Extruded high-voltage direct current cable systems transmit electric power over long distances. Numerical field simulation can provide access to the internal electrothermal behavior of cable joints, which interconnect cable sections. However, coupled nonlinear electrothermal field simulations are still a challenge. In this work, a robust numerical solution approach is implemented and validated. This approach allows for efficient parameter studies of resistively graded high-voltage direct current cable joint designs. It is assessed how the dielectric stress distribution between the conductor connection and the grounded cable sheath is influenced by nonlinear field and temperature dependent electric conductivity of the field grading material. Optimal field grading material parameters, which fulfill the field grading and power loss requirements, are suggested based on the simulation studies.

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Many optimization problems in electrical engineering consider a large number of design parameters. A sensitivity analysis identifies the design parameters with the strongest influence on the problem of interest. This paper introduces the adjoint variable method as an efficient approach to study sensitivities of nonlinear electroquasistatic problems in time domain. In contrast to the more common direct sensitivity method, the adjoint variable method has a computational cost nearly independent of the number of parameters. The method is applied to study the sensitivity of the field grading material parameters on the performance of a 320 kV cable joint specimen, which is modeled as a finite element nonlinear transient electroquasistatic problem. Special attention is paid to the treatment of quantities of interest, which are evaluated at specific points in time or space. It is shown that the method is a valuable tool to study this strongly nonlinear and highly transient technical example.