# Review of the AC Loss Computation for HTS using the H-formulation

## TL;DR

This review comprehensively discusses the $H$-formulation finite element method for calculating AC losses in high temperature superconductor devices, covering equations, modeling strategies, applications, and computational aspects.

## Contribution

It provides a detailed overview of the $H$-formulation FEM model, including equations, implementation, modeling strategies, and applications in HTS AC loss calculations.

## Key findings

- The $H$-formulation is widely used for AC loss modeling in HTS applications.
- Modeling strategies like multi-scale and homogenization improve efficiency.
- The $H$-formulation has advantages in ease of implementation but also some limitations.

## Abstract

This article presents a review of the finite element method (FEM) model based on the $H$ formulation of Maxwell's equations used to calculate AC losses in high temperature superconductor (HTS) tapes, cables and windings for different applications. This model, which uses the components of the magnetic field as state variables, has been gaining a great popularity and has been in use in tens of research groups around the world. This contribution first reviews the equations on which the model is based and their implementation in finite element method programs for different cases, such 2D longitudinal and axis-symmetric geometries, 3D geometries. Modeling strategies to tackle large number of HTS tapes, such as multi-scale and homogenization methods, are also introduced. Then, the second part of the article reviews the applications for which the $H$ formulations has been used to calculate AC losses, ranging from individual tapes, to complex cables and large magnet windings. Afterwards, a section is dedicated to the discussion of the $H$ formulation in terms of computational efficiency and easiness of implementation. Its pros and cons are listed. Finally, the last section draws the main conclusions.