Based on the general theory of fractional order derivatives and integrals, application of the Caputo–Fabrizio operator is analyzed to improve a mathematical model of a two-mass system with a long shaft and concentrated parameters. Thus, the real transmission of complex electric drives, which consist of long shafts with a sufficient degree of adequacy, is presented as a two-mass system. Such a system is described by ordinary fractional order differential equations. In addition, it is well known that an elastic mechanical wave, propagating along a drive transmission with a long stiff shaft, creates a retardation effect on distribution of the time–space angular velocity, the rotation angle of the shaft, and its elastic moment. The approach proposed in the current work helps to take in account the moving elastic wave along the shaft of electric drive mechanism. On this basis, it is demonstrated that the use of the fractional order integrator in the model for the elastic moment enables it to reproduce real transient processes in the joint coordinates of the system. It also provides an accuracy equivalent to the model with distributed parameters. The distance between the traditional model and the model in which the fractional integral is used for the elastic moment modelling in a two-mass system, with a long shaft, is analyzed.

Genetic algorithms are used to parameter identification of the model of oscillatory processes in complicated motion transmission of electric drives containing long elastic shafts as systems of distributed mechanical parameters. Shaft equations are generated on the basis of a modified Hamilton–Ostrogradski principle, which serves as the foundation to analyse the lumped parameter system and distributed parameter system. They serve to compute basic functions of analytical mechanics of velocity continuum and rotational angles of shaft elements. It is demonstrated that the application of the distributed parameter method to multi-mass rotational systems, that contain long elastic elements and complicated control systems, is not always possible. The genetic algorithm is applied to determine the coefficients of approximation the system of Rotational Transmission with Elastic Shaft by equivalent differential equations. The fitness function is determined as least-square error. The obtained results confirm that application of the genetic algorithms allow one to replace the use of a complicated distributed parameter model of mechanical system by a considerably simpler model, and to eliminate sophisticated calculation procedures and identification of boundary conditions for wave motion equations of long elastic elements.

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In the paper, based on interdisciplinary approaches to modeling, a mathematical model of a part of an opened extra-high voltage electrical grid, which key elements are two long power transmission lines with distributed constants is presented. Within this framework the analysis of transient processes in power transmission lines in a single-line arrangement is carried out. The results of transient processes are displayed by means of figures; they are under ongoing research.

Beginning with the classic methods, a mathematical model of an electromechanical system is developed that consists of a deep bar cage induction motor that, via a complex motion transmission with distributed mechanical parameters, drives a working machine, loading the drive system with a constant torque. The electromagnetic field theory serves to create the motor model, which allows addressing the displacement of current in the rotor cage bars. Ordinary and partial differential equations are used to describe the electromechanical processes of energy conversion in the motor. The complex transmission of the drive motion consists of a long shaft with variable geometry cardan joints mounted on its ends. Non-linear electromechanical differential equations are presented as a system of ordinary differential equations combined with a mixed problem of Dirichlet first-type and Poincaré third-type boundary conditions. This system of equations is integrated by discretising partial derivatives by means of the straight-line methods and successive integration as a function of time using the Runge–Kutta fourth-order method. Starting from there, complicated transient processes in the drive system are analysed. Results of computer simulations are presented in the graphic form, which is analysed.