Systems, Decision and Control in Energy IV: Volume I. Modern Power Systems and Clean Energy 3031224639, 9783031224638

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Studies in Systems, Decision and Control 454

Artur Zaporozhets   Editor

Systems, Decision and Control in Energy IV Volume I. Modern Power Systems and Clean Energy

Studies in Systems, Decision and Control Volume 454

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

The series “Studies in Systems, Decision and Control” (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control–quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the fields of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the worldwide distribution and exposure which enable both a wide and rapid dissemination of research output. Indexed by SCOPUS, DBLP, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science.

Artur Zaporozhets Editor

Systems, Decision and Control in Energy IV Volume I. Modern Power Systems and Clean Energy

Editor Artur Zaporozhets General Energy Institute National Academy of Sciences of Ukraine Kyiv, Ukraine

ISSN 2198-4182 ISSN 2198-4190 (electronic) Studies in Systems, Decision and Control ISBN 978-3-031-22463-8 ISBN 978-3-031-22464-5 (eBook) https://doi.org/10.1007/978-3-031-22464-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Reforming the energy sector remains a key factor in Ukraine’s sustainable growth. Ukraine is a strategic player in the transportation of energy resources and one of the largest regional producers of hydrocarbons. Despite the open energy market, state-owned enterprises maintain a dominant role in the energy sector. The largest energy producers are nuclear and hydropower enterprises. “Naftogaz Ukrayiny” and its subsidiaries play a key role in the supply of oil and gas to Ukraine and neighboring countries. However, new private companies are gradually entering to the market, mainly in the field of thermal generation, as well as companies involved in the distribution of electricity and natural gas. A significant number of new private enterprises in renewable energy should also be noted. In 2020, the total supply of primary energy to Ukraine was 86.402 million toe. The largest particles in its structure were natural gas (≈27.6%), coal and peat (≈26.4%), and nuclear energy (≈23.1%). Biofuels and waste (≈4.9%), wind, solar, and geothermal energy (≈0.9%) have relatively low particles so far. Thus, Ukraine has a great potential for the development of renewable energy sources. Despite the social and economic difficulties Ukraine has faced, it has shown a commitment to reforming the energy sector, which will put it on a path of sustainable growth. The occupation of the Crimean peninsula and part of the Donbass by Russia in 2014 broke the energy supply chain to Ukraine, since most of the mines are located in the Donetsk and Lugansk regions. However, after signing the Association Agreement with the European Union in 2014 and taking on international obligations, Ukraine began to work on promoting energy efficiency. A significant role was played by scientific developments carried out by Ukrainian scientists, including the authors of this book. Various approaches were also used to the economic deregulation of energy enterprises and economic incentives for end users of energy resources. Despite the war activities caused by the Russian invasion on February 24, 2022, and the destruction of a large number of energy generation and transmission enterprises, NPC “Ukrenergo” disconnected the Ukrainian energy system from Russia and Belarus and joined the unified energy system of continental Europe ENTSO-E. The physical interconnection operations were completed on March 16, 2022. The

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Preface

process of union of energy systems in conditions of military aggression, the introduction of active war activities, the destruction of critical infrastructure facilities, including energy enterprises, became possible only due to highly qualified specialists in the energy sector and modern scientific theoretical and applied developments that formed the basis for the work of many energy companies. This book consists of two volumes, and this volume consists of five parts: Cybersecurity and Computer Science, Electric Power Engineering, Heat Power Engineering, Fuels, and Renewable Power Engineering. Scientists from more than 20 leading scientific, educational, governmental and private Ukrainian institutions took part in the creation of the book. Among them are National Academy of Sciences of Ukraine (Kyiv), General Energy Institute of NAS of Ukraine (Kyiv), Institute of Engineering Thermophysics of NAS of Ukraine (Kyiv), State Institution “The Institute of Environmental Geochemistry” of NAS of Ukraine (Kyiv), Institute of Physics of NAS of Ukraine (Kyiv), Institute of Telecommunications and Global Information Space of NAS of Ukraine (Kyiv), Taras Shevchenko National University (Kyiv), National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” (Kyiv), Lviv Polytechnic National University (Lviv), National Aviation University (Kyiv), National Technical University ”Kharkiv Polytechnic Institute” (Kharkiv), Kharkiv National University of Radio Electronics (Kharkiv), Ivano-Frankivsk National Technical University of Oil and Gas (Ivano-Frankivsk), National University of Life and Environmental Sciences of Ukraine (Kyiv), Mykolayiv National Agrarian University (Mykolaiv), Cherkasy Bohdan Khmelnytsky National University (Cherkasy), Kyiv International University (Kyiv), Donetsk National Technical University (Pokrovsk), International Scientific and Educational Center for Information Technologies and Systems (Kyiv), Kharkiv National Air Force University (Kharkiv), Military Academy (Odesa), Verkhovna Rada of Ukraine (Kyiv), NPC “Ukrenergo” (Kyiv), and PJSC “Ukrnafta” (Kyiv). Also, scientists from Rzeszów University of Technology (Rzeszów, Poland) joined for the creation of this book. A major role in the preparation and creation of this volume of the book was played by Academician of the National Academy of Sciences of Ukraine, Doctor of Technical Sciences, Professor, Director of the General Energy Institute of the National Academy of Sciences of Ukraine (1997–2022) Kulyk Mykhailo Mykolayovych, and Corresponding Member of the National Academy of Sciences of Ukraine, Doctor of Technical Sciences, Professor, Acting Director of the General Energy Institute of the National Academy of Sciences of Ukraine Babak Vitalii Pavlovych. This book is for scientists, researchers, engineers, as well as lecturers and postgraduates of higher education institutions dealing with energy sector, power systems, ecological safety, etc. Kyiv, Ukraine March 2022

Artur Zaporozhets

Contents

Cybersecurity and Computer Science Development of Top-down and Bottom-up Methodology Using Risk Functions for Systems with Multiplicity of Solutions . . . . . . . . . . . . . Anatoly Zagorodny, Viacheslav Bogdanov, Yurii Ermoliev, and Mykhailo Kulyk

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Basic Matrix Forms of the System Input–Output and Their Fundamental Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mykhailo Kulyk

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Development and Application of New Price Models in the System of Means Input–Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mykhailo Kulyk

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Mathematical Models and Software for Studying the Elasticity of Building Structures and Their Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vitalii Babak, Artur Zaporozhets, Vladyslav Khaidurov, Leonid Scherbak, Ihor Bohachev, and Tamara Tsiupii Application of Discrete Hilbert Transform to Estimate the Characteristics of Cyclic Signals: Information Provision . . . . . . . . . . . Vitalii Babak, Artur Zaporozhets, Mykhailo Kulyk, Yurii Kuts, and Leonid Scherbak

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Using of Big Data Technologies to Improve the Quality of the Functioning of Production Processes in the Energy Sector . . . . . . . 117 Viktoria Dzyuba and Artur Zaporozhets Parametric Identification of Dynamic Systems Based on Chaotic Synchronization and Adaptive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Artem Zinchenko

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Detection Method of Augmented Reality Systems Mosaic Stochastic Markers for Data-Centric Business and Applications . . . . . . . 145 Hennadii Khudov, Igor Ruban, Oleksandr Makoveichuk, Vladyslav Khudov, and Irina Khizhnyak Method for Converting the Output of Measuring System into the Output of System with Given Basis . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Elena Revunova, Volodymyr Burtniak, Yuriy Zabulonov, Maksym Stokolos, and Volodymyr Krasnoholovets Electric Power Engineering Analysis of UAVs and Their Technical Parameters for Overhead Power Lines Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 Serhii Babak, Artur Zaporozhets, Oleg Gryb, and Ihor Karpaliuk Determination of Energy Characteristics for Choice of Surge Arresters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Sergii Shevchenko, Dmytro Danylchenko, Stanyslav Dryvetskyi, Natalia Savchenko, and Serhii Petrov Heat Power Engineering Methodology for Designing Precision Sensors Which Using in Thermal Conductivity Measurement Systems . . . . . . . . . . . . . . . . . . . . . . 223 Zinaida Burova, Svitlana Kovtun, Leonid Dekusha, and Valentina Vasilevskaya Methods of Ecologization of Gas-Consuming Industrial Furnaces by Using Waste Heat Recovery Technologies . . . . . . . . . . . . . . . . . . . . . . . . . 239 Nataliia Fialko, Vitalii Babak, Raisa Navrodska, Svitlana Shevchuk, and Nataliia Meranova Simulation Modeling of Vapor Compression Refrigeration Unit Temperature Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253 Andrii Bukaros, Oleg Onishchenko, Alexander Herega, Herman Trushkov, and Konstantin Konkov Methods for Diagnosing the Technical Condition of Heating Networks Pipelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 Vitalii Babak, Oleg Dekusha, Artur Zaporozhets, Leonid Vorobiov, and Svitlana Kovtun Thermal Power Plants’ Coal Stock Short Term Projection Method for Ensuring National Energy Security . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 Sergii Shulzhenko, Borys Kostyukovskyi, Olena Maliarenko, Vitalyi Makarov, and Maryna Bilenko

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Use of Improved Methodology to Determine the Total Power Efficiency of Energy Products in Their Co-production at Combined Heat and Power Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Vitalii Horskyi and Olena Maliarenko Physical Model of Structural Self-organization of Tribosystems . . . . . . . . 309 Vitalii Babak, Nataliia Fialko, Vitalii Shchepetov, and Sergii Kharchenko Fuels Effect of Diethyl Ether Addition on the Properties of Gasoline-Ethanol Blends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Viktoriia Ribun, Sergii Boichenko, Anna Yakovlieva, Lubomyr Chelaydyn, Dubrovska Viktoriia, Shkyar Viktor, Artur Jaworski, and Pawel Wos Efficiency of Electric Logging in Thin-Layer Sections of Hydrocarbon Deposits (Gas Fields of the Precarpathian Depression) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Oleksiy Karpenko, Mykyta Myrontsov, Yevheniia Anpilova, and Oleksii Noskov Formation Mechanisms and Overcoming Methods to Reducing Natural Gas Consumption in the Residential Sector . . . . . . . . . . . . . . . . . . 353 Olexandr Yu. Yemelyanov, Tetyana O. Petrushka, Anastasiya V. Symak, Kateryna I. Petrushka, and Oksana B. Musiiovska Research of Characteristics of Solid Waste as Energy Resource . . . . . . . . 371 Artur Voronych, Teodoziia Yatsyshyn, Petro Raiter, Lubomir Zhovtulya, and Serhii Maksymiuk Renewable Power Engineering Geothermal Heat Supply Development Pathways in Ukraine . . . . . . . . . . 385 Yulia Shurchkova, Sergii Shulzhenko, Anna Pidruchna, Volodymyr Deriy, and Vitaly Dubrovsky Environmental Aspects of Geothermal Energy . . . . . . . . . . . . . . . . . . . . . . . 397 Anna Pidruchna and Yulia Shurchkova Straw Pellets for Heat Supply in the Countryside: Economic, Environmental and Circular Economic Indicators . . . . . . . . . . . . . . . . . . . . 411 Valerii Havrysh and Vasyl Hruban Comparative Analysis of Energy-Economic Indicators of Renewable Technologies in Market Conditions and Fixed Pricing on the Example of the Power System of Ukraine . . . . . . . . . . . . . . . 433 Mykhailo Kulyk, Tetiana Nechaieva, Oleksandr Zgurovets, Sergii Shulzhenko, and Natalia Maistrenko

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Prospects and Energy-Economic Indicators of Heat Energy Production Through Direct Use of Electricity from Renewable Sources in Modern Heat Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 Volodymyr Derii, Oleksandr Teslenko, Eugene Lenchevsky, Viktor Denisov, and Natalia Maistrenko

Cybersecurity and Computer Science

Development of Top-down and Bottom-up Methodology Using Risk Functions for Systems with Multiplicity of Solutions Anatoly Zagorodny , Viacheslav Bogdanov , Yurii Ermoliev , and Mykhailo Kulyk Abstract There is a wide and important class of objects and systems with a hierarchical structure, which by their nature should be applied methodology TOP-DOWN– BOTTOM-UP (TD–BU), but in the current state of the most important problems of its study can not be solved existing models TD–BU. This class of tasks, first of all, includes forecasting the production of almost all types of products and services, demand for them in all sectors of the economy, social sphere and in the country as a whole, ensuring unambiguous performance indicators of upper and lower levels of government, banks, trade, transport networks, etc. For these systems, the key problem is the discrepancy between the corresponding indicators for the upper and their sum for the lower hierarchical levels. The problem of discrepancy was solved by developing special analytical dependencies for indicators of both upper and lower levels. However, the solution of the problem of discrepancy led to the problem of ambiguity of solutions, these analytical solutions have n − 1 (n—dimension of the system) modification, each of which provides the necessary equality of indicators of these levels. There was a problem of choosing the best solution from many. The problem of building a mathematical model and a corresponding method that would simultaneously solve the problems of both divergence and ambiguity was overcome in the work by combining the TD–BU methodology with the analytical apparatus of general risk theory. At the same time, using the TD–BU methodology, analytical dependences were obtained that provide a solution to the problem of discrepancy. Based on these dependencies, in combination with the apparatus of risk theory, solutions were determined for both levels that have zero risks. As a function of the risk function, the functionality of the classical least squares method was used, which (method) gives better results (zero risks) for this problem in comparison with others.

A. Zagorodny · V. Bogdanov · Y. Ermoliev National Academy of Sciences of Ukraine, Kyiv, Ukraine M. Kulyk (B) General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] Y. Ermoliev International Institute for Applied Systems Analysis, Laxenburg, Austria © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_1

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As a result of combining TD–BU methodology and general risk theory, a comprehensive method of researching a new, important class of problems in the field of TD–BU problems was synthesized. Keywords Top-down · Bottom-up · TD–BU · Risk theory · Hierarchy · Discrepancies · Risks

1 Introduction The interplay of Top-Down and Bottom-Up technologies, information processing strategies used in many and varied management and organizational tasks, enables researchers to exploit the strengths of both approaches. Most of the proposed methods of synthesis of Top-Down and Bottom-Up as a holistic methodology are a combination of analysis of the components of the analyzed hierarchical systems with iterative procedures and are characterized by high labor costs and convergence problems that arise. Despite these difficulties, researchers are constantly turning to the use of TopDown–Bottom-Up (TD–BU) methodology for analysis, optimization or synthesis of systems and structures of hierarchical nature, which indicates the high relevance of improving the TD–BU methodology. Here are just a few examples of the use of TD–BU in specific areas. Thus, in [1] a comprehensive analysis of energy policy was conducted, for which the technological details of the ascending models and the economic wealth of the descending ones were combined. At the same time, a combination of different mathematical formats—mixed complementarity and mathematical programming—was carried out, which allowed to overcome the limitations of the dimensionality of the analyzed systems. To develop cost-effective ways to combat karst rocky desertification (KRD)—a serious environmental problem threatening southwest China—a spatial model was developed to model KRD dynamics using TD–BU, which allowed to predict its potential expansion or contraction [2]. The need to develop effective measures to respond to rapid changes in the environment has led the authors [3] to use TD–BU methods to combine downstream large-scale software approaches with rising, initiated and managed at the community level, which together with indigenous and local knowledge compliance with the monitoring program and community priorities, as well as respect for indigenous peoples’ intellectual property rights. In [4], the combined TD–BU approach allowed the authors to create a model for assembling zeolite frames, according to which the fusion of zeolite minerals may be the result of several possible ways of crystal growth. The authors [5] used hybrid modeling of TD–BU to analyze problems related to energy systems, indicating that linking upstream industry (engineering) models with downward (macroeconomic) models is an important contribution to the design of energy systems compatible with steady economic growth. Thus, a number of problems in various fields are currently successfully solved by TD–BU methods. However, there are a wide range of important systems and facilities that, by their nature, should be subject to the TD–BU methodology, but this could not be done

Development of Top-down and Bottom-up Methodology Using Risk …

5

using existing TD–BU models. This class of tasks, first of all, includes the simultaneous forecasting of production volumes both at the national level and at the level of industries of almost all types of products and services, demand for them in all sectors of the economy, social sphere and the country as a whole. For such systems and facilities, the key issue is the discrepancy (mismatch) of the indicators for the upper and their sum for the lower hierarchical levels. The publication [6] shows that this discrepancy problem for this new class of problems can be solved by developing a generalized model of the TD–BU class and special analytical dependences for indicators of both upper and lower hierarchical levels. However, solving the problem of discrepancy leads to the problem of ambiguity of solutions, namely—these analytical solutions have n − 1 modification (n—dimension of the system), each of which provides the necessary equality of the upper and their sum for the lower levels. That is, there is a problem of choosing the best solution from many. This paper proposes the solution of the above complex problem by combining the TD–BU methodology using the above-mentioned special mathematical dependencies with the analytical apparatus of general risk theory and the formation of a generalized mathematical method. Currently, a wide range of risk assessment algorithms has been developed, and the choice of a specific one directly depends on the nature of the problems that constantly arise in various fields of technology, economics, finance, and others. In particular, to assess credit risk, which is the main focus of the financial and banking sectors in connection with recent financial crises, the function of the least squares method of reference vectors is used as a risk function [7], as it can turn quadratic programming into linear programming, thereby reducing computational complexity. The same method of risk assessment, namely, the method of least squares of reference vectors used in [8] to analyze the factors influencing the design of the construction industry in developing countries. To assess the risk of planning electrical networks, a model of least squares of reference vectors was created [9], based on the clipping algorithm. This is due to the fact that the application of the least squares method of reference vectors leads to a loss of sparseness, and the clipping algorithm makes the corresponding matrix sparse. The study [10] develops and tests a model to increase the accuracy and facilitate decision-making on project selection for international construction firms, while the data analysis uses the method of partial least squares, i.e., finds a model of linear regression by projecting predicted variables and existing variables into new space. For epidemiological studies, risk differences were estimated using modified least squares regression, which is a useful analytical tool for rare binary results on the number of distortion factors, which gave reliable results for such systems [11]. In [12] shows how the use of the least squares method of Monte Carlo for long-term modeling of economic balance can be implemented in practice. As can be seen from the analysis of literature sources, most of the problems of risk theory in the role of functionals use various modifications of the least squares method, or this method in its classical form. It will be shown below that the object of study of this work in the intermediate form is a redefined system of linear algebraic equations. It turned out that the best results in terms of risk indicators for such an object are provided by the risk function in the form of the least squares functional in its (method) classical interpretation.

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Mathematical model and methods of analytical determination of indicators of upper and lower levels in these problems that solve the problem of ambiguity were presented in [6]. The mathematical model is formed in such a way that provides an opportunity to find solutions for the upper and each of the lower (sectoral) levels in a unique, analytical form. Therefore, the search for solutions is non-iterative. It is carried out in two stages. On the first of them, using known (standard) methods, preliminary forecasts are developed for indicators of the upper and lower levels. At the second stage a special system of algebraic equations is formed, from which analytical dependences for calculation of refined indicators of both levels are defined. This ensures a complete match between the upper indicator and the sum of the lower levels indicators. These mathematical model and methods can be used quite reasonably to reconcile the reporting indicators of the upper and lower levels of the respective objects (management structures, banks, trade network, etc.). In this case the consensual decisions are formed in one stage.

2 Mathematical Model The source information in this study is the vector of predictive functions f , formed at a given period of time using certain mostly known forecasting methods f = [ f 1 , f 2 , f i , f n ]; ,

(1)

where f 1 —Top-level forecast, f i , i = 2 − n—Down-level forecasts. According to the problem f 1 /=

n .

fi .

(2)

i=2

The purpose of the study in mathematical terms is to find a solution to the system of equations x = f1, x2 = f 2 , xi = f i , xn = f n ,

(3)

in which x a —T-level solution, and x i , i = 2, n—D-level solutions, and these solutions are related by an equation

Development of Top-down and Bottom-up Methodology Using Risk …

xa −

n .

7

xi = 0.

(4)

i=2

The system of equations (3) and (4) in the matrix–vector form is Ax = F,

(5)

or 1 2 i n n+1

⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣

1 2 Ai n 1

⎤

⎥ ⎥ ⎥ 1 ⎥ ⎥ 1 ⎦ 1 −1 −1 −1 1

⎡

⎤ f1 xa ⎢ ⎥ f2 ⎥ ⎢x ⎥ ⎢ ⎥ ⎢ 2⎥ ⎢ ⎢ , × ⎢ ⎥ = ⎢ fi ⎥ ⎣ xi ⎦ ⎢ ⎥ ⎥ f ⎣ n⎦ xn 0 ⎡

⎤

(6)

;

in which the vector [f 1 , f 2 , f i , f n , 0] denote by F. The system of equations (5), (6) has n + 1 equation and n unknowns. Such a system is redefined and therefore does not have an exact solution. To find the best of the approximate solutions, we use the Gaussian transformation in the form A' Ax = A' F.

(7)

For the right-hand side of Eq. (7), the dependence is valid A' F = f ,

(8)

which is confirmed by multiplying A' by F. Therefore, Eq. (7) will be considered in the form Bx = f , B = A' A,

(9)

in which ⎡ 1 2 Ai n ⎤ ⎡ ⎤ ⎡ 1 2 Ai n n + 1 xa ⎡ ⎤ 1 1 1 1 ⎢ 1 ⎥ ⎢ x2 ⎥ ⎢ ⎢ ⎥ ×⎢ ⎥=⎢ 2 ⎢ −1 ⎥ ⎥ ⎢ ⎥ ⎢ ⎢ 1 ⎥ ×⎢ 1 ⎢ ⎥ ⎣ xi ⎦ ⎣ ⎣ ⎦ ⎢ ⎥ i 1 −1 ⎣ 1 ⎦ xn n 1 −1 1 −1 −1 −1

⎤ f1 f2 ⎥ ⎥ ⎥, fi ⎦ fn

or, in the final version, the mathematical model of the problem has the form

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1 2 i n

12 2 −1 ⎢ −1 2 ⎢ ⎣ −1 1 −1 1 ⎡

Bi −1 1 2 1

⎡ ⎤ ⎡ n xa ⎤ −1 ⎢x ⎥ ⎢ ⎢ 2⎥ ⎢ ⎥=⎢ 1 ⎥ ⎥ ×⎢ ⎣ xi ⎦ ⎣ ⎦ 1 xn 2

⎤ f1 f2 ⎥ ⎥ ⎥. fi ⎦

(10)

fn

3 Analytical Solutions In algebraic equations (9) and (10), the matrix B is square with dimension n, the vectors x and f also have dimension n, the determinant |B| /= 0, that is, the system of equations (9) and (10) has one solution. This system has a structure that provides a unique opportunity to find this solution in an analytical form. To do this, we apply another Gaussian transformation to system (10), reducing the matrix B to a triangular form and limiting itself to the dimension n = 3. As a result, we obtain an algebraic system (11) ⎤ ⎡ ⎤ ⎡ 1 2 3 f1 xa ⎤ 1 2 −1 −1 ⎥ ⎢ ⎥ ⎢ × ⎣ x2 ⎦ = ⎣ f 1 + 2 f 2 ⎦. 2 ⎣ 3 1⎦ x3 −2 f i + 2 f 2 − 6 f 3 3 −8 ⎡

(11)

We find analytical solutions for the two dimensions of the system (11), namely, for n = 2 and n = 3. For n = 2 we have: x2 = ( f 1 + 2 f 2 )/3 = f 2 + ( f 1 − f 2 )/3, 2xa = f 1 + x2 = f 1 + f 2 + f 1 /3 − f 2 /3, xa = 2/3 f 1 − 1/3 f 2 = f 1 − ( f 1 − f 2 )/3. For the case n = 3 we receive: −8x3 = −2 f 1 + 2 f 2 − 6 f 3 , 4x3 = f 1 − f 2 + 3 f 3 , x3 = f 3 + ( f 1 − f 2 − f 3 )/4; 3x2 = f 1 + 2 f 2 − f 3 − ( f 1 − f 2 − f 3 )/4, x2 = (1/3 − 1/12) f 1 + (2/3 + 1/12) f 2 − (1/3 − 1/12) f 3 = f 2 + ( f 1 − f 2 − f 3 )/4; 2xa = f 1 + x2 + x3 ; xa = ( f 1 + f 2 + f 3 )/2 + ( f 1 − f 2 − f 3 )/4 = f 1 − ( f 1 − f 2 − f 3 )/4.

Development of Top-down and Bottom-up Methodology Using Risk …

9

Analysis of the received decisions x a and x i , i = 1, 2 for both cases shows that these solutions have the same structure, namely, the top-level solution has the form xa = f 1 −

1 r, n+1

(12)

and sectoral decisions in this case take shape xi = f i +

1 r, i = 2, n, n+1

(13)

where r = f1 −

n .

fi ,

(14)

i=2

is the difference between the upper level indicator and the sum of sectoral data, n – dimension of the system (10), i = 2, n. To confirm the dependences (12)–(14) we will show that they are valid not only for the dimension n, but also for the dimension n + 1. To do this, consider the structure (10) with dimension n + 1, shown in Eq. (15). ⎡ ⎤ ⎡ xa ⎡ 1 2 Bi n n + 1 ⎤ ⎢ ⎥ ⎢ 2 −1 −1 −1 −1 x2 ⎥ ⎢ ⎢ −1 2 1 1 1 ⎥ ⎢ ⎢ ⎢ ⎢ ⎥ ×⎢x ⎥ =⎢ ⎢ ⎥ ⎢ i ⎥ ⎢ ⎥ ⎢ −1 1 2 1 1 ⎥ ⎢ ⎢ ⎢ ⎥ ⎣ xn ⎥ n ⎣ ⎦ ⎣ −1 1 1 2 1 ⎦ n+1 xn+1 −1 1 1 1 2 1 2 i

⎤ f1 ⎥ f2 ⎥ ⎥ fi ⎥ ⎥. ⎥ fn ⎦ f n+1

(15)

It is easily verified that the matrix B in the system (15) has the structure of the matrix B from Eq. (10) and differs only in the dimension. Analytically determine the unknown x a and x i , i = 2, n + 1 in the system (15) taking into account the dependences (12)–(14), in which the dimension n is increased by one. New unknown x n+1 determined from the last equation of the system (15) 2xn+1 − xa +

n .

xi = f n+1 ,

i=2

or 2xn+1 = f n+1 + f 1 − r/(n + 2) −

n . i=2

f i − r (n − 1)/(n + 2).

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Seeing that f1 −

n .

f i = r + f n+1 ,

i=2

we get the result xn+1 = f n+1 + r/(n + 2).

(16)

Unknown x a is determined from the first equation of the system (15) 2xa −

n+1 .

xi = f 1 ,

i=2

which, with considering (12)–(14) and (16), is transformed into a form 2xa = f 1 +

n+1 .

f i + r n/(n + 2),

i=2

or 2xa = 2 f 1 − r + r n/(n + 2), and as a result xa = f 1 − r/(n + 2). The dependence for x i in system (15) is determined from equation n .

2xi − xa +

xk = fi ,

k=2; k/=i

which is converted taking into account (12)–(14) and (16), (17) to the form n+1 .

2xi = f 1 −

f k − r n/(n + 2) + f i .

k=2; k/=i

Applying the identity f1 −

n+1 . k=2; k/=i

fk = r + fi

(17)

Development of Top-down and Bottom-up Methodology Using Risk …

11

we get the final xi = f i + r/(n + 2).

(18)

Dependencies for x m , m = 2, n, m /= i are obtained analogously to (18) with insignificant differences in their definition, and as a result, taking into account (16), formula (18) is true for all i = 2, n + 1. The validity of the dependences (16)–(18) is also confirmed by their direct substitution into the system (15). In particular, for the equation I, we have − f 1 + r/(n + 2) +

n+1 .

f k + r n/(n + 2) + f i + r/(n + 2) = f i .

k=2

Taking into account (14) we obtain the expression −r + f i + r (n + 2)/(n + 2) = f i , which is an identity. Thus, the dependences (12)–(14) are the solution of the system of Eq. (10). However, their substitution in Eq. (4) does not satisfy him and gives an error xa −

n .

xi = r/(n + 1).

(19)

i=2

This is quite natural, because the system (3), (4) does not have, as noted, an exact solution. However, it is noteworthy that the error r in the forecasts f, i = 1, n due to transformations (7)–(9) in the system (10) decreases according to (19) by n + 1 times. Therefore, it seems appropriate to organize the iterative process to ensure Eq. (4) Bx (1) = f , Bx (2) = x (1) , . . . , (m−1)

Bx (m) = x (m−1) , ||x||

(m)

− ||x||

≤ ε,

(20)

where E—permissible error, m—number of iterations. Decision x(1) after the first iteration in the form (12)–(14) already found. After the second iteration, it looks like ) ( 1 1 r, + x (2) = f − 1 a n + 1 (n + 1)2 ) ( (21) 1 1 x (2) + r, i = 2, n. = f + i i n + 1 (n + 1)2

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The solution of the iterative process (20) for the m-th iteration is determined using the method of complete induction. Considering (21), there is reason to assert that after the m-th iteration process (20) will provide a solution xa(m) = f 1 − s(m)r,

(22)

xi(m) = f i + s(m)r, i = 2, n,

(23)

s(m) =

m .

1/(n + 1)k .

