Electrical Engineering & Electromechanics http://eie.khpi.edu.ua/ <div id="focusAndScope"> <p><span id="result_box" lang="en"><strong><span class="alt-edited">Electrical Engineering &amp;</span> Electromechanics</strong> is a peer-reviewed open access scientific Journal, which publishes high-quality original articles with a strong focus on analytical, numerical and multiphysics techniques of modelling of electrophysical processes in electrical, electromechanical and electrical power installations and systems, on the development of new electrical devices and systems with improved technical, economic and environmental performance in such areas </span><span id="result_box" lang="en">as: <strong>theoretical electrical engineering</strong>; <strong>high electric and magnetic fields engineering, engineering electrophysics</strong>; <strong>electrical machines and apparatus</strong>; <strong>electrical complexes and systems</strong>; <strong>industrial electronics</strong>; <strong>electrical insulation and cable engineering</strong>; <strong>power stations, grids and systems</strong>.<br />Articles that form the scientific basis for further development in these areas, as well as original articles with specific solutions of actual engineering problems are also approved.<br />The <strong>aims and scope</strong> of the Journal is to present a forum for discussion and testing of techniques of modelling, calculation, experimental validation and development of new electrical devices and systems with improved technical, economic and environmental performance, as well as expanding the scope of their industrial use.<br />The advantages of the Journal are due to the fact that Founders are a union of research and educational centers in the field of electrical engineering. Founders' extensive collaboration with research institutions around the world allows peer review of submitted manuscripts by the world-leading experts and to engage cutting-edge research results to publication in the Journal.<br /></span></p> <p><strong>Year of Foundation:</strong> 2002</p> <p><strong>Co-founders:</strong><br /><strong><a href="http://www.kpi.kharkov.ua/eng/">National Technical University "Kharkiv Polytechnic Institute"</a></strong><br />Address:<br />2, Kyrpychova Str., 61002, Kharkiv, Ukraine<br />E-mail: omsroot@kpi.kharkov.ua<br />phone: +380 57 7001564<br /><a href="https://ipmach.kharkov.ua/en/administration/"><strong>Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine</strong></a><br />Address:<br />2/10, Komunalnykiv Str., 61046, Kharkiv, Ukraine<br />E-mail: admi@ipmach.kharkov.ua<br />phone: +380 572 930144</p> <p><strong>Publisher:<br />National Technical University "Kharkiv Polytechnic Institute" (NTU "KhPI")</strong> jointly with <strong>Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine (IEMS of NAS of Ukraine)</strong></p> <p><strong>Sections of Journal:</strong></p> <ul> <li><em><strong>Theoretical Electrical Engineering</strong></em></li> <li><em><strong>High Electric and Magnetic Fields Engineering, Engineering Electrophysics</strong></em></li> <li><em><strong>Electrical Machines and Apparatus</strong></em></li> <li><em><strong>Electrical Complexes and Systems</strong></em></li> <li><em><strong>Industrial Electronics</strong></em></li> <li><em><strong>Electrical Insulation and Cable Engineering</strong></em></li> <li><em><strong>Power Stations, Grids and Systems</strong></em></li> </ul> <p><strong>ISSN 2074-272X (Print), ISSN 2309-3404 (Online)</strong></p> <p>All articles have <strong>DOI </strong>number with prefix <strong>10.20998</strong>. For example, the first article in no.1 2016 has <strong>doi</strong>: <strong>10.20998/2074-272X.2016.1.01</strong></p> <p><strong>How to cite article in our journal.</strong> For example:<br />Montazeri Z., Niknam T. Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm. <em>Electrical Engineering &amp; Electromechanics</em>, 2018, no. 4, pp. 70-73. doi: <a href="https://doi.org/10.20998/2074-272X.2018.4.12">https://doi.org/10.20998/2074-272X.2018.4.12</a>.</p> <p><span id="result_box" class="short_text" lang="en"><strong>Indexing of Journal:<br /><a href="https://www.scopus.com/sourceid/21101066743">Scopus</a></strong> (from 2019), <strong><a href="https://mjl.clarivate.com/search-results?issn=2074-272X&amp;hide_exact_match_fl=true&amp;utm_source=mjl&amp;utm_medium=share-by-link&amp;utm_campaign=search-results-share-this-journal">Web of Science™ Core Collection: Emerging Sources Citation Index (ESCI)</a>,<br /></strong></span><span id="result_box" class="short_text" lang="en"><strong><a href="https://doaj.org/toc/2309-3404?source=%7B%22query%22%3A%7B%22filtered%22%3A%7B%22filter%22%3A%7B%22bool%22%3A%7B%22must%22%3A%5B%7B%22terms%22%3A%7B%22index.issn.exact%22%3A%5B%222074-272X%22%2C%222309-3404%22%5D%7D%7D%5D%7D%7D%2C%22query%22%3A%7B%22match_all%22%3A%7B%7D%7D%7D%7D%2C%22size%22%3A100%2C%22sort%22%3A%5B%7B%22created_date%22%3A%7B%22order%22%3A%22desc%22%7D%7D%5D%2C%22_source%22%3A%7B%7D%7D">DOAJ</a>, <a href="http://www.proquest.com/libraries/corporate/engineering-scitech/adv_tech_aero.html">ProQuest</a>, <a href="https://www.ebscohost.com/titleLists/asr-journals.htm">EBSCO Publishing INC.