Application of the Optimal Auxiliary Functions Method to a Permanent Magnet Synchronous Generator

Analysis and control of electrical and mechanical behavior of electrical machines devoted to capture the wing energy is a subject of huge interest nowadays, due to the need to respond to the actual demands related to green energy, more specific to the demand to convert the mechanical wind energy into electrical energy. The working regime of a permanent magnet synchronous generator associated with a wind turbine under a variable wind profile is investigated in this paper starting from the reality that the wind speed and especially its variation generate significant electrical and mechanical loads in the system, which could lead to various damages. A new and effective analytical technique, namely the Optimal Auxiliary Functions Method is employed to obtain approximate analytical solutions to the governing equations which are expressed in non-dimensional form. It is found that the analytical results obtained by means of our new method agree very well with numerical integration results, if an appropriate number of convergence-control parameters are employed in the construction of the auxiliary functions. A detailed analysis of the convergence of approximate analytical solutions is developed and it is concluded that the convergence of solutions greatly depends on the number of convergence-control parameters, whose optimal values are rigorously determined using various reliable procedures. Several numerical examples are developed in order to illustrate the capabilities of the proposed approach, which proves to be highly efficient and controls the convergence of the approximate solutions, ensuring a very fast convergence after only one iteration.