(24)

k=1

According to the method of complete induction, the solution after the m + 1 iteration should have the same form as in (22)–(24) with the difference that in it instead of the value of m will appear m + 1. According to (12)–(14) and using (20), (22)–(24), the solution after the m + 1 iteration is represented in the form ) ( n . 1 (m) (m) xi = − , x − n+1 a i=2 ) ( n . 1 (m+1) (m) (m) (m) xi xi = xi + . x − n+1 a i=2

xa(m+1)

xa(m)

(25)

(26)

Dependence (25) is revealed using (22)–(24): xa(m+1) = f 1 − s(m)r − (1/(n + 1)) ) ( n . × f 1 − s(m)r − ( f i + s(m)r ) i=2

= f 1 − r/(n + 1) − (1 − 1/(n + 1) − (n − 1)/(n + 1))s(m)r. Seeing that (1 − 1/(n + 1) − (n − 1)/(n + 1)) = 1/(n + 1), and s(m)/(n + 1) =

m+1 . k=2

dependence (27) is transformed into form

1/(n + 1)k ,

(27)

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13

x (m+1) = f 1 − s(m + 1)r, a which is according to the method of complete induction and confirms correctness of (22). The correctness of the dependence (23) is proved similarly. To further use solutions (22), (23) it is necessary to determine the sum (24) with an unlimited increase in the number of iterations m, i.e., it is necessary to establish a convergence limit c(n) = lim s(m) = lim m→∞

m→∞

m . ( ) 1/(n + 1)k .

(28)

k=1

) . ( k Series m coincides with all the attribute. k=1 1/(n + 1) The limit of convergence is determined by the assumption with its subsequent verification. Suppose that such a limit is a quantity c(n) = 1/n.

(29)

This assumption is justified, in particular, by the fact that the amount 4 .

1/(n + 1)k =0.0999931 at n = 10.

k=1

To prove (29) we form according to (24) the difference between c(n) and the partial sum s(m), which at m → ∞ must turn into zero p(m) = c(n) − s(m).

(30)

(Value p(m)) at m = 1 is equal to p(1) = 1/(n(n + 1)) and at m = 2 p(2) = 1/ n(n + 1)2 . By the method of complete induction we assume that the value of p(m) has the form ) ( p(m) = 1/ n(n + 1)m ,

(31)

and prove that this expression is valid for a series with m + 1 members, i.e., ) ( p(m + 1) = 1/ n(n + 1)m+1 . Denote n + 1 = ω then according to (30) we establish ( p(m + 1) = ω

( m+1

− (ω − 1)

m . k=0

)) ω

k

) ( / (ω − 1)ωm+1 .

(32)

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Revealing the amount

.m k=0

ωk , we receive

(ω − 1)

m .

ωk = ωm+1 − 1.

k=0

As a result ) ( p(m + 1) = 1/(ω − 1)ωm+1 = 1/n(n + 1)m+1 . This dependence proves that expression (31) is valid for all positive integers m. In this regard lim p(m) = lim 1/(n + 1)m = 0, that is, the dependence (29) is m→∞

m→∞

true. Thus, the dependence (31) is valid for all positive integer m. Then lim p(m) = m→∞

1 lim m = 0 at all positive integers n and m, and the dependence (21) is true. m→∞ n(n+1) The consequence of this is that the dependences (22), (23) take the form

xa = f 1 − r/n,

(33)

xi = f i + r/n, i = 2, n.

(34)

Substitution of dependences (33), (34) satisfies Eq. (4). However, although the problem of discrepancy for this set of problems has been overcome, the model (10), (33), (34), which solves it (the problem), provides not one but n − 1 solution. Indeed, if in system (3) with dimension n it is equivalent to combine any two equations of level . DOWN, we obtain a system with dimension n − 1, in which the values f 1 and ni=2 f i will be unchanged, i.e., r will not change either. But the decision xa will be determined not by dependence (33), but by another, xa = f 1 − r/(n − 1). Repeating this procedure until exhaustion, we obtain a system of n − 1 solution ⎫ ⎪ ⎪ ⎪ ⎪ = f 1 − r/(n − 1),⎪ ⎪ ⎬

x (n) a = f 1 − r/n, x (n−1) a ···

,

(35)

x (k) a = f 1 − r/k, k = 2, n.

(36)

x (3) a x (2) a

= f 1 − r/3, = f 1 − r/2,

⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭

or in a compact form

Thus, as a result of transformations (10)–(14), (20), (33), (34) of the original system of Eqs. (3)–(4) n − 1 solution for the indicator is obtained xa top level. That

Development of Top-down and Bottom-up Methodology Using Risk …

15

is, there is a problem of choosing the best of them from a set of solutions (36). A similar problem applies to sectoral indicators xi (34). According to the review of literature sources related to these problems of choice, they (problems) can be solved quite effectively by minimizing a certain mathematical form that is a function of risk [7–12]. This approach provides an approximation of the set of solutions, in particular, (36) one value of xa , which may differ from each solution x (k) a , k = 2, n. The module of such discrepancy serves as a measure of the risk of applying the selected risk function and provides an opportunity to determine the best solution from the set of acceptable ones. The performed literature analysis shows that the most popular risk function is the least squares functional and its modifications. Therefore, in this study the determination of the optimal values of the indicators as the top xa , and lower x i , i = 2, n levels is performed on the basis of the risk function by the classical method of least squares.

4 Determining the Best Solutions for the Upper and Lower Levels Based on the Least Squares Risk Function According to the method of least squares to determine the best solutions from the set (36) must first find a solution x, which minimizes functional in the form of the sum of squares of inconsistencies ϕ(x a ) =

n . (

x a − xa(k)

)2

→ min, k = 2, n.

(37)

k=2

For a fixed n, the functional (37) will have a minimum value when derived dϕ(x a )/d x a will be zero. This feature allows you to find the value x as x a = f 1 − S(n)r,

(38)

S(n) = C(n)/(n − 1),

(39)

where

C(n) =

n .

(1/k).

(40)

k=2

Having a dependency for x in the form (38), we can determine the overall dependence for sectoral indicators x. We will look for this dependence in the form x i = f i + a(n)r, i = 2, n.

(41)

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A. Zagorodny et al.

Then condition (4) takes the form xa −

n .

( f i + a(n)r ) = 0,

i=2

or f 1 − S(n)r −

n .

f i − (n − 1)a(n)r = 0,

i=2

whence we have finally (n) = (1 − S(n))/(n − 1).

(42)

The direct substitution of solutions (38) and (42) satisfies Eq. (4). That is, the decisions received on the basis of method of least squares, satisfy the basic requirement of the set task concerning equality of the T-level indicator of the sum of indicators of the DOWN level. Constants S(n) and a(n) are used not only to determine the values x a (38) and x i (41). In the future it will be shown that they are also needed when calculating the values of risks. Therefore, these constants are tabulated and listed in Table 1 for n from 2 to 20 inclusive. Dependencies x a (38) and xa(k) (36) provide an opportunity for the upper level indicators to determine the discrepancies from the functional (37) at a fixed n, namely. .a(k) = x a − xa(k) = (1/k − s(k))r, k = 2, n.

(43)

The set of discrepancies (43) has n − 1 values. From this set we choose the maximum modulo | (k) | |. | a max(k) = Ra (n) = |(S(n) − 1/n)r |.

(44)

In dependence (44) there is always (Table 1) inequality S(n) > 1/r , but r can be negative. In the future, the value Ra (n) will be used as a measure of risk (risk) when choosing the best solution from the set (36). The set of discrepancies for sectoral indicators is similar (43) .i(k) = x i − xi(k) = (a(n) − 1/k)r, k = 2, n , i = 2, n,

(45)

and the measure of risk (risk) for each of n − 1 of these sets is similar to the form (44) | | | | R(n) = |.i(k) | = |(a(n) − 1/n)r |, i = 2, n. (46) max(k)

0.202

0.0798

S(n)

a(n)

11

–

–

a(n)

1

0.5

0.5

0.0735

0.1912

12

2

Number of forecasts (n)

S(n)

Constants

Table 1 Constants S(n), a(n)

0.0682

0.1817

13

0.2917

0.4167

3 0.3611 0.213

0.0636

0.1732

14

4

0.0596

0.1656

15

0.1698

0.3208

5 0.29 0.142

0.0561

0.1587

16

6 0.2655 0.1224

0.053

0.1525

17

7

0.2454 0.1078

0.0502

0.1468

18

8

0.2286 0.0964

0.0477

0.1415

19

9

0.0454

0.1367

20

0.0873

0.2143

10

Development of Top-down and Bottom-up Methodology Using Risk … 17

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A. Zagorodny et al.

Using the dependencies for risks (43), (46) and indicators of Table 1 for S(n) and a(n). such important generalizations can be made. When using the least squares approximation for solutions of both the upper and sectoral levels, there are two values on the numerical axis n in which these risks are zero. These are points n = 2 and n = ∞. Point n = ∞ provides a formal. degenerate solution. because at this point the constants S(n) and a(n) reach zero values. As a result. a top-level decision is made x = f 1 . and sectoral decisions— x i = f i , i = 2, n , that is, at this point system (3), (4) degenerates into the initial system (3). At the point n = 2 according to Table 1 constant S(n = 2) = a(n = 2) = 1/2, and therefore risks Ra (n = 2) = R2 (n = 2) = 0. Thus, when approximating solutions of both upper and sectoral levels by the method of least squares, many solutions are obtained x(n) and x(n) power ( n − 1), among which the best in terms of risk are solutions x a (n = 2) and x i (n = 2), at the same time their risks Ra (2) and R2 (2) equal to zero. In the range of values 2 < n < N < ∞ the risk measures of these indicators are greater than zero. Therefore, to obtain the most reliable indicators of both upper and lower levels, you need to use the following comprehensive method. 1. On the first stage the original system of dimension n is aggregated into a system of dimension m = 2. 2. Top level indicator x a it is fixed as x a = f 1 − r/2 .

(47)

3. On the second stage the system is disaggregated with dimension m = 2 into the original system with dimension n. The following operations are performed. Sectoral adjustment factors are determined μi = f i / f s , f s =

n .

f i , i = 2, n.

(48)

i=2

4. The values of sectoral corrections are calculated pi = μi r/2 , i = 2, n .

(49)

5. Sectoral decisions are determined x i = f i + pi , i = 2, n .

(50)

Solutions (47), (48) provide the basic Eq. (4). Indeed, making their substitution in (4), we obtain n .

xi =

i=2

given (47) we have

n . i=2

fi +

n . i=2

μi r/2 = f s + (r/2 f s )

n . i=2

f i = f s + r/2;

Development of Top-down and Bottom-up Methodology Using Risk …

19

Table 2 The influence of the dimension of the system n on its solution x a (n), x i (n) and risks Ra (n), Ri (n) (f 1 = 200, r = 30, f i = 15) n

S(n)

x(n)

x(n)

Ra (n)

Ra (n), %

a(n)

x(n)

x(n)

Ri (n)

Ri (n), %

2

0.5

185

185

0

0

0.5

30

30

0

0

3

0.4167

187.5

190

2.5

1.3

0.2917

23.75

25

1.25

5.3

4

0.3611

189.2

192.5

3.3

1.7

0.213

21.39

22.5

1.11

5.2

5

0.3208

190.4

194

3.6

1.9

0.1698

20.09

21

0.91

4.5

6

0.29

191.3

195

3.7

1.9

0.142

19.26

20

0.74

3.8

10

0.2143

193.6

197

3.4

1.8

0.0873

17.62

18

0.38

2.2

15

0.1656

195

198

3

1.5

0.0596

16.79

17

0.21

1.3

20

0.1367

195.9

198.5

2.6

1.3

0.0454

16.36

16.5

0.14

0.9

f 1 − r/2 = f s + r/2; f 1 = f s + r ; f 1 = f 1 . This substitution gives identity, i.e. requirement (4) is satisfied. The obtained identity also gives grounds to claim that the application of the least squares method to approximate the solutions of the initial system (3), (4) provides solutions (47). Equation (50) with zero risks. At the end of the study, it is also advisable to analyze the risks and behavior of upper and lower level decisions in cases where the dimension of the system lies in a wide range 2 < n < ∞. In the Table 2 shows the results of such calculations for systems with dimensions from 2 to 20. For comparative analysis for all n the same data were selected: f 1 = 200, r = 30 and one sectoral indicator f i with value f i = 15. In the whole range n = 3 ÷ 20 decision x a (n) is less important than the decision x a (n). This is due to the fact that in this range is a constant S(n) exceeds 1/n. Comparison of solutions x i (n) and x i (n) in the same range n shows the same trend, x i (n) 0 , { } f (e) = f ∈ F : n e, f > 0 . If there are several objects that depend on one characteristic, then binary search should be used to find the required object. In the case of searching for characteristics of N alternatives, the number of binary queries q can be given by the formula q = log2 (N ). Establishing associated relationships between objects e and characteristics f minimizes the number of requests: ( q = log2

) |E| . |e( f )|

(1)

The presence of additional associations n e, f can be expressed in terms of the number of additional binary queries in order to further establish links with the required object. The increase in additional requests can be expressed as follows ( ) k = 1 + log2 n e, f .

(2)

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Thus, taking into account (1) the characteristic f significance for the object e and the importance factor (2), a significant number of binary queries can be represented as (3): ( ( )) I (e, f ) = 1 + log2 n e, f · log2

(

) |E| . |e( f )|

(3)

Using (3) allows one to predict the number of questions of existing objects e with different characteristics f . During studying the objects proximity degree E 1 and E 2 , it is necessary to use the basic laws of vector algebra, consider the distance between the vectors (V (e1 , f ), V (e2 , f ), ...), because each object e can be assigned weight V (e, f ). V (e, f ). Assessment of the distance between objects for each characteristic can be represented as follows . f

d(e1 , e2 ) = . f

|V (e1 , f ) − V (e2 , f )|

max(V (e1 , f ), V (e2 , f ))

.

(4)

Distance (4) depends on the number of existing characteristics, if it is normalized on the interval by dividing by the largest value of the distance, the dependence can be avoided [2, 4, 8]. Thus, a large-scale set of objects (domains, users, energy resources, reports, geolocations, etc.) and a data features repository (values of indicators, parameters, documents for data processing, dictionaries, etc.) are formed.

5.3 New Approach to the Search for Parameter Values in the Analysis of Energy Sector Data During BD processing in practice, the problem arises in maximizing the minimum value of the array after performing the specified operations. Let’s consider the operations of triple and double multiplication often used in the analysis of data in the energy sector [17, 18]. This is because when parameter values and their backups are stored, the distance between objects increased in 2 or 3 times. A successful solution of this problem lies in the use of software tools based on binary search. Let’s consider a binary search algorithm in the range [1, max(array)]: (1) let f = 1, while l—maximum element of the array, and res as INT _MIN; (2) perform a binary search at f ≤ l; (3) check if mid is the minimum element. For this its necessary to perform the “is_possible_min()” operation; (4) in the “is_possible_min()” function, it is necessary to iterate over the elements from the end (N-1) of the array to index 2 and check if “arr [i] < mid”. Then return 0 if the condition is performed. Otherwise, it’s necessary to calculate

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Fig. 1 Software implementation of the algorithm in the Python environment

the value 3 × which is attached to arr[i-1] as x and arr[i-2] as 2x. Next, it’s necessary to check the truth of the arr [0] ≥ mid and arr [1] ≥ mid conditions and output 1. Otherwise, it’s nesessary to return 0. The implementation of the described algorithm is shown in Fig. 1. If the “is_possible_min()” function evaluates to true when the algorithm is performed, then the mid value exists. Since the minimum value of max(res, mid) is stored in the res variable, it can be maximized the minimum value by moving to the right on step f = mid + 1. Otherwise, it can be tried moving left on step l = mid − 1. The computational complexity of mathematical operations for the proposed algorithm is defined as O(N*log(maxval)), where N—dimension of the original array, and maxval—maximum element of the array. Adequate processing power must be used to achieve the required speed of operations. In practice, this can be hundreds or thousands of servers that are capable to distribute data and to work together in a cluster architecture (Hadoop, Apache Spark). To date, establishing a high speed of computing in a cost-effective way is a rather problematic task.

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6 Discussion Conducting research within the framework of the topic of this section has shown that in connection with the rapid development of the latest technologies, a large-scale information accumulation is taking place. Using methods of BD analysis, humanity can qualitatively and quickly exctract benefit from this data array. The common advantage of BD is the provision of better services for the population, since each existing link in the public or private structure has the ability to optimize its processes. It has been established that BD arrays, in most cases, remain in an unprocessed form, and if further use is necessary, processing is carried out with the involvement of software or intelligent data processing. As confirmation, a binary search algorithm is presented to maximize the minimum value of the array. The mathematical representation of BD arrays arising in the energy sector in the form of a multidimensional hypercube model is detailed. The process of BD consolidating for analyzing and forecasting the development of the energy complex allows generating the following tasks: • growth of optimization of data receipt, processing and further use for making managerial decisions on energy facilities; • building new strategies for the development of the energy industry through the data analysis that are not included in the reports and are not taken into account during decision making; • regular monitoring of negative development trends for their further elimination. To ensure an integrated approach to the information analysis on energy facilities, it is necessary: (1) to store and to manage BD; (2) to process information from different databases (relational, multidimensional, XML, NoSQL, structured, unstructured, etc.); (3) to use combined approaches to obtain information data. The need for regular processing and BD high-speed transmission has led to a number of requirements for the original computing infrastructure. To avoid overloading a server or server cluster, the computing power provided for BD processing and transmitting must meet the established requirements. To create a local BD system, it is appropriate to use Apache open source technologies in addition to Hadoop and Spark, which contain the following structural elements: YARN (built-in resource manager and Hadoop work scheduler); MapReduce programming program, which is also the main component of Hadoop; Kafka (messaging platform and data transfer from program to program); HBase databases; SQL-on-Hadoop query systems such as Drill, Hive, Impala and Presto. For example, the use of the latest Hadoop-based appliances allows you to create a customized computing structure for implementing BD projects, where hardware and software are kept to minimum. Thus, the transfer of local BD sets and their processing is a rather cumbersome process for energy companies. This is due to ensuring the availability of data for

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analysts, in particular in distributed environments, which are a combination of diverse platforms and data storages. The solution is possible through the development of data catalogs containing metadata management functions and data line functions. That is, data quality and data management must be a priority to ensure that BD sets are used in a trustworthy manner.

7 Conclusions The chapter provides a rationale for the relevance of using BD technologies to improve the quality of the functioning of production processes in relation to energy facilities. The main directions of digitalization of the energy industry are considered and the main approaches to the further development of the energy complex are identified. Mathematical tools for BD representing and processing are analyzed, in particular, a multidimensional model in the form of a hypercube is considered in detail. A software implementation of the binary search algorithm for maximizing the minimum value of an array is presented. It has been established that the allowable dimensional values define the cells of the hypercube, which in practical use can be located densely or sparsely. Sparsity of the hypercube arises in the case of an increase in the number of dimensions and the establishment of measurement values. It should be noted the advantages and disadvantages of existing models for BD representing, namely: a multidimensional model allows to visualize and analyze data, along with this, the sparsity of a hypercube with heterogeneous data is a significant disadvantage during calculations; object model requires modification for the use of extensive data; the graph model is used to analyze and establish links between objects of a small number, since the computational complexity of search algorithms increases. Thanks to the successful analysis and BD processing, it is possible to achieve ultraaccurate forecasts to assess the effectiveness of production activities in a particular area. In addition, it can be determined the current geolocation for energy facilities and the necessary equipment; calculate the minimum and maximum loads in the network; effectively allocate the use of energy resources, etc. The conducted studies suggest that one of the topical areas of using BD technologies in the energy complex of Ukraine can be monitoring the functional state of power units to improve their operational properties. In general, the creation of a multi-level system for diagnosing and predicting the technical condition of energy facilities (turbines, pumps, substations, etc.) opens up new prospects for the development of the industrial infrastructure of the country. Therefore, the use of BD technologies in the energy sector is not only a tool for data processing and well-predicted management decisions, but also a promising way to transform the energy complex as a whole.

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References 1. Cavanillas, J.M., Curry, E., Wahlster, W.: New horizons for a data-driven economy. A roadmap for usage and exploitation of big data in Europe. In: Big Data Usage I. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-21569-3_8 2. Mashey, J.R.: Big data... and the next wave of infrastress. Slides from invited talk (2020) 3. Cha, J.M., Shin, J., Yeom, C.S.: A review on applicability of big data technology in nuclear power plant: focused on O&M phases. In: Transactions of the Korean Nuclear Society Spring Meeting (2015) 4. Vlasenko, R.V.: Big data concept in Ukraine: prospects for use in governmental bodies. Derzhava ta rehion 4(60), 97–101 (2017) 5. Roh, S.: Big data analysis of public acceptance of nuclear power in Korea. Nucl. Eng. Technol. 49(4), 850–854 (2017). https://doi.org/10.1016/j.net.2016.12.015 6. Jalal-Kamali, A., Hossain, M.S., Kreinovich, V.: How to Understand Connections Based on Big Data, T.10., pp. 63–87. Department of Computer Science, University of Texas at El Paso, El Paso (2014) 7. Elshenawy, L.M., Mohamed, A., Halawa, et al.: Unsupervised machine learning techniques for fault detection and diagnosis in nuclear power plants. Department of Industrial Electronics and Control Engineering, Faculty of Electronic Engineering, Menoufia University, Egypt (2021). https://doi.org/10.1016/j.pnucene.2021.103990 8. W., Qingyang, Li, G., Yan, J., Deguchi, Y.: Analysis of critical pipe break sizes leading to reactor pressure vessel liquid level collapse and core uncovery with APROS. Prog. Nucl. Energy 142, 104016 (2021). https://doi.org/10.1016/j.pnucene.2021.104016 9. Shakhovska, N., Veres, O., Bolubash, Y., Bychkovska, L.: Big Data information technology and data space architecture. Sens. Trans. 195(12), 69 (2015) 10. Sverdlova, A., Zaporozhets, A., Bohachev, I., Popov, O., Iatsyshyn, A., Iatsyshyn, A., Hrushchynska, N., et al.: Self-organizing network topology for autonomous IoT systems. In: CEUR Workshop Proceedings, vol. 2850, pp. 57–70. http://ceur-ws.org/Vol-2850/paper4. pdf (2021) 11. Zaporozhets, A., Babak, V., Sverdlova, A., Isaienko, V., Babikova, K.: Development of a system for diagnosing heat power equipment based on IEEE 802.11 s. In: Systems, Decision and Control in Energy II, pp. 141–151. Springer, Cham (2021). https://doi.org/10.1007/978-3030-69189-9_8 12. Kotenko, S., Nitsenko, V., Hanzhurenko, I., Havrysh, V.: The mathematical modelling stages of combining the carriage of goods for indefinite, fuzzy and stochastic parameters. Int. J. Integr. Eng. 12(7), 173–180 (2020) 13. Kalinichenko, A., Havrysh, V., Perebyynis, V.: Sensitivity analysis in investment project of biogas plant. Appl. Ecolo. Environ. Res. 15(4) 14. Havrysh, V., Kalinichenko, A., Mentel, G., Mentel, U., Vasbieva, D.G.: Husk energy supply systems for sunflower oil mills. Energies 13(2), 361 (2020). https://doi.org/10.3390/en1302 0361 15. IBM What is big data?—Bringing big data to the enterprise [Electronic Resours]. Access mode: www.ibm.com 16. Laney, D.: 3D Data Management: Controlling Data Volume, Velocity and Variety [Electronic Resours] / D.Laney. Access mode: https://blogs.gartner.com/doug-laney/files/2012/01/ad9493D-Data 17. I.C., Leshchenko: Levelised cost of hydrogen production in Ukraine. Prob. General Energy 2(65), 4–11 (2021). https://doi.org/10.15407/pge2021.02.004 18. Maliarenko, O.Y., N.Y., Maistrenko, Horskyi, V.V.: Forecast of fuel and coal consumption in Ukraine until 2040 by a complex method of forecasting energy consumption. Problems General Energy 3(66), 28–35 (2021). https://doi.org/10.15407/pge2021.03.028

Parametric Identification of Dynamic Systems Based on Chaotic Synchronization and Adaptive Control Artem Zinchenko

Abstract In this chapter algorithm of parametric identification based on chaotic synchronization and adaptive control is offered. It’s shown that noise influence on the nonautonomous dynamic system which is near to border of a synchronous mode establishment, leads to appearance in time realization intervals of synchronous dynamics interrupted with asynchronous intervals. Numerical simulations on Rössler system are presented to demonstrate the effectiveness of the proposed approach. Furthermore, the principal possibility of use of a method on small samples during observing a function from all system coordinates is shown. It also demonstrates results of comparison from a time delay method on which basis full reconstruction of Lorenz dynamic system is made. Keywords Parametric identification · Chaotic synchronization · Adaptive control · Rössler system · Lorenz system

1 Introduction Investigation of nonlinear dynamics in spatially distributed systems of different physical nature (in thermal physics, chaotic advection, hydromechanics, geophysics, chemistry, etc.) and identification of parameters and structures of mathematical models of complex processes and systems, based on accurate and incomplete measurements, is actively studied and attracts the attention of many researchers in recent times [1–4]. In this area, the interest of research is due to the great fundamental and practical value of this issue due to the fact that most important systems are dissipative, distributed and demonstrate complex, including chaotic modes of oscillation. Many problems of radiophysics, plasma physics, nanoelectronics, ecology, etc. are reduced to the analysis of space-continuous models that demonstrate space– time chaos and the processes of structure formation. The task of the investigation

A. Zinchenko (B) Kyiv International University, Kyiv, Ukraine e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_7

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is quite complicated if the information about the studied object is limited to a onedimensional implementation of one of the coordinates of the system or the presence of only the observed scalar time sequences (incomplete measurements). In this case, an algorithm of global reconstruction was proposed in [4] to build mathematical models which is implemented in several stages. At the first stage, it was visualized the series, highlight the trend, identify the transition mode, the process of data accumulation, the steady process of chaotic fluctuations, identify and analyze chaotic dynamics. In the second stage, we determined the dimension of the embedding space, time delay and reconstruct closed trajectories using Takens’s and Whitney’s embedding theorems for the scalar realization xi = x(i.t), i = 1, . . . , N of the system. In the third stage, we a priori defined a system of ordinary 1st-order differential equations of the selected structure and determine the evolution operator, for example, by the least squares method (LSM). For accurate data obtained from the chaotic mode of a dynamic system, we can skip the first step. It is clear that reconstruction algorithms (for example, the method of sequential differentiation) significantly depend on the error of approximation by regression analysis (for example, the recurrent LSM), the accuracy of derivative calculations, the presence of noise in data limiting the use of algorithms for large embedding spaces. Therefore, the reconstruction of nonlinear dynamic systems is not always successful, and the most common problems are the tasks of automatic nonlinear control—parametric identification with a known structure of the system. This paper considers the application of chaotic synchronization [5, 6] and adaptive control [7] to the problem of parametric identification. To accelerate the synchronization of unidirectional oscillators, it is proposed to use a relay algorithm which is a partial case of the standard high-speed pseudo-gradient algorithm. In addition, instead of the standard vector function of the rate of change of a smooth objective function, it is proposed to use a class of functions (for example, trigonometric) that fully satisfies the conditions of pseudo-gradient algorithm, the conditions of reachability, the conditions of existence of "ideal control" and the convexity of the feedback function on the corresponding state vector of the controlled system. The importance of the study of the zero Lyapunov exponent is shown. The example of the Lorentz system shows the efficiency of the vector function in comparison with the standard one. In addition, on the example of this system, parametric identification was performed by observing not only one coordinate of the system but function from all coordinates. For this case, the formulas are derived and the conditions of convergence of the method are given. Furthermore, on the example of the Lorentz system, we are showed the possibility of applying the algorithm for small samples, in particular, the results of the convergence of the method when observing the function from all coordinates of the system. To test the effectiveness of the algorithm, the results are presented to demonstrate comparing the proposed method with the standard based on approximations. In addition, based on the latter method, an example of a complete reconstruction of the dynamic Lorentz system is showed when observing the function from all coordinates of the system. The structure of the article is as follows: the first part provides general information about the chaotic synchronization of two oscillators and about the zero Lyapunov

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exponent, modifications are proposed to accelerate the convergence of the method; the second part presents the structure of the algorithm with proposals and it considers the standard method of identification from the family of approximation methods; the third part presents the results of the study.

2 Chaotic Synchronization of Two Unidirectional Coupled Oscillators Recently, there has been great interest in the study of synchronization in complex nonlinear systems consisting of a large number of elements with different connections. Currently, the basic laws of the phenomenon of chaotic synchronization are well studied for systems with a small number of degrees of freedom. There are several different types of synchronous behavior of connected chaotic systems: complete, generalized, noise-induced, asymptotic, phase, time-scale synchronization, and others. However, the use of chaotic synchronization for parametric identification of spatially continuous high-order self-oscillating systems is a new area of research, little studied and first proposed in [8–10]. That is why there is a need to give own definition of synchronization of dynamic systems for parametric identification. . Let’s consider k dynamic systems i (i = 1, . . . , k), each of which is formally described by 6 parameters: .

