We present a system approach to evaluating dynamic forms of interactions between elements of mechanical oscillatory systems, which can be applied as design diagrams of engineering objects used for transport or technology purposes. The approach of structural mathematical modelling was used, where a mechanical oscillatory system (with the finite number of freedom degrees) is compared to the block diagram of a dynamically equivalent automatic control system. The research object was represented by a family of mechanical oscillatory systems with the finite number of freedom degrees under the action of connected force harmonic disturbances. The main research focus was on a set of dynamic states of an engineering object, which are caused by the application of common-phase external force disturbances at various frequencies and characterised by a connection coefficient. For a family of chain mechanical oscillatory systems with two degrees of freedom, a method for interpreting a set of dynamic states in the form of oriented graphs was developed. A method for constructing a population graph of dynamic states based on the frequency response of system transfer functions was developed. Within the framework of the developed interpretation, the graphs of dynamic states can be considered as peculiar invariants that persist on sets of mechanical oscillatory system parameters. Using the methodology of structural mathematical modelling, a concept of dynamic invariants was developed, according to which the totality of dynamic invariants can be used to provide a general evaluation of the variety of dynamic states and forms of dynamic interactions between the elements of mechanical oscillatory systems. The proposed concept of dynamic invariants extends the methodology of structural mathematical modelling in relation to the problems of system analysis for ensuring the safety of engineering objects for transport and technology purposes under the conditions of connected vibrational loading.

The aim was to obtain a rough determination of the dimensions and shape of a sample for an experimental study of the mechanical characteristics of filamentary FDM-printing structures with a low filling at central tension. The sample geometry was designed based on the dimensions and shape provided in the GOST 17370-2017 “Cellular rigid plastics. Tension testing method”. The research methods included the finite element analysis of stress state parameters in an automated environment, elements of the stiffened shell theory and experimental testing of samples. The theory of stiffened shells was used to simplify the geometry of the finite element model for the studied samples. Finite element analysis was carried out in a linear formulation and, based on the results of its combination with the analysis of the technological model of a designed sample, a decision on transforming the sample geometry was made. The samples were produced using a “line” template with an orientation along the longitudinal axis of the sample. According to the results of testing the samples, a conclusion about the success of implied transformation was made. The success criterion involves the destruction of an FDM sample within the limits of the working part. As a result, both external and internal geometries of the prototype sample were transformed. This allowed the main emphasis in the work of the stretchable FDM sample to be shifted to its working part and the trajectory of power flows to be adjusted according to the FDM-printing specifics. Experimental testing of FDM samples with a low “line” template filling showed a consistently satisfactory result: fractures occurred in the working part of test samples. In the course of the studies, the general trend in the dependence of the force flow distribution over the sample volume on the combination of the printing thread trajectory with external and internal geometries of the sample was determined. Future work will focus on a more detailed analysis and formalisation of the obtained results with regard to various printing templates.

The feasibility of applying the method of two measurements in determining the parameters of equivalent circuits of electrical network elements for the highest harmonic components is analyzed. Experiments were carried out using a MATLAB Simulink model of the common coupling point that includes a distorting load in the form of a three-phase rectifier, a nondistorting linear load and a generalized power system without distortion sources. The parameters of an equivalent circuit in the form of active bipoles, consisting of current distortion and conductivity sources, were determined using the method of two measurements of mode parameters. Modes with variations in the active and reactive power of the studied distorting load and loads in the external electrical network were considered. The results of determining the equivalent circuit parameters under 20% and more variations in the power loading were established to be unstable (400% dispersion of actual values). Therefore, these parameter values appear to be unreliable due to their dependence on the value of external load power. At the same time, the simulation of random variations in loading parameters within 10% of the initial value allowed the parameters of an equivalent circuit to be correctly determined. It was shown that the equivalent circuit of a nondistorting linear load consists solely of conductivity, while the equivalent circuit of a distorting load can contain non-zero conductivity on the considered harmonic component. Thus, according to the performed study, the method of two measurements produces the results acceptable in terms of accuracy (deviation from actual values of less than 1%) not at a single significant variation in the mode parameters, but during a continuous monitoring of small natural variations in the parameters of the electric power system. The results obtained can be used when solving the problem of online assessing the effect of loads on the quality of electricity, since the initial data for this problem include the equivalent circuit parameters.

