Abstract
On the basis of interdisciplinary modelling methods the mathematical model of the electromechanical system, including power transformer, induction motors and synchronous motors, is formulated and presented in the paper. The motors are joined with the driven objects through a mechanical power transmission system. In addition, the transformer is loaded by nonlinear circuit RL. Differential state equations of the studied system are given as the Cauchy’s formulas. Numerical simulations of the system operation have been made for the selected cases. The results of computer simulation are presented in a graphic form.
Highlights
An interdisciplinary variational method has been used in order to formulate a general mathematical model of an electrical system
The electrical system (Fig. 1), consisting of transformer, one drive based on synchronous motor and two drives based on induction motor, has been analysed numerically
At the time t=40s the electromechanical oscillations are observed in the system. These oscillations are caused by synchronization of synchronous motor, whereas the moments of elasticity in transmission shafts are maximal at the time of achievement of subsynchronous speed
Summary
An interdisciplinary variational method has been used in order to formulate a general mathematical model of an electrical system. The method is based on a modification of Hamilton’s principle [1, 4]. The electromechanical system including transformer, induction motors and synchronous motors as well as nonlinear load RL is analysed. Differential equations describing operation state of the system are derived by formulation of modified Lagrangian terms using the abovementioned method [2, 3]
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