (above 220 kV) infrastructures for efficiently transferring electricity from remote renewable energy sources locations to urban centers due to minimal energy loss. Superconducting high-voltage lines present a promising alternative for managing extremely high power levels (in the GW range) over long distances at relatively lower voltage levels (up to 220 kV), simplifying the design, management, and safety. Transferring the same amounts of power using superconducting cables at low or medium voltages would require employing large quantities of expensive tape or operating at temperatures significantly colder than LN\({}_{2}\), both of which pose challenges. The methodology reported in [35; 36] is revised and improved here for HTS HVAC coaxial cables. To the authors' knowledge, no standardized structure exists for superconducting coaxial cables, known to be produced by manufacturers such as Southwire Company and Nexans. Therefore, its conceptual design was adjusted based on what the authors considered the most reliable guidance from the literature. Sections 2-6 will describe the complete optimization procedure, highlighting the key modifications made to the original code and covering the approach's overview and the implemented cost, loss, and constraint functions.