The impact of oil leakages in a turbine on the main power system parameters is investigated in reactive hydraulic turbines with adjustable-blade runners (Kaplan turbines) installed at Maynskaya, Nizhne-Bureiskaya and Vilyuyskaya hydroelectric power plants. The main theoretical relations and conclusions were obtained by the methods of mathematical simulation and integral calculations in the MATLAB software environment. A method is proposed for monitoring leakages in the housing of an adjustable-blade runner and smoothing the fluctuations of various parameters (amplitude, rotational velocity, phase angle, active power and generator current) of the power system in the case of oil leak-ages. The control is performed by means of a sensor installed in the runner, a fiber-optic cable and an optical-electrical converter located along the shaft from the runner blades to the oil receiver of the corresponding hydraulic unit. The performed analysis of the obtained mathematical model (frequency response and Nyquist plots were built) relative to the basic parameters of the electrical energy generated by a hydraulic unit showed that the proposed method of monitoring oil leakages contributes to an increase in the operational stability of a hydraulic unit. When constructing the model, the following parameters of the hydraulic unit were taken into account: rotational angle of runner blades and opening angle of hydraulic turbine guide vanes. The developed block diagram can be used to compare variations in the parameters both without oil leakage control and taking into account the automated control system proposed by the authors. It is shown that the obtained logarithmic Nyquist plot can be used to monitor variations in the amplitude, as well as its smoothening, both under normal conditions and taking into account oil leakages in the hydraulic turbine housing.

We investigate the effect of modernizing the main condensate scheme applied at the power unit No.5, CHP-10 of Baikal Energy Company LLC, on its energy and economic efficiency using a customized simulation model. Simulation modelling was carried out in the Machine Program Building System software environment. The constructed model was verified using the results of measuring control parameters in several operating modes according to a three-stage procedure of verifying the mathematical models of complex thermal power units. We propose an original approach to modernizing the main condensate thermal scheme at the power unit under study in order to reduce the specific fuel consumption for balance-of-plant needs. The idea was to expand the main condensate scheme by including an additional sealing pump to the feedwater electric pumps of the 1Кs-20-110 unit in order to avoid the incorrect selection of condensate pumps. The study showed that the redistribution of the main condensate flow between the existing condensate pumps and the proposed 1Ks-20-110 sealing pump leads to a reduction in the specific fuel consumption for the electric energy generation to 0.32 g of fuel per kWh across the range of electrical loads from 137 to 150 mW. As a result, the net efficiency of the power unit can be raised by 0.03%. It should be noted that the proposed modernization project may reduce the consumption of electricity for balance-of-plant needs when the feedwater electric pump is switched to the standby mode during an emergency shutdown of the power unit. Based on the performed energy and economic calculations, energy savings for the period of 2019 comprise 82,653 kWh, while the total annual savings are estimated at 78,030 rubles. Thus, the conducted research demonstrates the high efficiency of applying simulation modelling in the study and optimization of existing thermal power plants.

In this study, we set out to develop a methodology for calculating insolation of a photovoltaic power plant taking into account the maximum number of significant input parameters and its territorial adaptation. To this end, simulation modelling implemented in the MATLAB environment was used. Functional possibilities for the synthesis of models using existing elements with the integration of algorithms and modelling results between the blocks of the Simulink sub-system were used. In terms of significant input parameters, geographical coordinates, local time, tilt of the receiving solar panel, modelled day, atmospheric transparency coefficient, albedo and azimuthal angle were considered. A computer model of a photovoltaic power plant was developed for investigating the operation of photovoltaic cells depending on the coordinates of their installation, geometric parameters of solar panels, as well as the temperature and reflectivity of the environment. The performed modelling of the photovoltaic power plant operation visualised graphic dependences of insolation on the tilt of the solar panel, atmospheric transparency coefficient, geographical coordinates of the object and the current month or day. According to the analysis, 15 variations in the solar panel tilt modifies insolation by 10–15%, while variations in the atmospheric transparency coefficient result in 30–50% variations of insolation. As a result, the daily insolation values for the city of Angarsk throughout a year can be modified by 1000–6500 W/m2. The presented results of investigating a regionally adapted photovoltaic power plant demonstrated the need for accounting for location-based and weather parameters during the calculation of insolation for determining the applicability of a plant. The proposed mathematical model for calculating insolation of a photovoltaic power plant can be used for the design and optimization of power supply systems in combination with the specified photovoltaic solar power plants.