</a>, <a href="http://galesupport.com/trialsite/php/generate_trial.php?un=8617324">Gale/Cengage Learning</a>, <a href="http://ulrichsweb.serialssolutions.com/login">Ulrich’s Periodical Directory</a>, <a href="https://scholar.google.com.ua/citations?hl=uk&amp;user=of_7RnkAAAAJ">Google Scholar</a></strong></span></p> <p><strong>Frequency Journal:</strong> 6 times per year</p> <p><strong>Language of Publications: </strong>English, Ukrainian (for online version all articles necessarily are translating in English by Journal's Editorial Board)</p> <p><strong>Editor-in-Chief:</strong> Sokol Yevgen, Professor, Corresponding Cember of NAS of Ukraine, Rector of NTU "KhPI"</p> <p><strong>Executive secretary:</strong> Grechko Oleksandr, PhD</p> <p><strong>Address of the Journal:</strong> National Technical University "Kharkiv Polytechnic Institute", Kyrpychova Street, 2, Kharkiv, Ukraine, 61002</p> <p><strong>Phones:</strong> +380 57 7076281, +380 67 3594696</p> <p><strong>E-mail:</strong> <a href="mailto:%20a.m.grechko@gmail.com">a.m.grechko@gmail.com</a></p> <p>Online pdf version of Journal <strong>"Electrical Engineering &amp; Electromechanics"</strong> - free of charge</p> </div> en-US <p><strong>Authors who publish with this journal agree to the following terms:</strong></p><p>1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a <a href="http://creativecommons.org/licenses/by/3.0/" target="_new">Creative Commons Attribution License</a> that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.</p><p>2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.</p><p>3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.</p> a.m.grechko@gmail.com (Grechko Oleksandr) a.m.grechko@gmail.com (Grechko Oleksandr) Thu, 02 Jan 2025 00:17:57 +0200 OJS 3.2.1.2 http://blogs.law.harvard.edu/tech/rss 60 Computer-economical optimization method for solving inverse problems of determining electrophysical properties of objects in eddy current structroscopy http://eie.khpi.edu.ua/article/view/305610 <p><strong><em>Introduction. </em></strong><em>The problems of determining the profiles of electrophysical material properties are among the inverse problems of electrodynamics. In these studies, the focus is on the creation of a computer-economical method for reconstructing the profiles of electrical conductivity and magnetic permeability of metal planar objects under testing. These parameters can include the information about the results and quality of the production process or the effects of exposure to an aggressive environment. Registration of changes in electrophysical properties by means of eddy current testing allows for prompt adoption of effective management decisions regarding controlled processes. The simultaneous determination of these parameters because of non-contact indirect measurements of the electromotive force (EMF) by surface eddy current probes over the surface object with the subsequent restoration of the parameter distributions along its thickness by numerical methods is an urgent task. <strong>Objective. </strong>To create a computer-economical method for determining the electrophysical properties of objects by means of surrogate optimization with the accumulation of additional apriori knowledge about them in neural network metamodels with nonlinearly reduced dimensionality to improve the accuracy of simultaneous profile determination. <strong>Methodology. </strong>The method for determining the electrophysical properties of objects is based on homogeneous designs of experiments, surrogate optimization with the accumulation of apriori knowledge about them in metamodels with nonlinearly reduced dimensionality. <strong>Originality. </strong>Integration of multiple capabilities in the surrogate model that combine the advantages of high-performance computing and optimization algorithms in the factor space reduced by the Kernel PCA </em><em>(</em><em>Principal Component Analysis</em><em>) </em><em>method. The accumulated additional apriori knowledge about objects is incorporated into the neural network metamodel. This makes it possible to implicitly identify complex patterns hidden in the data that are characteristic of the eddy current measuring process and take them into account during reconstruction.