= {T , Ui , X i , Yi , φi , h i }, i = 1, . . . , k,

i

where T – total set of time points; Ui , X i , Yi – set of inputs, states and outputs, respectively; φi : T × X i ×Ui → X i – display of transitions; h i : T × X i ×Ui → Yi — display of outputs. Assume that given l functionals g j : ϒ1 ×ϒ2 ×· · ·×ϒk ×Ti → R1 , i = 1, . . . , l. Here ϒi are the sets of all functions on T with values in ϒi , so ϒi = {y : T → Yi }. We will assume that the set of moments T is either a positive axis T = R1 (continuous time) or a set of natural numbers T = 1, 2, . . . (discrete time). For any τ ∈ T we define στ as a shift operator on τ, so στ : ϒi → ϒi is defined y(t +τ) for any y ∈ ϒi and t ∈ T. Let yi (·) denotes the output function as (στ y)(t) = . t ∈ T , i = 1, . . . , k. Let x (1) (t), . . . , x (k) (t) of the system i :yi (t) = h(x .i (t), t),. are solutions of the system 1 , . . . , k defined for all t ∈ T with initial states x (1) (0), . . . , x (k) (0), respectively. Then we can define the synchronization of dynamic systems. . . Definition 1 In systems 1 , . . . , k , processes x (1) (t), . . . , x (k) (t) will be called synchronized (and systems will be called fully synchronized) in relation to functionals g1 , . . . , gl , if the identities of g j (στ1 y1 (·), . . . , στk yk (·), t) ≡ 0, j = 1, . . . , l are true for all t ∈ T and some τ1 , . . . , τk ∈ T .

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. . Definition 2 We will also call the 1,..., k systems asymptotically synchronized in relation to functionals g1 , . . . , gl , if for some τ1 , . . . , τk ∈ T lim g j (στ1 y1 (·), . . . , στk yk (·), t) = 0, j = 1, ..., l. t→∞

. . Definition 3 Let’s call systems 1 , . . . , k approximately synchronized with respect to functionals g1 , . . . , gl , if there exists ε > 0 and τ1 , . . . , τk ∈ T , such that inequalities || || ||g j (στ y1 (·), . . . , στ yk (·), t)|| ≤ ε, j = 1, . . . , l 1 k performed for all t ∈ T . In our further studies, we will focus on the problem of asymptotic coordinate synchronization or global exponential synchronization, which is optimal with respect to convergence and synchronization errors [11, 12] for the parametric identification of dynamical systems. We will understand it as the fulfillment of the relation || || lim ||x (1) (t) − x (2) (t)|| = 0,

t→∞

(1)

where x (1) , x (2) —state vectors of synchronized dynamic systems. Let us describe a general method for solving such problem. For simplicity, let’s assume that there are two subsystems described by affine models: x˙1(1) = f 1 (x1(1) ) + g1 (x1(1) )u 1 , x˙1(2) = f 2 (x1(2) ) + g2 (x1(2) )u 2 .

(2)

The original systems are not interconnected. We pose the problem of asymptotic coordinate synchronization of subsystems—to find a control algorithm u i = Ui (x1(1) , x1(2) ), i = 1, 2 to ensure the control goal (1). The solution of the problem is trivial if the right parts of (2) can be changed arbitrarily and independently, that is, if the following conditions are satisfied m = n,g1 (x1(1) ) = g2 (x1(2) ) = In , where In —identity matrix n × n. Then, taking, for example, u 1 = 0, u 2 = K (x1(1) − x1(2) ), where K > 0—amplification factor, we obtain the synchronization error equation in the form: e˙ = f (x1(1) (t)) − f (x1(1) (t) − e) − K e,

(3)

where x1(1) (t)—solution of the first Eq. (2) on a given time interval at u 1 = 0. If the Jacobi matrix A(x (2) ) = ∂ f(2) (x (2) ), j = 1, . . . n is bounded in some zone . ∂x j

containing a solution to system (2), then for sufficiently large K > 0 the eigenvalues of the symmetric matrix A(x (2) ) + A T (x (2) ) − 2K In lie to the left of the imaginary axis at x (2) ∈ .. In this case, the system itself will have the property of convergence in .,, that is, all its trajectories lying in ., coincide at t → ∞ to a single limited solution. And since e(t) ≡ 0 is such a solution, then all trajectories converge to it.

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Thus, the synchronization of two systems takes place when the feedback between the subsystems whose parameters should be estimated is strengthened. Note that the smoothness of the right-hand sides and the existence of the Jacobian matrix are not required of | systems: |it is sufficient to require the Livshitz | | for synchronization | | | (1) (2) | condition | f (x1 ) − f (x1 )| ≤ L |x1(1) − x1(2) | to be satisfied for some L > 0 [12]. As a control algorithm (adaptation method) in this work, a relay (sign) algorithm was chosen, which is a special case of the standard velocity pseudogradient algorithm [12]. The latter is written like this: u(t) = u 0 − γψ(x(t), u(t)), where γ > 0—scalar step multiplier (amplifier factor or feedback constant), u 0 —some initial (reference) control value (usually u 0 = 0), and vector-function ψ(x, u) satisfies the pseudogradient condition ψ(x, u)T ∇u w(x, u) ≥ 0, where w(x, u)—velocity change of a smooth objective function (feedback function), and ∇u = { ∂u∂ 1 , . . . , ∂u∂ n }T —gradient vector. Since to estimate the parameters of the leading system in the state vector xi , i = 1, . . . , n, the control is u = xi' , where xi' — corresponding state vector of the controlled system, then the relay (sign) algorithm will take the form: x˙ i' (t) = f i (x ' ) − γ sign∇xi' w(x(t), x ' (t)),

(4)

where sign for a vector is understood as by component, for state vector x ' = col(x1' , . . . , xn' ) we have sign(x ' ) = col(sign(x1' ), . . . , sign(xn' )). For the convergence of this algorithm, a number of conditions are required [12], the main of which are the convexity of the function w(x, x ' ) at xi' and the existence of an “ideal control”—vector x∗' such that the condition w(x, x∗' ) ≤ 0 for all x is satisfied (accessibility condition). In numerical simulation of synchronization for the parametric identification of the Ressler, Lorentz, Van der Pol, Rayleigh and other systems, it was found that the use of some feedback functions that satisfy the above conditions accelerates synchronization and improves adaptation. So, at choosing the feedback function γsign∇xi' ar ctg(x ' (t) − x(t)), in contrast to the standard [5, 6] γ(x ' (t) − x(t)) for synchronization and proposed in [8–10] for parametric identification using synchronization, with the same choice of initial conditions, the method coincides approximately at 2 times faster. The simulation results for the example of the Lorenz system are presented below (Figs. 3 and 4). Let’s consider now the behavior of two unidirectional coupled oscillators x˙ = H (x, α), x˙ ' = G(x ' , α' ) + γw(x, x ' ),

(5)

where x = (x1 , x2 , . . . , xn ), x ' = (x1' , x2' , . . . , xn ' )—state vectors of the leading and controlled “drive-response” systems, respectively, H and G define the vector field

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of the considered systems, α and α' are parameter vectors, component w is responsible for unidirectional communication between systems, and parameter γ—feedback constant that determines the strength of the connection between these systems. The behavior of unidirectional coupled oscillators (5) for the dimensions of the phase spaces n and n ' , respectively, can be characterized using the spectrum of Lyapunov characteristics λ1 ≥ λ2 ≥ · · · ≥ λn+n ' . Since the behavior of the leading system does not depend on the state of the controlled oscillator, the spectrum of Lyapunov characteristic exponents can be divided into two parts: Lyapunov indicators of the leading system λ1 ≥ λ2 ≥ · · · ≥ λn and conditional Lyapunov indicators λ'1 ≥ λ'2 ≥ · · · ≥ λ'n ' , characterizing the behavior of the controlled system. When the feedback parameter γ is changed, the Lyapunov indicators of the leading system remain unchanged, since the dynamics of the leading system does not depend on the intensity of the connection, while the values of the conditional Lyapunov indicators change. Obviously, this approach can also be applied to describe the non-autonomous behavior of an oscillator under external influence: in this case, it is appropriate to consider only the spectrum of conditional Lyapunov indicators λ'1 ≥ λ'2 ≥ · · · ≥ λ'n ' , responsible for the behavior of systems (5), and the feedback value γ should be interpreted as a controlled parameter, which determines the amplitude of the external action. Although, as shown above, the main synchronization condition is the convergence condition: the eigenvalues of the Jacobi matrix A(x ' ) = ∂∂xf' (x ' ), j = 1, . . . , n ' j are uniformly negative for all values x ' , and this condition is much easier to verify than the condition for the negativity of all conditional Lyapunov indicators, however, the research of the Lyapunov indicators spectrum of coupled systems near the synchronization limit (of any kind) is important. Interacting systems can be characterized by both chaotic and periodic dynamics. If we consider chaotic dynamical systems, then the leading Lyapunov exponents of each of them (at least λ1 and λ'1 ) are positive. In any case, in the absence of a connection between the systems (γ = 0), in each of the spectra of the Lyapunov exponents, there necessarily exists a zero Lyapunov exponent (λi = 0 and λ'j = 0, respectively), which is responsible for the evolution of a small perturbation, which describes the displacement of the graphic point along the phase trajectory in the phase space of the considered system. In the case of periodic systems, these zero Lyapunov exponents are older (i.e. i = 1, j = 1). With an increase of the connection parameter γ between systems, the zero Lyapunov exponent of the leading system remains zero, and the conditional zero Lyapunov exponent characterizing the behavior of the controlled system can change. It is known [6], that for a system with periodic behavior in the absence of noise .0 becomes negative precisely when the controlled system is synchronized by the periodic signal (control) acting on it, which is acting on it from the side of the leading system. A more complicated situation arises when the leading system is affected by noise (deterministic or random). In this case, as shown in [13], the Lyapunov exponent .0 becomes negative even before the start of the synchronous regime, and its value depends on the feedback parameter as follows:

Parametric Identification of Dynamic Systems Based on Chaotic …

. .0 (γ) ≈

135

1 − |γ−γ , γ < γc , | c| √ | | | ln 1 − β γ − γc , γ > γc ,

where γ—feedback parameter between interacting oscillators; γc parameter corresponds to the bifurcation value of the feedback parameter, at which, in the absence of noise, the synchronous mode is established; β parameter is determined by the properties of the studied systems. The change in the sign of the Lyapunov exponent indicates, in general, the qualitative changes that have taken place in the dynamics of the system. The transition of one Lyapunov exponent to the zone of negative values is associated with the occurrence of synchronous behavior, for example, in the case of synchronization of periodic oscillations or the establishment of complete chaotic synchronization. At the same time, for coupled chaotic oscillators, when the regime of asymptotic coordinate synchronization is established, the conditional Lyapunov exponent .0 is already essentially negative [14]. Therefore, taking into account the negativity of the zero Lyapunov exponent, it must be assumed that in this case, below the phase synchronization limit, some properties of synchronous behavior should appear themselves, although the synchronization mode itself has not yet been established and, therefore, the use of parametric identification in such cases is inappropriate. That is why studies of the zero Lyapunov exponent are often used as a criterion for the established synchronous coupling and for finding the feedback parameter corresponding to the synchronization boundary.

3 Assessment of Unknown Parameters Despite the ability to successfully synchronize two unidirectional dynamical systems according to formula (4) with the fulfillment of all synchronization conditions, it is impossible to assess the unknown parameters of the leading system. For this purpose, ∂g adaptive control by an unknown parameter is used αl' = h((xi' (t) − xi (t), ∂α ' ), i = l ' ' 1, . . . n, i /= l, n = n , where αl —unknown parameter, which must be estimated. In works [9, 10, 13] it is proposed to use adaptive control (adaptive control equation) of .' ∂g the following form: αl = −δ(xi' (t) − xi (t)) ∂α ' , where δ – adaptation parameter. In l this paper, we will follow to algorithm (4). Then, in the general case, system (5) using the proposed algorithm (4) for synchronization and the equation of adaptive control over the unknown parameter αl , l = 1, . . . , n, l /= i will be written as follows: x˙ = H (x, α), x˙k' = f k (x ' , {α j | j /= l}, αl' ) − γsign∇xk' w(xk , xk' ) = f k (x ' , {α j | j /= l}, αl' ) − γsign∇xk' .(xk' (t) − xk (t)), x˙i' = f i (x ' , {α j | j /= l}, αl' ), i = 1, . . . , n, i /= k

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α˙ l' = −δsign∇xk' ar ctg(xk' (t) − xk (t))

∂ fk , ∂αl'

(6)

where xk (t)—k-th coordinate of the leading system that we observe (control or controlled variable [10]), ( f 1 , . . . , f k , . . . , f n ) = G from system (5)—controlled system. In cases of assessing unknown parameters during controlling other coordinates x, ˙ differentiation difficulties arise. In [10], the following formula was proposed for this case. Let us consider the growth of the controlled variable in one step of time discretization of the controlled system under the conditions of algorithm convergence (4): ∂ fs ' 2 ' .xk' ≈ . f k dt ≈ ∂∂ xfk' .xs' dt ≈ ∂∂ xfk' . f s (dt)2 ≈ ∂∂ xfk' ∂α ' .αl (dt) , where x s —ss s s l ' th coordinate of xk (t), equation of which consist unknown parameter αl . Then we ∂ fk ∂ fk ∂ fs can write that ∂α . In the case when the unknown parameter appears in ' ≈ ∂ x ' ∂α' s

l

l

∂ fk different coordinates of the vector x by m times, the calculation ∂α ' is made as l follows [10]. Let’s consider again the growth of the controlled variable per one step of time discretization of the controlled system under the conditions of algorithm convergence (4):

.xk' ≈ . f k dt ≈ ≈{

. ∂ fk ∂ fk ∂ fs } .αl' (dt)3 . ' ' ∂α' ∂ x ∂ x s k l m

∂ fk Then ∂α ' ≈ { l

. ∂ fk ∂ x ' ∂ fs ∂ fk ∂ fk m ' 2 .x dt ≈ . f (dt) ≈ { } .αl' (dt)2 s s ' ∂ x ' ∂α' ∂ xs' ∂ xs' ∂ x m s l m

. m

∂ fk ∂ fm ∂ fs } . Further, in order to numerically assess of the unknown ∂ xm' ∂ xs' ∂αl'

parameter αl of the leading system, it is necessary to simultaneously solve two systems (6) by an iterative method, for example, the fourth or fifth order Runge–Kutta method with a variable numerical integration step, for example, with the DormandPrince corrective procedure, which makes it possible to ensure local accuracy order of magnitude at O(10−12 )–O(10−15 ). Note that the synchronization error (3) for this method is defined as e(αl' , t) = .(xk' − xk )2 , where xk (t)—control variable. From this equation, we can write that the error in assessing the unknown parameter ∂e(α' ,t) ∂x' α˙ l' ≺ −sign∇xk' .(xk' − xk ) ∂αk' , because α˙ l' ≺ − ∂αl' . For small orders dt the l

l

gain of the controlled variable can be written as .xk' = ∂ x˙ '

∂ x˙k' .αl' dt. ∂αl'

From this α˙ l' ≺

−γ sign∇xk' .(xk' − xk ) ∂αk' . l Since the chaotic synchronization of two unidirectional coupled oscillators essentially depends on the initial conditions, the proposed scheme of the parametric identification algorithm coincides for sufficiently small sample sizes of observations of the controlled variable (about 30 basic oscillations of the Lorentz system). In this case, the final conditions for the divergence of the method are assumed by the initial

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conditions, and the method is started again. The results of the research are shown in Fig. 6. If instead of one coordinate of the leading system xk (t), we observe the function F(x1 , x2 , . . . , xn ),F : Rn → R1 , then for the equation of adaptive control and synchronization, the author proposes to use a vector-function of the following form: ψ(x, u) = γsign∇x ' .(F ' − F), where F ' = F(x1' , x2' , . . . , xn' ). In this case, in addition to the general conditions of algorithm (4) and synchronization, it’s add a ' condition ∂∂ Fx ' /= 0, where xk' takes from the system (6). k To compare the effectiveness of the method, let’s compare it with the standard time delay method [15–17], which uses approximation (recursive LSM) for identification. The only clear advantage of this method is the guaranteed possibility of a global reconstruction of a dynamical system, provided that the system functions are successfully expanded into the required series. Let’s set the structure of the dynamical system by ordinary differential equations of the 1-st order x˙ = F j (x), j = 1, . . . , n. Then, in order to obtain a specific form of the evolution operator of the function F j is represented as a decomposition by some basis, while being limited to a finite number of decomposition components. In a simpler case, the F j specification can be carried out by a polynomial of some degree v: v .

F j (xi ) =

C j,1 ,l2 ,...,ln

l1 ,l2 ,...,ln =0 n .

n .

lk xs,i , j = 1, . . . , n,

s=1

ls ≤ v,

s=1

where C j,1 ,l2 ,...,ln —unknown coefficients necessary to be found. To calculate these coefficients, it is necessary to solve a system of N linear algebraic equations: x j,i+1 =

v . l1 ,l2 ,...,ln =0

C j,l1 ,l2 ,...,ln

n .

lk xs,i , i = 1, . . . , N , j = 1, . . . , n,

(7)

s=1

with unknowns C j,1 ,l2 ,...,ln , in which N—the number of points in the pseudo-phase reconstruction of the scalar time series xi (t) used to approximate the right-hand sides, and v—polynomial degree. Legendre polynomials may be used for the approximation, or a more complex technique may be used. For given n and v, the number of polynomials coefficients K (7) in the general case can be determined by the formula: K = (n + v)!/(n!v!). Usually N ≥ K , therefore, to specify the evolution operator, the system of equations (7) is solved by the LSM. In the end, the mathematical model is complex, but with a good choice of the general form of nonlinear functions, its solution is successful. It is clear that for parametric identification this algorithm always coincides and is much more accurate, but the approximation error remains.

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4 Research Results: Ressler and Lorenz Models Let us consider the behavior of two unidirectionally coupled oscillators—the Ressler system, which is on the verge of the asymptotic coordinate synchronization regime. The equations of interacting oscillators at controlling the first coordinate will be written as: x˙ ' = −ω' y ' − z ' − γsign∇x ' ar ctg(x ' (t) − x(t)), x˙ = −ωy − z, y˙ ' = ω' x ' + ay ' , i ' y˙ = ωx + ay, z˙ = b + z ' (x ' − c), z˙ = b + z(x − c), a˙ ' = −δsign∇x ' ar ctg(x ' (t) − x(t)),

(8)

where (x, y, z) i (x ' , y ' , z ' )—the vectors of the leading and controlled oscillator, respectively; γ—feedback parameter; δ—adaptation parameter, ω—parameter that determines the main natural oscillation frequency (it was chosen ω = 0.93, ω' = 0.95); other standard options were chosen as follows a = 0.15, b = 0.2, c = 10. With this choice of controlled parameters, coupled systems show coordinate-coherent synchronization. As it was written above, the spectrum of Lyapunov indicators of the leading system (λ1 > λ2 > λ3 ) does not depend on the value of the connection parameter γ, , while the conditional Lyapunov exponents (λ'1 > λ'2 > λ'3 ) change with increase coefficient γ. Figure 1 shows the dependences of 4 Lyapunov exponents on the value γ. The other two Lyapunov exponents are essentially negative (≈−10), so they do not affect on synchronization. To calculate the Lyapunov exponents, the Bennettini algorithm was used [1, 18, 19]. The exponents λ1 > 0 and λ2 = 0 correspond to the behavior of the host system, so their values are constant. If connection between the systems is absent (γ = 0), then we have λ'1 > 0 and λ'2 = 0. Since it is the first exponent that characterizes the chaotic dynamics of the controlled system, then λ'2 = .0 —zero exponent with an increase in which already at γ = 0.03, as can be seen from Fig. 2, the partial chaotic synchronization mode is established. A negative value λ'2 = .0 causes synchronization of the oscillators (8), although not all conditional Lyapunov exponents are already negative. Coordinate synchronization Fig. 1 Dependence of the Lyapunov exponents on the feedback parameter γ

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occurs at some time intervals near the steady state limit, but the asymptotic coordinate synchronization mode is not fully established. Therefore, we apply parametric identification to the second coordinate of the vector (x, y, z). The simulation results are shown in Fig. 2. Modeling of all drawings was carried out in the Java programming language.

Fig. 2 Asymptotic coordinate synchronization of two unidirectional Ressler oscillators (8) and estimation of an unknown parameter a at γ = 1 and δ = 1, b = 0.2, c = 10, ω = 0.93, ω' = 0.95.

Fig. 3 Asymptotic coordinate synchronization of two unidirectional Lorentz oscillators (9) and assessment of the unknown parameter σ at γ = 1 and δ = 1 with a standard choice of the function w(x, x ' ) = γ(x ' (t) − x(t)) for the proposed algorithm (4) (observing the control function F(x1 , x2 , x3 ) = 1/2x 2 + 1.1y)

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Fig. 4 Asymptotic coordinate synchronization of two unidirectional Lorentz oscillators (9) and assessment of an unknown parameter σ at γ = 1 and δ = 1 with the proposed choice of function w(x, x ' ) = γsign∇xi' ar ctg(x ' (t) − x(t)) for algorithm (4) (observing the control function F(x1 , x2 , x3 ) = 1/2x 2 + 1.1y)

Let us now consider the behavior of two unidirectionally coupled Lorentz systems at observing the control function F(x1 , x2 , x3 ) = 1/2x 2 + 1.1y:

x˙ = σ (y − x), y˙ = r x − y − x z, z˙ = x y − bz

x˙ ' = σ (y ' − x ' ) − γ sign∇x ' ar ctg(1/2x '2 + 1.1y ' − (1/2x 2 + 1.1y)), ' y˙ = r x ' − y ' − x ' z ' , z˙ ' = x ' y ' − bz ' , σ˙ ' = −δsign∇x ' ar ctg(1/2x '2 + 1.1y ' − (1/2x 2 + 1.1y))(y ' − x ' ).

Jacobi matrix of this system can be writtem as follows: ⎛ ⎜ ⎜ ⎜ J =⎜ ⎜ ⎜ ⎝

'

−σ − γsign(x ' ) 1+(1/2x '2 +1.1yx' −1/2x 2 −1.1y)2 r −z y −δsign(x ' )(−ar tng(1/2x '2 + 1.1y ' − 1/2x 2 − 1.1y) 1 + (y ' − x ' ) 1 + (1/2x '2 + 1.1y ' − 1/2x 2 − 1.1y)2

σ − γsign(x ' ) 1+(1/2x '2 +1.1y1,1' −1/2x 2 −1.1y)2 −1 x −δsign(x ' )(ar tng(1/2x '2 + 1.1y ' − 1/2x 2 − 1.1y) 1, 1 + (y ' − x ' ) '2 1 + (1/2x + 1, 1y ' − 1/2x 2 − 1, 1y)2

⎞ 0 y' − x ' −x 0 ⎟ ⎟ ⎟ −b 0 ⎟. ⎟ ⎟ 0 0 ⎠

(9)

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Fig. 5 Convergence of the method depending on the parameters for system (9). In the zone (−) there is convergence, in the zone (+)—no convergence

Figures 3 and 4 show the parametric identification of the unknown parameter σ of the Lorenz system during observing the function F(x1 , x2 , x3 ) = 1/2x 2 + 1.1y using algorithm (4) with the standard choice of the vector-function w(x, x ' ) = γ(x ' (t) − x(t)) (Fig. 3) and with the proposed choice of the vector-function w(x, x ' ) = γsign∇xi' ar ctg(x ' (t) − x(t)) (Fig. 4). As can be seen from the graphs above, the method coincides with the proposed choice of the vector-function w(x, x ' ) approximately by 10 times faster (with t ≈ 1 in dimensionless time units). At the same time, the assessment accuracy using the fifth-order Runge–Kutta method with the Dormand-Prince corrective procedure for a variable step of numerical integration was 10–7 . Figure 5 shows the selection ranges of the controlled parameters (adaptation and feedback) for which the method coincides, that is, when all real parts of the eigenvalues of the Jacobi matrix J are less than zero. Let’s present the structural and parametric identification of dynamical systems using the example of the Ressler system for the scalar implementation of system (8) and the chosen parameters a = 0.15, b = 0.2, c = 10 under the initial conditions x(t0 ) = y(t0 ) = z(t0 ) = 0.001. In this case, the method of successive differentiation, the recurrent LSM and the mentioned Runge–Kutta method of the fifth order with the corrective procedure of Dormand-Prince were used. The results of the recurrent LSM assessment are shown in Table 1. From the above table, it is observed that the best assess of the unknown parameter was 0.15008583965282281 at 25,000 values of the scalar realization of the first coordinate of the Ressler system (8). Assessing the unknown coefficients of the system (8), which is shown on the left, we obtain the Ressler system reconstructed from observations (only 100,000 observations) (on the right):

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Fig. 6 Ressler attractor for the reconstructed system (8) (a) and the convergence of the method for system (9) on a small sample of observations (20 basic oscillations) at replacing the final values of the divergence with the initial ones (b)

Table 1 Assessment of the unknown parameter a of the Ressler system .

Number of observations, n

Assessment of the unkmown parameter a

Student’s t-test

(yi −yiM ) n

2

5000

0.15279989073271564

16.11550727420384

0.00051349525955

10,000

0.15179031214712582

21.7848638879715

0.00037518457237

15,000

0.15023587771954774

24.780482729799697

0.00021788606654

20,000

0.14991215402599043

28.15722213497546

0.00013270174521

25,000

0.15008583965282281

31.755325001013514

0.00007546570353

30,000

0.14958778332228523

33.92477404405509

0.00034885192906

35,000

0.14975804834261507

36.9612833901198

0.00023395394712

⎧ ⎪ ⎨ x˙ = −ωy − z, y˙ = ωx + ay, ⎪ ⎩ z˙ = b + z(x − c).

⎧ x˙ = y, ⎪ ⎪ ⎪ ⎨ y˙ = z, ⎪ z˙ = −0.2 − 10x + 0.5y − 9.85z ⎪ ⎪ ⎩ +1.0225x y + yz − 0.15x z − 0.15y 2 − 0.15x 2 + 0z 2 .

Figure 6b shows the convergence of the method for system (9) with a small sample, observing the function F(x1 , x2 , x3 ) = 1/2x 2 + 1.1y using algorithm (4) with the selected vector-function w(x, x ' , t) = γsign∇xi' ar ctg(x ' (t) − x(t)). The simulation found that even with 20 basic steady state oscillations in the sample, the method coincides.

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5 Conclusions In this chapter, for the problem of parametric identification, a new algorithm based on chaotic synchronization and adaptive control is proposed. Thus, the acceleration of synchronization of unidirectional oscillators occurs due to the use of a relay algorithm as an adaptation method, which is a special case of the standard speed pseudogradient algorithm. In addition, it is proposed to use, instead of the standard vector function of the rate of change of a smooth objective function, a class of functions (for example, trigonometric) that satisfies the conditions of pseudo-gradient, reach, existence of “ideal control” and convexity of the feedback function with respect to the corresponding state vector of the controlled system. It was found that using a vector-function ar ctg(x), that fully satisfies these conditions, with the same choice of initial conditions of the dynamic system, the method coincides approximately faster at 2 times. This feedback function was also used in the adaptive control equation to estimate unknown parameters. Using the Ressler system as an example, the influence of the zero Lyapunov exponent on the synchronization of two unidirectional coupled oscillators of this system under the control of the first coordinate is shown, and the spectrum of Lyapunov characteristic indicators is calculated. In this case, although asymptotic coordinate synchronization occurs due to the negativity of the zero Lyapunov exponent, however, it is interval-phase, so identification is impossible. The example of the Lorenz system shows the effectiveness of the vector-function ar ctg(x) in comparison with the standard one. In addition, using the example of this system, parametric identification was made during observing not only one coordinate of the system, but also a function of all coordinates. For this case, formulas are derived and conditions for the convergence of the method are given. Also, on the example of the Lorentz system, the possibility of applying the algorithm for small samples is shown, in particular, the results of the convergence of the method during observing a function of all coordinates of the system are given. To check the effectiveness of the algorithm, the results of comparing the proposed method with the standard one based on approximation are presented. In addition, on the basis of the last method, an example of a complete reconstruction of the dynamical Lorentz system is given at observing a function of all coordinates of the system.