This paper presents a modification of the analytic hierarchy process in order to increase its efficiency for a multi-criteria comparison of mixes of generating plants in local energy areas during their development. The multi-criteria problem of selecting the most effective ratio of rated capacities is considered for power plants representing a single mix of generating plants during the development of a local energy area in the Khabarovsk Krai. The energy sources are represented by thermal, solar, wind and diesel power plants. The following estimation criteria for alternative solutions were accepted: levelized cost of electricity, ecological effeciency estimation; estimation of public opinion about the consequences involved with the establishment of power plants. In order to solve the multi-criteria problem, the analytic hierarchy process (AHP) was used. When using the original AHP for the set problem, a large quantity of alternatives at the stage of pairwise comparisons were found to represent a perceptible load on a decision maker. Thus, already during the estimation of 10 alternatives according to 5 criteria, decision makers should conduct 225 pairwise comparisons, which may eventually result in an unacceptable consistency of the results. In addition, this requires a procedure accounting for the uncertainty of the decision maker's preferences. The proposed solution represents a method of forming matrices of pairwise comparisons upon criteria. This method consists in generating an interval or fuzzy model of the decision maker's preferences for evaluating pairs of estimates according to the criterion. The proposed method was verified using a numerical example of solving the set problem. The obtained optimum mix of power plants consists of thermal, solar and diesel plants with a power of 30, 35 and 39 mW, respectively. The proposed method ensures a high consistency of the results obtained during alternative pairwise comparisons. In addition, the modified analytic hierarchy process takes into account the non-linear nature of the decision maker's preferences for estimating alternatives according to criteria.

This study is aimed at improving the efficiency of photovoltaic plants operated in the electric networks of various densities by adjusting the synthetic inertia algorithm and automatic frequency control circuits. To this end, the automatic control system of a photovoltaic plant was investigated using hybrid modelling methods in an all-mode online simulation complex of electric power systems. It was shown that the stability of photovoltaic power plants could be improved through the use of synthetic inertia. According to the conducted research, effective operation of this algorithm can be ensured by a correct determination of the bandwidth of automatic frequency control. Operation of this automatic frequency control circuit can lead to the oscillations of various frequencies during the installation of photovoltaic power plants in low-current electrical networks (electrical networks with the short circuit coefficient of less than 10 a.u.) and, subsequently, negatively affect the operability of the synthetic inertia algorithm. In addition, in high-current networks with an increased bandwidth of the automatic frequency control unit, the value of the network frequency reduction decreases (optimal bandwidth of 50 Hz). Conversely, in low-current networks, the automatic frequency control unit, under an increase in the bandwidth, decreases the response rate of the synthetic inertia algorithm, which leads to an increase in the frequency reduction value (optimal bandwidth of 0.3 Hz). Thus, the conducted investigations showed that the automatic frequency control circuit in the control system of a photovoltaic power plant can be used to alter the operation of the synthetic inertia algorithm. However, the nature of this effect depends on the electrical network density and can be both positive and negative. The effect observed in the tested power system was confirmed for a real-dimension power system.

This study aims to improve the accuracy of forecasting the electricity consumption of an enterprise based on an analysis and preliminary processing of input data, as well as at evaluating the effect caused by feature selection on the results of various forecast models. A woodworking enterprise located in Nizhniy Novgorod was selected as a forecast object. Two types of machine learning methods, including neural network and ensemble models, were compared. An approach to selecting the most significant parameters (features) from a time series was considered in order to improve the results of the following ensemble models based on decision trees: adaptive busting (AdaBoost), Gradient Boosting and Random Forest. The most significant features of the initial time series were determined using the calculation of correlation coefficients between the values of electricity consumption in forecasted and previous hours. For the considered forecast object, the most significant features were established to be the consumed energy in hours lagging behind the forecasted hour by the multiple number of days. The schedule of repair works for woodworking machines was used as an additional feature. According to the obtained results, decision tree ensembles can surpass artificial neural networks provided that significant features are selected correctly. Thus, the smallest average error of a neural network model on a test sample comprised 7.0%, while an error of 5.5% was obtained for a Gradient Boosting ensemble model. The use of a repair schedule was demonstrated to additionally increase the forecast accuracy: for the considered ensemble models, the error reduced from 20 to 30%.

