The aim of the paper is to analyze the basic principles of design the protection zone of a complex system of air-termination rods according to the rolling sphere method, which, at the moment, is the main in the field of lightning protection and meets the requirements of modern European standards. The problem of determining the minimum number of air-termination rods required to calculate the surface of the protection zone of any complexity, with their arbitrary height and location, is solved. Through the use of the stereometry laws of, for the first time in Ukraine, a mathematical model was developed to build such a protection zone. The operation of this model was tested on the example of an electrical substation with a voltage of 110 kV using a test computer program with a real arrangement of air-termination rods with different heights. The result of this program is a three-dimensional display of the protection zone with the possibility of visual analysis of the protection of objects from direct lightning strike with a given probability. The value of the work lies in the possibility of practical implementation of the rolling sphere method to protect power facilities of Ukraine from direct lightning strikes in accordance with the modern standard EN 62305. References 12, figures 5.

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Mathematical analysis of the rolling sphere method was performed to develop a model for constructing of volume protected by rod air-termination in accordance with EN 62305:2012 for the protection of nuclear power plants objects from direct lightning strike. The necessity of development of the corresponding mathematical model for similar objects is shown, and the direction of its realization with the help of decomposition method is proposed. The mathematical models for calculation of protection zones of single and double air-termination rods of arbitrary height and location are developed. Directions of further researches are formed.

Introduction. Within the framework of European integration of Ukraine, the international Standard IEC 62305 has been harmonized, which provides for a full inspection of lightning protection devices with a frequency of 0.5-4 years, which significantly increases the volume of work. Problem. The adopted Standard is stricter than those for which external lightning protection systems (LPS) of power plants and substations, which are objects of critical infrastructure, have been designed. There is no clear algorithm of actions to bring the existing LPS of existing energy facilities of Ukraine in accordance with the requirements of IEC 62305. Due to the need to modernize the existing LPS facilities, there is a need to develop a single algorithm for these works. Goal. Development of an algorithm for evaluation of the current state LPS for existing power plants and substations. Methodology. Based on the analysis of IEC 62305, three stages of evaluation are proposed: experimental (based on geodetic and electromagnetic method of determining the configuration of the object and components of LPS), calculation (based on the topographic survey method and the electromagnetic method for determining the configuration of the object and components of the LPS) and stage of analysis and development of recommendations. Results. Three stages, which are a basis of analysis of a condition of LPS based on the created algorithm, are considered in detail. An example of the analysis LPS condition of the existing substation with a voltage of 35 kV, created according to the specified method, is given. The program report in 3D form illustrates the unprotected parts of the object. Originality. For the first time, an algorithm for analysis the state of LPS of operating energy facilities according to the IEC 62305 standard has been developed. Practical value. Typical remarks to the existing LPS are formed. The results of the work can be used to inspection and modernize the LPS energy facilities, as well as buildings and structures of public importance. References 18, tables 1, figures 3.