analytical calculation of the basic electromagnetic losses of the energy of the frequency-regulated asynchronous engine in positioning

Purpose. Obtaining analytical dependencies for the calculation of the main electromagnetic energy losses of a frequency-controlled induction motor in positioning modes with small displacements for various types (linear, parabolic and quasi-optimal) of its velocity variation. Methodology. Similarity methods, differential and integral calculus, analytical interpolation, mathematical analysis. Findings. Analytical dependencies for calculation of current electromagnetic power losses and basic electromagnetic energy losses of a frequency-controlled asynchronous motor in the modes of positioning with small displacements for various types (linear, parabolic and quasi-optimal) of its velocity are obtained. A universal form of the analytical dependence for calculating the optimal acceleration and deceleration times for a frequency-controlled asynchronous motor for positioning with small displacements, corresponding to minimization of the main electromagnetic energy losses of this engine with the indicated positioning for various species (linear, parabolic and quasi-optimal), is obtained. A comparative quantitative assessment of the change is made: the optimum values of the main electromagnetic energy losses of the frequency-controlled asynchronous engine and the corresponding maximum speed and optimal acceleration and deceleration times, in the function of the set prescribed small displacements for the various engine speed trajectories under consideration. Originality. For the first time, analytical dependencies for the calculation of the main electromagnetic energy losses of a frequency-controlled asynchronous motor are obtained for positioning with small displacements as a function of the set values of the movement of the motor shaft and the set values of its acceleration and deceleration times for the specified specified displacements. For the first time, dependences are obtained for a quantitative estimate of the minimum fundamental electromagnetic energy losses of an induction motor and the corresponding maximum speed and optimal acceleration and deceleration times in the function of the set given small displacements for a linear, parabolic and quasi-optimal trajectory of the engine speed during positioning. Practical value.  The calculated analytical dependencies obtained are intended for a quantitative estimation of the main electromagnetic energy losses of a frequency-controlled induction motor in the small-displacement mode. By determining, using the proposed analytical dependencies of the maximum speed values and the optimum acceleration and deceleration times of the frequency-controlled asynchronous motor, minimization of its main electromagnetic energy losses is achieved by positioning for linear, parabolic and quasi-optimal velocity trajectories.