We study the effect of preheating the air entering a gas turbine compressor using a standard closed air heating circuit system with heat supply from the heat network of the Urengoy city district power plant on the efficiency of a PGU-450 unit and this power plant as a whole. An analysis was conducted to compare the data obtained as a result of assessing the existing plant characteristics of GTE-160 gas turbines (SGT5-2000E), the adopted operating modes of air heating systems (closed air heating circuit and anti-icing system) and the effect of the operation of these systems on the specific fuel consumption of a PGU-450 unit and the Urengoy city district power plant according to the daily calculated technical and economic parameters of the power unit operation. As a result of full-scale tests carried out with the air heating system at the nominal load of a PGU-450 power unit, the optimal temperature was established to be +6.4°C. During the air heating from -5.0°C to +6.4°C, the specific consumption of the conventional fuel per 1 kWh of electricity decreased by 1.4 g. The reduced specific consumption of the conventional fuel for the supply of electric energy at an increase in the extraction ratio comprised 2.43 and 2.35 g for the equipment of the backup thermal power station and the power plant as a whole, respectively. Thus, the use of a closed air heating circuit with the unutilized network water heating leads to a positive thermal efficiency effect. The preheating of the air entering the gas turbine compressor leads to an increase in its efficiency by 0.3%. A further increase in excess of the optimum temperature leads to a decrease in the available capacity of the combined cycle plant by 3.1 MW per each degree.

The paper is aimed at developing technical and organizational measures to reduce the losses of electrical energy during its transmission via main and distribution electrical grids, in power transformers and electric power trans-mission lines. The focus of the study was on electrical grid modes in the Namangan Region of Uzbekistan (voltages of 220/110/35/10/6 kV), which were analyzed via technological calculation-based research methods using an equivalent circuit representing the linear circuit currently employed in the regional electric energy system. In addition, electrical grids were simulated using the software package “Program for calculating electrical grid modes” followed by the processing of calculation results by means of the Microsoft Excel package. The paper calculates electrical modes for the equivalent circuit of the regional electric energy system, as well as offering technical measures (installation of reactive power compensation devices; adjustment of transformation ratios in power transformers) aimed at adjusting voltage to improve electric power quality in terms of voltage deviations and lower power losses. Voltage deviations in most grid nodes were found to be inconsistent with GOST 32144-2013. Thus, in 35 kV, 10 kV, and 6 kV nodes, the largest underdeviation amounted to 12.45 kV, 3.26 kV, and 2.09 kV, respectively. For the placement of reactive power compensating devices having a total power of 67.82 MV∙Ar, 35 kV nodes were used; in addition, the values of transformer ratios at transformer substations (35–110 kV) were determined. Calculations indicate that the conducted activities can normalize voltage in the 35 kV, 10 kV, and 6 kV nodes while reducing power losses in the electrical grid by 9.35 MW. It is estimated that the proposed measures will be paid back in approximately three years. By means of compensating reactive power and adjusting transformer ratios, these measures can reduce electrical energy losses during transmission in the considered objects and maintain a given voltage level.

A mathematical model representing the temperature mode of an overhead power line wire and taking into account the axial heat transfer was developed. Processes in overhead power lines were analyzed using analytical and numerical methods for solving differential equations, including the finite difference method. The equation of thermal conductivity for AS-240/32 and SIP-2 3х95+1х95 wires was solved for the case of current variations along the line length. An analytical solution to the equation of thermal conductivity was proposed for the steady-state operation of an overhead wire under the same current in all sections of the line, taking into account the temperature dependence of active resistance. The results obtained by the analytical method agree well with those obtained by the method of finite differences. The boundary conditions at the beginning and at the end of the line were established to affect the line temperature only within a few meters. At the same time, despite the slight increase in the degree of this effect at an increase in the current due to the temperature dependence of heat emission, it remains small up to emergency level currents. Therefore, the calculations of the line thermal mode require no high accuracy in setting boundary conditions. A line with a uniformly distributed load demonstrates differing results at large current variations along the wire length. Thus, the absolute error of the analytical solution (compared to the finite difference method) for the maximum temperature equals 77.9°C, while the relative error for losses equals 10%. The same errors in temperature calculations for an infinitely long wire in terms of the length function comprise 2.5°C and 0.1%, respectively. Therefore, despite the high thermal conductivity of a metal, a model with a zero thermal conductivity along the wire axis gives more accurate results as compared to a model with an infinitely high thermal conductivity. The obtained results are applicable when clarifying the total loss of active power, as well as for estimating the line capacity according to the maximum permissible temperature, which depends on the type of wires and comprises 70 and 90°C for uninsulated steel-aluminum and self-supporting insulated wires, respectively.

