Papers [6, 7] demonstrate contemporary requirements to technical means and mathematical software for ICS for STC in APCS in terms of life cycle, reliability, safety, and failure-free operation considering the number of control points for technological parameters. One of the main criteria to ensuring high reliability of ICS for STC in APCS is the criterion of realization of the set of assigned algorithms and programs to process information for reliability in a real-time mode. Thus, to improve the reliability of operation of ICS for STC in APCS at a power plant under non-standard modes 4

It is shown that in the existing models of the solar cell, assumptions were made about the ideally smooth surface topography, which had a significant impact on the calculation of the output parameters. It is proposed to take into account the real working area of the receiving surface of the solar cell to improve the accuracy, linearity and stability of the current-voltage characteristics. A geometric model of the structure of the receiving surface of a solar cell has been developed, which describes and takes into account geometric changes in the structure of a semiconductor conducting layer, in the presence of damaging defects in the form of local inhomogeneities, micropores and macrocracks. It was found that the receiving surface with damaging defects is a porous inhomogeneous structure and has fractal properties: self-similarity, invariance, scalability. It is proposed to determine the real working area, to use the method of the theory of fractal geometry and, as an effective quantitative parameter for assessing the change in fractal structure, to choose the value of the fractal dimension. The obtained analytical expressions for the improved model establish the relationship between the output parameters and determine the degree of filling of the current-voltage characteristic for the output power and efficiency. The computational experiment showed that the real area can be much less than the geometric area of the topological relief and is quantitatively related to the change in fractal dimension in the range from 2.31 to 2.63. The obtained data on the real area, when solving analytical expressions for the solar cell model, play an important role in ensuring the stability and linearity of the current-voltage characteristic, increasing its accuracy up to 5 %.

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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.

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.