Shape Sensitivity Analysis and Optimization of Current-Carrying Conductor for Current Distribution Control

This paper proposes a sensitivity analysis for the shape optimization of current-carrying conductor in the dc system. The design variable for the current-carrying conductor problem is the outer boundary of the conductor, which has the homogeneous Neumann condition. The 3-D shape sensitivity formula is derived using the material derivative concept from continuum mechanics and the adjoint variable technique. The evolution of the conductor shape is expressed by using the level set method. Three numerical examples are tested to show the usefulness of the proposed method.