The sensitivity analysis using adjoint method in numerical modeling of electric potential distribution of the transmission lines

This paper proposes a new methodology for sensitivity analysis evaluation, fast and with high precision of the electric potential distribution near the transmission lines (TL's). The TL is modeled by the finite element method and the sensitivity of the cable positions is obtained using the adjoint method. The sensitivity of the objective function during the optimization process by using methods based on gradient information is obtained by using the adjoint method. The exact sensitivity obtained by the adjoint method concerning the numeric model of the TL's results in new geometries of the bundles conductors with high surge impedance loading. These geometries are not possible to get using analytic models. The sensitivities of a large number of conductors by phase are obtained with high precision and very low computational cost using adjoint sensitivities, which are independent of the number of design variables. The central finite difference method is used to calculate the sensitivities and to validate the adjoint method. With this methodology, the FEM model of the TL can be used during the optimization process without compromising the required computational processing time.