Electric Power Engineering Research Articles

Extreme weather and electricity markets: Key lessons from the February 2021 Texas crisis

Todd Levin is a principal energy systems engineer in the Center for Energy, Environmental and Economic Systems Analysis (CEEESA) at Argonne National Laboratory. His research interests focus on utilizing advanced optimization and simulation methodologies to model complex interactions in electricity markets and quantify the implications of domestic energy policies and regulations. He also maintains a strong interest in international energy development, examining optimal centralized and decentralized rural electrification strategies and a range of global energy security issues. Dr. Levin holds a BA in physics from Northwestern University and a PhD in industrial engineering from the Georgia Institute of Technology. Audun Botterud is a principal energy systems engineer in CEEESA at Argonne National Laboratory with a co-appointment in Laboratory for Information and Decision Systems at Massachusetts Institute of Technology. He analyzes the complex interactions between engineering, economics, and policy in electricity markets, in support of the transition toward a cost-efficient and reliable low-carbon energy system. He is particularly interested in grid integration of renewable energy and energy storage. Audun holds an MSc (industrial engineering) and PhD (electrical power engineering) from the Norwegian University of Science and Technology and was previously with SINTEF Energy Research in Trondheim, Norway. W. Neal Mann is a postdoctoral appointee in CEEESA and the Nuclear Science and Engineering Division at Argonne National Laboratory. His research interests include energy system modeling and design, nuclear energy, and energy storage for climate change mitigation and adaptation. He holds a BA in physics and music from Southwestern University and an MSE and PhD in mechanical engineering (nuclear and radiation engineering focus) from the University of Texas at Austin. Jonghwan Kwon is an energy systems engineer in CEEESA at Argonne National Laboratory. His research interests include operations research applied to electric power systems, power systems operations and planning, management of distributed energy resources, and market design and pricing. Dr. Kwon holds a PhD in electrical engineering power system from Arizona State University. Zhi Zhou is a principal computational scientist in CEEESA at Argonne National Laboratory. His research interests include optimization, machine-learning-based forecasting, decision making under uncertainty, and applications to power grid, electricity markets, renewable energy, and the interdependency between power grids and other infrastructure systems. Zhi Zhou received his BE in computer sciences from Wuhan University, MS in operations research and statistics, and PhD in decision sciences and engineering systems from Rensselaer Polytechnic Institute.

ОПЫТ РЕАЛИЗАЦИИ РОССИЙСКО-КИТАЙСКОЙ СОВМЕСТНОЙ ПРОГРАММЫ ПОДГОТОВКИ СТУДЕНТОВ ИЗ КИТАЙСКОЙ НАРОДНОЙ РЕСПУБЛИКИ ПО НАПРАВЛЕНИЮ «ЭЛЕКТРОЭНЕРГЕТИКА И ЭЛЕКТРОТЕХНИКА»

The paper deals with the Chinese-international education cooperation. The brief overview of structure and current state of international education programs are given. On the example of the Far Eastern State Transport University, the experience of implementing a joint Russian-Chinese educational program for students involved in electric power and electrical engineering education programs is considered. Examples of successful scientific work of Chinese students during their studies in Russia are given.

Types of smart systems and their application in power grids

With the development of modern technologies, opportunities for an exchange of the increasing amount of information at ever higher speeds are created. The use of smart systems in electric power engineering creates conditions for improving the systems for monitoring, archiving, analysis and management. It is necessary to collect the basic information about the emergency modes automatically for analysis of the operation of the equipment and the parameters of the regimes in the power grids. The main questions to be decided are: what type of information is needed, how to use this information and at what are the different access levels, what should be the systems - local or global, how to exchange data. Smart systems for power grids and switchgears have been developed on a modular basis by almost all global manufacturers, as well as by many companies on individual assignments. The publication discusses the existing types of smart systems and the data they process. Suggestions have been made for the volume and structure of data that are needed for the analysis process.

ИНТЕРАКТИВНЫЙ ТРЕНАЖЕР ДЛЯ ОБУЧЕНИЯ ПЕРСОНАЛА ОАО «РЖД» НАВЫКАМ ОПЕРАТИВНЫХ ПЕРЕКЛЮЧЕНИЙ

The paper is devoted to decrease of a number of accidents and electrical injuries in electrical power engineering organizations. The author proposes an interactive complex of training exercises aimed at training electrical personnel of alternating current railways in safe methods of operating switching in schemes of electric substations. Practising a skill of virtual operating switching on a training simulator will allow the personnel to decrease the probability of mistakes in future, which will contribute to reduction of a number of accidents and injuries in operation. The developed training simulator adapts to the scheme of any traction substation on the JSC «RZD» railway network, which creates the possibility for replication of the product, enlargement of its functional possibilities and exchange of experience of its use.