<strong> Results. </strong>The reduction of the search space is a considerable result. It was possible due to the nonlinear Kernel-PCA transformations with the analysis of the eigenvalues of the kernel matrix and the restriction on the number of PCA principal components. The results confirmed the validity of a significant reduction in space without major loss of information. Another indicator of the effectiveness of the method is a high precision of the created surrogate models. The accuracy of the reduced dimensional metamodels was achieved by using a homogeneous computer design of experiment and deep learning networks. The adequacy and informativeness of the constructed surrogate models have been proved by numerical indicators. The efficiency of the method is demonstrated on model examples. </em>References 36, table 5, figures 6.</p> V. Ya. Halchenko, R. V. Trembovetska, V. V. Tychkov Copyright (c) 2025 V. Ya. Halchenko, R. V. Trembovetska, V. V. Tychkov http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/305610 Thu, 02 Jan 2025 00:00:00 +0200 Multispheroidal model of magnetic field of uncertain extended energy-saturated technical object http://eie.khpi.edu.ua/article/view/317959 <p><strong><em>Problem</em></strong>. <em>The implementation of strict requirements for magnetic silence of elongated energy-saturated technical objects – such as </em><em>naval vessel</em><em> and submarines is largely determined by the adequacy of mathematical models to the signatures of a real magnetic field. </em><strong><em>Aim</em></strong><em>. </em><em>Simplification of mathematical modeling of the magnetic field of an uncertain extended energy-saturated object based on the development and application of a multispheroidal model of its magnetic field instead of the well-known multidipole model</em><em>. </em><strong><em>Methodology. </em></strong><em>Coordinates of the geometric location and magnitudes of spatial extended spheroidal harmonics of spheroidal sources of multispheroidal </em><em>model </em><em>of</em><em> magnetic field calculated as </em><em>magnetostatics geometric inverse problems </em><em>solution </em><em>in the form of</em><em> nonlinear minimax optimization problem based on near field measurements for prediction far </em><em>extended technical objects</em><em> magnetic field magnitude. Nonlinear objective function calculated as the weighted sum of squared residuals between the measured and predicted magnetic field COMSOL Multiphysics software package used. Nonlinear minimax optimization problems solutions calculated based on particle swarm nonlinear optimization algorithms. </em><strong><em>Results. </em></strong><em>Results of </em><em>prediction </em><em>far magnetic field magnitude</em><em> of extended technical objects</em><em> based on </em><em>designed multispheroidal model of the magnetic field in the form of spatial </em><em>prolate </em><em>spheroidal harmonics in </em><em>prolate sphe</em><em>roidal coordinate system </em><em>using </em><em>near field measurements with consideration of </em><em>extended technical objects</em><em> magnetic characteristics uncertainty. </em><strong><em>Originality. </em></strong><em>For the first time t</em><em>he method for design of </em><em>multispheroidal model of magnetic field</em> <em>of</em><em> uncertain </em><em>extended energy-saturated </em><em>technical </em><em>object </em><em>based on </em><em>magnetostatics geometric inverse problems solution and magnetic field spatial spheroidal harmonics calculated in</em><em> prolate </em><em>spheroidal coordinate system taking into account of technical objects magnetic characteristics uncertainties</em><em> developed. </em><strong><em>Practical value. </em></strong><em>It </em><em>is shown the possibility to reduce the </em><em>number of spheroidal sources of the magnetic field for adequate modeling of the real magnetic field based on the developed multispheroidal model compared to the number of </em><em>well-known</em><em> dipole sources of the magnetic field in the multidipole model of the magnetic field. </em>References 48, figures 4.</p> B. I. Kuznetsov, T. B. Nikitina, I. V. Bovdui, K. V. Chunikhin, V. V. Kolomiets, B. B. Kobylianskyi Copyright (c) 2024 B. I. Kuznetsov, T. B. Nikitina, I. V. Bovdui, K. V. Chunikhin, V. V. Kolomiets, B. B. Kobylianskyi http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/317959 Thu, 02 Jan 2025 00:00:00 +0200 Optimization of fractional PI controller parameters for enhanced induction motor speed control via indirect field-oriented control http://eie.khpi.edu.ua/article/view/314455 <p><strong><em>Introduction.