This paper considers the physical processes in the structure of the material for a heat-emitting fuel element (FE) shell, caused by various damaging defects, on its outer and inner surfaces, and affecting the change in the geometric parameters of a nuclear reactor’s FE. The task to improve the model of damage to an FE shell is being solved, taking into consideration structural and phase changes in the material of the shell with damaging defects on the outer and inner surfaces, in order to establish the actual criterion for assessing the FE hermeticity degree. It is proposed to study the structure of the shell material with damaging defects (macropores and microcracks), which is a porous heterogeneous structure with fractal properties of self-similarity and scalability, to use the apparatus of fractal geometry. A physical model of the FE shell has been built and proposed, in the form of a geometric cylinder-shaped figure, which makes it possible to investigate the fractal properties of the structure of the material of the damaged shell and their influence on a change in the geometric parameters of FE An improved model of damage to the FE shell was derived, which makes it possible to take into consideration fractal increases in the geometric parameters of FE, for the established values of the fractal dimensionality. Experimental studies of the FE shell, using the skin effect, confirmed the theoretical results and showed the validity of the choice of practical use of the fractal dimensionality parameter as an effective criterion for assessing the hermeticity degree of an FE shell. It has been experimentally established that the value of the fractal dimensionality of 2.68 corresponds to the maximum degree of damage to the shell for a leaky FE.

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The analysis of the criteria for improving the technical and economic efficiency in the operation of the electric power equipment of power units of power plants. It is indicated that the existing methods for calculating the technical and economic effect do not take into account the factors that lead to technical and economic costs when the power unit is stopped and the load of electricity consumers is reduced. A significant factor in increasing the technical and economic efficiency in the operation of automated control systems for technological processes at the power unit of the power plant is operational control to identify information with a low level of reliability. It is shown that the reliability of the functioning of the technological equipment of the power unit significantly depends on the efficiency of automated control in emergency situations, when unauthorized shutdowns of the power unit occur due to false alarms. It was found that the reason for false alarms is information about the parameters of the technological process of the power unit, which is characterized by a low degree of reliability. It is shown that unforeseen unauthorized shutdowns of the power unit and a decrease in the load for power consumers lead to significant economic and material losses, and, consequently, to a decrease in technical and economic efficiency with automated control of the power unit. It is shown that the applied technical and economic models do not take into account financial and material costs that occur due to an unauthorized shutdown of the power unit and a decrease in the load for electrical consumers in case of false alarms in real time. A unified integrated economic and mathematical model has been developed, which allows calculating the economic effect, taking into account the change in the reliability of the technological equipment of the power unit, due to the timely prompt detection of false alarms and information with a low degree of reliability. To calculate the economic effect on the basis of the developed unified economic and mathematical model, a modular block of the mode of emergency situations is proposed, associated with the modules of false positives and emergency signs, taking into account the static and operational technical and economic components. Practical recommendations are given for using the technical and economic module in the software and hardware complex of the power unit, which allows calculating the technical and economic effect based on statistical data coming from the data memory and current data from the power unit.

The analysis of the existing methods of control of the surface of the fuel element cladding material was carried out, which showed that their use for detecting surface and internal defects, such as local inhomogeneities, micro- and macropores, various cracks, axial looseness, etc. is characterized by low efficiency, is a laborious process that requires additional surface treatment, material of the fuel elements cladding. In addition, the investigated methods of controlling the surface of the fuel element cladding material make it possible to visually identify only rough external cracks and large slag inclusions, small cracks and non-metallic inclusions invisible under the slag layer. It is proposed to assess the quality of the surface of the shell material in case of its damage and destruction, the use of a computational apparatus based on the method of the theory of fractals. It is proposed to use the fractal properties of the shell material structure and a quantitative fractal value – the fractal dimension, which makes it possible to determine the degree of filling of the volume of the shell material structure during fuel element depressurization. A mathematical model of damage to the structure of the fuel element cladding material is developed depending on the simultaneous effect of high temperature and internal pressure caused by the accumulation of nuclear fuel fission products between the nuclear fuel pellet and the inner surface of the fuel element cladding, taking into account the fractal increases in the geometric parameters of the fuel element cladding. It is shown that damaged structures of the fuel rod cladding material depend on the pressure and temperature inside the fuel rod cladding, as well as the fractal increase in geometric parameters, such as: volume and surface area, outer and inner diameters, height and cross-sectional area, cladding length and height of nuclear pellets, gap between the inner surface of the cladding and nuclear fuel. A criterion for assessing the integrity of the fuel rod cladding is determined, which depends on the change in geometric values in the event of damage and destruction of the structure of the fuel rod cladding material. Practical recommendations are given on the use of the proposed method for monitoring the tightness of the fuel element cladding for processing information obtained from the computational module of the system for monitoring the tightness of the cladding for the automated process control system of the nuclear power plant power unit, which makes it possible to detect the depressurization of fuel elements at an earlier stage in comparison with the standard procedure.

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