This study is aimed at improving the efficiency of monitoring and automated control over the technological state of electrolytic cells during copper refining using the recognition and identification of short circuits between the electrodes. Experimental works were performed on a laboratory bench consisting of two cells connected in series to the electrical circuit. The method of detecting short circuits is based on measuring infrared radiation using a scanning thermal imager (Оptris PI 400i / PI 450i) for determining areas with elevated temperatures of electrode and electrolyte surfaces. A short-circuit detection algorithm was developed and tested in MATLAB environment using the Image Processing Toolbox MATLAB functions. The proposed method for recognizing and identifying short circuits between the electrodes of an electrolytic cell is based on using a scanning digital thermal imager. This method allows a comprehensive assessment of the contact area, determination of both the start time of a short circuit and the degree of electrode heating in the short-circuit zone, as well as establishment of temperature values in all areas, including the electrolyte temperature in the entire volume of the cell. An algorithm for searching for short-circuit locations in an electrolytic cell is proposed. This algorithm involves the collection of data and its comparison for adjusting the inter-electrode distance, ensuring a stable energy mode for the entire electrolytic line, and determining the exact position of each cathode in the cell using the threshold processing of infrared images obtained by a thermal imager. It was established that timely identification of short circuit locations in the electrolytic bath (since the onset of a contact between the electrodes), as well as recording of the growth rates of a dendritic coalescence area and electrolyte temperature, ensure timely elimination of technological disturbances during the operation of electrolytic baths. Thus, the developed method of short circuit identification for comprehensive determination and recognition of the technological state of an electrolytic cell during the electrolytic refining of copper can be used to reach a stable energy mode with minimum deviations in the process temperature.

The process of extraction/re-extraction of copper from heap leaching solutions using the Acorga M5774 Solvay extractant (Sytec, Belgium/USA) representing a modified aldoxime (5-nonylsalicylaldoxime) was studied. This extractant is characterized by a high effectiveness and a large selectivity of copper to iron, thus enabling a more rapid phase separation. During experiments, a pregnant leach solution obtained after the percolation leaching of the Sayak deposite ore (Republic of Kazakhstan) was used, g/dm3: H2SO4 – 11.67, Сu – 2.44, Fe – 2.613, Al – 0.345, Si – 0.127, Zn – 0.05, рН = 1.85. The main parameters and effectiveness of the extractant were studied by plotting extraction and re-extraction isotherms, as well as by simulating the closed cycle processing sequence and determining the level of copper extraction at the liquid extraction stage. The extraction/re-extraction of copper from pregnant leach solutions was studied. An aliphatic product of Elixore 205 (Total, France) was used as an extractant diluent, with the amount in the organic phase equal to 90%. Based on the conducted studies, extraction and re-extraction isotherms were plotted. In the liquid extraction process, simulated using the obtained isotherms, the extraction of copper comprised 96.18% (at an organic/aqueous phase ratio of 1.1) with a reagent saturation of 79%. The dependence of iron transfer from the organic phase on the saturation of organic phase with copper was obtained. Thus, the performed studies confirmed the effectiveness of the Acorga M5774 extractant for the purposes of extracting copper from pregnant leach solutions obtained during heap leaching of the Sayak deposit ore.

In this work, we develop a digital twin of a tube digester and a software application automatically calculating the aluminate solution quality based on mass balance equations with the purpose of improving the quality of hydro-chemical process management at the Rusal Achinsk JSC alumina plant. A mimic diagram of the nepheline sinter leaching process was visualized using the Wonderware InTouch software package. Quick scripts were created to display the process animation. The input parameters include the solution temperature, the consumption of sinter and recycled solution, as well as the chemical composition of raw materials. The air temperature, vibrations and equipment malfunction were used as the main disturbing effects. Output parameters consisted of sludge and aluminate solution yields, power consumed by the drive and the silicon ratio of the resulting solution. Based on the mass balance of sinter and recycled solution, calculated using industrial laboratory data, an algorithm for modelling variations in the digestion process and a software application for calculating the quality of aluminate solution were developed using the InTouch built-in capabilities of scripting in its own programming language. A digital twin of a tube digester was developed on the basis of an operating unit utilized at the Rusal Achinsk JSC. It was shown that the developed software application predicts the quality of the finished product (aluminate solution) using a simple balance model under variations in both the composition of raw materials (cake and recycling solution) and the rate of fed raw materials, as well as present the results of calculations performed using a mimic diagram of the process. Thus, the developed interface can be used to simulate various technological operations performed in a tube digestor, including solution drainage, sludge discharge and variations in the inlet flows. At the same time, it becomes possible both to observe current changes in process parameters and archive plots, as well as to select the optimal composition of raw materials to obtain an aluminate solution of higher quality.

Viktor Elshin, Doctor of Technical Sciences, Professor, Head of the Department of Automation and Control of the Irkutsk National Research Technical University celebrates two anniversaries on October 3, 2022: his 75th birth anniversary and the 50th anniversary of his scientific and pedagogical activity.