Abstract
A mathematical model is developed of the master circuit of an electric driver system including a power transformer and susceptible motion transmission of asynchronous and synchronous drives. Electric motors drive water pumps by means of motion transmission that comprises two elastic couplings of lumped mechanical parameters and a long shaft of distributed mechanical parameters. Differential equations for oscillatory processes for the long shaft and the elastic couplings are different. The shaft is described with partial derivative Euler–Poisson equations, which, combined with the boundary conditions, form mixed problems from the mathematical point of view. The elastic couplings, on the other hand, are described with the ordinary second type Lagrange equations. Based on the theory of electromagnetic field, the partial differential equations describe the skin effects across the rotor age bars. Vertical pumps are presented by means of a loading torque waveform as a function of the input shaft’s angular velocity. The complex mathematical model serves to analyse electromechanical transient processes across the integrated drive system. Starting from there, conditions of stabilisation of the drive system voltage are determined. Electromechanical state equations are presented in the normal Cauchy form and integrated using the fourth-order Runge–Kutta method. Results of computer simulations are shown with graphics, which are interpreted and described.
Highlights
The process of water supply plays an important part in contemporary society
Asynchronous drives are normally used to power-pumping systems that use susceptible motion transmissions to drive pump rotors
Asynchronous motors have a range of advantages over other electric motors, they suffer from the fundamental drawback of consuming high magnetising currents that can reach values of several times the rated currents in transient processes [6,7,8]
Summary
The process of water supply plays an important part in contemporary society. There is a global trend towards high-quality centralised water supply for increasing numbers of consumers. The elements of the assembly are a power transformer and asynchronous and synchronous pump drives with flexible transmission of motion with distributed parameters. Analysis of the power system depending on the value of the excitation current of synchronous motors, taking into account the oscillating mechanical processes in the transmission of motion;. The purpose of this study is to analyse transient processes in a drive system including a power transformer, asynchronous and synchronous pump systems of susceptible motion transmission, and long torsional elements of lumped and distributed mechanical parameters. The main approach of formulating the model is to use the concept of electromechanical energy conversion: electrical components of devices are described by electromagnetic equations taking into account the phenomenon of current displacement in deep-bar cage induction motors. Electromagnetic torque of the synchronous motor will be computed in the ordinary manner [9]:
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