The paper addresses the problem of modeling a smooth contour interpolating a point series belonging to a curve containing no special points, which represents the original curve with specified accuracy. The contour is formed within the area of possible location of the parts of the interpolated curve along which the curvature values are monotonously increased or decreased. The absolute interpolation error of the point series is estimated by the width of the area of possible location of the curve. As a result of assigning each intermediate point, the location of two new sections of the curve that lie within the area of the corresponding output section is obtained. When the interpolation error becomes less than the given value, the area of location of the curve is considered to be formed, and the resulting point series is interpolated by a contour that lies within the area. The possibility to shape the contours with arcs of circles specified by characteristics is investigated.

The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that if a sequence of points can be interpolated by a monotone curve, then the reference curve on which these points have been assigned is monotone, provides the opportunity to implement the proposed approach to estimate the interpolation error of a point series of arbitrary configuration. The proposed methods for forming a convex regular contour by arcs of ellipses and B-spline ensure the interpolation of any point series in parts that can be interpolated by a monotone curve. At the same time, the deflection of the contour from the boundaries of the area of the possible location of the monotone curve can be controlled. The possibilities of the developed methods are tested while solving problems of the interpolation of a point series belonging to monotone curves. The problems are solved in the CAD system of SolidWorks with the use of software application created based on the methods developed in the research work.

During the design of extra-high-voltage transmission lines, studies of the influence of asymmetry due to the phase difference of the parameters on its processes and the electrical network were performed. To compensate for this source of asymmetry for transmission lines longer than 100 km, a relatively simple technical means was proposed and implemented—phase transposition (change of the mutual location of phase wires in space). However, at the same time transposition causes additional capital costs in construction and reduces reliability during operation, so when designing a specific transmission line, extra-high-voltage is desirable to evaluate the effectiveness of the use of this measure in the real electricity network. Thus, under certain conditions, even for a transmission line 600 km in length, it was possible to perform either an incomplete transposition cycle, or abandon this measure altogether.

Winter wheat is one of the widespread crops in Ukraine. The search for methods to increase the yield and consumer properties of wheat, without compromising environmental safety, is one of the important scientific problems. The principles of precision agriculture point to the proper positioning of the seeds, recommending the method of “upward germination” (positioning the wheat germ vertically). The main objective of this study was to develop a new geometric model of wheat grain with a displaced centre of mass, as well as to conduct the theoretical research and numerical experiments on the orientation of grains using their multiple impact interaction with inclined surfaces. A new model of germ consisting of two different end semispheres and amid-line truncated cone was proposed, with a displaced centre of mass. Taking into account the physical properties of the objects, the concept of arrangement of gravity orientation of seeds in a stream was applied. This concept was based on various ratios of kinetic parameters of bodies with a displaced centre of gravity following an impact. The results showed that the orientation process can be controlled by changing the inclination angles and the length of the walls of the tray orientator within the working velocity range. This must be done before impact interaction of 0.2-0.3 m s−1 when the inclination angles of the impact interaction planes are 24-32°C.

The aim of this study is to investigate changes in the wind power plant energy production parameters under the conditions of sudden wind changes and voltage drop. To achieve these goals, a simulation of operation of wind power plants was performed. Twelve wind turbines with variable rotational speed equipped with a Fuhrländer FL 2500/104 asynchronous double-fed induction generator (DFIG) were used, each with an installed capacity of 2.5 MW. A general scheme of a wind power plant has been developed using a modular-trunk power distribution scheme. The system consists of wind power modules and a central substation, which allows total power to be supplied to the power system at a voltage of 35 kV. The central substation uses two high voltage switchgears. Four modules were used, each of them consisting of three wind turbines, with a power of 7.5 MW. The simulation of the wind turbines was performed in the MATLAB® Simulink® software environment. The mode of response of the turbines to a change in wind speed, a voltage drop in the 35 kV voltage system, and a one-phase short circuit to the ground in the system of 10.5 kV voltage was explored. The results show that a sudden voltage drop and the appearance of short circuits influence the wind power plant (WPP) operation in a different way independent of regulation mode. The power generation from WPP will be limited when voltage drop occurred for both AC and Voltage regulation mode and during short circuits while WPP is set on AC regulation mode.