This article considers the criteria for the existence of established modes of power systems. Nonlinear nodal equations of steady-state modes are presented, which have many solutions or do not have any physically realizable solutions. Criteria for the existence of solutions are given based on derivatives of power losses depending on the parameters of the power system modes. Equivalent circuit of the electrical system was performed using the South-Western MEN (MAIN ELECTRIC NETWORKS). The paper highlights the results of calculations of steady-state modes of the electrical system at weighted values of node 12. The maximum normal modes of electrical systems for the power of nodes was determined by the criteria are set ∂ Δ P c ∂ Π i = ∞ .

The aim of the study is to study and analyze the physical, mechanical and technological properties of soils from under winter grain crops in the hot climate of Uzbekistan. The results of determining the moisture content, density, hardness and resistance to various deformations of soils after harvesting winter wheat are presented. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. Studies have found that, in the layer 0-30, the soil moisture for ten days after harvesting winter cereals decreases by 12.1-16.3%, and the soil hardness increases by 10.7-16.4% and are 3.22-5.14 MPa. At the same time, at an average humidity of 12-14%, the resistance of the soil to breakage and torsion, respectively, is 1.3-1.8 and 1.0-1.1 times higher than the resistance of the soil to shear. The resistance of the soil to shear is 87.9 kPa, and to breakage and torsion-69.7 and 78.6 kPa, respectively.

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