Двухканальный безмостовой корректор коэффициента мощности

This paper discusses the analysis and design details of a bridgeless power factor corrector. The circuit topology of the proposed power converter is based on the combination of two DC/DC converters forming a two-channel structure of the power processing path. To meet the safety requirements, the converter circuit is equipped with a common ground link between the AC input voltage source and the DC output. The two-channel bridgeless power factor corrector operates under a power factor close to one and is robust to a short circuit fault. The resonance mode of the converter circuit prevents unpredictable overvoltage across the converter semiconductors. The device was modelled and simulated using MATLAB/Simulink software environment under varying load conditions. The results of numerical investigations have confirmed predicted device performance parameters and operational characteristics. The paper content will attract the attention of researchers and engineers working in the areas of electrical power engineering and power supplies.

РАЗРАБОТКА СХЕМЫ И МОДЕЛИРОВАНИЕ РЕЗОНАНСНОГО ТРАНСФОРМАТОРА НА БАЗЕ МНОГОФУНКЦИОНАЛЬНОГО ИНТЕГРИРОВАННОГО ЭЛЕКТРОМАГНИТНОГО КОМПОНЕНТА

Relevance The use of functional integration methods in power electrical engineering makes it possible to achieve a reduction in the weight and dimensions of the finished device, as well as to increase the reliability and efficiency of the system. The use of hybrid components in the development of transformers makes it possible to implement the resonant mode of operation of the system, thereby reducing losses. Aim of research This article discusses the development of a circuit and modeling of a resonant transformer based on a multifunctional integrated electromagnetic component. The main tasks are to determine the electrical circuit of the resonant transformer implemented on the basis of a multifunctional integrated electromagnetic component and the analytical calculation of the parameters of the multifunctional integrated electromagnetic component. Research methods In this study, the following methods were used: patent review, the study of scientific literature, computer simulation performed in the MatLab software package. Results The authors have developed a computer model in MatLab of a resonant transformer based on a multifunctional integrated electromagnetic component. The design and functional features of component make it possible to implement the resonant mode of operation of the transformer, since the finished component is both a capacitive and an inductive load. An equivalent circuit of a multifunctional integrated electromagnetic component is presented and adapted to the MatLab software package. As a result of the simulation, a graph of the magnetizing current of the transformer was obtained. The analysis of the possibility of practical implementation of the system was carried out.

Finance and Innovation Solutions to Implement Investment Programs in Electric-Power Complex of the Russian Federation

Today we observe changes in concepts of organizing power - engineering industry and tariff pricing. While estimating the pressure of sanctions, everybody agrees that the worst damage is caused by finance tools. Therefore, innovation in electric-power sector is started with finance innovation. It is also necessary to bear in mind the future earnings of stakeholders and households that plan to re-orient their investment from oil sector to electric-power engineering. This trend is being discussed right now, though for Russia with its gas reserves and customer preferences the process of investment changes can be rather long. The finance platform in this industry is not fundamental yet. It is possible to start innovation only after accumulating some funds. For instance, it is planned to change elements in the structure of power and fuel potential, to reform technical and technological elements of infrastructure (chat-bots with geographic and product applications, drones, quadrocopters, which can be used for linear and high buildings). In the future it is planned to develop new customer clusters with certain social index. In the article the authors study finance and innovation solutions to implement innovation programs in electricpower complex in conditions of digitalization and imperative indices of investment, though digitalization is called the key anti-ecological factor in this sector.

Construction Technology and Quality Control of Power and Electrical Engineering Based on Convolutional Neural Network

In the context of the Internet era, more and more parties have begun to store, process, and analyze data, but the accompanying question is whether people are reasonable about the data under the impact of massive data, effective and efficient analysis, especially the problems faced in this project. This article aims to study the quality control problems faced by electric power and electrical engineering in the construction process through the use of convolutional neural networks. Under this idea, this article proposes a multilayer convolution method. The experimental results show that the use of the improved multilayer convolution method for the convolution method of the convolutional neural network can effectively improve the multiple analysis problems of small datasets in the construction of electric power and electrical engineering; in this way, the relevant data are analyzed; by controlling the quality of construction, the quality problem has been greatly improved. After comparison, it is concluded that the overall construction quality has increased by 35%.

