This paper presents a method for refining the forecast schedule of renewable energy sources (RES) generation by its intraday adjustment and investigates the measures for reserving RES with unstable generation in electric power systems (EPSs). Owing to the dependence of electricity generation by solar and wind power plants (PV and WPPs, respectively) on natural conditions, problems arise with their contribution to the process of balancing the power system. Therefore, the EPS is obliged to keep a power reserve to compensate for deviations in RES from the planned generation amount. A system-wide reserve (mainly the shunting capacity of thermal and hydroelectric power plants) is used first, followed by other means of power reserve: electrochemical, hydrogen, or biogas plants. To analyze the technical and economic efficiency of certain backup means, mathematical models based on the theory of similarity and the criterion method were developed. This method is preferred because it provides the ability to compare different methods of backing up RES generation with each other, assess their proportionality, and determine the sensitivity of costs to the capacity of backup methods with minimal available initial information. Criterion models have been formed that allow us to build dependencies of the costs of backup means for unstable RES generation on the capacity of the backup means. It is shown that, according to the results of the analysis of various methods and means of RES backup, hydrogen technologies are relatively the most effective. The results of the analysis in relative units can be clarified if the current and near-term price indicators are known.

We study the physical processes occurring in electrotechnical complexes with turbo mechanisms and pipelines. The strategy for improvement of the methods and means is defined for analyzing the operating modes of electrotechnical complexes with controlled pumping stations for energy efficiency raising of their operation. Subsystem classification of such complexes is proposed; an element-wise and general analysis of the current state of their modeling is carried out. It is shown that, in spite of a large number of works devoted to this topic, a systematic approach to mathematical modeling of processes occurring in such complexes has not been developed to date. In connection with the greatest potential for energy saving of powerful complexes, the necessity of creating an effective means of their analysis is justified, particularly, in the steady-state regimes. Based on the formalized approach, a mathematical model of the generalized electrotechnical complex of the power supply system of a pumping station has been developed. The model was successfully tested in the calculation of stationary modes of power supply systems for oil pumping station and a sewerage station. It is advisable to use the proposed model for analyzing the modes of both operating and projected objects, as well as for creating automatic control systems for such objects.

The development of a mathematical model of a three-phase ultrahigh voltage transmission line with two overhead ground wires is presented in the paper. The mathematical model is based on differential equations of state of a long line with partial derivatives in the matrix-vector form. The boundary conditions of the second kind (Neumann's conditions) are used, which enables obtaining functions of unknown coordinates of the overhead ground wires mode at the beginning and at the end of the voltage transmission line to solve the transmission line equation. Some results of computer simulations of transients during switching on and a single-phase short circuit of the line are presented in the form of corresponding graphic functions of its mode coordinates.

A review and analysis of different approaches to modelling the operating modes of an asynchronous electric drive with centrifugal units of pumping stations has been performed. It has been shown that modern researches of this subject are mainly focused either on the control systems of the electric drive of pumps, or on the hydraulic subsystem, or on the optimization of energy and economic macro indicators of pumping stations in general. As a rule, in most works only one of the subsystems of the pumping station is modelled in an expanded form: either electromechanical or hydraulic; the other one is usually presented in a very simplified way (by approximating the experimentally obtained tabular data). This significantly limits the ability to study efficiently the physical processes that take place simultaneously in these inextricably linked subsystems, and extends the range of the proper specialists involved in solving relevant tasks. One way to solve this problem may be to develop a mathematical model in which both subsystems would be presented with a comparable level of detailing. The paper proposes a mathematical model of dynamic operating modes of an asynchronous electric centrifugal pump unit with a pipeline, in which the electromechanical and hydraulic subsystems are presented with a balanced level of detailing. The equations of the mathematical model are formed in orthogonal d-q coordinates rigidly connected to the rotor of the asynchronous machine in relative units using a system of basic quantities and are solved with respect to the first derivatives. The proposed model can be used for analyzing the operating modes of the existing high-capacity pumping stations and their power supply systems without making physical experiments, and for designing new facilities as well.

MATHEMATICAL MODELING OF MULTI-UNITS PUMPING STATION WITH ASYNCHRONOUS ELECTRIC DRIVE OF CENTRIFUGAL PUMPS

The paper is devoted to the development of a mathematical model of a high-capacity controlled pumping station with automatic pressure stabilization. The purpose of the work is to increase the efficiency of the liquid transportation process through main and large distribution pipelines. The proposed model with a comparable level of detail describes the electromechanical and hydraulic subsystems as a single entity. The parameters of the centrifugal pump model are calculated based on the geometry and dimensions of its elements, taking into account the influence of the physical properties of the working fluid. This makes it possible to conduct a comprehensive study of such objects without physical impact on them, taking into account the mutual dependence of both subsystems and changes in the parameters of the elements of the hydraulic subsystem. The paper suggests directions for use and ways to expand the functionality of the developed model