References 1. Zinchenko, A.Yu.: Computer Modeling of Deterministic Chaos in Complex Nonlinear Systems (2021). ISBN 978-617-651-225-7 2. Proskurnikov, V., Matveev, A.S.: Tsypkin and Jury-Lee criteria for synchronization and stability of discrete-time multiagent systems. Autom. Remote Control 79(6), 1057–1073 (2018). https:// doi.org/10.1134/S0005117918060061 3. Tomashevich, S., Andrievsky, B.: Adaptive control of quadrotors spatial motion in formation with implicit reference model. In: Sivasundaram, S. (ed.) AIP Conference Proceedings, p. 2046. Amer Inst Physics UNSP 020103 (2018). https://doi.org/10.1063/1.5081623

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4. Crutchfield, J.P., McNamara, B.S.: Equations of motion from a data series. Complex Systems 1, 417–452 (1987) 5. Pikovsky, M., Rosenblum, Kurths, J.: Synchronization. A Universal Concept in Nonlinear Sciences, p. 432. Cambridge University Press, Cambridge (2001). https://doi.org/10.1017/CBO 9780511755743 6. Boccaletti, S., Kurths, J., Osipov, G.V., Valladares, D.L., Zhou, C.T.: The synchronization of chaotic systems. Phys. Rep. 366, 1–101 (2002). https://doi.org/10.1016/S0370-1573(02)001 37-0 7. Huberman, B.A., Lumer, E.: Dynamics of adaptive systems. IEEE Trans. Circ. Syst. 37, 547– 550 (1990) 8. Wang, J., Wang, X.: Parametric adaptive control in nonlinear dynamical systems. Int. J. Bifurcation Chaos. 8, 2215–2223 (1998). https://doi.org/10.1142/S0218127498001807 9. Yang, T., Yang, C.M., Yang, L.B.: A detailed study of adaptive control of chaotic systems with unknown parameters. Dyn. Control 8, 252–267 (1998). https://doi.org/10.1023/A:100825840 3620 10. Maybhate, Amritkar, R.E.: Use of synchronization and adaptive control in parameter estimation from a time series. Phys. Rev. E 59, 284–293 (1999). https://doi.org/10.1103/PhysRevE.59.284 11. Gonzalez-Miranda, J.M.: Synchronization and Control of Chaos: An Introduction for Scientists and Engineers, p. 224. Imperial College Press (2004). https://doi.org/10.1142/p352 12. Fradkov, A.L.: Cybernetical Physics: From Control of Chaos to Quantum Control. Springer, Heidelberg, p. 236 (2007). https://doi.org/10.1007/978-3-540-46277-4 13. Hramov, A.E., Koronovskii, A.A., Kurovskaya, M.K.: Zero Lyapunov exponent in the vicinity of the saddle-node bifurcation point in the presence of noise. Phys. Rev. E. 78, 36–212 (2008). https://doi.org/10.1103/PhysRevE.78.036212 14. Hramov, A.E., Koronovskii, A.A., Kurovskaya, M.K.: Two types of phase synchronization destruction. Phys. Rev. E. 75, 36–205 (2007). https://doi.org/10.1103/PhysRevE.75.036205 15. Anishchenko, V.S., Astakhov, V., Neiman, A., Vadivasova, T., Schimansky-Geier, L.: Nonlinear dynamics of chaotic and stochastic systems. In: Tutorial and Modern Developments, p. 446. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-38168-6 16. Hassanibesheli, F., Boers, N., Kurths, J.: Reconstructing complex system dynamics from time series: a method comparison. New J. Phys. 22, 073053 (2020). https://doi.org/10.18452/22317 17. Anishchenko, V.S., Vadivasova, T.E., Strelkova, G.I.: Deterministic Nonlinear Systems. A Short Course, p. 294. Springer International Publishing, Switzerland (2014). https://doi.org/10.1007/ 978-3-319-06871-8 18. Benettin, G., Galgani, L., Giorgilli, A., Strelcyn, J.M.: Lyapunov characteristis exponents for smooth dynamical systems and for Hamiltonian systems: a method for computing all of them. Part 1. Mechanic 15, 9–20 (1980) 19. Benettin, G., Galgani, L., Giorgilli, A., Strelcyn, J.M.: Lyapunov characteristis exponents for smooth dynamical systems and for Hamiltonian systems: a method for computing all of them. Part 2. Mechanic 15, 21–30 (1980)

Detection Method of Augmented Reality Systems Mosaic Stochastic Markers for Data-Centric Business and Applications Hennadii Khudov , Igor Ruban , Oleksandr Makoveichuk , Vladyslav Khudov , and Irina Khizhnyak Abstract The paper proposes the method of detection of mosaic stochastic markers of augmented reality systems for data-centric business and applications. A description of the well-known markers of augmented reality systems, their advantages and disadvantages is given. Determined that the finding of angles or special areas of reference of well-known markers is a quick method, but requires unambiguous detection of all four points of well-known markers. The detection method of mosaic stochastic markers for augmented reality systems has been improved. The main stages of the method are: the preprocessing of the input image; the finding the marker area; to determine the bit container. Results of the experiments of the method of detection of mosaic stochastic markers for augmented reality systems has been given. Keywords The mosaic stochastic marker · The detection · The method · Bit · The system of augmented reality · Data-centric business application

1 Introduction Nowadays the virtual and augmented reality technologies capture the imagination. But we perceive them, rather, as an entertainment component of life, gaming applications are by far the largest and most interested investors in this area. But thanks to the development of augmented and virtual reality technologies at the expense of gaming giants, technologies are also being developed that allow augmentation of reality to help other areas of business [1]. The technology of creating augmented reality (AR) in any field includes three mandatory components [2–5]: . mobile device (smartphone, tablet) with a built-in video camera; . a specially designed application containing virtual information; H. Khudov (B) · I. Khizhnyak Kharkiv National Air Force University, Kharkiv, Ukraine e-mail: [email protected] I. Ruban · O. Makoveichuk · V. Khudov Kharkiv National University of Radio Electronics, Kharkiv, Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_8

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. a label, Global Position System (GPS) coordinates, or a marker (a real object, its part or a printed image), which launch the mobile application. A marker or tag allows the program to bind augmented reality information to the outside world and transfer the image to a smartphone display or to special glasses. But these three components are not always enough; various fields of application of AR technologies have their own specifics [6]. To see an AR object, you need to point the camera at a mark or marker, and the image will appear on the screen of a smartphone or tablet. AR can be formed not only on the basis of an image, but also include, for example, readings of a compass, gyroscope, 3D model—without this, it is impossible to create a three-dimensional object visible from different angles [1]. Augmented reality allows to make a presentation anywhere, show how the object will look from all sides, and even make the perception of the object interactive. To do this, you only need a program (application), a display with a camera and a marker printed on a sheet. When you point the camera at the printout, an object will appear on the screen. True, for the full effect of presence, spectators will need special glasses or a helmet [1, 4]. In medical diagnostics, there is not always direct access to the information base on which additional reality is built. In this case, AR technology uses data from highprecision diagnostic devices, such as magnetic resonance imaging, computed tomography, ultrasound diagnostics, X-rays, etc. They are the basis to which augmented reality is tied, and certain organs or points are markers. An image of the patient’s internal state appears on the doctor’s monitor [7, 8]. AR-devices that help patients cope with illness exist in psychiatry and psychotherapy. Barcelona-based Psious Inc. has developed a technology that allows to simulate situations that provoke phobias, for example, the fear of enclosed spaces, flying in an airplane or spiders [7, 8]. Under the supervision of specialists, a person suffering from a phobia undergoes a phased adaptation to a stressful situation. For the field of distance education, AR technologies are a universal tool [9]. There are certain best practices for conducting classes in a virtual laboratory or applications that create the effect of being present at a real operation in a remote operating room or on a battlefield in the distant past. Japanese publishing house Tokyo Shoseki has prepared a special AR English textbook. It has built-in cameras that project onto the pages of animated characters [10, 11]. AR allows to translate sign or digital information into a more easily perceived visual and make the process of perceiving information interactive. In the use of AR-devices when monitoring the environment while the car is moving, feedback is provided. Data management is carried out in voice mode [12, 13]. Architectural visualization is a demonstration of an object under construction from any point of view and from the inside. This requires special markers in the building itself. By pointing a video camera at them, you can get a variety of images, and with the help of simple manipulations on the display, turn the object at any angle, see the internal structure or disassemble the building by floors [14].

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The marker and unmarked AR systems are presented in approximately the same way, with unmarked systems most often used in gaming and travel applications. In unmarked systems, the location of the user (his geographical coordinates) obtained by GPS is used as a marker. Additional information is most often downloaded from a remote server, where the coordinates and orientation of the smartphone’s camera are transmitted. This naturally binds the system to one place and makes it inaccessible for use to moving objects, which narrows its scope [13, 15]. In order to obtain additional information about arbitrary objects, augmented reality marker systems will be used in the vast majority of cases, which will be considered in this paper. The main existing types of AR markers are given in [2, 3, 11–13, 16, 17]: . the template markers—black and white markers that have a simple image inside a black frame (Fig. 1); . the 2D barcode markers—which consist of black and white cells that code data bit by bit, and sometimes frames or synchronization areas (Fig. 2). Most often, quick response (QR) codes are used as barcode AR-markers; . the circular markers—similar to barcode markers (Fig. 3). But the bits are encoded not in rectangular cells, but in black and white circular slices; . the images (image markers)—ordinary color images are used as markers (Fig. 4). Its may contain a frame or other landmarks to identify and find a position. The image markers are usually identified by searching by pattern or by image feature.

Fig. 1 The template marker

Fig. 2 The 2D barcode marker

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Fig. 3 The circular marker

Fig. 4 The image marker

Theoretically, an AR marker can be any figure (object), but in practice we are limited by the resolution of the camera, the features of color reproduction, lighting and computing power of the equipment. Therefore, for work in real time, a simple black and white marker of a simple shape is usually chosen. This is usually a rectangle or square with an inscribed image inside. The paper [18] describes the main types of template markers and compares the recognition performance of different implementations of markers (Fig. 5). A typical method of processing a template marker consists of the following steps [18, 19]: . . . . . .

the transition to grayscale; the threshold determination and image binarization; the finding closed areas; the selection of contours; the finding the angles of the marker; the finding the parameters of projective transformation and coordinate transformation.

Analyzing the known types of AR-markers, we can conclude that each of them has its advantages and disadvantages: (1) all AR-markers allow to determine the position of the camera, but this uses different methods:

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Fig. 5 The main types of template markers [18]: a ArToolKit (ATK); b Institut Graphische Datenverarbeitung (IGD); c Siemens Corporate Research (SCR); d Hoffman marker system (HOM)

. finding image angles (template markers); . finding special areas of reference (bar code and circular markers); . finding special points of the image and their descriptors (image markers). (2) some of them (bar codes and circle markers) contain additional information (messages), such as links to information resources, which is a clear advantage because it allows to expand the scope.

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Fig. 6 The mosaic sustainable marker for augmented reality systems [14, 17]

Finding angles or special areas of reference is a quick method, but requires unambiguous detection of all 4 points, finding special points of the image and building their descriptors requires more computing resources, but is much more stable, part of the image can be obstructed, however, this method allows to correctly determine the position of the camera. In [14, 17] a new type of mosaic sustainable markers of augmented reality systems is proposed. Its form is shown in Fig. 6. So, we will develop the mosaic sustainable marker detection method for augmented reality systems.

2 The Method of Detection of Mosaic Stochastic Markers for Augmented Reality Systems To detect a mosaic stochastic marker of augmented reality, a method is proposed, the block diagram of which is shown in Fig. 7.

2.1 The Preprocessing of the Input Image The preprocessing of the input image (Fig. 6) involves the transition from color to grayscale. Formally, this can be written as (1): g=

1 (0.2989R + 0.587G + 0.114B), 255

(1)

Detection Method of Augmented Reality Systems Mosaic Stochastic … Fig. 7 The block diagram of the mosaic stochastic marker detection method for augmented reality systems

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The image

The processing

The filtration

The segmentation

The morphological processing

The mask of AR-marker

where R, G, B—the corresponding color components of the original image in RGBrepresentation; g—grayscale image; conversion factors are the same as those for the Y-channel (luminance) in the transition from RGB to NTSC-representation; coefficient 1/255 is introduced for convenience—to normalize the dynamic range of brightness from 0.0.255 to 0.0.1. The grayscale image is shown in Fig. 8. Fig. 8 The grayscale image

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2.2 The Finding the Marker Area It is proposed to use the operation of finding the local standard deviation over the square area for the AR-marker of detection on the image f (Fig. 8) because the AR marker contains only 3 grayscale values {0, 1/2, 1}. At the border between the ARmarker cells, the local standard deviation will be maximum and small for smooth image areas. Since all coordinates in the images are set in integers, it is convenient (for symmetry) to choose the size of the region as an odd number. Figure 9 shows an image of σ, this is the result of calculating the local standard deviation over an area of size (3 × 3). For a square area of size (2a + 1)x(2a + 1) centered at a point with coordinates (x, y), we have expression (2): σ (x, y) =

a a . . 1 (f(x + m, y + n) − μ(x, y))2 , (2a + 1)2 m=−a n=−a

(2)

where μ(x, y) is the local average, which is calculated according to expression (3): μ(x, y) =

a a . . 1 (f(x + m, y + n)). (2a + 1)2 m=−a n=−a

(3)

The next step is to binarize the image (Fig. 9). Since the histogram of the local standard deviation image is unimodal in the general case (Fig. 10), then the standard binarization by Otsu’s method. It works well for bimodal distributions. But this will give an overestimated threshold, which will lead to the loss of some useful information (Fig. 11). We will carry out binarization using k-means segmentation. The simplest way is segmentation into k = 2 classes (background and object) [20, 21]. But in this Fig. 9 The image of local standard deviation

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Fig. 10 The histogram image of the local standard deviation

Fig. 11 The result of binarization by Otsu’s method (some information is lost)

case it will give results that will be close to binarization by Otsu’s method [20, 21]. Therefore, it is proposed to use k = 3 classes—background, intermediate values and object (Figs. 7 and 12). Then the binary image is obtained as a union of class masks that are not related to the background. Background is defined as the class that has the lowest average luminance value. Since the background occupies the largest area, the best is determined. An increase in the number of classes k > 3 does not significantly change the results and is impractical. The result of binarization by the proposed method is shown in Fig. 13. To compare the results in Fig. 14 shows fragments of binary masks obtained by the Otsu method and the proposed method. You can see that the proposed method gives significantly better results—all cell contours are well distinguished.

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Fig. 12 The index image—the result of segmentation into 3 classes

Fig. 13 The result of binarization by the proposed method

The resulting binarized image is processed using operations of mathematical morphology. It is proposed to use the morphological closure operation with a square window for to fill the inner areas. In this case, the size of the window sets the maximum size of the voids that will be filled. In this work, it is proposed to use a window (63 × 63). The results are shown in Fig. 15. Next, the largest 4-connected area is found (Fig. 16). In the future, it makes sense to discard uninformative image areas. And as the area of the AR-marker, take a rectangular fragment in which its mask is inscribed (Fig. 17). All further operations will be performed only for the part of the image that is highlighted by this mask (Fig. 18).

Detection Method of Augmented Reality Systems Mosaic Stochastic … Fig. 14 The comparison of binarization results: a Otsu’s method (some of the contours are missing); b the proposed method

Fig. 15 The result of filling the inner areas

Fig. 16 The most connected area

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Fig. 17 The mask of AR-marker

Fig. 18 The image of AR-marker

2.3 To Determine the Bit Container To determine the bit-containers (information elements cells, the colour of which encodes the information bits), it is proposed to use the segmentation of the AR-marker image into k = 3 classes using the k-means algorithm (similar to the definition of the AR-marker area). The result of segmentation is shown in Fig. 19. It should be noted that the k-means algorithm assigns class indices in an arbitrary manner. And to obtain a picture that will look more similar to the original image, the resulting indices should be sorted according to the growth of the average brightness of each class. The result of this ordering is shown in Fig. 20. In this case, the dark cells (encoding bits 0) will belong to the class with the minimum index value, which is equal to 1. Gray (border)—of the class with index = 2. White (coding bit 1)—class with index = 3.

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Fig. 19 The index image of segmentation of AR-marker

Fig. 20 The result of ordering of class index (to compare with Fig. 18)

If there are correctly ordered class indices, then we can select the cell masks that correspond to each bit. Bit 0 is coded in black. It will correspond to the class with the lowest index, which is 1 (Fig. 21). Bit 1 is coded white. It will correspond to the class with the highest index, which is 3 (Fig. 22). The next step is filtering the bit container masks. This operation is efficiently performed with a square window morphological opening operation. The problem is the choice of the window size. It should be such that artifacts are filtered out as much as possible. This did not remove information items. To select the optimal window size, the following is proposed. Let’s count the number N(a) of 4-connected areas

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Fig. 21 The mask for cells with index 1 (bit 0)

Fig. 22 The mask for cells with index 3 (bit 1)

in the binary image that remain after the morphological opening operation. We will count it as a function of the filtering window size a (Fig. 23). The function N(a) first falls. As the size of the window increases, more and more areas are filtered out. Further, for a certain range of sizes, we reach a plateau— the number of areas remains unchanged. Since the window size is smaller than the typical cell size. With a further increase in the window size, the function N(a) will fall again. Since the cells will start to filter out. Thus, to determine the size of the window, it is necessary to find the point at which the function N(a) reaches a plateau. This will mean that the noise has already been filtered, and the cell is not yet. Since the function N(a) is nonincreasing, it is sufficient to find the first maximum of the

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Fig. 23 The function N(a) for each bit of container mask

derivative dN/da to find this point (Fig. 24). The results of morphological filtration are shown in Figs. 25 and 26. Taking into account the perspective distortions of the image, the described behavior of the function N(a) is made less certain. Since some of the cells in the far area of the image will be smaller than the noise in the near area. However, as the experiments have shown, the proposed method for determining the optimal filter window size gives good results. It will be shown further for the proposed algorithms that the loss of a certain number of information cells is less critical than the presence of noise areas. Morphological filtration effectively removes only those areas that are smaller than the cell size. To filter areas that are significantly larger than this size—you must use a different method. If small artifacts arise through binarization defects, then the nature of this noise is different. It is either interference that obscures part of the container’s area (such as a hand or other object). Or a part of the cells that “stuck” together due to uneven lighting. To eliminate such noise, it is proposed to use statistical filtering by the size of connected regions. All areas with an area greater than three standard deviations from the mean are filtered out. To increase efficiency, this method is used iteratively. The number of iterations is 3. The results of statistical filtration for each mask are shown in Figs. 27 and 28. The result of the merge of the masks is shown in Fig. 29. Thus, we have obtained the mosaic sustainable marker detection method for augmented reality systems. It is based on the binarization of the local variance, detects the marker area in the original image and finds the masks of bitcontainers.

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Fig. 24 The plots of derivative dN/da for each mask of bit-container. The circle indicates the point of the first maximum: a for 0; b for 1

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Fig. 25 The result of morphological filtration of the mask of bit-container (bit 0)

Fig. 26 The result of morphological filtration of the mask of bit-container (bit 1)

This is done by segmentation and subsequent morphological filtration of the masked area of the image.

3 Conclusions In this paper we have obtained the method of detecting mosaic stochastic markers of augmented reality systems for data-centric business and applications. It is based on the binarization of the local variance, detects the marker area in the original image

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Fig. 27 The result of statistical filtration of the mask of bit-container (bit 0)

Fig. 28 The result of statistical filtration of the mask of bit-container (bit 1)

and finds the masks of bit-containers. This is done by segmentation and subsequent morphological filtration of the masked area of the image. Areas for further research are: . the development of a method for determining the parameters of projective transformation. This is necessary to align the image and determine the position of the camera; . the development of a method for decoding the mosaic sustainable marker of augmented reality systems.

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Fig. 29 The result of the marge of the mask

References 1. Ivanova, A.V.: VR & AR technologies: opportunities and application obstacles. Strat. Decis. Risk Manag. 3, 88–107 (2018). https://doi.org/10.17747/2078-8886-2018-3-88-107 2. Thomas, D.J.: Augmented reality in surgery: the computer-aided medicine revolution. Int J Surg. 36(A), 25 p (2016). https://doi.org/10.1016/j.ijsu.2016.10.003 3. Cui, N., Kharel, P., Gruev, V.: Augmented reality with microsoft holo lens holograms for near infrared fluorescence based image guided surgery. Molecular-guided surgery: molecules, devices, and applications III. Int. Soc. Opt. Photon. 10049, 100490I (2017). https://doi.org/10. 1117/12.2251625 4. Smelyakov, K., Chupryna, A., Hvozdiev, M., Sandrkin, D.: Gradational correction models efficiency analysis of low-light digital image. In: 2019 Open Conference of Electrical, Electronic and Information Sciences (eStream), 25–25 April 2019, pp. 34–39. Vilnius, Lithuania 5. Barsom, E.Z., Graafland, M., Schijven, M.P.: Systematic review on the effectiveness of augmented reality applications in medical training. Surg. Endosc. 30, 4174–4183 (2016) 6. Smelyakov, K., Shupyliuk, M., Martovytskyi, V., Tovchyrechko, D., Ponomarenko, O.: Efficiency of image convolution. In: 2019 IEEE 8th International Conference on Advanced Optoelectronics and Lasers (CAOL), 6–8 Sept. 2019, pp. 578–583. Sozopol, Bulgaria 7. Khudov, H., Ruban, I., Lysytsya, V., Kuzyk, P., Symkanych, O., Khudov, R.: The method for determination of bone marrow cells in photographic images. Int. J. Emerg. Trends Eng. Res. 8(9), 5681–5687 (2020). https://doi.org/10.30534/ijatcse/2020/131892020. 8. Khudov, H., Symkanych, O., Kovalenko, A., Kabus, N., Lysytsya, V., Khudov, R.: The comparative assessment of the quality of cytological drugs image processing. Int. J. Adv. Trends Comput. Sci. Eng. 9(5), 8645–8653 (2020). https://doi.org/10.30534/ijatcse/2020/250952020 9. Smelyakov, K., Ponomarenko, O., Chupryna, A., Tovchyrechko, D., Ruban, I.: Local feature detectors performance analysis on digital image. In: 2019 IEEE International ScientificPractical Conference Problems of Infocommunications, Science and Technology (PIC S&T), 8–11 Oct 2019, pp. 644–648. Kyiv, Ukraine 10. Khudov, H., Tyurina, V., Ovod, Y., Kozyr, M., Chala, A., Khizhnyak, I.: The ways of psychological and pedagogical barriers overcoming between teachers and students during COVID-19 pandemic. Syst. Rev. Phar. 11(11), 373–379 (2020). https://doi.org/10.31838/srp.2020.11.55

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11. Akçayır, M., Akçayır, G.: Advantages and challenges associated with augmented reality for education: a systematic review of the literature. Educ. Res. Rev. 20, 1–11 (2017). https://doi. org/10.1016/j.edurev.2016.11.002 12. Augmented Reality and Virtual Reality Market by Offering (Hardware & Software), Device Type (HMD, HUD, Handheld Device, Gesture Tracking), Application (Enterprise, Consumer, Commercial, Healthcare, Automotive), and Geography—Global Forecast to 2023. Markets and Markets. 2018. [Electronic resource]. URL: https://www.marketsandmarkets.com/MarketRep orts/augmented-reality-virtual-reality-market-1185.html. Accessed at: 11 Dec 2018 13. Kaiser, R., Schatsky, D.: For more companies, new ways of seeing. Momentum is building for augmented and virtual reality in the enterprise. Deloitte University Press. [Electronic resource]. URL: https://www2.deloitte.com/content/dam/insights/us/articles/3768_Sign als-for-Strategists_Apr2017/DUP_Signals-for-Strategists_Apr-2017.pdf. Accessed at: 12 Nov 2019 14. Ruban, I., Khudov, H., Makoveychuk, O., Khizhnyak, I., Khudov, V., Lishchenko, V.: The model and the method for forming a mosaic sustainable marker of augmented reality. In: 2020 IEEE 15th International Conference on Advanced Trends in Radioelectronics, Telecommunications and Engineering (TCSET), February 2020. https://doi.org/10.1109/TCSET49122.2020. 235463 15. Siltanen, S.: Theory and applications of marker-based augmented reality. Espoo 2012. 198 p 16. Magee, D., Zhu, Y., Ratnalingam, R., Gardner, P., Kessel, D.: An augmented reality simulator for ultrasound guided needle placement training. Med. Biol. Eng. Comput. 45, 957–967 (2007) 17. Khudov, H., Makoveychuk, O., Khizhnyak, I., Yuzova, I., Irkha, A., Khudov, V.: The mosaic sustainable marker model for augmented reality systems. Int. J. Adv. Trends Comput. Sci. Eng. 9(1), 637–642 (2020). https://doi.org/10.30534/ijatcse/2020/89912020 18. Zhang, X., Fronz, S., Navab, N.: Visual marker detection and decoding in AR systems: a comparative study. In: Proceedings of the International Symposium on Mixed and Augmented Reality, pp. 1–7 (2002) 19. ARToolKit: Computer Vision Algorithm [Electronic resource]. URL: http://www.hitl.washin gton.edu/artoolkit/documentation/vision.htm. Accessed at: 19 Jan 2020 20. Ruban, I., Khudov, H.: Swarm methods of image segmentation. Adv Spatio-Temporal Segment Visual Data 53–99 (2019) 21. Gonzalez, R., Woods, R.: Digital Image Processing, 4th edn. Prentice Hall, Upper Saddle Rever (2017)

Method for Converting the Output of Measuring System into the Output of System with Given Basis Elena Revunova , Volodymyr Burtniak , Yuriy Zabulonov , Maksym Stokolos , and Volodymyr Krasnoholovets

Abstract The chapter reviews the methods of data processing aimed at improving the accuracy of measurements in radiation monitoring systems. The accuracy of radionuclide activity determination using model selection criteria has been studied. It is shown how the output of a linear measured system to a system with specified properties can be converted. The mentioned specified properties are classified and considered. Preliminary processing has been performed by the method of converting the output of the measuring system into the output of the system with a given basis. The method has successfully been applied for the study of spectra of radionuclides 137 Cs, 134 Cs and 60 Co. Keywords Model selection criteria · Measuring system · Transformation of the output · Radionuclide activity

1 Introduction Identification and determination of the activity of weak sources of radioactive radiation is an urgent task of radiation monitoring [1]. This article reviews the methods of data processing aimed at improving the accuracy of measurements in radiation monitoring systems, as well as the accuracy of determining the activity of radionuclides using the output transformation method of the measuring system.

E. Revunova (B) International Research and Training Center for Information Technologies and Systems of the NAS of Ukraine and the MES of Ukraine, Kyiv, Ukraine e-mail: [email protected] V. Burtniak · Y. Zabulonov · M. Stokolos State Institution “The Institute of Environmental Geochemistry of National Academy of Sciences of Ukraine”, Kyiv, Ukraine V. Krasnoholovets Institute of Physics, National Academy of Sciences of Ukraine, Kyiv, Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_9

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2 Methods of Data Processing in Radiation Monitoring Systems and Factors Complicating Processing The requirement for the mobility of monitoring systems, together with the need to measure sources with low levels of radioactivity, determines the choice of a scintillation detector as a detecting element, which does not require a cooling system and has a high detection efficiency (compared to semiconductor detectors). The disadvantage of scintillation detectors is their low energy resolution compared to semiconductor detectors. The choice of these types of detectors affects the requirements for methods of processing the spectrum of ionizing radiation. As is known, the full spectrum of gamma radiation includes three main characteristic regions (zones of interest): the total absorption peak, the backscatter peak, and the Compton part. The shape and severity of the characteristic regions of the gamma spectrum is determined by the properties of the detector and the measurement geometry. Thus, the low energy resolution of a scintillation detector, together with the requirement to measure the activity of objects with a complex (previously unknown) spectral composition, leads to the need to process spectra that have such features as overlapping peaks, complete masking of the peak of one of the elements by the peak or ‘Compton’ part of the other. On the other hand, in almost all monitoring activities aimed at ensuring the radiation safety of nuclear fuel cycle facilities, the problem arises of processing gamma radiation spectra measured in complex (non-fixed) geometry. To process spectra of complex composition measured in non-fixed geometry, we have developed full spectrum processing methods [2–4], which take into account the number of gamma quanta recorded in the entire measured energy range. The essence of the full spectrum processing methods is as follows. The measured spectrum is presented as a combination of the response functions of the radionuclides that make up the radiation source, weighted by the activities. The task of processing is to determine from the measured spectrum which response functions and with which weighting factors are activities formed the observed spectrum. The initial information is a set of detector response functions (DRF) to the impact of gamma quanta with energies in the range of 100 keV–2 meV. Programs have been developed that make it possible to obtain DRF by simulating the process of propagation of gamma radiation. The measured spectrum of gamma radiation is modeled as the sum of DRF weighted by coefficients proportional to the activity. The basic hypothesis about the composition of the spectrum is the assumption that the spectrum includes all possible spectral lines in the range of 100 keV–2 meV: Ax+ε=b where A is the DRF matrix of size m × n, x is the vector of weights proportional to the activity of radionuclides, ε is the intrinsic noise vector of the measuring path, b is the output vector of the measuring system of size m. When digitizing the energy range with a step of 16 keV and n = 125 the observed emission spectrum is modeled as a weighted sum of 125 DRF (with a step of 7.8 keV and 256 DRF). The weighting coefficients corresponding to the radionuclides present in the

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measured spectrum are proportional to the activity of these nuclides, and all other weighting coefficients are zero. The use of a preliminary hypothesis that the spectrum includes all possible spectral lines of the measured range is a hallmark of our approach. In the traditional approach, a preliminary hypothesis about the composition of the spectrum is the hypothesis that the spectrum is composed of nuclides of a certain group, for example, thoriumradium. Using the assumption that the spectrum includes all possible spectral lines of the energy range under study makes it possible to avoid the situation when a nuclide that is not included in the model appears in the measured spectrum. When the spectrum is processed by traditional methods, the appearance in the spectrum of a nuclide that is not included in the model leads to an increase in the error in determining the activity of all nuclides present in the spectrum, and if the activity of a nuclide that is not included in the model is high, it also leads to errors in identifying the nuclides present. However, a large number of terms in the preliminary spectrum model, together with the presence of additive intrinsic noise in the measured spectrum, leads to the fact that the determination of activity, for example, by the least squares method (LSM) is unstable. The instability manifests itself in the fact that zero weights (corresponding to lines of nuclides that are not present in the spectrum) are assigned certain values (both positive and negative) by the LSM. As a result, nuclides that are not actually present in the spectrum are erroneously identified. This behavior of the LSM is due to the fact that the multicomponent model tries to approximate not only the real function of the spectrum, but also the additive noise. Modern methods that work stably in the presence of noise are the methods of model selection [5] and sparse approximation [6]. Model selection methods, through the use of model selection criteria [7, 8], provide a balance between the approximation accuracy (spectrum functions) and the number of basic functions (response functions) included in the model, thereby preventing the model from “tuning” to noise. The use of the methods of this group makes it possible to avoid such a situation when the spectrum model includes the response functions of elements that are not actually present in the spectrum; which, in fact, is an attempt to approximate the diurnal fluctuations of the background radiation spectrum by the model. The model selection criteria are formulated in such a way that they automatically reduce the model dimension with increasing noise level. For various model selection criteria, a study was made of the dependence of the model dimension and activity determination accuracy of the noise level. The comparison has shown that the best accuracy is provided by the criterion that retains the true dimension of the model longer than others with increasing noise level. Suppose the measured spectrum includes four monochrome sources of gamma radiation, in this case the true dimension of the model is four. However, the true dimension is unknown, and a preliminary hypothesis about the composition of the spectrum is the hypothesis that it includes 125 DRF. The use of model selection criteria makes it possible to exclude from the model lines that are absent in the measured spectrum. However, as the noise level increases, the criterion for choosing the model begins to reduce the dimension of the model,

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making it less true, due to the exclusion from the model of lines of nuclides with low activities that are not much higher than the noise level. Thus, the value of the minimum detectable activity (MDA) is overestimated. Relevant is the development of methods for processing gamma spectra, free from this drawback. In work [9], a model selection criterion (the l0 -optimality criterion) has been proposed, which does not explicitly link the model dimension with the noise level, but allows testing the validity of the hypothesis about the composition of the model. We have carried out computational experiments, the purpose of which is to compare the accuracy of determining the weight coefficients of the model using the criteria: Cr , MDL and l0 -optimality. Experiments have shown that with an increase in the noise level, the error in determining the weight coefficients of the model according to the l0 -optimality criterion is much less than the error for the model selection criteria Cr and MDL [10]. However, the l0 -optimality test has drawbacks because it is not applicable to any system of basic functions. For example, the system of basic functions formed from the responses of a scintillation detector does not meet the requirements for the test for l0 -optimality. The signal model can be tested for l0 -optimality if the value of the cumulative connectivity function μ [9] for the system of basic functions that form the model is less than one. Otherwise, the test for l0 -optimality is not applicable. To overcome such a shortcoming, we can use the output conversion method. The output of a linear measuring system is a spectrum measured using a scintillation detector. The system of response functions of the detector has μ > 1 and can be converted into the output of a measuring system having a cumulative connectivity of less than one.