</em></strong><em> Induction Motors (IM) possess advantages such as stability, reliability, and ease of control, making them suitable for many purposes; the literature elucidates control methodologies for IM drives, primarily focusing on scalar and vector control techniques; the conventional method utilized in manufacturing is scalar control, which unfortunately demonstrates optimal performance solely in steady-state conditions. The absence of significant instantaneous torque control restricts flux and dissociated torque, resulting in subpar dynamic responsiveness. Indirect Field Oriented Control (IFOC) for IM drives has proven beneficial for various industrial applications, particularly electric vehicle propulsion. The primary advantages of this approach include the decoupling of torque and flux characteristics and its straightforward implementation. <strong>The novelty</strong> of the work consists of a proposal for a driving cycle model for testing the control system of electric vehicles in Mosul City (Iraq), and using a Complex Fractional Order Proportional Integral (CFOPI) controller to control IMs via IFOC strategies, the Artificial Bee Colony (ABC) algorithm was applied, which is considered to be highly efficient in finding the values of controllers. <strong>Purpose.</strong> Improvement IFOC techniques for the regulation of IM speed. <strong>Methods.</strong> Using the ABC algorithm in tuning the two unique CFOPI controller, and a Real Fractional Order Proportional Integral (RFOPI) controller, to regulate the speed of a three-phase IM via IFOC techniques. <strong>Results.</strong> The CFOPI controller outperforms the RFOPI controller in obtaining the best performance in controlling the IM. <strong>Practical valu</strong>e. The CFOPI controller demonstrates superiority over the RFOPI controller, as evidenced by the lower integral time absolute error in motor speed tracking during the driving cycle 2.1004 for the CFOPI controller compared to 2.1538 for the RFOPI controller.</em> References 27, tables 5, figures 4.</p> I. I. Alnaib, A. N. Alsammak Copyright (c) 2025 I. I. Alnaib, A. N. Alsammak http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/314455 Thu, 02 Jan 2025 00:00:00 +0200 Optimal tuning of multi-stage PID controller for dynamic frequency control of microgrid system under climate change scenarios http://eie.khpi.edu.ua/article/view/306189 <p><strong><em>Introduction. </em></strong><em>In recent years, the use of renewable energy has become essential to preserve the climate from pollution and global warming. To utilize renewable energy more effectively, the microgrid system has emerged, which is a combination of renewable energies such as wind and solar power. However, due to sudden and random climate fluctuations, energy deviation and instability problems have arisen. To address this, storage systems and diesel engines have been incorporated. Nevertheless, this approach has led to another issue: frequency deviation in the microgrid system. Therefore, most recent studies have focused on finding ways to reduce frequency deviation. The <strong>goal</strong> of this work is to study and compare various improvement methods in terms of frequency deviation. <strong>Methodology</strong>. We first simulated the microgrid system using the PID controller based on the following algorithms: krill herd algorithm (KHA) and cuckoo search algorithm (CSA). In the second phase, we replaced the PID controller with the multi-stage PID controller and optimized its parameters using the KHA and the CSA. In the final phase, we tested the response of the microgrid system to these methods under a range of influencing factors. <strong>Results.</strong> The results initially showed the superiority of the KHA over the other algorithms in improving the parameters of the PID controller. In the second phase, the results showed a significant advantage of the multi-stage PID controller in terms of speed and stabilization time, as well as in reducing the frequency deviation compared to the PID controller. <strong>Practical</strong> <strong>value</strong>. Based on the tests conducted on the microgrid system, we can conclude that the multi-stage PID controller based on the KHA can be relied upon to solve these types of problems within the microgrid system. </em>References 36, tables 4, figures 10.</p> B. Alouache, M. Helaimi, A. B. Djilali, H. A. Gabbar, H. Allouache, A. Yahdou Copyright (c) 2025 B. Alouache, M. Helaimi, A. B. Djilali, H. A. Gabbar, H. Allouache, A. Yahdou http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/306189 Thu, 02 Jan 2025 00:00:00 +0200 Type-2 fuzzy logic controller-based maximum power point tracking for photovoltaic system http://eie.khpi.edu.ua/article/view/311414 <p><strong><em>Introduction</em></strong><em>. Photovoltaic (PV) systems play a crucial role in converting solar energy into electricity, but their efficiency is highly influenced by environmental factors such as irradiance and temperature. To optimize power output, Maximum Power Point Tracking (MPPT) techniques are used. This paper introduces a novel approach utilizing a Type-2 Fuzzy Logic Controller (T2FLC) for MPPT