An Artificial Neural Network Developed in MATLAB-Simulink for Reconstruction a Distorted Secondary Current Waveform. Part 1

Recently, there has been an increased interest in the use of artificial neural networks in various branches of the electric power industry including relay protection. Аrtificial neural networks are one of the fastest growing areas in artificial intelligence technology. Recently, there has been an increased interest in the use of аrtificial neural networks in the electric power engineering, including relay protection. Existing microprocessor-based relay protection devices use a traditional digital signal processing of the monitored signals which is reduced to a multiplying the values of successive samples of the monitored current and voltage signals by predetermined coefficients in order to calculate their RMS values. In this case, the calculated RMS values often do not reflect the real processes occurring in the protected electrical equipment due to, for example, current transformer saturation because of the DC component presence in the fault current. When the current transformer is saturated, its secondary current waveform has a characteristic non-periodic distorted form, which is significantly differs from its primary (true) waveform, which causes underestimation of the calculated RMS value of the secondary current compared to its true value. In its turn, this causes to a trip time delay or even to a relay protection devices operation failure. The use of аrtificial neural networks in conjunction with a traditional digital signal processing provides a different approach to the functioning of both the measuring and logical parts of the microprocessor-based relay protection devices, which significantly increases the speed and reliability of such relay protection devices in comparison with their traditional implementation. A possible application of the аrtificial neural networks for the relay protection purposes is the fault occurrence detection and its type identification, current transformer secondary current waveform distortion restoration due to its saturation up to its true value, detection the distorted and undistorted sections of the current transformer secondary current waveform during its saturation, primary power equipment abnormal operating modes detection, for example, power transformer magnetizing current inrush. The article describes in detail the stages of the practical implementation of the аrtificial neural networks in the MATLAB-Simulink environment by the example of its use to restore the distorted current transformer secondary current waveform due to saturation.

Destruction of polymer insulation and threshold amplitudes of current pulses of different temporal shapes for electric wires and cables in the low- and high-current circuits of pulse power engineering, electrical engineering and electronic devices

Goal. Development of engineering method for settlement of threshold amplitudes Impk of single-pulse current ip(t) of different temporal shapes for electric wires and cables with polyethylene (PET), polyvinylchloride (PVC) and rubber (R) half-length insulation, used in modern pulsed power engineering, electrical engineering and electronics in their low- and high-current circuits. Methodology. Basis of the theoretical and applied electrical engineering, electrical power engineering, electrophysics bases of technique of high-voltage and large pulsed currents, bases of low- and high-current electronics, measuring technique, electromagnetic compatibility and standardization. Results. Development of engineering method is executed on close calculation determination of threshold amplitudes Impk of single-pulse axial-flow current ip(t) of different temporal shapes for electric wires and cables with copper (aluminum) current-carrying parts and PET, PVC and R half-length insulation, used in the ow- and high-current circuits of pulsed electrical power engineering, electrical engineering and electronics. Electrothermal resistibility of half-length insulation of the examined cable and wire products (CWP), proper maximum to the possible temperatures of heating of current-carrying and insulating parts of the probed wires and cables and shutting out the offensive of the phenomenon destruction in the indicated insulation of CWP, was fixed based on this method. Calculation analytical correlations are obtained for finding in probed CWP of threshold numeral values of Impk amplitudes of pulses of current ip(t), time-varying both on aperiodic dependence of type τf/τp with duration of their front τf and duration of their pulses τp and by law of exponential attenuation sinewave. It is shown that at Imp>Impk destruction of their half-length insulation, resulting in the decline of service life of CWP, will come from the thermal overheat of current-carrying parts of the examined electric wires and cables. The examples of practical application of the offered method are resulted upon settlement for a radiofrequency coaxial cable RC 50-4-11 with middle sizes is easily soiled with continuous PET insulation of threshold amplitudes of Impk of standard aperiodic pulses of current ip(t) from nano-, micro- and millisecond temporal ranges of shape of τf/τp=5 ns/200 ns, τf/τp=10 μs/350 μs and τf/τp=7 ms/160 ms. It is shown that with the proper growth of parameter τp>>τf for flow on a continuous copper tendon and split copper shell of radiofrequency coaxial cable RC 50-4-11 with middle sizes is easily soiled indicated homopolar pulses of current ip(t) substantial diminishing of their threshold amplitudes of Impk (with 531,2 кА for the nanosecond pulse of current of type 5 ns/200 ns to 1.84 кА for the millisecond impulse of current of type of 7 ms/160 ms takes place). Originality. An engineering method is first developed for close settlement of threshold numeral values of Impk amplitudes of single-pulse axial-flow current ip(t) of arbitrary peak-temporal parameters for electric wires and cables with copper (aluminum) current-carrying parts and PET, PVC and R half-length insulation. Practical value. Application in electrical engineering practice of the offered engineering method for determination of threshold amplitudes Impk of the indicated pulses of axial-flow current ip(t) for the probed electric wires and cables will allow considerably to increase service life of examined CWP.

