This paper presents a methodology for the calculation of the flux distribution in power transformer cores considering nonlinear material, with reduced computational effort. The calculation is based on a weak coupled multi-harmonic approach. The methodology can be applied to 2D and 3D Finite Element models. The decrease of the computational effort for the proposed approach is >90% compared to a time-stepping method at comparable accuracy. Furthermore, the approach offers a possibility for parallelisation to reduce the overall simulation time. The speed up of the parallelised simulations is nearly linear. The methodology is applied to a single-phase and a three-phase power transformer. Exemplary, the flux distribution for a capacitive load case is determined and the differences in the flux distribution obtained by a 2D and 3D FE model are pointed out. Deviations are significant, due to the fact, that the 2D FE model underestimates the stray fluxes. It is shown, that a 3D FE model of the transformer is required, if the nonlinearity of the core material has to be taken into account.

The present work is aimed at geometrical optimization and optical analysis of a small-sized parabolic trough collector (PTC). Improving the performance of parabolic trough collectors can greatly justify the use of solar energy. An optimized curvature geometry, the location of the absorber tube, and the heat flux distribution along the circumference of the absorber tube are major features in the geometric optimization and optical modelling of parabolic trough collectors. Rim angle, aperture width, the diameter of the absorber tube, receiver position, and the optimum value of heat flux are the major parameters considered in this work for geometrical and optical analysis. The Monte Carlo ray tracing method has been adopted for analysis. The non-uniform heat flux distribution profile obtained from optical analysis of the proposed parabolic trough collector has been compared with the profile available in the literature, and good agreement has been obtained, which proves the feasibility and reliability of the model and method used for this study. An experimental new small-sized parabolic trough collector has been fabricated for the optimized rim angle of 90 deg after a successful laser light feasibility test. The effect of the absorber tube position along the optical axis on the heat flux profile was analysed and found to be substantial. Furthermore, the sensitivity analysis of the parabolic trough collector using the software applied has been discussed separately.