in PV systems. The <strong>novelty</strong> of the proposed work lies in the development of a T2FLC that offers enhanced adaptability by managing a higher degree of uncertainty, we introduce an original method that calculates the error between the output voltage and a dynamically derived reference voltage, which is obtained using a mathematical equation. This reference voltage adjusts in real-time based on changes in environmental conditions, allowing for more precise and stable MPPT performance. The <strong>purpose</strong> of this paper is to design and validate the effectiveness of a T2FLC-based MPPT technique for PV systems. This approach seeks to enhance power extraction efficiency in response to dynamic environmental factors such as changing irradiance and temperature. The <strong>methods</strong> used in this study involve the implementation of T2FLC to adjust the duty cycle of a DC-DC converter for continuous and precise MPPT. The system was simulated under various environmental conditions, comparing the performance of T2FLC against T1FLC. The <strong>results</strong> show that the T2FLC MPPT system significantly outperforms traditional methods in terms of tracking speed, stability, and power efficiency. T2FLC demonstrated faster convergence to the MPP, reduced oscillations, and higher accuracy in rapidly changing environmental conditions. The findings of this study confirm the <strong>practical value</strong> of T2FLC logic in improving the efficiency and stability of PV systems, making it a promising solution for enhancing renewable energy technologies.</em> References 33, tables 4, figures 10.</p> A. Boudia, S. Messalti, S. Zeghlache, A. Harrag Copyright (c) 2025 A. Boudia, S. Messalti, S. Zeghlache, A. Harrag http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/311414 Thu, 02 Jan 2025 00:00:00 +0200 Improved grey wolf optimizer for optimal reactive power dispatch with integration of wind and solar energy http://eie.khpi.edu.ua/article/view/311526 <p><em>The <strong>aim</strong> of this paper is to present a new improved grey wolf optimizer (IGWO) to solve the optimal reactive power dispatch (ORPD) problem with and without penetration of renewable energy resources (RERs). It is a nonlinear multivariable problem of optimization, with multiconstraints. The purpose is to minimize real power losses and improve the voltage profile of a given electric system by adjusting control variables, such as generator voltages, tap ratios of a transformer, switching VAr sources, without violating technical constraints that are presented as equalities and inequalities. <strong>Methodology</strong>. Metaheuristics are stochastic algorithms that can be applied to solve a wide variety of optimization problems without needing specific problem structure information.</em> <em>The penetration of RERs into electric power networks has been increased considerably to reduce the dependence of conventional energy resources, reducing the generation cost and greenhouse emissions. It is essential to include these sources in power flow studies. The wind and photovoltaic based systems are the most applied technologies in electrical systems compared to other technologies of RERs. Moreover, grey wolf optimizer (GWO) is a powerful metaheuristic algorithm that can be used to solve optimization problems. It is inspired from the social hierarchy and hunting behavior of grey wolves in the wild. <strong>The novelty. </strong>This paper presents an IGWO to solve the ORPD problem in presence of RERs<strong>. Methods. </strong>The IGWO based on enhancing the exploitation phase of the conventional GWO. The robustness of the method is tested on the IEEE 30 bus test system. For the control variables, a mixed representation (continuous/discrete), is proposed. The obtained <strong>results</strong> demonstrate the effectiveness of the introduced improvement and ability of the proposed algorithm for finding better solutions compared to other presented methods. </em>References 40, tables 3, figures 9.</p> F. Laouafi Copyright (c) 2025 F. Laouafi http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/311526 Thu, 02 Jan 2025 00:00:00 +0200 Robust adaptive fuzzy type-2 fast terminal sliding mode control of robot manipulators in attendance of actuator faults and payload variation http://eie.khpi.edu.ua/article/view/307034 <p><strong><em>Introduction.</em></strong> <em>This study presents a robust control method for the path following problem of the PUMA560 robot. The technique is based on the Adaptive Fuzzy Type-2 Fast Terminal Sliding Mode Control (AFT2FTSMC) algorithm and is designed to handle actuator faults, uncertainties (such as payload change), and external disturbances</em><em>.