3 Method for Converting the Output of Measuring System into the Output of System with Given Basis Let some object emit a signal x. The linear measurement system A converts the signal emitted by the object into the measured output b by linear transformation using a matrix A (the matrix of basic functions) Ax = b0 and addition with the noise vector ε: b = b0 + ε. The observed output b may not meet user requirements or be incompatible with further processing methods. Let some other measurement system C have a set of basic functions (detector response functions) that provide the required output. In this case, we can set the problem of finding the transformation of the observed output b into the output of the system C. We will look for the output transformation as a linear transformation. For the case when the noise vector is known and its covariance matrix is not degenerate, and also the matrix of basic functions A, weighted by the noise covariance matrix, is not degenerate, it has been proposed [11] to obtain the desired transformation using the inversion A. However, if A has a high condition number and the series of its singular

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Fig. 1 Complication of the measurement system

values smoothly decreases to zero, the solution obtained using the inverse matrix (the result of transformation into the output of the system C) is unstable. The instability manifests itself in the fact that small changes in b correspond to large changes in the solution, and the error in the solution is large. So a kind of decomposition should be introduced (Fig. 1). The approach we are developing to a stable solution of the output transformation problem is based on the use of a truncated singular value decomposition [12–14]. The estimate of the output of system C obtained using the k-component of the singular value decomposition of A, looks as below. dk' = CA+ k b = Tk b; Tk =

CA+ k

) ϕi UT dk' , = CVdiag σi

(1)

(

(2)

where C is the matrix that performs the transformation Cx = d0 , A+ k = V diag

(

) ϕi UT , σi

(3)

where ϕi = 1 if i ≤ k, otherwise ϕi = 0. −1 T Here, A+ k = V S U is the pseudoinverse matrix (n × m) obtained of k (k < n) components of the singular value decomposition, U = (u1 , ..., uk ) is the matrix of left singular vectors, V = (v1 , ..., vk ) is the matrix of right singular vectors, S = diag(σ1 , ..., σk ) is the singular value matrix. The optimal number k of singular value decomposition components can be found using the model selection criteria. Figure 2 shows the approach is function in principle.

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Fig. 2 Operation of the matching method

4 Improving the Accuracy of Estimating the Vector of Parameters by Converting a Linear System to a System with Specified Properties When solving a class of problems related to the processing of information received from various sensors (problems of protection against interference, identification, diagnosis, interpretation, etc.) there is a problem of effective analysis of noisy signal mixtures. In a number of such problems, the measured data are the result of summation of the effects generated by the physical process and weighted .by the coefficients, which leads to the use of linear parameters of the form y = Nj=1 ϕ j (z)β j where (β1 , β2 , ..., β N ) is the vector of parameters β ∈ R N , (ϕ1 (z), ϕ2 (z), ..., ϕ N (z)) is the vector of values of basic functions ϕ ∈ R N . The input vectors ϕ i form the matrix of inputs . ∈ R L ×N , the output values yi form the output vector y ∈ R L . If a possible set of basic functions is known (for example, a set of detection system response functions to known influences), but it is not known which of them formed the observed output, the solution of the approximation problem can be obtained by sparse approximation methods (see, e.g. Refs. [12–14]). For the output vector y0 not distorted by noise, the problem of sparse approximation is set as the problem of minimizing the number of nonzero components in the parameter vector under the condition y0 = . β. If the output vector is distorted by noise, the problem of sparse approximation is set as the problem of minimizing the number of nonzero components in the vector of parameters under the condition ||y − .β|| ≤ δ, where δ is a (small) value proportional to the noise vector ε. In connection with the solution of the problem of sparse approximation of the noisy output vector, the concept of “l0 -optimal solution” was introduced a solution that provided both the minimum approximation error and the maximum possible sparseness. However, the disadvantage of the approach to solving the problem of

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sparse approximation using the test for l0 -optimality is that the test cannot be applied to any system of basic functions. It is necessary to develop methods that allow the use of a wider class of basic functions for sparse approximation. However, the approach to solving the problem of sparse approximation using the l0 -optimality test has a drawback: the test cannot be applied to any system of basic functions. It is necessary to develop methods that allow the use of a wider class of basic functions for sparse approximation.

4.1 The Matching Method with the Conversion of the Output of a Linear System to a System with Specified Properties To solve the problem of sparse approximation with a noisy output vector, a modified matching method (MMM) is proposed. The method works as follows. Starting with k = 0 and f0 = 0, at the (k + 1)th pass the selection of the vector ϕ k+1 ∈ R L (columns of the matrix .) and calculation of the parameter βk+1 are performed, which minimizes the square of the residual norm: (βk+1 , ϕ k+1 ) = arg min ||rk − β ϕ|| 2 where rk = y − fk . After that the next appoximation fk+1 = fk + βk+1 ϕ k+1 is calculated. The vector of parameters β∗k obtained at the kth pass is checked for l0 -optimality. If the conditions of l0 -optimality are satisfied, the method ends. The test for l0 -optimality is as follows: the value of β∗k is a solution with the maximum possible sparsity and the smallest approximation error if d1 + d2K < 0.5 × (1 − μ(2k − 1)) × max |βi | and μ(2k − 1) < 1,

(4)

. where d K = ( j=K ||)1/2 , K is the number of largest scalar products of the remainder r with all ϕ j , μ(s) is the function of cumulative connectivity. Note that with respect to the l0 -optimality test, expression (4) uses the value of the maximum (by module) component of the vector of parameters (max j |β j |). The cumulative connectivity function is calculated for normalized vectors ϕ j by the rule: . μ(s) = max max ||, (5) /I card(I ) ≤ s j ∈

i∈I

where s is the number of nonzero parameters, I is the set of indices of functions that form the subspace under consideration, i indicates an element from the subspace for all possible decompositions of card(I )-members of the output vectors y (card(I ) = 1, 2, ..., s),i = 1, ... , card(I ), i ∈ I andcard(I ) ≤ s. These conditions mean that the power of the set of indices (subspace dimension) varies from 1 to s. Since the ‘basis connectivity condition’ μ(2k − 1) < 1 is not satisfied for any system of basic functions, we propose to stop the MMM according to the criterion of model selection. Comparative studies of the accuracy of estimating the vector of

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parameters of MMM with a stop on the criterion of model selection and the test for l0 -optimality showed that the accuracy of restoration of the vector of parameters on the criterion of model selection is worse than the l0 -optimality test. This forces us to look for ways to extend the class of basic functions used for sparse approximation. In the context of expanding the class of basic functions, we propose to transform the existing output vector to the output of a linear system formed by a system of basic functions that satisfy the condition of connectivity of the basis. The MMM algorithm with the conversion of the output vector consists of the following sequence of actions. Step 1.1. Form the matrix of inputs A ∈ R L × N , L 0 is satisfied, which corresponds to the dynamic equilibrium of the processes of destruction and restoration of secondary structures. The thickness of the destroyed film is a function of the vector g (block V(g)). The block diagram corresponds to the following system of equations: Spl = S − f ; f = Sp − Sb ; Sp = α1 (q)Spl ; SB = β(V)Sp ; i = khSp ; z = γ(g); α1 (g) = α[q, z(g)]. Therefore, we can write: i = [kSγ (q1 C)α1 (q1 C)]/1 + α1 (q1 C)[1 − β(v, C)]. The expression explicitly contains the vector C, the components of which are the parameters of materials and working media. Self-regulation as a phenomenon of friction is a logical expression of the universal phenomenon of structural adaptability. In fact, new phases appear on rubbing surfaces under conditions of adaptability (as a result of mass transfer with the medium and structural-chemical transformations), while friction acts as the creator of new materials that are extremely resistant to destruction during friction (surface structures) [18, 19]. To describe the regularity of the phenomenon of structural adaptability, which consists in the fact that in a certain (for a given combination of materials and boundary conditions of the scale, external temperature, physical and chemical means of the medium) range of loads and movement speeds, all types of interactions are localized in a minimum volume and such a spectrum of dissipative metastable structures and such a distribution of their volumes and dissipative flows between them, in which the total production of entropy would be minimal, a physical model of self-regulation is proposed, which is shown in Fig. 3. The following designations are used to describe the model under consideration: Sf is the area of actual contact, Sy is the area of juvenile areas on the surface of

f1

τ-ψ

Wоb WЕ

∫

Sy Spl

Wр Sf f2

q(t) Fig. 3 Dynamic model of self-regulation of metals and environment in the friction zone

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actual contact, formed as a result of destruction and wear of films, Wp is the rate of destruction of films (an increase in their area per unit time), g(τ) is the generalized loading parameter, depending on the value of the specific load p(τ), f1 and f2 are functions expressing the dependences of the rates of formation and destruction of films of secondary structures on the corresponding parameters, ψ is the time between the moments of destruction and wear of films (the formation of juvenile areas) and the appearance of new films in these areas. The parameter ψ is mainly characterized by the penetrating ability of the medium and the rate of physicochemical interaction between the medium and the juvenile metal surface. The following dependences correspond to the considered physical model: dSpl /dτ = Wob (τ) − Wp (τ) = WE (τ); Wob (τ) = f1 [V(τ), Sy (τ − ψ)]; Wp (τ) = f2 [g(τ)]; Sy (τ) = Sf − Spl . The film formation rate is proportional to the sliding velocity and the area on which their formation is possible and can be written as Wob = kW(τ)Sy (τ − ψ) where k is the film formation intensity factor. Taking into account the independence of the mechanical effects of the specific load and the speed of movement, it can be written that Wp [g(τ)] = a1 (V(τ) + a2 p(τ)), where a1 and a2 are coefficients depending on film strength [20]. Thus, the process of formation and destruction of secondary structures is described by a first-order differential equation and a retarded argument dSpl /dτ + k(τ)Spl (τ − ψ) = V(τ)(kSf − a1 ) − p(τ)a2 , which for p, v = const describes the state of selfregulation and stationarity of the processes of destruction and formation of films of secondary structures. Based on the analysis of the physical model of the transformation of surface layers during friction and the results of structural changes, taking into account the thermodynamic processes of mechanical energy dissipation, it was found that the physical and chemical wear mechanisms are invariant with respect to materials during friction. In addition, the indicated processes and mechanisms determine the nature and patterns of wear of both metal and metal-polymer friction units, regardless of the conditions of their loading and lubrication.

3 Conclusions 1. The evolution of the structure of surface layers of metallic materials and coatings under contact interactions is considered. A physical model of self-organization of surface layers during friction and an analysis of the state of surface structures subjected to energy impact are presented. 2. It is shown that one of the fundamental theoretical and applied achievements underlying the fundamental sequence of friction processes and the implementation of the physical wear mechanism is the structural adaptability of materials under friction loading. 3. The process of self-organization of materials under conditions of structural adaptability, which stimulates the regularity and adequacy of the formation of protective hardened dissipative structures, is considered. On the basis of the structural

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scheme of self-organization of wear processes, it is presented that the regeneration and destruction of secondary structures is described by a first-order differential equation with a retarded argument. 4. The mechanism of self-organization, which causes the appearance of normal wear and the occurrence of damage, is considered, the condition of dynamic equilibrium of the processes of destruction and restoration of secondary structures during friction is established. It is emphasized that the state of the contact surface, due to the ordered dynamics of the shielding structures, corresponds to the minimum values of the friction parameters and corresponds to normal mechanochemical wear. 5. The activated changes in the structure of a thin surface layer in the process of self-organization under friction loading are described, on the basis of which a sufficiently complete and consistent physical model is constructed that meets the fundamental principles of thermodynamics of irreversible processes. 6. Based on the analysis of the physical model of self-organization of surface layers during friction and the results of their structural changes, taking into account the thermodynamic processes of dissipation of mechanical energy, it has been established that the physicochemical wear mechanisms are invariant with respect to the materials of friction pairs.

References 1. Makhesana, M.A., Patel, K.M.: Performance assessment of CaF2 solid lubricant assisted minimum quantity lubrication in turning. Procedia Manuf. 33, 43–50 (2019). https://doi.org/ 10.1016/j.promfg.2019.04.007 2. Antonyraj, I.J., Singaravelu, D.L.: Tribological characterization of various solid lubricants based copper-free brake friction materials—a comprehensive study. Mater. Today 1, 2650–2656 (2020).https://doi.org/10.1016/j.matpr.2019.11.088 3. Antsupov, A.V., Fedulov, A.A., Antsupov, A.V., Antsupov, V.P. An application of antifriction coatings to increase the lifetime of friction units. MATEC Web Conf. 346, 03024 (2021). https://doi.org/10.1051/matecconf/202134603024 4. Matuszewski, M., Słomion, M., Mazurkiewicz, A., Wojciechowski, A.: Mass wear application of cooperated elements for evaluation of friction pair components condition. MATEC Web Conf. 351, 01006 (2021). https://doi.org/10.1051/matecconf/202135101006. 5. Babak, V.P., Shchepetov, V.V., Nedaiborshch, S.D.: Wear resistance of nanocomposite coatings with dry lubricant under vacuum. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetuthis link is disabled 1, 47–52 (2016). nbuv.gov.ua/UJRN/Nvngu_2016_1_9 6. Babak, V.P., Shchepetov, V.V., Harchenko, S.D.: Antifriction nanocomposite coatings that contain magnesium carbide. J. Frict. Wear 40(6), 593–598 (2019). https://doi.org/10.3103/S10 68366619060035 7. Vilhena, L., Ferreira, F., Oliveira, J.C., Ramalho, A.: Rapid and easy assessment of friction and load-bearing capacity in thin coatings. Electronics 11, 296 (2022). https://doi.org/10.3390/ele ctronics11030296 8. Zaytsev, A.N., Aleksandrova, Y.P., Yagopolskiy, A.G.: Comparative analysis of methods for assessing adhesion strength of thermal spray coatings. BMSTU J. Mech. Eng. 5(734), 48–59 (2021). https://doi.org/10.18698/0536-1044-2021-5-48-59

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9. Zhang, Y.-L., Li, H.-J., Yao, X.-Y., et al.: Oxidation protection of C/SiC coated carbon/carbon composites with Si-Mo coating at high temperature. Corros. Sci. 53, 2075–2079 (2011) 10. Huang, J.-F., Wang, B., Li, H.-J., et al.: A MoSi2 /SiC oxidation protective coating for carbon/carbon composites. Corros. Sci. 53, 834–839 (2011) 11. Zhi-Qiao, Y., Xiang, X., Peng, X., et al.: A multilayer coating of dense SiC alternated with porous Si–Mo for the oxidation protection of carbon/carbon silicon carbide composites. Carbon 46, 149–153 (2008) 12. Agüero, A., Muelas, R., Pastor, A., Osgerby, S.: Long exposure steam oxidation testing and mechanical properties of slurry aluminide coatings for steam turbine components. Surf. Coat. Technol. 200, 1219–1224 (2005) 13. Agüero, A., Muelas, R., Gutierrez, M., Van Vulpen, R., Osgerby, S., Banks, J.P.: Cyclic oxidation and mechanical behaviour of slurry aluminide coatings for steam turbine components. Surf. Coat. Technol. 201, 6253–6260 (2007) 14. Chroctek, T.: Tribological wear of Fe–Al coatings applied by gas detonation spraying. Tech. Sci. 24, 245–256 (2021) 15. Kochanov, G.P., Rogova, A.N., Kovalev, I.A., Shevtsov, S.V.: Preparation of niobium carbidebased high-temperature ceramics by direct niobium carburization. Inorg. Mater. 57, 1077–1082 (2021) 16. Kim, D., Lee, S., Kwon, S.: Evaluation of thermal conductivity of thermal barrier coating by a laser flash method and a differential scanning calorimeter. J. Korean Phys. Soc. 79, 953–960 (2021) 17. Abreu-Castillo, H.O., Bueno, B.P., d’Oliveira, A.S.: In situ processing aluminide coatings with and without tungsten carbide. Int. J. Adv. Manuf. Technol. (2021) 18. Karlov, V.I., Krykhtin, Y.I.: Investigation of the composition, structure and properties of new porous powder friction coatings obtained by plasma sputtering. MATEC Web Conf. Les Ulis 346, 45–77 (2021) 19. Wang, Q.: Mechanical and tribological evaluation of CrSiCN, CrBCN and CrSiBCN coatings. Tribol. Int. 130, 146–154 (2019) 20. Poplavsky, A.: The effect of vacuum annealing on the structure and properties of the electrically conductive a-CN coating. Vacuum 184, 109–119 (2021)

Fuels

Effect of Diethyl Ether Addition on the Properties of Gasoline-Ethanol Blends Viktoriia Ribun , Sergii Boichenko , Anna Yakovlieva , Lubomyr Chelaydyn , Dubrovska Viktoriia , Shkyar Viktor , Artur Jaworski , and Pawel Wos

Abstract This paper presents experimental studies carried out to investigate the effect of diethyl ether on the properties of gasoline-ethanol blends. The solubility of ethyl alcohol of different dehydration degrees in gasoline and stability of gasolineethanol blends was studied. It is shown that higher degree of dehydration provide better stability of gasoline-ethanol blends. The anti-knock properties of ethanolcontaining gasolines with different content of ethanol and diethyl ether additive was studied. The synergistic effect of anhydrous ethanol/diethyl ether mixtures on the properties of composite gasoline is shown. A mathematical model for calculating the octane number of gasoline-ethanol-diethyl ether blends has been developed. Amounts of some exhaust gases emission of gasoline and ethanol-containing fuels were studied experimentally and compared. Keywords Anhydrous ethanol · Diethyl ether · Stability · Synergistic effect · Octane number · Exhaust gases · Emissions

V. Ribun Chemical-Analytical Laboratory of the PJSC Ukrnafta, Kyiv, Ukraine S. Boichenko (B) · D. Viktoriia · S. Viktor Institute of Energy Saving and Energy Management, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine e-mail: [email protected] A. Yakovlieva Ukrainian Research and Educational Center of Chemmotology and Certification of Fuels, Lubricants and Technical Liquids, National Aviation University, Kyiv, Ukraine L. Chelaydyn Department of Environmental Protection Technology, Ivano-Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine A. Jaworski · P. Wos Department of Automotive Vehicles and Transport Engineering, Rzeszów University of Technology, Rzeszów, Poland © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_19

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1 Introduction Modern transport sector is strongly dependent on non-renewable energy resources (oil, coal, gas), which are used to produce motor fuels—gasoline, diesel fuel and liquefied petroleum gas. However, taking into account scarcity of fossil fuels and negative impact of transport on environment (transportation is responsible for about 14% of global carbon dioxide emissions), during last decades countries actively promote introduction of alternative motor fuels. Among the great variety of existing today biofuels, bioethanol is considered as one of the most promising alternatives to substitute petroleum-derived gasoline completely or partially in a form of gasolineethanol blends (GEBs). For Ukraine GEBs are currently considered as a way to reduce the consumption of light petroleum products and to improve the ecological characteristics of the environment. Actually, more than half of ethanol, produced worldwide is used as an additive to fuels for internal combustion engines. Many countries, including the United States, Brazil and Sweden, use fuels with an ethanol content of up to 85%, therefore road vehicle manufacturers produce cars equipped with engines, which are already adapted to gasoline-ethanol fuels. For example, in France fuel containing 5% ethanol is widely used [1]. In general, the dynamics of biofuel usage in the world is constantly growing. Consuming about 200 million tons of fuel and energy resources annually, Ukraine is considered an energy-deficient country because it does not fully cover the needs for energy resources and imports up to 85% of petroleum products. Such a state of the energy economy causes dependence of Ukraine on oil and gas exporting countries and threatens the country’s national energy security. Operating only 30% of its total capacity, the alcohol industry of Ukraine fully satisfies the domestic needs for the alcoholic beverage production [2]. That is why the study of properties of gasoline-ethanol blends (GEBs) containing various additives, finding out and elimination of the main drawbacks of these fuels is an important scientific and applied problem.

2 Literature Overview Internal combustion engines (ICEs) can operate with different types of fuel if the temperature is high enough to initiate fuel ignition at the end of the compression stroke [3]. So the use of blended fuels for internal combustion engines is appropriate and efficient [4, 5]. Oxygen-containing additives such as diethyl ether (DEE) and ethanol are used in the internal combustion engine (ICE) to eliminate the drawbacks of fuel combustion in the internal combustion engine in order to increase engine efficiency and control the combustion. Moreover, mixing DEE and ethanol is a promising way to prepare additives for blended fuels as DEE is higher reactive than most fuels, has appropriate evaporation heat, high oxygen content, low ignition temperature, which boosts ignition and cold start of the engine [7, 8]. Ethanol (E) is high octane biofuel

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made from crops with a higher heat of vaporization, rate of laminar flame spread and additional oxygen atoms compared to gasoline [9, 10]. Several studies show that DEE and ethanol, due to their higher oxygen content in its chemical structure, reduce CO, unburned hydrocarbons and soot emissions [11, 12]. The authors [13] showed that DEE contributes to the completeness of fuel combustion. In addition, some authors claim that at the engine speed of 1500 rpm butanol-gasoline mixtures have an earlier ignition time than ethanol-gasoline mixture containing the same fraction of alcohol. Results of the studies on using ethanol mixtures with gasoline are considered in [14]. However, there is a lack of researches on the use of DEE and ethanol mixtures in different proportions as additives to gasoline for improving the octane number of gasoline as anti-knock property and the stability of blended fuels for spark ignition ICE. Taking into account the mentioned above the study of cumulative effect of DEE and ethanol use for improving octane rating of gasoline seems to be relevant. Over the past decade, transport’s greenhouse gases emissions have increased at a faster rate than any other energy using sector. Rising of road traffic causes the need in improvement of fuel efficiency and decreasing exhaust gases emissions from motor transport [15]. Taking into consideration this urgent problem, the use of oxygen-containing additives in motor fuels may significantly contribute to reduction of exhaust gases during fuels combustion. Despite the numerous studies devoted to evaluation of emissions during ethanol-containing fuels combustion, there is a lack of studies of DEE effect on emissions reduction. The aim of the work is to study the synergistic effect of DEE and ethanol on the operation and physical–chemical properties of blended gasoline fuels. To achieve the aim of the study the following tasks should be fulfilled: . to study experimentally physical stability of GEBs; . to study the effect of DEE additives on physical stability of GEBs; . to study the influence of DEE and ethanol additives on the octane number (ON) of blended gasoline fuels; . to propose optimal composition of GEBs with DEE additives; . to study experimentally amounts of exhaust gases emission in a result of GEBs combustion.

3 Materials and Methods of the Study For determining physical stability of GEBs gasoline of grade A-92-Euro 5 and samples of ethyl alcohol of different purity were used. For blending with gasoline we have used industrially produced rectified alcohol (96% vol.)—E96, industrially produced alcohol (90% vol.)—E90 and anhydrous ethyl alcohol (100% vol.)—E100. Anhydrous ethyl alcohol was synthesized with calcium oxide and distilled using calcium chloride tube [13]. To determine the composition of ethanol samples we performed infrared spectral analysis of the original 96%, industrial 90% and absolute ethanol received in a result of synthesis.

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The following GEBs were studied 100/0, 90/10, 80/20, 70/30, 60/40, 50/50, 0/100 (were first number is ration of gasoline, and second is ration of ethyl alcohol). To study the influence of ethanol and DEE on ON of GEBs the samples were prepared using gasoline of grade A-80 and anhydrous ethyl alcohol containing 2.343% of diethyl ether. The following samples were prepared: 0.5% diethyl ether + 0.5% ethanol + 99% gasoline, 1% diethyl ether + 1% ethanol + 98% gasoline, 1.5% diethyl ether + 1.5% ethanol + 97% gasoline. Physical stability of GEBs was studied by means of optical methods by parameters of optical density, light transmission and refractive index. Measurements were done using photoelectric colorimeter KFK-2. Density of GEBs was determined using standard method for determination of density of oil products using set of areometers. Anti-knock properties of GEBs were studied by the parameter of ON. ON was measured using octane/cetanometer Shatox 100, research and empirical methods for ON determining as well. The principle of operation octane/cetanometer is to determine the detonation resistance of gasoline on the basis of measuring its dielectric constant and resistivity. Determination of the ON of gasoline mixtures was performed by the research method using reference mixtures of isooctane and n-heptane. Empirical determination of ON of GEBs was performed using the calculation method according to the formula: ONGEB = [26.44−0.29(ONo )] ln CE + [1.32(ONo )−29.49],

(1)

where ONGEB —ON gasoline-ethanol blend, ONo —ON of base gasoline, CE — ethanol content in gasoline-ethanol blend, % (vol.) To evaluate the amount of exhaust gases emissions formed during the complete combustion of gasoline with the amount of gases formed during complete combustion of the developed ethanol-containing fuels, the theoretical volume of air required for complete combustion of 1 kg of fuel was calculated according to the formulae 2. The theoretical volume of the content of products of complete fuel combustion was calculated according to the formula 3–7. V =

( ) H S O mol C + + − , 0.21 12 4 32 32

(2)

where C, H, S, O—mass content of elements in fuel; V mol —volume of 1 mol of air; 0.21—volumetric content of oxygen in air. VCO2 = 22.4

C ; 12

(3)

VO2 = 0.21(α − 1)V ;

(4)

VN2 = 0.79 · α · V ;

(5)

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H VH2 O = 22.4 ; 2

(6)

S , 32

(7)

VSO2 = 22.4

where V —volume of air necessary for complete combustion of 1 kg of fuel. The theoretical content (%) of chemical elements in ethanol, DEE, and ethanolcontaining fuel was calculated according to the formula (8). Data on the content of chemical elements in gasoline are taken from the reference literature. ωelement =

n · Ar element , Mr f uel

(8)

where n—number of atoms of the element; Ar —atomic mass of element; M r —molar mass of element. The theoretical content (%) of chemical elements in ethanol-containing fuel was calculated according to the formula (9): E blend =

.

K i Ei,

(9)

where E blend —content of element in fuel blend, %; K i —content of i-th component in fuel blend; E i —content of element in i-th component of blend.

