Analytical study on electromechanical wave propagation in a non-uniform continuum power system

According to the differential equations set of describing electromechanical wave propagation in a general lossless non-uniform continuum, firstly, while both the per unit length susceptance and the rotor's inertia of non-uniform continuum change in the form of power functions of spatial coordinate, this paper obtains the Lommel equation about electromechanical wave propagation, presents the exact solutions expressed by Bessel functions. Then the characteristic impedance and the wave speed expressions of electromechanical wave propagation are also derived in the non-uniform condition. Secondly, the WKBJ approximate analytical solutions are studied while the per unit length susceptance and the rotor's inertia of the non-uniform continuum are slow-variation functions of spatial coordinate. Finally, based on an example with typical parameters, the result of electromechanical wave propagation in a non-uniform continuum power system validate the rationality and correctness of the conclusions presented in this paper.