</em><em> The <strong>aim </strong>of this study is to utilize the Fast Terminal Sliding Mode Control (FTSMC) approach in order to ensure effective compensation for faults and uncertainties, minimize tracking error, reduce the occurrence of chattering phenomena, and achieve rapid transient response. A novel adaptive fault tolerant Sliding Mode Control (SMC) approach is developed to address the challenges provided by uncertainties and actuator defects in real robotics tasks.</em> <strong><em>Originality. </em></strong><em>The present work combined the AFT2FTSMC</em><em> algorithm in order to give robust controllers for trajectory tracking of manipulator’s robot in presence parameters uncertainties, external disturbance, and faults. We use an adaptive fuzzy logic system to estimate the robot’s time-varying, nonlinear, and unfamiliar dynamics. A strong adaptive term is created to counteract actuator defects and approximation errors while also guaranteeing the convergence and stability of the entire robot control system. <strong>Novelty.</strong> The implemented controller effectively mitigates the chattering problem while maintaining the tracking precision and robustness of the system. The stability analysis has been conducted using the Lyapunov approach. </em><strong><em>Results.</em></strong><em> Numerical simulation and capability comparison with other control strategies show the effectiveness of the developed control algorithm.</em> References 53, table 1, figures 8.</p> H. Rahali, S. Zeghlache, B. D. E. Cherif, L. Benyettou, A. Djerioui Copyright (c) 2025 H. Rahali, S. Zeghlache, B. D. E. Cherif, L. Benyettou, A. Djerioui http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/307034 Thu, 02 Jan 2025 00:00:00 +0200 Impact of transmission line lightning performance on an operational substation reliability considering the lightning stroke incidence angle http://eie.khpi.edu.ua/article/view/307431 <p><strong><em>Introduction</em></strong><em>. This study investigates substation failures caused by lightning strikes, which significantly affect operational reliability. Given the random nature of lightning strikes, a robust statistical approach is essential for accurately assessing their effects. <strong>Method.</strong> The research develops a comprehensive procedure to analyse the random distribution of non-vertical lightning strikes on transmission lines using the Monte Carlo method, a widely recognized statistical simulation technique. The <strong>goal</strong> of this work is to evaluate the performance of air-insulated substations under various lightning strike scenarios affecting the connected transmission lines. This is assessed in terms of mean time between failures (MTBF), determined by the basic insulation level of the equipment. The study incorporates both vertical and non-vertical strikes to address a critical gap in the literature, offering practical insights to enhance the reliability and safety of air-insulated substations. By considering the angle of lightning strikes, the study improves the accuracy of evaluating lightning performance using precise modelling of system components. <strong>Result</strong><strong>s</strong>. MATLAB and EMTP software were used to simulate and analyse the substation’s response to lightning-induced surges at various strike angles. The results are more representative of real-world conditions and reveal that non-vertical lightning strikes significantly reduce MTBF, underscoring the importance of advanced protective measures. <strong>Practical value.</strong> The findings highlight the necessity of accounting for the angle of lightning strikes when assessing substation reliability. </em>References 32, table 4, figures 13.</p> T. Hamel, S. Bedoui, A. Bayadi Copyright (c) 2025 T. Hamel, S. Bedoui, A. Bayadi http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/307431 Thu, 02 Jan 2025 00:00:00 +0200 The impact of parasitic capacitances on the accuracy of scale transformation of high-voltage dividers http://eie.khpi.edu.ua/article/view/317957 <p><strong><em>Purpose. </em></strong><em>The <strong>aim</strong> of this work is the determination of the parasitic capacitance’s influence on the accuracy of scale transformation of high-voltage dividers. Analyzing the possibilities of reducing such influence is a pressing <strong>problem</strong> for high voltage measurement, especially at high frequency range of input voltage. <strong>Methodology</strong>. Mathematical modeling of the voltage divider equivalent circuit, considering parasitic capacitances and inductances has been performed in the QUCS circuit simulator software under sinusoidal alternating current conditions in the range from 100 Hz to 1 MHz. Using the FEMM software, the finite element method was used to simulate the density distribution of capacitive currents in the module with capacitance graded insulation of the high-voltage arm of the