4 Results and Discussion 4.1 Analysis of Physical–Chemical Properties of Gasoline-Ethanol Blends The physical–chemical properties of the GEBs were analyzed. Samples were prepared by blending gasoline with ethyl alcohol (E100, E96 and E90) in different ratios. In order to understand the solubility of ethyl alcohol of different dehydration degrees (E100, E96 and E90), photo colorimetric and refractometric analysis of gasoline-ethanol blends was performed. The curves of the optical density, light transmittance and refractive index of the blends are shown in the Figs. 1, 2 and 3 respectively. Some trends can be observed from Figs. 1, 2 and 3, namely, adding small quantities of ethyl alcohol to gasoline (up to 10%) leads to the separation of gasoline-ethanol blends. Gasoline, alcohol and water form an emulsion, because in the presence of fine water droplets the stability of gasoline-ethanol mixtures is disturbed. Due to the alkyl residue and high polarity, ethanol molecules have affinity to both water and gasoline

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Fig. 1 Dependence of optical density of GEBs on the ethanol dehydration degree and its content in the blends

Fig. 2 Dependence of light transmission coefficient of GEBs on the ethanol dehydration degree and its content in the blends

and can serve as stabilizers. However, if the amount of ethanol molecules is low, they cannot provide emulsification of water and gasoline molecules. Visually, this can be seen as turbidity. Deviation from the linear dependence of optical density and light transmission coefficient on the content of hydrous ethanol in GEBs at an ethanol fraction of 10 vol. % (Figs. 1 and 2) proves the inability of small amounts of ethyl alcohol to emulsify the water-gasoline system. However, the use of anhydrous ethanol solves this problem and a tendency to linear dependence on the curve of anhydrous alcohol can be observed.

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Fig. 3 Dependence of refractive index of GEBs on the ethanol dehydration degree and its content in the blends

Additionally, the refractive index of GEBs with different content of ethanol and in different ratios was studied (Fig. 3). The high content of ethanol (50% vol.) significantly changes the refractive index of the original gasoline (1435). However, the introduction of small amounts of alcohol (up to 20% vol.) does not significantly change the refractive index of GEBs. As can be seen from Figs. 1, 2 and 3, addition of small amounts of ethyl alcohol to gasoline (up to 10%) leads to the separation of GEBs. The use of absolute ethanol does not provide such effect, and the curve of absolute alcohol can be traced to linear dependence of GEBs stability on ethanol content. Since density is an important physicochemical parameter for fuels, the effect of ethanol concentration and content on the density change of gasoline-ethanol fuels was studied. From Fig. 4 it can be concluded that the addition of 90% and 96% ethyl alcohol in a volume up to 30%, and absolute alcohol up to 50% does not cause a significant change in density. The curves of the dependences of the GEBs density on the content of ethanol and its concentration express a linear relation. The higher the ethanol content the higher the density of ethanol-containing gasoline as the alcohol density is higher than the gasoline density.

4.2 Analysis of Anti-knock Properties of Gasoline-Ethanol Blends After studying the physical–chemical parameters of GEBs, a study of the anti-knock properties of ethanol-containing fuels was conducted. Synthesized by the authors [13]

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Fig. 4 Dependence of density of GEBs on the ethanol dehydration degree and its content in the blends

dehydrated ethanol containing 2.343% diethyl ether (DEE) was mixed with gasoline and its effect on the octane number (ON) of blended fuels was investigated. The physicochemical characteristics of some oxygen-containing additives for gasoline were previously analyzed (Table 1). As it can be seen from Table 1, DEE is similar in density and molecular weight to A-92 gasoline, and the boiling point of DEE (Tb = 34.6 °C) is close to the boiling point of A-95 gasoline (initial boiling point Tb = 40 °C). These properties are really useful for operating boosted gasoline engines in winter, when ignition is complicated because of low temperatures (< −10 °C). Therefore, to evaluate the combustion of GEBs prepared with anhydrous ethanol containing DEE, the ON of such mixtures (with an anhydrous ethanol content of 10– 95 vol. %) was determined by experimental and empirical methods (Fig. 5) [14]. The blends were prepared using gasoline of grade A-80 and anhydrous ethanol containing DEE. Table 1 Physical–chemical characteristics and ON of some oxygen-containing additives and gasoline No

Oxygen-containing additives/gasoline

Molecular weight, g/mol

Density ρ, kg/m3

Boiling temperature tb , °C

ON

1

Dimethyl ether

46.07

0.002

−24.9

105

2

Diethyl ether

74.12

713

34.6

110

3

Methanol

32.04

792

64.5

156

4

Ethanol

46.07

789

78.29

132

5

Gasoline A-92

72

730–780

40–205

95

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Fig. 5 Dependence of ON of gasoline A-80 on the volume of anhydrous ethyl alcohol containing DEE (99.95%)

ON of GEBs, determined experimentally, are significantly higher comparing to those determined by the empirical method (Fig. 5). This difference is explained by the fact that the empirical method for determining the ON takes into account only the content of gasoline and ethanol in the GEBs [14]. Based on experimental data, it can be assumed that the increase in ON of GEBs is due to the presence of DEE in those blends. Further experimental studies were performed to determine the ON of GEBs without DEE, GEBs containing DEE and pure DEE. It was found that ethercontaining anhydrous ethanol increases the ON of GEBs. Based on experimental data, a mathematical model for determining the ON of GEBs containing DEE was developed. . 4

C D E E ))) . · ln(C E + (1.32 · (ON0 ) − 29.49)

ONG E B = (26.44 − 0.29 · (ON0 − (4.6 ·

(10)

Thus, ether-containing ethyl alcohol enhances the gasoline ON more intensely. At a content of 20–40% vol. of such ethanol, the gasoline ON increased to 91–95 units (Fig. 6). At a content of 20–40% of such ethanol, the gasoline ON increased to 91–95 units. At the same time, according to empirical calculations, this content of dehydrated ethanol should increase the octane number of A-80 gasoline to 85–88 units (Figs. 4 and 5) therefore not so intensely. At the maximum possible content of anhydrous ethanol (80–90%) in gasoline A-80 octane number according to calculations should reach 91–93 units (Figs. 4 and 5), however, introducing the same amount of ether-containing anhydrous alcohol into gasoline causes much more effective increasing in the octane number and it reaches 97–97.5 units (Figs. 4 and 5).

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Fig. 6 ON of blends determined by experimental and empirical methods

Empirical model adequacy Sad was verified using Fisher’s test (F), which can be calculated by the following formula: . F=

2 2 Sad /S y2 , i f Sad > S y2 2 2 , 2 2 S y /Sad , i f S y > Sad

(11)

2 2 where Sad —adequacy variance; Sad —adequacy of experiment. The adequacy variance is determined by following formula:

.N 2 Sad

=

1=1 (yic

− yie )2

f

,

(12)

where yic —calculated values of the parameter; yie —experimental values of the parameter; f —the number of degrees of freedom. The number of degrees of freedom is determined by the formula: f = N − K.

(13)

The number of experiments is chosen within 10–99% of the ethanol content in the blend. For this study N = 13. The number of approximation coefficients depending on the ON of ethanol was calculated as the number of all numerical coefficients in the formula, taking into account the exponents and bases of logarithms (1). In this case, k = 7. Then the number of degrees of freedom f = 13–7 = 6. The variance of the experiment was calculated from the values obtained in a series of repeated experiments following:

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.N S y2

=

2 i=1 (yi− y)

f

,

(14)

where yi —values obtained in each experiment; y—the average values of the measured parameters; n—the number of repeated experiments. The number of repeated experiments at each point was 3. The arithmetic mean was taken as a result of the experiment at each point. The model can be considered adequate with a corresponding reliable probability, if the calculated value of the Fisher criterion does not exceed the tabular data. The reliable probability is 95%. Due to the fact that GEBs prepared on the basis of absolute ethanol can get some water during storage, transportation and operation, the effect of diethyl ether (DEE) on the stability of blended fuels and their octane numbers was examined. Since the lowest stability is found in GEBs containing less than 20% of ethanol, they were chosen to study the effect of diethyl ether on the stability of gasolineethanol fuels. As we can summarize from Figs. 7 and 8 diethyl ether has a positive effect on the stability of gasoline-ethanol fuels, causing increasing the light transmittance and decreasing the optical density of the examined compositions. Namely, these properties characterize the stability of GEBs: the higher the transmittance and lower optical density, the more stable GEBs are. Diethyl ether as well as ethyl alcohol has better performance than gasoline. In particular, the octane number of both oxygen-containing additives exceeds the octane number of gasoline by 20–30 units. However, ethyl alcohol has a significant disadvantage, namely, low saturated vapor pressure. To address these weaknesses of diethyl ether containing ethyl alcohol was blended into gasoline.

Fig. 7 Dependence of light transmission of GEBs containing 5% diethyl ether: 1—100% gasoline; 2—a blend containing 90% gasoline and 10% additives; 3—a blend containing 80% gasoline and 20% additives; 4—a blend containing 70% gasoline and 30% additives

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Fig. 8 Dependence of optical density of GEBs containing 5% diethyl ether: 1—100% gasoline; 2—a blend containing 90% gasoline and 10% additives; 3—a blend containing 80% gasoline and 20% additives; 4—a blend containing 70% gasoline and 30% additives

To study the effect of diethyl ether on the ON of GEBs, several reference mixtures were prepared. ON of blends were measured using a Shatox 100 octanometer (Fig. 9). DEE and ethanol have a synergistic effect on engine performance. The addition of only pure ethanol or only DEE in the amount of 1, 2 and 3% increases the ON of fuel blends by 2–3 units, and the addition of DEE/E mixtures containing ethanol E (0.5% DEE + 0.5% E; 1% DEE + 1% E and 1.5% DEE + 1.5% E) increases ON by 4–6 units.

Fig. 9 The effect of the oxygenated additives on the octane number of gasoline

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4.3 Analysis of Exhaust Gases Emissions from Gasoline-Ethanol Blends Combustion Automobile exhaust gases are a complex mixture of toxic components, including nitrogen oxides, carbon dioxide and carbon monoxide, sulfur oxides, unburned hydrocarbons, soot, aldehydes, and others. The composition of the exhaust gases is not constant and may vary depending on the fuel composition, type of internal combustion engine, its operating mode, load and technical condition of the vehicle [15–19]. Complete combustion of fuel results in emissions of carbon dioxide, sulfur dioxide, water, and nitrogen oxides [3, 6, 7]. To compare the amount of exhaust gases produced during the complete combustion of gasoline with the amount of exhaust gases produced during complete combustion of the developed GEBs, the theoretical volume of air required for complete combustion of 1 kg of fuel and the theoretical volume of products of complete fuel combustion were calculated. We have used a GEB sample that was composed of 75% gasoline (G) and 25% absolute ethanol (E) containing 2.34% of DEE was selected. This amount of DEEcontaining absolute ethanol increases the ON of A-80 gasoline by 12.4 units to 92.4. Table 2 shows the component composition of the studied fuel samples. Table 3 provides results of calculation of the theoretical amount of air required for complete combustion of 1 kg of fuel sample and the volume of products of complete fuel combustion. After theoretical calculations, the experimental study of CO2 and SO2 in exhaust gases was performed using gas analyzers. Portable gas analyzers of the “Dozor” type Table 2 Elemental composition of studied fuel samples Content, %

Fuel sample

C

H

S

O

Gasoline

85

14.95

0.05

Ethanol

52.17

13.04

–

13.79

DEE

64.84

13.51

–

21.65

GEB (75% gasoline + 25% DEE containing ethanol)

76.87

17.57

0.02

0.05

5.54

Table 3 Composition of exhaust gases during complete fuel combustion Fuel sample

Volume of air, Vair , m3

Volume of combustion products V, m3 CO2

H2 O

SO2

O2

N2

Gasoline

11.43

1.59

1.67

0.0004

0.96

3.36

Ethanol

6.96

0.97

1.46

–

1.02

9.33

DEE

8.64

1.21

1.51

–

1.64

3.45

GEB (75% gasoline + 25% DEE containing ethanol)

7.464

1.22

1.26

0.0004

0.98

4.83

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Fig. 10 The amount of air required for the combustion of gasoline (G) and its mixtures with DEE-containing ethanol (E) and the amount of carbon dioxide emissions in the exhaust gases

were used to analyze the composition of exhaust gases during the operation of the carburetor engine on A-95 and GEBs (75% gasoline + 25% DEE containing ethanol and 50% gasoline + 50% DEE containing ethanol). The studies were performed at the minimum crankshaft speed nmin = 800 min−1 ± 100 min−1 and at the maximum crankshaft speed nmax = 2200 min−1 ± 100 min−1 . Figure 10 presents the comparative analysis of theoretical and experimental amounts of CO2 in the exhaust gases of gasoline and GEBs and the amount of air required for their combustion. Therefore, the presence of ethanol and DEE in motor fuels reduces the amount of air required for fuel combustion and the amount of carbon dioxide in the exhaust gases. Moreover, the higher the percentage of additives, the more significant its effect. This effect is explained by the presence of oxygen atoms in ethanol molecules.

5 Conclusions In the result of this study the physical–chemical and operation properties of gasolineethanol fuels were studied. The obtained results allow us concluding the following: 1. The use of mixtures of DEE and absolute ethanol has further research prospects for improving the operational and physical-chemical characteristics of blended oxygenated fuels. 2. It is shown that ethyl alcohol blending into gasoline reduce the stability of ethanolgasoline blended fuels. However, increasing ethanol concentration and the DEE introduction stabilize blended fuels. 3. The DEE additives cause a synergistic effect on the ON of GEBs. 4. It has been developed the mathematical model for determining the ON of GEBs blends containing diethyl ether.

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5. It is shown that ethyl alcohol blending into gasoline allows improving environmental properties of fuels. Mainly, it allows reduction of carbon dioxide emissions and amount of air required for fuel combustion The fulfilled study allows us solving an important scientific and applied problem of the rational use of gasolines with ethanol content. The results of the study may be used during developing technology of production of oxygen-containing additives from domestic raw materials and new compositions of motor fuels with improved operational and environmental properties.

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Efficiency of Electric Logging in Thin-Layer Sections of Hydrocarbon Deposits (Gas Fields of the Precarpathian Depression) Oleksiy Karpenko , Mykyta Myrontsov , Yevheniia Anpilova , and Oleksii Noskov Abstract The non-trivial task of searching for and diagnosing oil and gas deposits in the sections of wells represented by thin-layer deposits remains relevant. Existing traditional methods of interpreting logging data are focused on other types of sections. In thin-layer deposits, the effectiveness of logging methods is much lower. Anisotropy and the mutual influence of the characteristics of neighboring strata eliminate anomalies in geophysical curves. This leads to numerous gaps in productive formations and objects in the well sections. Thickness values for the thickness of thin single layers sufficient to determine their geophysical characteristics, and further—and reservoir properties, are not suitable for bundles or layers of thin-layer thickness of the section. Despite significant advances in the theory and practice of interpreting these electrical methods data, geophysical characteristics or logging curves in front of thin-layer intervals of well sections in most cases do not allow direct effective quantitative and qualitative geophysical and geological interpretations for individual strata. Only the integration of these geophysical methods, the use of new approaches to the interpretation of logging data can increase the effectiveness of exploratory research. The statistical approach to the creation of new synthetic parameters allows the formation of contrasting anomalies in front of gas or oil-saturated formations. The research is devoted to this and the results are presented below. Keywords Thin-layered section · Well logging · Electrologging · Gas deposit · Electrical resistivity · Interpretation

O. Karpenko (B) Taras Shevchenko National University of Kyiv, Kyiv, Ukraine e-mail: [email protected] M. Myrontsov · Y. Anpilova · O. Noskov Institute of Telecommunications and Global Information Space of the National Academy of Sciences of Ukraine, Kyiv, Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_20

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1 Introduction The thin-layered type of section of sedimentary rocks is interpreted differently by specialists—representatives of different geological disciplines. The concept of “layer” in general geology is “an elementary unit of layered texture of sedimentary rocks, which differs from adjacent similar units in material composition, particle size, mineralogy, rock structure, nature of inclusions, staining, etc.“; in field geology, “layer” is defined as “an elementary unit in the description of a section.“ In stratigraphy, it is “a term of free use to denote small lithostratigraphic subdivisions, which often have local development” [1, p. 544]. “Layering” is characterized as “the texture of sedimentary rocks, which is expressed in the alternation of thin layers with a thickness of 1 mm to 1 cm” [1, p. 544]. Common in these definitions is the property of the rocks of the layer to differ from the rocks that contain it, some characteristics that are the subject of study of a particular geological science. Thus, the widely used term—“thin-layer section” should have distinctive features in different geological and geophysical disciplines. In geophysics, the term “fine-grained” is associated with the geometric resolutions of research methods. In the field of well logging, “thinlayering” is the property of a section consisting of a sequence of individual layers of rocks that differ from each other in lithological and reservoir characteristics, which creates anomalies in the curves of geiphysical methods, the width of which is to quantify the geophysical and geometric parameters of these layers. Naturally, when geologically interpreting the results of well logging on such anomalies, it is impossible to accurately estimate the lithological, reservoir or industrial characteristics of the layers (using standard methods of interpretation). Thus, Siberian scientists V. G. Mamyashev and I. G. Glazunov set the lower limit for estimating the electrical resistivity of layers in the layered thickness of about 2 m [2]. They divide the layering into levels: the first—macrolayer and the second—microlayer. The first level of stratification is characterized by layers of rocks from 2 m and less—to the lower limit of the resolution of the methods—0.4– 0.6 m. If the inhomogeneity is significantly less than the vertical resolution of the method (stratification is not distinguished by the shape of the curves), then use the “method of anisotropic formation” according to V. P. Zhuravlyov, also using the data of electrical methods [3]. When applying the above methods, it is possible to obtain only approximate values of geophysical parameters (electrical resistivity) of individual lithological components of the layered strata. The often used expression “thin-layer section” without reference to a specific geological or geophysical field of study creates difficulties in comparing the results of the diagnosis of rocks by different methods. Thus, even for different logging methods in the study of oil and gas wells, the vertical resolution varies significantly—from the first tens of centimeters (micromethods, LL and caliper) to 2–4 m (electrical gradient probes of large size). For most conventional measuring devices of radioactive, acoustic, electric focused methods, this value is 0.4–0.8 m. The figures are approximate, because the resolution property, in each case, depends on the well conditions, the ratios of the measured parameters of closely spaced layers and layers,

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the frequency of alternation of layers with different properties. For example, for a single layer it is possible to determine the value Rz (resistivity of the invaded zone) by the data only of small gradient probes with a thickness of at least 1 m [4, p. 103]. This is the maximum size of the layer sufficient to obtain the optimal value of resistivity. Determining the resistivity Rt of a layer using large gradient probe readings requires an even greater limit thickness of a single layer. In the sonic log method (SL), it is advisable to determine the value of the interval time when the thickness of the single layer is greater than the base of the probe, usually—0.4 m. These limit values of the thickness of thin single layers, sufficient to determine their geophysical characteristics, and then—and capacitive properties, are not suitable for bundles or layers of thin-layer thickness of the section. Due to the mutual influence on the probe readings (especially large, with a significant radius of the study area) of a number of adjacent layers and strata with different values of geophysical parameters, the resulting log curve will have a smoothed appearance; the integral characteristic of the thin-layer section of the well will be observed and registered. Thus, in the above we can highlight the following: it is necessary to specify the definition of the term “thin layer” for geological objects studied by well logging and use it for such types of sections, the geometric properties of which do not allow using conventional (standard) methods of interpretation to carry out a quantitative assessment of geophysical parameters and geological properties separately for each layer (layer) of small thickness of a certain lithological affiliation. From the analysis of the content of numerous scientific publications and production reports, it should be noted that, despite significant advances in the theory and practice of interpretation of electrical logging methods, geophysical characteristics or logging curves opposite thin-layer intervals of well sections in most cases do not allow directly perform qualitative geophysical and geological interpretations for individual layers of rocks of small thickness. This also applies to the data of other, non-electric methods.

2 Purpose and Objectives of the Study Issues related to the study of thin-layer rock deposits are considered. Such rocks are common in the sections of numerous gas fields of the Outer Zone of the Precarpathian Depression. Rocks of terrigenous composition, macro- and microlayered, predominate in the deposits of the Neogene system, as well as in the Neocomian and Senonian sections of the Cretaceous system. Lower Sarmatian sediments (Lower and Upper Dashava subsuites) are composed of layers of gray and dark gray shale, argillite-like clays and light gray, gray, greenishgray multigrained calcareous sandstones and siltstones and thin layers of tuffs. Tuffs and tuffites have been found to be largely pyritized, as a result of which they are easily distinguished on logging diagrams by very low values of electrical resistivity. In fact, these deposits, as well as the rocks of the Kosiv suite, are the main objects of research in this paper.

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It has traditionally been believed that gas reservoirs in thin-layer Neogene deposits of the Outer Zone of the Precarpathian Depression are the thin layers, layers of sandstones and siltstones, which are often lenticular in shape and lie among impermeable layers and clay strata. Some researchers (O. O. Orlov, A. V. Loktev, etc.) develop a hypothesis about the gas-bearing reservoir of the clay layer directly, in which with increasing content of psammitic material appear collector conditioning properties [5]. General well-logging geophysical characteristics of typical thin-layer deposits. Most methods of interpreting well-logging data are based on factual information about the properties of geological objects obtained in a petrophysical laboratory or (often more reliably) in formation tests. The quality of quantitative or qualitative interpretation depends largely on the presence and magnitude of systematic and random errors in the recording of geophysical parameters, most often—on the accuracy of registration of a single parameter. Serious shortcomings that affect the effectiveness of most methods of interpretation of well logging data are: . common errors about higher accuracy and reliability of laboratory analyzes of core material in comparison with geophysical data; . unrepresentative diversity of lithotypes of rocks in the section of the well core material; . insufficient amount of core material to build reliable petrophysical models of section rocks; . discrepancy between the physical volumes of research in core analysis and geophysical research (corresponding to different hierarchical levels of the structure of the geological object from the standpoint of systems analysis); . methodological differences in measurement technologies by laboratory and well installations; . others. In addition to the above, traditional methods of interpretation, like any other, have their natural limitations in terms of accuracy and reliability of the final results. In the conditions of thin-layered terrigenous sections of gas fields of the Outer Zone of the Precarpathian Deflection, the efficiency of using the electrical resistivity Rt of formations, its ratio to the resistivity of the invasion zone Rt/Rz, or the saturation parameter Fs = Rt/Ro (where Ro—electrical resistivity of water saturated rock/formation) as a diagnostic sign of gas bearing reservoir formation, is low due to the manifestation of the known effect of anisotropy of thin-layer strata, increased clayness, the large invasion zones and too small thicknesses of individual layers [6–9]. The Dashava and Kosiv suites are very complex objects for geophysical research, and special methods and techniques of research and interpretation must be used here. Unfortunately, due to various reasons, logging methods in the open wellbore of exploration and prospecting wells are not very suitable for detecting reservoirs and productive strata in the low-resistivity thin-layer section. With the increase in the specific content of clayey sand-siltstone and clay layers, which is typicaly for most gas deposits of the Outer Zone, direct separation of

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water-saturated, gas-saturated and “dry” intervals or strata by geophysical parameters becomes impossible. Only the experience and intuition of interpreters and geologists allows, according to the standard set of geophysical studies of wells to establish the nature of the saturation of individual parts of the sections and offer them for testing. However, there are practically no quantitative geophysical signs of gas-bearing reservoir of thin-layered strata, ie, significant differences in the values of readings of individual methods by the nature of saturation. According to the results of research to identify the limit values of the parameters for the separation of water-saturated and gas-saturated rocks of the Upper Dashava subsuite and low-sandy intervals of the Lower Dashava, the following is established. Practically for almost every field, vague boundaries of geophysical parameters have their own meanings. The coefficient of separation efficiency by the nature of saturation for each parameter does not exceed 60–70%. Histograms of distribution of characteristics for rocks (strata) with different nature of saturation practically oveRtap. A small difference in the average values (or median) of the electrical resistivity, the intensity of radiation according to GR or NGR, the interval time for sonic log does not always allow to reliably determine the saturation of rocks. The thickness of individual layers and layers, as noted above, is much smaller than the size of gradient probes of resistivity log. As a result, the effect of parallel inclusion of thin layers is cleaRty manifested here—the curves of resistivity log probes are pooRty differentiated, the electrical resistivity of productive and water-saturated strata is quite low, in the range of 2–4 .·m. Studies of the spread over the area of gas-saturated strata within individual fields indicate a predominantly lenticular structure of deposits. Many productive or watersaturated strata opened by wells, when detailed by well-logging methods, are the “brushes” made of thin layers of reservoirs and clays. Externally hidden cyclic structure of strata and horizons is revealed by mathematical processing of curves of well-logging methods by mathematical filtering of data of separate methods on a well section [10–12]. At the same time contrasting anomalies of a high-frequency component on the logging curves recorded by probes with rather low vertical resolution on electrical resistivity R, for example, 2.25 or 4.24 m gradient probes are shown. The use of the method with the number of resistivity gradient probes (BKZ) in order to identify productive and water-saturated reservoirs in this type of section does not give noticeable positive results. Partly low efficiency of BKZ is connected with a thin-layered structure of a thickness, partly—with application of the traditional processing techniques calculated for homogeneous layers of considerable thickness [13, 14]. Unfortunately, geophysical surveys in wells in the Precarpathians use standard sets of methods and techniques suitable for qualitative and quantitative processing of well logging data in simpler types of sediments.

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3 Research Methods In recent years, work has been done to identify geological and geophysical conditions, the feasibility of effective application of new methods of rapid interpretation of well logging data with the involvement of specialists of industrial and geophysical organizations in order to establish in thin layers of productive objects. It should be emphasized that these works were supported by the management and specialists of a number of geophysical and oil and gas production organizations. When developing new methods and techniques, the following tasks were set: firstly, to use the data of conventional well logging methods, which are included in the mandatory complex of well logging; secondly, to develop quantitative criteria for the detection of productive (oil and gas-saturated) objects—strata and bundles of layers in thin-layered deposits of different types. Using the relaxation parameter of electrical resistivity to detect gas-saturated layers and section intervals. An analogue of the following approach to the detection of productive thin-layer parts of the section is a known method of determining the nature of fluid saturation of the reservoir rock in the well section by determining the value of electrical resistivity or resistivity increase parameter (parameter of saturation)—Fs. As already noted, the efficiency of separation of thin-layered rocks by the value of electrical resistivity is extremely low, as with other geophysical parameters and known criteria, so you should look for other ways to solve this problem. The resistivity increase parameter (or saturation parameter) is calculated as follows: Fs =

Rt Rt = , Ro F · Rw

(1)

where Rt—electrical resistivity of the rock, determined according to electrical logging methods; Ro—calculated electrical resistivity of a similar rock under the condition of 100% filling of the pore space with formation water; F—formation resistivity factor—relative parameter that characterizes the porosity of the rock; Rw—electrical resistivity of formation water. In the practice of well logging or geophysical works, the value of the electrical resistivity of rocks R is determined only by resistivity gradient probes (BKZ) or by other electrical methods using probes of large radius of study and, accordingly, low vertical resolution. It follows that the ability to determine the values of R layers of different thickness is limited by the size of large probes of electrical logging, and in thin layers it is impossible to determine the electrical resistivity of individual layers to assess the saturation of specific layers of reservoir rocks by (1). Practically critical value of the Fs parameter in homogeneous low-clay oil and gas saturated rocks in the separation of productive and water-saturated intervals is 6–8. From (1) it follows that the separation efficiency of reservoir rocks by saturation is determined by the difference between electrical resistivity. This method of detecting productive gas-bearing and oil-bearing formations and intervals according to existing electrical research methods is ineffective in thinlayer sections of wells. The values of electrical resistivity measured in the well

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in productive and water-saturated thin-layer strata are close in magnitude to the values characteristic of the general background of clay rocks and are, as a rule, units of Ohm·m. Significant oveRtap of the ranges of electrical resistivity of productive and water-saturated rocks in clays or thin-layer sections does not allow the use of electrometry methods to detect oil or gas saturated intervals in well sections using Fs or absolute values of electrical resistivity. The main purpose of the new method is to allocate intervals with different nature of fluid saturation in the sections of wells of thin-layer types according to the values of electrical resistivity of rocks, which are registered by conventional probes of electrical well studies. To do this, based on the data of R logging probes of different sizes of the BKZ method, the transformation of well logging information is performed in order to obtain parameters that characterize the presence of productive (oil or gas saturated) intervals in terms of clay layers in the presence of layers with high sand content. The essence of the new method of detecting productive intervals is that the interpretation uses not the absolute values of the electrical resistivity of individual probes, and the statistical characteristics of high-frequency components of the curves R, we called the curves of “residual apparent resistivity” Rf . The parameter Rf at the depth zi of the section of the well is determined by the procedure of digital filtering of logging curves, for example by the method of a moving strip: R f (z i ) = R(z i ) − R(z i ),

(2)

where zi —the depth of the well section at the point i taking the electrical resistivity of the probe; R f (z i )—residual electrical resistivity of the probe at depth z i ; R(z i )— counting the electrical resistivity of the probe at depth z i ; R(z i )—smoothed (average) value of the electrical resistivity of the probe in the depth range from (zi —0.5·Δz) do (zi + 0.5·Δz), calculated for depth zi (.z—the depth interval in which the averaging of the electrical resistivity of the probe is performed; for a typical thin-layer section, it is recommended to choose about 2 m). Figure 1 shows a typical interval of a thin-layered section of the Kosiv suite, where the repetition of almost all anomalies from thin layers (less than 1 m) on BKZ pribe curves, which are more contrasting after filtering by moving strip, is cleaRty visible. This pattern is observed in all, without exception, curves of BKZ gradient probes with a length of 0.45–4.25 m inclusive, recorded in wells of thin-layer sections of all types in the hydrocarbon deposits covered by our research. Example of Fig. 1 is a confirmation of the possibility that local layers of small size form noticeable anomalies on the curves of not only small but also large of the gradient probes, which is often underestimated in the detailed interpretation of well logging data. This makes it possible to determine the bundles of productive layers and layers of rocks because in front of water-saturated or clayey impermeable thin-layer intervals there is a rapid damping of oscillations of this component with increasing size or radius of the logging probe. In contrast, in productive thinlayered intervals, significant differentiation of the Rf parameter is preserved on the curves of large probes with a significant study radius. For comparison: in a thin-layer

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Fig. 1 An example of the reflection of anomalies of electrical resistivity from individual layers of rocks on the curves of the gradient probes BKZ in the sediments of the Kosiv suite in the well of Bohorodchany gas field: R1–R4—curves of electrical resistivity 0.45–4.25 m gradient probes BKZ; R1f –R4f —curves of residual electrical resistivity after filtering the curves of the gradient probes

section according to R values taken from the curves of imaginary apparent resistivity of electric logging probes of different sizes, it is impossible to effectively divide the section into aquifers and gas-bearing intervals, and Rf curves already have a marked degree of attenuation with increasing probe size saturation of rocks. This is explained by the fact that due to the presence of the ivasion zone in reservoir rocks (characterized by increased sandiness in clay strata) on the curves of small probes, the differentiation of Rf values is determined only by the ratios of thicknesses and resistivity values of impermeable clay and permeable layers, filled with filtrate of drilling mud fluid. If the section is represented by alternating layers of clay rocks and permeable reservoirs, then on the residual apparent resistivity curves of large probes significant fluctuations in Rf values are observed only opposite the productive intervals, when reservoir layers outside the penetration zone due to oil or gas saturation have increased electrical resistivity values. in relation to the electrical resistivity of clay rocks (Fig. 2). In the presence of layers of water-saturated rocks, the electrical resistivity of which differs little from the resistivity of clay rocks, the differentiation of Rf curves of large probes will be much smaller than in the presence of oil or gas-saturated layers [2, 9, 15]. Figure 2a also shows the case of alternation of clayey rocks of sandstones and compacted rocks-non-reservoirs with high electrical resistivity. Similar intervals are distinguished on the curves of small gradient probes by a high degree of differentiation, which also naturally decreases in the direction of increasing the probe size.