TRAINING OF FUTURE ENERGY SPECIALISTS TO SOLVE PRACTICAL PROBLEMS ON THE BASIS OF PHYSICAL PROJECTS

Formulation of the problem. In the field of higher education, general and special competencies are acquired, which have in common the ability to apply knowledge in practical situations. Therefore, the formation of mental and practical skills and abilities of future energy specialists to solve practical problems is becoming more and more important. The effectiveness of solving practical problems in the field of power engineering, electrical engineering and electromechanics depends on the understanding by future specialists of energy profile the theories and methods of physics. There is a need to develop and implement effective teaching methods, in particular on the basis of physical projects. Materials and methods. The analysis of research in the field of education, the National Qualifications Framework, the standard of higher education in the specialty 141 "Electricity, Electrical Engineering and Electromechanics" for the first (bachelor's) level of higher education to theoretically substantiate the requirements for mental and practical skills of future energy specialists to solving practical tasks and advantages of physical projects in their formation was carried out; pedagogical experiment was carried out for testing the effectiveness of the use of physical projects in the training of future energy specialists; diagnostics (using the 16-factor personal questionnaire of R. Cattell and the method of analysis of products of activity as projects) was for evaluation the levels of ability of future energy specialists to solve practical problems using theories and methods of physics; statistical calculations, such as quantitative and qualitative data processing, graphical presentation of results, were for tracking the dynamics of the levels of formation of the ability of future energy specialists to solve practical problems and establishing the scientific reliability of the results of the study. Results. The essence of physical projects and features of their using are theoretically substantiated on the example of discipline "Alternative energy", the maintenance of which is directed on formation of ability to apply the received theoretical knowledge, scientific and technical methods for the decision of scientific and technical problems and problems of power. Such criteria as personal, content-procedural, evaluation-regulatory, indicators and diagnostic tools for testing the ability of future energy specialists to solve practical problems with the using of physics methods are characterized. The analysis of experimental data showed significant qualitative changes in the levels of formation of the ability of future energy specialists to solve practical problems by EG physics. That is confirmed by calculations of Pearson's criterion (17,61> 7,8).

Discussion on the Application of Electric Power Automation Technology in Electric Power Engineering

Discussion on the Application of Electric Power Automation Technology in Electric Power Engineering

CONTROL AND PROTECTION OF AC/DC HYBRID MICROGRIDS

Future trends in electrical power engineering predict the development of dispersed generation, accumulation and microgrids. Besides many of the various benefits and efficiency increase, the operation of hybrid AC/DC networks brings also specific requirements for control and protection. This paper analyses the key challenges of hybrid AC/DC network operation. The paper deals with operation and protection issues respecting different levels of short-circuit power in different operating states and focuses on specific properties of short circuit current shutdown in terms of protection of hybrid microgrids. Specific issue of line to ground fault detection and tripping in microgrid are verified using laboratory experiment. The paper provides a comprehensive view on some specific requirements for the protection and control of AC/DC hybrid microgrids.

Formation of Scientific Foundations of Technosphere Safety Among Students of the Direction of Training "Electric Power and Electrical Engineering”

The article deals with issues related to the formation of scientific foundations of technosphere safety in the training of students and specialists in the field of electric power industry. Technosphere safety in the field of electric power engineering should be formed on the theoretical basis of the subjects of ecology and life safety.