voltage divider. <strong>Results</strong>. The results of the calculations show that the percentage of parasitic capacitive currents decreases exponentially depending on the ratio of the outer radii of the shielding disks to the distance between them. However, even with the outer radii of the shielding disks of about 3 m, capacitive currents still make up about 1 % of the total current flowing in the measuring circuit of the voltage divider. Instead of increasing outer radii, it is proposed to use high-voltage capacitance graded insulation between the shielding disks. As a result, a stable error of large-scale voltage transformation was obtained when the values of parasitic capacitances change, and it is proposed to manufacture the high-voltage arm of the voltage divider from the same type of high-voltage modules. <strong>Originality</strong>. The results of modeling the dependence of the accuracy of the voltage divider scale transformation on the ratio of the structural elements geometric parameters of its high-voltage arm were obtained. The solution has been proposed that involves changing the design of the high-voltage arm of the voltage divider, which significantly reduces the dependence of its scale transformation error on significant changes in the parasitic capacitances of the structure components on grounded surfaces. <strong>Practical value</strong>. The results of mathematical modeling of the characteristics of the voltage divider high-voltage arm make it possible to design, for the purpose of serial production, the same type of high-voltage modules for assembling on-site broadband voltage dividers for any nominal voltage, which will have the possibility of integration into Smart Grid systems. </em>References 23, tables 1, figures 8.</p> Y. O. Haran, Y. O. Trotsenko, O. R. Protsenko, M. M. Dixit Copyright (c) 2024 Y. O. Haran, Y. O. Trotsenko, O. R. Protsenko, M. M. Dixit http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/317957 Thu, 02 Jan 2025 00:00:00 +0200 Distribution of volumes of plasma channels components between metal granules in working liquids http://eie.khpi.edu.ua/article/view/307759 <p><strong><em>Introduction.</em></strong><em> Expanding the capabilities of a number of modern technologies and improving quality of their products require detailed spark and plasma erosion processes control in metal granules layers (MGL). <strong>Problem.</strong> Traditional measurement of exclusively electrical parameters of these processes, even in the case of multi-electrode systems, provides only a general vision, not allowing monitoring processes in individual plasma channels. Optical control methods make it possible to simultaneously have information about almost every plasma channel in the MGL. The <strong>aim</strong> of the article is to study the characteristic components of plasma channels arising as a result of the flow of discharge currents in the MGL and to establish the laws of distribution of their volumes and their ratios. <strong>Methodology</strong>. During the experiments, photographs of plasma channels resulting from the flow of discharge current pulses between Al granules immersed in distilled water were obtained. Using the specialized ToupView program, the volumes of equivalent ellipsoids of rotation, approximating the colored halos and white cores of the plasma channels were determined. Discrete distributions of the volumes of the halo and cores of plasma channels, as well as their ratios were constructed both with and without procedures for screening out «anomalous» results. The efficiency of approximation of discrete distributions obtained in practice by continuous theoretical distributions Weibull, Rosin-Rammler and log-normal was estimated. <strong>Results.</strong> It is shown that of all the considered theoretical distributions of halo and cores of plasma channels volumes, as well as their ratios, the most adequate is the log-normal one. <strong>Originality.</strong> For the first time distributions of volumes of halo and cores of plasma channels were studied and their comparative analysis with the size distributions of erosion particles and dimples on the surface of Al granules was given. <strong>Practical significance.</strong> Taking into account the new obtained results, a technique for constructing distributions of volumes of halo and cores of plasma channels and determining their parameters has been developed.</em> References 53, figures 7, tables 5.</p> N. A. Shydlovska, S. M. Zakharchenko, M. F. Zakharchenko, M. A. Kulida, S. A. Zakusilo, R. A. Yakovenko Copyright (c) 2025 N. A. Shydlovska, S. M. Zakharchenko, M. F. Zakharchenko, M. A. Kulida, S. A. Zakusilo, R. A. Yakovenko http://creativecommons.org/licenses/by-nc/4.0 http://eie.khpi.edu.ua/article/view/307759 Thu, 02 Jan 2025 00:00:00 +0200