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Fig. 2 Examples of reducing the differentiation of curves of gradient probes with increasing probe size in a thin-layered clay-sand section of the well: a—interval with compacted layers of sandstone; b—interval with water-saturated layers of sandstones; c—interval with gas or oil-saturated layers of sandstones; R1f, R3f, R4f —curves of residual electrical resistivity of 0.45 m, 2.25 m and 4.25 m of gradient probes, respectively

The phenomenon of preserving significant differentiation of residual resistivity curves with increasing probe size (for example, gradient probes of electric logging— up to 2.25, 4.25 m with an average thickness of layers of rocks 0.3–0.8 m opposite the productive intervals) is reliably confirmed in typical thin layers Neogene deposits in gas fields of the Outer Zone of the Precarpathian Depression, where currently revealed gas-saturated horizons, which were missed in the past in some areas due to the impossibility of their allocation by conventional methods of interpretation of logging data in well sections. To assess the degree of differentiation of the residual electrical resistivity curve at each depth point zi of the logging probe curve, statistical evaluation of the variability of Rf values, such as variance, is performed in a certain depth window on both sides of this point zi —0.5·Δz (for a thin-layer type of section, it is desirable to set the value of Δz about 2 m). Thus, the residual electrical resistivity curves are converted into a parameter curve called the “residual electrical resistivity variance DRf or the standard deviation of the residual electrical resistivity σ Rf ”. Table 1 shows the average values of the distributions of the specified parameter σ Rf depending on the size of the probe and the nature of the saturation of the formations, established by industrial tests in exploration wells of Rubanivske gas field, Orkhovitske oil and gas field, Lyubeshivske, Vereshivske, Khidnovitske, Teysarivske, Bohorodchanske gas fields.

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Table 1 Distribution of σ Rf values depending on the nature of saturation of thin-layer layers and the size (L) of the gradient probes BKZ The nature of saturation

Values of σ Rf , Ohm·m of gradient probes: L = 0.45 m

L = 1.05 m

L = 2.25 m

L = 4.25 m

Number of test intervals

Gas

0.225

0.426

0.522

0.429

20

Water

0.487

0.458

0.087

0.074

23 12

“Dry”

0.495

0.833

0.241

0.176

Gas + water

0.033

0.056

0.031

0.031

5

All groups

0.363

0.489

0.258

0.209

60

4 Research Results From the data in Table 1 it is seen that in all cases of saturation of thin-layer strata or the layers except gas-saturated, there is a decrease in the differentiation of Rf curves on large 2.25 and 4.25 m probes relative to 0.45 m. Data on 1.05 m gradient probe were excluded from consideration and use due to the fact that its readings and configuration of the curve are significantly influenced not only by the features of the washed formation zone or invariant part, but also by the variability of invasion zone diameter. its neither as a “detector of lithology” in the near zone, nor as a “detector of saturation of the formation”—under the influence of an invariable part of the formation. In the calculations in order to use quantitative indicators of the presence of the productive interval, it is proposed to introduce a value called “parameter of radial relaxation of residual electrical resistivity” or “parameter of relaxation of residual electrical resistivity” Pr [12]: Pr = f

σ (R f l) , σ (R f sm)

(3)

where Pr—relaxation parameter of the residual electrical resistivity; σ Rfl and σ Rfsm—respectively, the value of the standard deviation of the residual electrical resistivity of the high-frequency component of the readings of the logging probes curves of large and small size in a certain window depth of 0.5 · Δz on both sides of the observation point; f —function or constant value to improve the visual rePrentation of the Pr curve. The limit value of the relaxation parameter of the residual electrical resistivity is set using reference samples. When using the decimal logarithm of the ratio of the corresponding standard deviations of the residual electrical resistivity instead of the function f : Pr = lg

σ (R f l) . σ (R f sm)

(4)

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The Pr parameter is usually in the range of −2 to +2 for typical terrigenous thin-layered sediments. It is established that gas-bearing productive horizons in thinlayered sections exist where the values of the relaxation parameter are greater than 0. The value 0 is the limit value Pr1, Pr2, which is set for Dashava and Kosiv suites deposits in the depths of 500–2500 m) (Figs. 3 and 4) using cumulative curves of parameter distributions for rocks with different nature of saturation. Comparison with the test results of the intervals of thin-layered sections of wells found that the efficiency of separation of rocks into water-saturated and productive using standard methods of interpretation of the usual complex of well-logging and geophysical research averages no more than 59% in Neogene deposits for different gas fields of Precarpathian. During the experimental use of the relaxation parameters of the residual electrical resistivity Pr at the Orkhovitske and Lyubeshivske gas fields (gradient probe data of 4.25 and 0.45 m were used), the efficiency of separation into productive and aquifer intervals in these areas increased on average to 87%. When using the same Pr parameters for two pairs of probes with sizes of 4.25 and 0.45 m and 2.25 and 0.45 m, the efficiency of separation of rocks into water-saturated and gas-saturated was 92%. Fig. 3 Distribution of average mean square deviations of residual electrical resistivity σ Rf for curves of BKZ gradient probes and relaxation parameters of residual electrical resistivity Pr depending on the nature of saturation in the intervals of thin-layered sections of gas fields

Fig. 4 Determination of limit values of residual electrical resistivity parameters Pr for Neogene rocks

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Figure 5 shows diagrams of electrical resistivity, residual electrical resistivity and relaxation parameters of residual electrical resistivity of gradient probes of different sizes: in the range of depths of thin-layered water-saturated rocks and in the range of depths of gas-saturated rocks of the Kosiv suite of the well Bohorodchanske gas field. It should be noted that the formation with a positive anomaly of electrical resistivity (1503.0–1503.8 m in Fig. 5) within the interval of the section, where the gas flow of 36 thousand m3 /day, can be attributed to the tight lay in accordance with the anomalies Pr1, Pr2, and the main productive reservoir here should be considered a thin-layer pack at a depth of 1500–1505 m. The inflow of formation water from the upper perforation interval is confirmed by the Prence of small values of the relaxation parameter of the residual resistivity.

5 Discussion and Conclusions A detailed analysis of the field of effective application of the parameters Pr1, Pr2 notes that it can already be noted that studies indicate the possible existence of false positive extremes of the parameter opposite the layers, where there is a sharp change in electrical resistivity. For example, in the presence of individual high-resistivity strata thicker than 0.6–0.8 m, or—pyritized tuffs and tuff with very low values of R, even against the background of low-resistivity clay-sandy rocks Dashava and Kosiv suites. That is, the use of the method of radial relaxation of residual electrical resistivity as with all other existing methods and techniques, competent analysis of the results in order to prevent or reduce the likelihood of erroneous conclusions about the existence or absence of oil and gas intervals in the section of the well. Using a new method of the radial relaxation parameter of the residual electrical resistivity, thin-layered potentially gas-saturated strata of rocks were recommended for testing horisons VD-13, VD-14 of well 12-Makunivska, where industrial gas inflow was obtained from the recommended depth intervals and, thus, a new gas deposit was discovered in the formations of Upper Dashava subsuite. Earlier we found that the limit value of Pr1, Pr2, which separates water-saturated or impermeable clay thin-layered intervals from gas-saturated, is 0. For typical thinlayered sediments with frequent alternation of layers of clays, siltstones and sandstones mostly less 0.4–0.6 m, the specified value of the relaxation parameter is quite stable for different depth intervals. However, with increasing sand content of the section and the thickness of individual layers (0.8–1.6 m), a sharp decrease in the value of Pr1 or Pr2 is often observed, even in gas-saturated intervals. This phenomenon is due to the fact that the layer ceases to be thin-layered in relation to the size of the applied gradient probes BKZ (0.45; 2.25 m). Anomalies in the curves of electrical resistivity in front of gas-saturated permeable layers increase sharply, including for small gradient probes. Under such conditions, the values (or curves) of the relaxation parameter of the electrical resistivity are in the negative area, which is not due to the nature of the saturation of the stratum, but to the fact that the sandy-clay stratum ceased to satisfy the thin layer. In connection with the above, this thickness

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Fig. 5 Example of detection of gas-saturated thin-layered rocks in the well section of Bohorodchanske gas field

is the part of the well section, which clearly stands out individual layers on all curves BKZ; curves are characterized by sharp differentiation. The preconditions on which the determination and use of the relaxation parameter were previously based (for thin-layered strata, poorly differentiated by electrical resistivity) in this case are not met. The issue of identifying the area of effective application of the parameters Pr1, Pr2, has led to additional research related to the existence of different types of thin-layered well sections. As mentioned eaRtier, under a thin-layered section (in

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relation to the geometric characteristics of probe devices of well-logging methods) we consider layering of layers with thicknesses less than or equal to 0.7–0.6 m, with small amplitudes of geophysical anomalies, which in most cases cannot be used for quantitative geological interpretation according to standard methods. However, just such noted features of the thin-layered section are a prerequisite for the effective application of the parameters Pr1, Pr2 in the detection of productive thin-layered strata in the thin-layered terrigenous section.

References 1. Dictionary of Petroleum Geology. Leningrad, Nedra, pp. 1–679 (1988). https://www.geokniga. org/books/216 2. Mamyashev, V.G., Glazunov, I.G.: Methods of petrophysical support for the interpretation of electrometry data of heterogeneous-layered sandy-clay reservoirs. In: Efficiency of Geophysical Studies in the Exploration of Oil and Gas Fields in the Tyumen Region: Collection of sc. papers, Tyumen, Zapsibneftegeofizika, pp. 34–41 (1988) 3. Zhuravlyov, V.P.: Determination of the electrical resistivity of anisotropic formations. Appl. Geophys. 51, 170–187 (1968). Moskov, Nedra 4. Itenberg, S.S.: Interpretation of Well Logging Results. Moskov, Nedra, pp. 1–375 (1987). https://www.geokniga.org/books/8435 5. Loktev, A.V.: Reasons for the omission of productive horizons in the clay layer of the Neogene of the Outer Zone of the Precarpathian DePrsion and measures to prevent them. Explor. Dev. Oil Gas Fields 3, 123–126 (2003). Ivano-Frankivsk, http://elar.nung.edu.ua/bitstream/123456 789/5440/1/30p.pdf 6. Izotova, T.S., Bondarenko, O.V.: Computer technology of interpretation of well logging data for thin- and microlayered sections of Miocene of the Precarpathian DePrsion. In: Theoretical and Applied Problems of Oil and Gas Geophysics, Kyiv, UkrDGRI, pp. 113–117 (2001) 7. Karpenko, O.M., Loktev, A.V.: Increasing the informativeness of well logging in the study of clay-sandy sections of thin-layered structure. Nauk. IFNTUNG newsletter, 1, Ivano-Frankivsk, pp. 20–24 (2001). http://elar.nung.edu.ua/handle/123456789/749 8. Kondrat, R., Khaidarova, L.: Research of influence of characteristics of opening of gas-bearing layers by perforation on production possibilities of a well. Explor. Dev. Oil Gas Fields 73(4), 46–53 (2019). https://doi.org/10.31471/1993-9973-2019-4(73)-46-53 9. Myrontsov, M., Karpenko, O.: Radial characteristics of lateral logging in thin-bedded formation. In: Conference Proceedings, Geoinformatics, vol. 2021, pp. 1–7 (2021).https://doi.org/ 10.3997/2214-4609.20215521045 10. Dech, V.N., Knoring, L.D.: Unconventional Methods of Complex Processing and Interpretation of Geological and Geophysical Observations in the Sections of Wells. Leningrad, Nedra, pp. 1– 192 (1978). https://www.twirpx.com/file/3095326/ 11. Karpenko, O.M., Fedorishin, D.D.: Estimation of productivity of a section of wells at a limited complex of well logging. Sc. Bull. IFNTUNG 1(2), 16– 20 (2002). https://studres.ru/product/ots-nka-produktivnost-rozr-zu-sverdlovini-pri-obmezh enomu-kompleks-promislovo-geof-zichnikh-dosl-dzhen 12. Karpenko, O.M., Onishchuk, O.M.: Morphological characteristics of logging curves in the aspect of solving applied geological and geophysical problems. In: Theoretical and Applied Aspects of Geoinformatics, pp. 99–107 (2008). http://dspace.nbuv.gov.ua/handle/123456789/ 12604 13. Karpenko, O., Myrontsov, M., Karpenko, I., Sobol, V.: Detection conditions of gas-saturated layers by the result of complex interpretation of non-electrical well logging data. In: Conference Proceedings, XIV International Scientific Conference “Monitoring of Geological Processes and

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Formation Mechanisms and Overcoming Methods to Reducing Natural Gas Consumption in the Residential Sector Olexandr Yu. Yemelyanov , Tetyana O. Petrushka , Anastasiya V. Symak , Kateryna I. Petrushka , and Oksana B. Musiiovska Abstract The authors simulated the barrier formation mechanisms on the way to improving the natural gas use efficiency in the residential sector and suggested effective ways to overcome these barriers. Regularities of barriers formation on the way to reduction of consumption of natural gas in apartment houses are considered. Grouping of these obstacles was carried out. Factors affecting the level of these barriers have been identified: shortage of necessary resources, insufficient level of resource quality, insufficient level of investors competence (i.e. persons who decide on the implementation of investment measures to save natural gas consumption in residential buildings), political and institutional factors, as well as insufficient level socio-economic results from the implementation measures to save natural gas consumption in the residential sector. A number of barrier model mechanisms have been built to improve the efficiency of natural gas use in the residential sector. The quantitative measurement method of the financial and economic barriers level that arise during the measure’s implementation for the purpose of natural gas saving by households is proposed, in case of financing these measures by borrowed funds. A grouping of ways to overcome barriers on the course to reducing natural gas consumption in the residential sector has been made. An optimization model for the state programs formation of financial support for measures for the purpose of reducing natural gas consumption in residential buildings has been developed. According to the analysis of the sample of Ukrainian households, the most significant barriers to the measures implementation with the object of reducing natural gas consumption by the surveyed households are obstacles caused by shortage of necessary resources and obstacles caused by shortage of investor competence. The forecast indicators of the state financial supporting program of those households seeking to implement measures with the object of reducing natural gas consumption on the basis of thermal modernization of residential buildings were calculated. Keywords Energy consumption · Barrier · Modeling · Overcoming · Residential building · Thermal modernization · Natural gas O. Yu. Yemelyanov · T. O. Petrushka · A. V. Symak · K. I. Petrushka · O. B. Musiiovska (B) Lviv Polytechnic National University, Lviv, Ukraine e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_21

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1 Introduction For many countries around the world, the problem of ensuring proper economic growth is acute. Solving this problem is a necessary condition for improving the welfare of the population [1], improving employment [2] and reducing the budget deficit [3]. At the same time, significant rates of economic growth are often accompanied by increased use of various energy resources types, especially non-renewable energy sources [4]. Such an increase usually has a negative impact on the environmental situation [5], worsens the energy security of countries [6] and reduces their opportunities for sustainable development [7]. Therefore, exists a contradiction between the urgent need for sustainable economic growth and the need for economical consumption of fossil energy resources. This contradiction is resolved by the transition to sustainable energy-saving economic development [8], which is accompanied by long-term economic growth while reducing the consumption of non-renewable energy. Whereas the transition to this economic development type requires the implementation of various technical, technological, organizational and other measures [9, 10] aimed at improving the efficiency of non-renewable energy [11], particularly by replacing them with renewable energy [12]. In many countries around the world a significant share of the energy consumption places such non-renewable energy resources as natural gas [13]. Therefore, reducing the use of natural gas is one of the main ways to ensure energy-saving economic development [14]. In recent years, there has been a significant reduction in the consumption of this energy resource in a number of countries. As a consequence, further reduction of its use with the simultaneous growth of gross domestic product may be associated with significant difficulties [15]. One of the prospective overcoming methods of these difficulties is to accelerate reduction rate of natural gas consumption in those economic sectors that do not have a significant impact on the value of gross domestic product. Particularly, this includes residential sector. At the same time, as for any other economic sector, the projects implementation to reduce natural gas consumption in residential buildings faces various barriers [16]. Identifying overcoming methods of these barriers requires preliminary study of their formation mechanisms [17] and the development of effective assessing tools for the level of these barriers [18].

2 Literature Review and Setting Research Objectives A significant amount of scientific work has been devoted to the assessment and overcoming of barriers to the implementation of energy-saving projects in both enterprises and households. Meanwhile, there are some differences between the authors’ views on the peculiarities of the formation of these barriers. In particular, scientists identify different types of the most important of them. Including in particular, in [19] the main

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obstacles to the implementation of energy-saving technological change projects are economic barriers. A similar opinion is expressed in [20], where the delay in the implementation of energy saving projects is explained by the lack of appropriate financial incentives. Some other researchers point out that management barriers play a crucial role. Particularly, in the study [21] has been showed that due to lack of rationality, lack of energy saving among the main goals and shortcomings in information support, businesses abandon energy saving projects, which are instead quite effective. The importance of information barriers as a factor that determines the slow implementation of energy-saving projects is also noted in the study [22]. Also, some authors, particularly in the study [23], among the barriers to energy efficiency, pay special attention to the significant level of risk in the implementation of many energy-saving programs and projects. However, the implementation of such programs and projects often requires large investments [24], while many businesses and households lack the necessary financial resources. Meanwhile, lending as the most common external source of financing for energy saving measures is often not attractive enough for the persons who plan to implement these measures [25]. One of the barriers that can hinder the implementation of energy reduction projects is the low level of energy prices, which makes projects unprofitable. At the same time, scientists are ambivalent about the significance of this barrier. Thus, in [26] it was found that the volume of electricity consumption changes with changes in its prices, however, for example, in [27] this pattern is not found. In general, we can agree with the statement made in [28] that an exhaustive list of barriers to energy efficiency has not yet been provided and the possibility of such a presentation is questionable. The fact that different scientists identify different types of barriers that arise in the process of implementing energy saving measures may be due to the lack of attention paid by most researchers to the relationships that exist between certain types of these barriers. Therefore, it should be noted the study [29], which distinguishes three types of such relationships, namely: causal, hidden and synergistic. In the meantime, the formation regularities of these barriers, particularly their sequence formation, have not been fully studied. The same applies to the barrier’s assessment, as there are currently no generally accepted tools for measuring them. At the same time, a significant number of scientists are limited to qualitative barriers analysis to energy efficiency, as was done, for example, in the study [30], which studies the Finnish construction sector. Researchers also used the results of a survey of energy managers to assess these obstacles [31]. Among the more objective methods of estimating barriers to the implementation of energy-saving projects is the measurement of these barriers in the study [32] using graph-analytical models and a hierarchical approach. The presence of a significant number of factors that hinder the implementation of measures to save non-renewable energy resources, naturally leads to the existence of various ways to overcome barriers to such implementation. According to the context of the study [30] the main way is to provide complete and up-to-date information on energy efficiency measures. The study [33], which researches Swedish municipal

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energy saving programs, notes the need for both comprehensive information support for those seeking energy saving measures and the mastery of these individuals’ skills in processing such information. A number of scientists consider providing energy saving projects with the necessary amounts of financial resources as one of the most important ways to reduce the consumption of non-renewable energy sources. To this end, scientists propose measures to improve the investment climate [34], the implementation of programs to subsidize projects for the transition to clean energy [35], the use of soft loans [36], in particular the introduction of such loans for small businesses [37]. However, the relationship between the necessary parameters of soft loans and the level of barriers that arise in the implementation of energy saving measures, which are expected to be overcome through the provision of soft loans, remains unexplored. Some authors consider overcoming barriers to energy efficiency on the basis of improving management, in particular, due to improved methods of energy audit [38] and improved motivation mechanisms [39]. Regarding the formation mechanisms of certain barriers’ types on the way to reducing the consumption of natural gas in residential sector, the modeling of these mechanisms requires the specifics consideration of each of them. Particularly, the most common are barriers associated with insufficient financial resources and (or) insufficient cost-effectiveness of measures to improve the use of natural gas in residential buildings. Hereinafter, we will call these barriers financial and economic. It should be noted that the formation mechanism of financial and economic barriers depends on what sources of funding for energy saving measures can be potentially used. For many households, bank credit is almost the only source. Then, in order for a certain household to be interested in taking a loan to implement measures to save natural gas consumption, two basic conditions must be met. First, the cost saving of paying for thermal energy must be not less than the amount of interest on the loan. Second, households must have sufficient income to repay the loan and pay interest on it. For the case of natural gas consumption and considering the possible change in its prices, these two conditions can be formalized as follows: E g · l · T pg ≥ Cig · (1 − α) · l;

(1)

Cbg · (1 − α) ≤ Rh − E g · l · T pg ,

(2)

where E g —annual household expenditures for heat energy at the basic level of natural gas prices, monetary units; l—the reduction share of thermal energy consumption after the measure implementation to reduce natural gas consumption; T pg —the growth rate of natural gas prices compared to the base price level; C ig —investment expenditures required for the measure implementation to reduce the consumption of natural gas, monetary units; α—the share of investment expenditures for the measure implementation by the household to reduce the consumption of natural gas, which may be hypothetically covered by certain third parties, the share of the unit; r— annual interest rate, unit share; C bg —annual expenses for servicing and repayment

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of the loan, provided that there is no partial compensation by third parties for household expenses for the measures implementation to save natural gas, monetary units; Rh —the maximum possible part of the household income that it can use to pay for thermal energy and to service and repay the loan, monetary units. From expressions (1) and (2) we obtain: E g · l · T pg ; Cig · l

(3)

Rh − E g · l · T pg , Cbg

(4)

αmin 1 = 1 − αmin 2 = 1 −

where α min 1 —the minimum possible value of α, for which inequality (1), the fraction of one; α min 2 —the minimum possible value of α, for which inequality (2), the fraction of one. Given that the indicator α can’t be negative, we finally get: αmin = max{0; αmin 1 ;αmin 2 },

(5)

where α min —the minimum share of investment expenditures for a certain natural gas saving measure, which is reimbursed by third parties, at which it is economically advantageous for the household to obtain a loan to finance this measure. Therefore, expression (5) can be used to quantify the level of financial and economic barriers to the measures implementation to save natural gas by households, provided that these measures are financed through borrowed funds. On the other hand, the above formulas (1)–(5) are essentially a model of the formation mechanism of these barriers.

3 Justification of Ways to Overcome Barriers on the Way to Reducing Natural Gas Consumption in the Residential Sector There are many ways to overcome barriers to natural gas efficiency in the residential sector. At the same time, the implementation subjects of these methods can be both households and state or local authorities (Table 1). As follows from the data presented in Table 1, important ways to overcome barriers on the course to increase the natural gas efficiency use in the residential sector are: improving the information and financial support for the development and implementation of measures, namely: (1) improving the provision of households—consumers of natural gas with complete, accurate and relevant information on future measures to reduce its use. For this purpose, the following main tasks need to be solved: to find and generate

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Table 1 Grouping methods of overcoming barriers on course to increasing natural gas efficiency use in the residential sector by types of these barriers and the implementation subjects of appropriate methods to overcome them Barriers types on course to increasing natural gas efficiency use in the residential sector

Methods to overcome barriers according to their implementation subjects Households

State and local authorities

1. Obstacles associated with shortage of necessary resources volume

Upgrading the ability to find sufficient resources needed to improve the natural gas efficiency in the residential sector

Households assisting in finding sufficient resources to improve the natural gas efficiency use in the residential sector (including providing financial and information support to households)

2. Obstacles associated with insufficient quality of necessary resources

Upgrading the ability to find the resources of proper quality needed to improve the natural gas efficiency in the residential sector

Households assisting in finding the resources of proper quality needed to improve the natural gas efficiency in the residential sector (including providing financial and information support to households)

3. Obstacles associated with insufficient competence of investors

Upgrading the investors competence in the development and implementation of measures to improve the natural gas efficiency in the residential sector

Households assisting in upgrading their competence by the development and implementation of measures to improve the natural gas efficiency in the residential sector

4. Political and institutional obstacles

Improving the investors competence in cases when the political and institutional factors in the development and implementation of measures to improve the natural gas efficiency in the residential sector should be considered

Perfection the legal framework for the implementation of measures to improve the natural gas efficiency in the residential sector; improving the state energy saving policy; increasing the availability of loan financing measures to improve the natural gas efficiency use in the residential sector

5. Obstacles caused by insufficient level of socio-economic results of implementation measures to improve the efficiency of natural gas use in the residential sector

Improving the investors competence in choosing the best options for implementing measures to improve the natural gas efficiency in the residential sector

Financial support for measures to improve the natural gas efficiency in the residential sector, implemented by households; natural gas price regulation; improving the regulation of energy-saving materials and equipment manufacturers

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data sets on prospective measures to reduce the use of natural gas in the residential sector; to structure the array of source information on socio-economic results of measures to reduce the use of natural gas in the residential sector; identify the best channels for transmitting information on prospective measures to reduce the use of natural gas in the residential sector for different consumer groups of this information; determine the rational composition and architecture of the developed web resources, which contain input information on prospective measures to reduce the use of natural gas in the residential sector; to determine the rational composition and architecture of the developed web resources, which provide consumers (households) with information on the socio-economic results of the measures implementation to reduce the use of natural gas in the residential sector; (2) improving the competencies of households in the development and implementation of measures to improve the natural gas efficiency use in the residential sector. Such improvement requires conducting initial courses, seminars, trainings, etc. to raise public awareness of the methods and techniques of developing and implementing measures to reduce the consumption of natural gas in residential buildings; (3) stimulating the state and local authorities in the process of implementing measures by households to improve the efficiency of natural gas use. With this end in view, it is necessary to solve the following main tasks: promotion of relevant measures by state and local authorities; advising state and local authorities on households—consumers of natural gas on prospective areas and specific measures to reduce the use of this type of energy; search and attraction of additional financial resources by state and local authorities to finance measures to reduce household gas consumption; financial support from state and local authorities of those households that seek to implement investment measures to reduce natural gas consumption, on the basis of soft loans; financial support from the state and local authorities of those households that seek to implement investment measures to reduce natural gas consumption, on the basis of non-repayable funding for these measures. Particularly, an important method to overcome barriers on the course to reduce natural gas consumption in the residential sector should be recognized as preferential lending for measures to reduce such, which shell be carried out at the expense of the state budget (similar programs can be implemented at the local government level). Then the task to substantiate the program preferential crediting of measures to reduce household gas consumption can be formulated as follows: let there be a set of households divided into classes according to the average income of the members of these households. Also, let there be a set of measures aimed at reducing the consumption of natural gas in the residential sector (in this case, the same type of measures can be combined into groups; under such conditions, the measures indicators are averaged within each of their groups). Then it is necessary to establish such a share of reimbursement by the state of household expenditures for the implementation of each group of measures (the rest of the expenditures shall be financed by loans provided

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by state banking institutions), to maximize the reduction of natural gas consumption in the residential sector: E = I1 · e1 + . . . + Ii · ei + . . . + In · en =

n .