Resilience in supply systems – What the food industry can learn from energy sector

Drastic events such as pandemics, earthquakes or other disasters not only threaten the immediate living conditions of people but also indirect circumstances such as energy supply, infrastructure and food production. To ensure that damage and failures in these areas do not lead to a disaster, special requirements are placed on this critical infrastructure. In this context resilience, which is defined as the resistance of a system to external effects, is required. A field that is indeed part of the critical infrastructure, but which has not been considered as intensively as the energy sector, is food production.The investigation focuses on how fundamental principles of thermodynamics, system theory and reliability theory can be applied to the modelling of food production processes to obtain a measure of resilience. Using known state and process variables from thermodynamics and electrical power engineering, analogous variables are derived for the food industry. These variables serve as an evaluation standard for a quality measure Q. In addition to system-theoretical considerations, it is investigated how existing evaluation criteria of power engineering, such as System Average Interruption Duration Index (SAIDI) and Customer Average Interruption Duration Index (CAIDI), can be transferred to food production.Design: The investigation focuses on how fundamental principles of thermodynamics, system theory and reliability theory can be applied to the modelling of food production processes to obtain a measure of resilience. Using known state and process variables from thermodynamics and electrical power engineering, analogous variables are derived for the food industry.Purpose: Drastic events such as pandemics, earthquakes or other disasters not only threaten the immediate living conditions of people but also indirect circumstances such as energy supply, infrastructure and food production. To ensure that damage and failures in these areas do not lead to a disaster, special requirements are placed on this critical infrastructure. In this context resilience is required.Findings: The aforementioned state and process variables serve as an evaluation standard for a quality measure Q. In addition to system-theoretical considerations, it is investigated how existing evaluation criteria of power engineering, such as SAIDI and CAIDI, can be transferred to food production.Originality: This paper fulfils an identified need to study a part of the critical infrastructure that has not been as extensively looked at as the energy sector, namely food production.

Problems of Remote Temperature Measurement of Small Objects of Electricity Power Systems—On the Example of Lashing Clamps of Bridge Connections on High Voltage Poles

The article presents problems occurring during remote temperature measurement of lashing clamps of bridge connections on high voltage poles using thermal imaging cameras. The basic metrological parameters of thermal imaging cameras are described. On this basis, typical errors made during the inspection of high voltage lines supplying power substations are presented using infrared cameras. Researching the possible solutions for the problems of remote temperature measurement of small objects of electricity power systems—on the example of lashing clamps of bridge connections on high voltage poles in the proposed paper and showing the basic metrological aspects and parameters of thermal imaging cameras are important because, in this way, it is observed to eliminate costly interruptions in the supply of electricity associated with the breaking of power lines. Small objects are quite difficult to be controlled and monitored on large grids and on large powerline poles; thus, it is very challenging to interpret the data offered by thermograms. The problem of remote temperature measurement of small objects in electrical power engineering is very important from the point of view of the quality and reliability of electricity supply. Obtaining early warning information about the occurrence of overheating, e.g., on lashing clamps of bridge connections, is very important, as it eliminates costly interruptions in the supply of electricity associated with the breaking of power lines supplying high voltage switchgears or substations.

Research on Construction Technology and Quality Control of Transmission Line in Electric Power Engineering

Research on Construction Technology and Quality Control of Transmission Line in Electric Power Engineering

Preface

We are glad to introduce you the proceedings of the 2021 2nd International Conference on Clean Energy and Electric Power Engineering (ICCEPE 2021). ICCEPE 2021 is to bring together innovative academics and industrial experts in the field of clean energy and electric power engineering to a common forum. The primary goal of the conference is to promote research and developmental activities in clean energy and electric power engineering and another goal is to promote scientific information interchange between researchers, developers, engineers, students, and practitioners working all around the world. The conference will be held every year to make it an ideal platform for people to share views and experiences in clean energy and electric power engineering and related areas.As we may aware, the World Health Organization officially declared the novel coronavirus COVID-19 a pandemic. Governments around the world are now issuing restrictions on travel, gatherings, and meetings in an effort to limit and slow the spread of the virus. The health and safety of the author and research community is our first priority and we are supporting these efforts. Therefore, the ICCEPE 2021 conference was held virtually on July 02-04, 2021.During the conference, the conference model was divided into three sessions, including oral presentations, keynote speeches, and online Q&A discussion. In the first part, some scholars, whose submissions were selected as the excellent papers, were given about 5-10 minutes to perform their oral presentations one by one. Then, keynote speakers were each allocated 30-45 minutes to hold their speeches. In the third part, followed by a question and answer by the participants with a direct questioning system, through chat forums and Q&A forums provided by the zoom application. The number of participants who joined the zoom room was recorded around 60 participants.In the second part, we invited three professors as our keynote speakers. The first one, Prof. M. Shahidul Islam, from Department of Mechanical and Manufacturing Engineering, Universiti Malaysia Sarawak. He presented his insightful speech: Waste Biomass the Potential Renewable Energy Source: A 2021 Update. A. Prof. Jia Cui, from Shenyang University of Technology. He had outstanding research in Multi-disciplinary research on clean energy consumption, intelligent control of energy internet and power big data technology area. The last keynote speakers, Prof. Jinghong Zhou, from School of Electrical Engineering and Information Technology, Changchun Institute of Technology. His speech title is Research on the Market Mechanism of Power Demand Side Adjustable Resources Participating in Grid Interaction. The speech mainly introduced the relevant research progress at home and abroad, the organization mode and market mechanism of power demand side resources participating in the grid interaction. Their insightful speeches had triggered heated discussion in the third session of the conference. Every participant praised this conference for disseminating useful and insightful knowledge.The proceedings of ICCEPE 2021 span over 3 topical tracks, that include: Clean energy, Power Engineering, Smart Grid and Energy Science. All the papers have been through rigorous review and process to meet the requirements of International publication standard.We would like to acknowledge all of those who have supported ICCEPE 2021. Each individual and institutional help were very important for the success of this conference. Especially we would like to thank the organizing committee for their valuable advices in the organization and helpful peer review of the papers. We hope that ICCEPE 2021 will be a forum for excellent discussions that will put forward new ideas and promote collaborative researches. We are sure that the proceedings will serve as an important research source of references and the knowledge, which will lead to not only scientific and engineering progress but also other new products and processes.The Committee of ICCEPE 2021List of Committee member, Conference Chairman, Program Committees, Technical Program Committees are available in this pdf.

