The article provides a brief analysis of the processes that occur when starting an electric motor. Mathematical relations modeling the process of starting a direct current motor are presented. Graphical dependences allowing to determine parameters of a thermistor providing an optimum start-up of a direct current machine have been obtained.

Keywords: starting current, thermistor, starting rheostat, thermal characteristic, DC motor, boundary conditions, torque resistance, idealized rheostat, heat loss, economical starting

The article gives a brief analysis of thermal processes occurring during the start-up of an electric motor. Mathematical relations modeling the distribution of thermal energy in the thermistor during the process of starting the DC motor are presented. Graphic dependences are presented, which allow to make arrangement of thermoresistors for the starting rheostat and to determine parameters of the starting rheostat obtained in this way. Application of the starting rheostat made on the basis of thermistors, provide an optimal starting of a DC motor.

Keywords: control gears, thermistor, starting rheostat, DC motor, temperature, dynamic characteristic, form of starting current

The article considers variants of arrangement of various reactive power compensation devices, the choice of location of which took into account both modes of operation of power grids and voltage levels in the nodes. Mathematical modeling made it possible to form an optimal calculation algorithm based on a multi-criteria approach, taking into account the possible voltage increase at the corresponding substations. However, this approach is accompanied by some increase in active power losses, so the final conclusions should be based on expert procedures.

Keywords: reactive power compensation, mathematical modeling, installation site, power losses, multi-criteria approach, calculation algorithm, power system, substation, compensating devices

The choice of the installation location of compensating devices is determined by various factors that must be taken into account when performing calculations. The location of reactive power compensation devices is determined based on the results of mathematical modeling and the optimal operating mode of individual sections of electrical networks. The paper presents the results of modeling, considers the uncertainties encountered in solving the problem of placement of compensating devices.

Keywords: compensating devices, electric power industry, active power losses, minimum reduced costs, uncertainty, power gain, optimization criteria, electrical node, damage vector, optimization

When determining the locations of compensating devices, it is necessary to make complex calculations that take into account various factors (included in the equations in the form of variables). To get results, calculations are performed repeatedly. Newton's method with coefficients in the form of a Jacobi matrix is widely used. An algorithm for solving the necessary equations by the Gauss method is considered, and the required number of iterations is determined to obtain reliable results.

Keywords: compensating devices, electric power, network state, nodal conductivity matrix, Gauss method, algorithm, Newton's method, electrical nodes, iterations, convergence, algorithm

The article provides a brief analysis of the starting processes of electrical devices. The mathematical formulation of the problem of synthesis of starting rheostats is formulated and its solution is proposed. The main condition for optimal starting of electric motors using thermistor rheostats is presented. Optimal diagrams of the starting current and set of revolutions are given. and also, the change in heat losses in the anchor chain. Recommendations on the layout of starting rheostats are given.

Keywords: thermistor rheostat, optimal start-up, thermal start-up characteristic, optimal control problem, DC motor, boundary conditions, speed

The description of the conveyor device intended for transportation of easily damaged goods is presented. A special feature of the device used is a conveyor belt containing ferromagnetic rods. Moving the conveyor belt and fixing the element on the conveyor belt is determined by the location of the coils on the frame and the speed of switching the voltage supplied to these coils.

Keywords: conveyor devices, the device is easy to damage the conveyer belt, the ferromagnetic cores of electromagnetic coils

The article considers the methods of calculation of electric networks when choosing the locations of compensating devices of consumers. The basic network and calculation module of a complex network transformed into a full polygon is analyzed

Keywords: reactive power compensation, optimization, power line, consumer compensating devices, analytical model, reactive load, power system

The Calculations of the electric network modes are based on the determination of electric power losses during transportation.The calculation methods used are based on the Newton method and the Jacobi matrix. The considered version of the calculation (by a number of transformations) with a small number of iterations allows to obtain the same results as when using the Newton method.

Keywords: matrix of nodal resistances, complex resistivity specific increments, losses of electric energy, compensating devices, algorithm, quadratic model, mathematical model

High-current semiconductor polycrystalline thermistors of high power of coaxial type have a large mass and consequently, considerable heat capacity and heat resistance. Due to this, the thermophysical and electrophysical processes in them are different in the steady and transient regimes, which is especially important in regimes. which lasts a fraction or a unit of seconds. The main variants of operation of such thermistors in dynamic modes are considered and various characteristics are given.

Keywords: Thermistor, thermal and electrophysical characteristics, electric motors, electrophysical and thermal characteristics of semiconductor thermo-resistors of coaxial type

Overhead contact system is a part of electric traction network which doesn’t have safety margin of a construction that’s why its using in winter becomes much difficult. The most heavy overhead contact system work is the operating regime in wind and ice loading because of wind and increasing not only on wires and suspension strands but on supporting structures. Ice loading on wires makes current-collecting conditions much worse and taking into account operational factors it can be a cause of a traffic accident and trains stop. The authors examine some methods of ice prevention, their efficiency effect and the capacity of their combining. In connection with this it is very important to trace ice load as early as possible. Equipment set for thermodynamic method instantiation and its fixing variant are represented.

Keywords: traction power system, overhead contact system, contact wire line, ice loading, loading, testing methods

The problem of distribution of compensating devices of consumers between separate nodes of the power system is considered in the article. The analytical model and the algorithm for optimizing reactive power compensation are presented. Criteria of optimality of reactive power compensation are singled out. The account is taken of poorly formalized, technological factors.

Keywords: Keywords reactive power compensation, multicriteria, information uncertainty, consumer compensating devices, analytical model, optimality criteria, normalized factors

The model of reactive power compensation system calculation in industrial enterprises and power systems electric networks is developed. The authors take into account three main problems: multidimensionality, informational fragmentation and incompleteness of information. The quadratic model of  reactive power compensation is examined. The calculation method main phases which uses all the advantages of quadratic model and methods of its improvement are given.

Keywords: compensating devices, reactive power compensation, power system, industrial enterprises electric networks, quadratic model, mathematical model, incompleteness of information

Contact network work in winter conditions is much more difficult than usual. The most hard contact network mode of operation is the mode of ice with wind, which increase wind and ice load on wires and cables, reference and supporting structures. Ice loading on the wires and wind effects significantly impair the conditions of current pick-off and coupled with operational factors can cause an accident and lead to a trains stop. From this perspective the detection of glaze-ice and rime deposition in the early stages with its minimal thickness becomes of vital importance. The article examines the methods of early detection of icing which are used on the transmission lines and the ability of these methods to be used in the contact network. The terms of the contact network and power lines are different that’s why not all methods used on the transmission lines can be used. The thermodynamic method of determining the ice is observed as the main. The set of equipment that implements this method and the installation option on the contact network part have been represented.

Keywords: overhead construction, contact wire, span wire, icing, workload, detection system, control methods, glaze-ice and rime deposition, power dispatcher, the thickness of the deposits, wire breakage, information

Thermoresistors nowadays are used not only as parts of temperature sensors and flowmeters but they are used as components of starting and control devices. Use of low-powered thermoresistors as starting and control devices parts needs a lot of devices that reduces equipment reliability. Current step-up running through motor-starting devices simplifies control circuit. For using thermoresistors in electric circuits with high-discharge rate it is necessary to use special constructions in order not to let termoresistor body be overheated. Thermoresistor expansion results in changing of thermal fields distribution pattern inside this semiconductor. The authors show calculated characteristics which let determine proportions and shapes of semiconductor subject to thermoresistor temperature.

Keywords: high power thermoresistors, thermoresistors of coaxial type, current density, temperature, analogy criterion, thermal conductance, temperature gradient, thermal field, stability criterion