Computational Design Scheme for Wind Turbine Drive-Train Based on Lagrange Multipliers

Abstract

The design optimization of wind turbines and their subsystems will make them competitive as an ideal alternative for energy. This paper proposed a design procedure for one of these subsystems, which is the Wind Turbine Drive-Train (WTDT). The design of the WTDT is based on the load assumptions and considered as the most significant parameter for increasing the efficiency of energy generation. In industry, these loads are supplemented by expert assumptions and manipulated to design the transmission elements. In contrary, in this work, the multibody system approach is used to estimate the static as well as dynamic loads based on the Lagrange multipliers. Lagrange multipliers are numerical parameters associated with the holonomic and nonholonomic constraints assigned in the drive-train model. The proposed scheme includes computational manipulations of kinematic constraints, mapping the generalized forces into Cartesian respective, and enactment of velocity-based constrains. Based on the dynamic model and the obtained forces, the design process of a planetary stage of WTDT is implemented with trade-off’s optimization in terms of gearing parameters. A wind turbine of 1.4 megawatts is introduced as an evaluation study of the proposed procedure, in which the main advantage is the systematic nature of designing complex systems in motion.