Experimental Efficiency Study of Project Technology as a Means of Formation Foreign Language Competence of Future Electric Power Engineers

The paper covers the ways of building foreign language competence of students majoring in electrical engineering in the process of their vocational training. The purpose of the article is the practical substantiation of the process of forming the future energy engineers’ foreign languagecompetence by means of project technology and carrying out diagnostic measures to check its effectiveness in foreign language learning. The methods used in this research are theoretical (analysis, comparison, systematization, generalization), empirical research methods (observations, surveys, pedagogical experiment), and statistical (non-parametric Pearson's criterion.). The results. The efficiency of project technology in the indicated process has been substantiated. A number of factors that determine the choice of such a learning technology has been specified, namely they are the following: student-oriented approach, foreign language learner autonomy, building project-oriented skills in specialty metalanguage, relationship between project work as a form of performing educational assignments and types of engineering activity. Author’s definition of project technology has been provided. By this notion a system of active and practical methods of learner-centered education aimed at programmed organization of students’ project activity, creation of educational projects that involve developing skills of independent knowledge acquisition, their practical handling, development of critical and creative thinking and key competences, is meant. The efficiency of project technology in the educational process has been experimentally verified by the example of developing foreign-language competence of students doing Master’s degree in electrical engineering. In order to determine the efficiency of project technology in the process of foreign language teaching to students in the master’s programme compared to traditional teaching methods, control groups and experimental groups with such attributes as reproductive properties, constructability and creativity were formed. Foreign language competence forming according to motivational, communication, professional, projecting and performance indicators was implemented in the process of executing profession-oriented projects. In order to assess the results of future power engineers’ project work, 100-point scale was developed. Conclusions. According to the results of the performed project work, it was determined that the level of foreign language competence in the experimental groups was higher than the one in the control groups. Generalized maturity indices of motivational, communication, professional, projecting and performance components in the control groups and in the experimental groups differed significantly. Group inhomogeneity and the significant differences were confirmed with the help of statistical non-parametric Pearson’s test χ². The obtained results of the pedagogical experiment have proved the efficiency of the suggested project technology and its rationale for implementing in the process of future electric power engineers’ foreign language teaching.

$G$-deviations of polygons and their applications in Electric Power Engineering

For any metric space $X$ endowed with the action of a group $G$, and two $n$-gons $\vec x=(x_1,\dots,x_n)\in X^n$ and $\vec y=(y_1,\dots,y_n)\in X^n$ in $X$, we introduce the $G$-deviation $d(G\vec x,\vec y\,)$ of $\vec x$ from $\vec y$ as the distance in $X^n$ from $\vec y$ to the $G$-orbit $G\vec x$ of $\vec x$ in the $n$-th power $X^n$ of $X$. For some groups $G$ of affine transformations of the complex plane, we deduce simple-to-apply formulas for calculating the $G$-deviation between $n$-gons on the complex plane. We apply these formulas for defining new measures of asymmetry of triangles. These new measures can be applied in Electric Power Engineering for evaluating the quality of 3-phase electric power. One of such measures, namely the affine deviation, is espressible via the unbalance degree, which is a standard characteristic of quality of three-phase electric power.