Ii · ei → max,

(6)

i=1

where E—is the expected total natural volumes of reduction of natural gas consumption in the residential sector due to the implementation of the state program of preferential lending; I i —total expected volumes of investment expenditures in the implementation of the measures group to reduce natural gas consumption, which shall be financed by concessional government lending, monetary units; ei —natural volumes of reduction of natural gas consumption in the residential sector by a group of measures for such reduction per one monetary unit of investment expenditures in the implementation of these measures; n—number of measures groups to reduce natural gas consumption in the residential sector. The indicator I i can be presented as follows: Ii =

m .

Ii j ,

(7)

j=1

where m—the number of household groups differentiated by the average income of their members; I ij —the expected amount of investment expenditures in the implementation of measures group to reduce natural gas consumption, which shall be financed by concessional government lending, a group of households, monetary units. The following restrictions must also be met: (1) on the total amount of compensation from the state of household expenditures for the implementation of measures to reduce natural gas consumption: I1 · α1 + . . . + Ii · αi + . . . + In · αn =

n .

Ii · αi ≤ B,

(8)

i=1

where α i —the generalized level of financial and economic barriers to the implementation of measures group to save natural gas consumption, the share of the unit; B—the general limit of compensations from the state of households’ expenses on measures implementation for reduction of natural gas consumption, monetary units. In this case, α i shall be determined using the following expression: { αi = max αi1 , . . . , αi j , . . . , αim } ,

(9)

where α ij —is the generalized level of financial and economic barriers to the measures implementation to save natural gas consumption by the group of households (this level is determined using expression (5));

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(2) the value of the indicator I ij (condition of their inseparability): Ii j ≥ 0.

(10)

The use of the proposed optimization model (6)–(10) in the practice of public authorities shall provide an opportunity to increase the state programs validity of financial support for reducing measures of natural gas consumption in residential buildings.

4 Empirical Barriers Analysis on the Course to the Measures Implementation for the Purpose of Reducing Natural Gas Consumption in the Residential Sector In order to assess barriers to the measures implementation with the object of reducing natural gas consumption by households, a survey of 400 Ukrainian households was conducted. It turned out that out of the total number of respondents, 128 tried to implement measures with the object of saving natural gas during 2020–2021. However, not all of these households overcame certain barriers to the successful implementation of these measures (Table 2). Based on the data presented in Table 2, it is possible to assess the relevant barriers level on the course to the measures implementation with the object of reducing natural gas consumption by the surveyed households. This level, as mentioned above, can be defined as the ratio of the households’ number that couldn’t overcome the barrier to the households’ number that approached it. The results of the corresponding calculations are given in Table 3. As follows from the data presented in Table 3, the most significant barriers to the measures implementation with the object of reducing natural gas consumption by the surveyed households include obstacles due to shortage of necessary resources and obstacles due to insufficient investor competence. The removal of barriers of the first type according to formula (1) would increase the level of measures implementation for the whole set of households from 0.246 to 0.246/(1 − 0.491) = 0.483 for measures to install heat-saving windows on balcony doors and from 0.258 to 0.258/(1 − 0.548) = 0.571 for measures to insulate the exterior walls of buildings. As mentioned above, the level of financial and economic barriers on the course to the measures implementation with the object of saving natural gas by households can be significantly affected by its price. Using expression (5), the generalized level of financial and economic barriers on the way to the implementation of natural gas saving measures by the surveyed households was calculated. At the same time, the baseline was the average level of prices for this type of energy resources for household consumers, which developed in Ukraine as of December 31, 2021. The results of the calculations are presented in Table 4. According to the data presented in this table,

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Table 2 Number of households that, according to the survey results, overcame the relevant type of barriers to the measures implementation for the purpose of reducing natural gas consumption Barriers types on the course to the measures implementation for the purpose of reducing natural gas consumption

Measures groups to reduce natural gas consumption Installation of heat-saving windows on balcony doors

Insulation of external walls of buildings

Replacement of gas boilers for solid fuel boilers

Installation of air temperature controllers

Installation of heat recuperators of ventilation air

1. Obstacles associated with shortage of necessary resources volume

29

14

11

3

5

2. Obstacles associated with insufficient quality of necessary resources

27

13

11

3

5

3. Obstacles associated with insufficient competence of investors

21

10

8

2

4

4. Political and institutional obstacles

18

9

7

2

4

14 5. Obstacles caused by insufficient level of socio-economic results of implementation measures to improve the efficiency of natural gas use in the residential sector

8

6

2

3

(continued)

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Table 2 (continued) Barriers types on the course to the measures implementation for the purpose of reducing natural gas consumption The total number of surveyed households that sought to implement a relevant measures group for the purpose of reducing natural gas consumption

Measures groups to reduce natural gas consumption Installation of heat-saving windows on balcony doors

Insulation of external walls of buildings

Replacement of gas boilers for solid fuel boilers

Installation of air temperature controllers

Installation of heat recuperators of ventilation air

57

31

24

7

9

Source By authors

the increase in natural gas prices for most of the measures to save it in this case does not cause a reduction in the general level of financial and economic barriers. The existence of a certain level of financial and economic barriers on the course to the measures implementation with the object of reducing natural gas consumption by the surveyed households requires state financial support from these households. This support may take the form of preferential lending relevant measures by stateowned banks with reimbursement of a certain share of the principal loan amount. Based on the data on the surveyed households and using the optimization model developed above (6)–(10), some forecast indicators of the financial support program of households seeking to implement measures with the object of reducing natural gas consumption were calculated. Particularly, this applies to the expected efficiency of public expenditures to reimburse the initial loans amount for thermal modernization of residential buildings and the proposed shares of such reimbursement (Table 5). As follows from the data presented in Table 5, despite the rather significant proposed share of state reimbursement of the initial loans amount received by households on the course to implement measures with the object of natural gas saving, the expected effectiveness of such reimbursement is quite high (ranging from 4.07 to 8.54 m3/USD).

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Table 3 The barriers level on the course to the measures implementation with the object of reducing natural gas consumption according to a survey of households in Ukraine Barriers types on the course to the measures implementation for the purpose of reducing natural gas consumption

Measures groups to reduce natural gas consumption Installation of heat-saving windows on balcony doors

Insulation of external walls of buildings

Replacement of gas boilers for solid fuel boilers

Installation of air temperature controllers

Installation of heat recuperators of ventilation air

1. Obstacles associated with shortage of necessary resources volume

0.491

0.548

0.542

0.571

0.444

2. Obstacles associated with insufficient quality of necessary resources

0.069

0.071

0.000

0.000

0.000

3. Obstacles associated with insufficient competence of investors

0.222

0.231

0.273

0.333

0.200

4. Political and institutional obstacles

0.143

0.100

0.125

0.000

0.000

0.222 5. Obstacles caused by insufficient level of socio-economic results of implementation measures to improve the efficiency of natural gas use in the residential sector

0.111

0.143

0.000

0.250

(continued)

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365

Table 3 (continued) Measures groups to reduce natural gas consumption

Barriers types on the course to the measures implementation for the purpose of reducing natural gas consumption

Installation of heat-saving windows on balcony doors

The actual level 0.246 of a measure implementation by respondents for the purpose of improving the natural gas efficiency in the residential sector

Insulation of external walls of buildings

Replacement of gas boilers for solid fuel boilers

Installation of air temperature controllers

Installation of heat recuperators of ventilation air

0.258

0.250

0.286

0.333

Source By authors

Table 4 Results of assessing the changes impact in natural gas prices for household consumers on the general level of financial and economic barriers to the measures implementation by households with the object of saving this energy resource The growth rate of natural gas prices relative to their base level

Generalized level of financial and economic barriers by household groups on the way to the implementation of the surveyed households’ measures to save natural gas by groups of these measures Installation of Insulation of heat-saving external walls windows on of buildings balcony doors

Replacement of gas boilers for solid fuel boilers

Installation of air temperature controllers

Installation of heat recuperators of ventilation air

0.6

0.39

0.41

0.30

0.33

0.32

0.8

0.31

0.30

0.17

0.27

0.20

1.0

0.23

0.19

0.22

0.21

0.26

1.2

0.15

0.24

0.30

0.15

0.32

1.4

0.33

0.29

0.38

0.27

0.38

Source By authors

5 Conclusions In the current scientific literature, the mechanisms of creating obstacles to the implementation of energy-saving projects, including measures to reduce natural gas consumption in the residential sector, remain incompletely studied. Accordingly, most of the presented ways of overcoming these obstacles require a more thorough

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Table 5 Expected efficiency of public expenditures on state reimbursement of the initial loans amount received by households in order to implement measures with the object of natural gas saving, and the proposed share of such reimbursement Indicator name Measures groups to reduce natural gas consumption Installation of heat-saving windows on balcony doors Expected efficiency of public expenditures to reimburse the initial amount of loans received by households in order to implement measures to save natural gas, m3/USD

7.12

Proposed state 28.1 reimbursement share of the initial loans amount received by households in order to implement measures to save natural gas, %

Insulation of external walls of buildings 6.46

23.5

Replacement of gas boilers for solid fuel boilers 8.54

26.4

Installation of air temperature controllers 5.39

24.8

Installation of heat recuperators of ventilation air 4.07

30.1

Source By authors

justification, which would be based on knowledge of the laws of their formation. Having this in view, there is a need to model the barriers mechanisms to improve the efficiency of natural gas in the residential sector and develop scientifically sound ways to overcome these barriers. The process of obstacles modeling to improving the efficiency of natural gas use in residential buildings should be based on pre-grouping the types of such barriers. Particularly, this grouping can be carried out by stages of the development process and measures implementation to save natural gas in the residential sector. Under such conditions, the formation mechanism of these obstacles is described by a certain sequence of their occurrence. Another grouping way the studied obstacles follows from those presented in the work five groups of factors that directly affect the formation of these barriers. These groups include: shortage of necessary resources,

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insufficient level of resource quality, insufficient level of investors competence (i.e. persons who decide on the implementation of investment measures to save natural gas consumption in residential buildings), political and institutional factors, as well as insufficient level socio-economic results from the implementation measures to save natural gas consumption in the residential sector. An important way to overcome barriers on the course to reducing natural gas consumption in the housing sector is to recognize concessional lending for such reductions, which will be carried out at the expense of the state budget. The use of the optimization model proposed in this paper for the state programs formation of financial support for measures to reduce natural gas consumption in residential buildings in the practice of public authorities shall provide an opportunity to increase the parameters validity of these programs. Calculations using this model on a sample of households seeking to implement measures with the object of natural gas saving showed that, despite the rather significant proposed size of the reimbursement shares of the initial loans amount received by households to implement measures for the purpose of natural gas saving, the expected efficiency such compensation is quite high.

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Research of Characteristics of Solid Waste as Energy Resource Artur Voronych , Teodoziia Yatsyshyn , Petro Raiter , Lubomir Zhovtulya , and Serhii Maksymiuk

Abstract In Ukraine, about 10 million tons of municipal solid waste (MSW) are generated annually, of which less than 10% is recycled. On average, the formation of MSW per capita is 220–250 kg/yr, and in large cities up to 380 kg. Thus, MSW is a major environmental problem. Accordingly, landfills are currently overcrowded and cause a difficult environmental situation in the surrounding areas. Solving this problem is a multi-stage process: starting with producers of various products and creating the conditions for them to prevent waste generation, public awareness of the importance of reducing waste flows, as well as consideration of already established solid waste as a resource. The morphological composition of MSW is analyzed. An approximate percentage of MSW suitable for energy recovery from the total mass of MSW entering landfills has been established. The level of reduction of mass of MSW by burning is determined. Some characteristic parameters of heat treatment of MSW by experimental method are determined. Thus, the emissions during combustion of the samples, fuel consumption for their combustion, excess oxygen and combustion temperature were analyzed. Determination of the calorific value of the samples was the basis for determining the energy potential of solid waste in Ivano-Frankivsk region. Keywords Municipal solid waste · Waste management strategy · Recycling waste management · Separate waste

A. Voronych · T. Yatsyshyn (B) · P. Raiter · L. Zhovtulya · S. Maksymiuk Ivano Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine e-mail: [email protected] T. Yatsyshyn State Institution “The Institute of Environmental Geochemistry” of NAS of Ukraine, Kyiv, Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_22

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1 Introduction Ivano-Frankivsk region is located in southwestern Ukraine. The area of the region is 13.9 thousand km2 , which is 2.4% of the area of Ukraine. Ivano-Frankivsk—regional center of Ivano-Frankivsk region, economic and cultural center of Prykarpattia. Municipal solid waste is waste that is generated in the course of human life and activities and accumulates in residential buildings, social and cultural institutions, public, educational, medical, commercial and other institutions (this is food waste, household items, garbage, fallen leaves, waste from cleaning and current repair of apartments, waste paper, glass, metal, polymer materials, etc.) and have no further use at the place of their formation. Currently, there are about 18 landfills and dumps where municipal solid waste is collected in the Ivano-Frankivsk region. But only 8 such facilities have passports. There are also a large number of unauthorized landfills. In Fig. 1 the main landfills and dumps in the region are given. The Ivano-Frankivsk landfill near Rybne village is the largest in the Ivano-Frankivsk region. According to the Ministry of Development of Communities and Territories of Ukraine, as of September 1, 2019, separate collection of solid waste has been introduced in 65 settlements. Glass, paper, and plastic are collected separately (all three fractions, or only some of them, depending on the settlement). Biomass is collected separately in Halych. In 2019, the share of settlements with separate collection of solid waste to the total number of settlements in the region is 8%. At the same time, according to the additional monitoring of the Ministry of Regional Development, only 7 landfills meet the state construction requirements for landfills. Only the landfill in Ivano-Frankivsk has a filtrate collection and purification system, landfill gas collection and utilization of seven landfills, and three landfills have only filtrate collection systems.

Fig. 1 Operating landfills in Ivano-Frankivsk region

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Fig. 2 Handling MSW in Ivano-Frankivsk region [1]

In accordance with the data of the Ministry for Communities and Territories Development of Ukraine, from 2015 to 2017, there was a tendency to an increase in the volume of solid waste generation in Ivano-Frankivsk region. In 2019, the volume of municipal waste generated was 1,027,000 m3 , which was 29% more than in 2011. Municipal solid waste generated in Ivano-Frankivsk region is currently a major environmental problem. Imperfect system of solid waste management causes their constant accumulation and burial in landfills (Fig. 2). According to the calculated data, and taking into account the fact that the service for the removal of household waste in 2019 covered only 78.2% of the region’s population, the estimated average waste generation rate will be 0.96 m3 /person/yr or 180 kg/person/yr. The actual volumes of household waste generation are larger, since usually the volumes of waste removal are equated to the volumes of waste generation, and waste generated in villages, where the service is not provided, is not accounted to it. Therefore, according to expert estimates, the real volume of solid waste generation in Ivano-Frankivsk region may be about 1,256,000 m3 . According to the annual environmental passports of Ivano-Frankivsk region, the average value of solid waste generation is 207829.1 tons/yr [2–6]. The data were analyzed for 2017 and 2018, as data on MSW generation from previous years are not available. The morphological composition of MSW is quite diverse and variable both in time and geographically. Municipal solid waste that is taken to the landfill is waste from residential buildings—food waste, room and yard waste, glass, leather, rubber, paper, metal, waste from apartment renovations, ash and slag, large household items, as well as household waste of trade enterprises and cultural and welfare institutions, waste of catering enterprises, waste of markets, medical institutions, street waste, industrial

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Fig. 3 Determining the percentage composition of MSW

and construction waste of hazard class IV. The average indicators of the composition of MSW in Ivano-Frankivsk are shown in Fig. 3) [7]. It significantly depends on the season due to the increase in food waste content from 20–25% in spring to 40–55% in autumn. Therefore, the percentage ratio between various components of MSW can be given only conditionally or for a specific batch of waste. Establishing the mass of MSW suitable for energy recovery makes it necessary to analyze the morphological composition of solid waste. Not all landfills of the region have data from the study of the morphological composition of MSW, therefore, there has been studied the information on the receipt of solid waste of the largest operating landfill in the region, located in Rybne village near Ivano-Frankivsk. This solid waste landfill serves the settlements of Ivano-Frankivsk City Council, Tysmenytsya, Nadvirna, Kosiv and Kolomyia districts. In 2020, the enterprise plans to accept 110 thousand tons of household waste for disposal, of which 1.0 thousand tons of recyclable materials will be sorted, and the rest will be buried [8]. There was determined the approximate percentage of solid waste suitable for energy recovery from the total mass of solid waste supplied to landfills, which was 67.61%. These components of MSW include: paper (cardboard), rubber and leather waste, plastic, wood, biowaste and unsorted residues suitable for incineration. About 32.4% of MSW is unsuitable for energy production—it is unsorted (non-combustible) residue, glass, metal. Thus, based on the obtained value of the total amount of solid waste, which is 207,829.1 t/yr, there has been established an approximate value of solid waste suitable for energy recovery by incineration in Ivano-Frankivsk region, which accounts for 140,513.2 t/yr. It should be taken into account that the composition of MSW varies

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Fig. 4 The composition of wastes used for incineration

throughout the year and depends on the area. Figure 4 shows the percentage of solid waste that is suitable for energy recovery in the total mass of waste.

2 Research Methods According to the standard method for determining the moisture content, the MSW samples were weighed and then placed in a drying cabinet, where the temperature did not exceed 105 °C. The weight of the samples was monitored periodically and there was established the moment when the decrease in their weight stopped. According to the found masses of wet and absolutely dry sample, the relative humidity is determined for each sample. Determination of the pH of MSW samples was carried out by analyzing the water extract of the waste using a pH meter. The electrical conductivity of the test samples was determined by impedance spectroscopy using an Autolab PGSTAT 12/FRA-2 modular potentiostat at room temperature [9, 10]. The study of the chemical composition of the studied samples was carried out by the method of X-ray fluorescence analysis in Laboratory of gamma-resonance spectroscopy with analysis of electron conversion, gamma and X-ray radiation (Vasily Stefanik Precarpathian National University) [11]. The method is based on the analysis of the fluorescence spectra of radiation elements during the adsorption of highenergy radiation. The method allows obtaining data on the chemical composition of a substance in a wide range with an accuracy of 1–10 ppm. The experiments were

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carried out on an EXPERT 3L Precision Analyzer with a constant supply of helium to the collimator channels. Analytical methods The assessment of the morphological composition of MSW was carried out on the basis of the averaged data of MSW indicators in 2017–2018, provided by the Municipal Solid Waste Landfill and obtained according to the recommendations [12]. MSW sampling was carried out at the landfill near Rybne village. This landfill is equipped with a sorting line with a capacity of 50 tons/day, which has been operating since 2018. The expedition to the landfill was carried out in the winter, therefore, at the time of sampling, the sorting line was not working due to the lack of a cover over the conveyor. 5 samples of 10 kg each were taken from the waste collection vehicles of MSW. At the next stage, there was performed sorting by morphological composition of municipal solid waste. 1 group of 5 samples were prepared according to the established composition, shown in Fig. 4 in a form of 1 kg. It was prepared for analyses to determine the physical and chemical characteristics, as well as to establish the calorific value of MSW using a calorimeter. To carry out the analyses envisaged by the project, the constituent samples were grounded by the component with a knife grinder to a particle size of no more than 0.1 mm. The grounded samples were stored in closed glass containers. Depending on the requirements for the analysis, the samples were subjected to subsequent processing: • a water extract was prepared to define the pH; • to determine the chemical composition, the sample preparation needed heating in a muffle furnace at a temperature of 700 °C until the waste was completely converted into ash [13]; • for analysis in the calorimeter, MSW samples were compacted using a press to one-gram Tablets, provided by the method. Determination of energy recovery potential from MSW was carried out in two stages: stage I—experimental determination of the heat released by MSW combustion suitable for energy recovery using IKA C1 calorimeter; stage II—calculation method for determining the lower heat of combustion and calculating the energy potential of the MSW mass. There was formed a sample of fuel from the selected and appropriately prepared samples of MSW using a press. All components of the sample were formed in accordance with the percentage composition of MSW, suitable for energy recovery according to the data shown in Fig. 4. The mass of the filling corresponded to 1 g ± 0.05. 1 ml of distilled water was introduced into the bomb and placed in a calorimeter for conducting an experiment to determine the heat of combustion.

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3 Research Results The study of MSW characteristics is a prerequisite for establishing the energy potential of MSW in the region. Physical and chemical analysis of MSW samples provided for the determination of the following indicators: • humidity and pH; • electrical conductivity and redox potential; • elemental composition of solid waste. The total humidity for the five samples ranges from 48.97 to 55.24%. High humidity values are associated with a significant content of bio-waste, as well as the ingress of external moisture from precipitation, since containers for collecting MSW are mostly without shelter. The average value of obtained pH values is 5196 with deviation 0.09. This corresponds to the moderately acidic reaction. As a result, there were obtained the dependences of the electrical conductivity of the samples on the frequency (Fig. 5). In general, the properties of all samples are close to those of dielectrics. As can be seen in Fig. 5, all test samples have a conductivity in the range of 1*10–4 –3*10–4 .−1 m−1 at constant current. As the frequency rises to 100–150 Hz, the conductivity increases rapidly (which is typical for dielectrics). At frequencies exceeding 150 Hz, the dynamics of the growth of conductivity decreases, which indicates a complex case of superposition of various types of conductivity, which is characteristic of both semiconductors and metals. -3

2,5x10

-3

2,0x10

1 2 3 4 5

-3

σ'

1,5x10

-3

1,0x10

-4

5,0x10

0,0 -3

10

-2

10

-1

10

0

10

1

10

2

10

Frequency, Hz

Fig. 5 Relation of test sample conductivity to frequency

3

10

4

10

5

10

6

10

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Table 1 Chemical composition of MSW, % Chemical element

Sample 1

Sample 2

Sample 3

Sample 4

Sample 5

O

23.201

26.021

23.706

27.069

25.069

Al

0.198

0.905

0.524

0.469

1.021

Si

1.886

3.143

1.524

4.164

4.516

P

0.0

0.0

0.0

0.0

0.289

S

0.762

1.132

0.546

1.089

0.942

Cl

19.307

13.259

16.722

13.116

17.017

K

12.568

13.683

11.353

9.171

17.289

Ca

34.921

30.803

42.07

34.541

28.16

Ti

1.285

1.523

0.391

1.855

0.911

Cr

0.275

0.805

0.094

0.479

0.206

Mn

0.234

0.26

0.183

0.256

0.162

Fe

4.521

7.083

2.448

6.505

3.389

Ni

229 × 10–5

0.0 259 ×

Cu

316 ×

Zn

0.538

Br

0.199

10–5

10–5

198 × 10–5

152 × 10–5

333 ×

322 ×

10–5

10–5

3.389 0.14

0.892

0.319

0.742

0.551

0.316

0.0

0.4

0.149

Sr

495 ×

0.113

0.067

0.057

0.067

Nb

0.0

381 × 10–5

0.0

0.0

0.0

Ag

0.0

0.0

0.0

405 × 10–5

0.0

Cd

0.0

0.0

0.0

0.0

197 × 10–5

Pb

0.0

0.0

0.0

0.0

0.082

10–5

The analysis of chemical composition was performed for 5 samples of MSW. As a result of processing the spectra, the average chemical composition of the experimental samples was obtained (Table 1). As can be seen from the data of Table 1 the samples differ greatly in their chemical composition. So, basically, the samples contain such chemical elements as Ca, Si, Fe. The amount of other chemical elements included in the sample products is less than 0.01%. The main chemicals and compounds that are encountered in the analysis of these samples can probably be attributed to construction waste (SiO2 , Fe2 O3 , CaO). Another group of chemical compounds are the remains of organic compounds, probably food and plant products (K2 O, P2 O5 ). Also, a significant part is made up of compounds that can be components of various paints and dyes (TiO2 , Fe2 O3 ). As a result of the experiments determination of the heat of MSW combustion, there was obtained the calorific value (higher heat of combustion) of MSW five samples, given in Table 2. The obtained experimental data do not take into account the humidity values, since the use of dried samples is envisaged for the experiment with the calorimeter.

Research of Characteristics of Solid Waste as Energy Resource Table 2 Data of experimental determination of MSW calorific value

379

Sample no

q_(V,gr,d), [J/g]

Sample No 1 Ua

24,333

Sample No 2 Ua

24,772

Sample No 3 Ua

26,195

Sample No 4 Ua

25,942

Sample No 5 Ua

24,624

Thus, it becomes necessary to take this factor into account by carrying out additional calculations. The energy recovery potential of a territory or region is defined as the product of the amount of MSW produced in a specified region during the year by the value of the net calorific value of the specified MSW. The value of the lowest calorific value of experimental MSW samples is obtained using the experimentally determined values of their calorific value (higher calorific value) according to the conversion formula [14, 15]: qp, net, m = {q V , gr, d − 206W H, d} · (1 − 0.01M T ) − 23.05M T ,

(1)

where qp,net,m—lower heating value, J/g; qV,gr,d—calorific value (higher calorific value), J/g; WH,d—hydrogen content in MSW, %; MT —humidity of MSW, %. The values of humidity for each component of MSW and the calculated values of humidity for MSW for each of the experimental samples are experimentally determined during physical and chemical analysis of MSW. The moisture that enters the firebox is non-combustible and does not give heat. But, in the process of high-temperature combustion of solid waste in the furnace, hydrogen is released, which must be added to the main component of hydrogen, which is already present in the components of MSW, as one of the chemical elements, chemical reactions during the combustion of which lead to the production of thermal energy. Therefore, it is necessary to carry out calculations of the total amount of hydrogen (percentage), which is present in MSW, the calorific value of which is being investigated. For this purpose, on the basis of typical data on the content of “combustible” chemical elements—carbon, hydrogen, oxygen, sulfur—in different components of MSW, there were performed calculations of the amount of these chemical elements in grams. However, these calculations include the mass of hydrogen contained in the socalled “dry” part of MSW. To determine the mass of hydrogen that is released from water during the incineration of MSW with a certain humidity, there was applied the formula [16]: H ydr ogen mass (H ) = H ydr ogen in Dr y Mass+ 2 + · (W et Mass o f M SW − Dr y Mass o f M SW ), 18

(2)

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Table 3 Calculation results of the hydrogen content

Sample no

Hydrogen mass(H2), g

Hydrogen mass(H2) part in MSW, %

Sample 1 Ua

461.9

21.45

Sample 2 Ua

456.6

21.13

Sample 3 Ua

452.7

18.41

Sample 4 Ua

462.3

20.97

Sample 5 Ua

459.9

21.43

where Hydrogen mass (H) is the mass of the hydrogen element in MSW, g; Hydrogen in Dry Mass is the hydrogen contained in the so-called “dry” part of MSW, g; Wet Mass of MSW is the mass of wet MSW, g; Dry Mass of MSW is the mass of dry MSW. Table 3 shows the results of calculating the values of hydrogen content in each of the MSW samples. According to the formula (1), there were calculated the values of the lower calorific value of experimental MSW samples, given in Table 4. These values made it possible to calculate the average value of the lower heat of MSW combustion obtained from the results of the study of the calorific value of five samples of MSW in Ivano-Frankivsk region. Energy recovery potential of the territory or district of Ivano-Frankivsk region was defined as the product of the amount of solid waste produced in the specified region during 2018, by the average value of the lower calorific value of the mentioned MSW indicated in Table 5. The results of calculations of the Energy recovery potential for the Ivano-Frankivsk region are shown in Table 5. Table 4 Calorific value and Net Calorific Value Sample no

Calorific value, qV,gr,d, [J/g]

Total moisture, MT [%]

Hydrogen content of the sampel, WH,d, [%]

Net Calorific Value (NCV), qp,net,m, [J/g] or [kJ/kg]

Sample 1 Ua

24,333

55.24

21.45

7640.1

Sample 2 Ua

24,772

54.65

21.13

8000.5 10302.2

Sample 3 Ua

26,195

48.98

18.41

Sample 4 Ua

25,942

54.35

20.97

8617.9

Sample 5 Ua

24,624

55.20

21.43

7782.3

Average

8468.6

Research of Characteristics of Solid Waste as Energy Resource

381

Table 5 Energy recovery potential of MSW per year and Energy potential of electricity and thermal energy per year in Ivano-Frankivsk region Mass of waste per year suitable for energy recovery by incineration

Mass of waste per year Energy recovery suitable for energy potential of MSW per recovery by year incineration—without ash

Energy potential of electricity and thermal energy per year

kg

kg

[MJ/yr]

[kWh/yr]

80%, [kWh/yr]

140,513,200

134,976,980

1143062.8

317 518

254014.4

4 Discussion and Conclusions The work is carried out study the possibilities of completing the management of municipal solid waste (MSW) in the Ivano-Frankivsk region by thermal treatment methods for recovery of energy. Physical and chemical analysis of MSW was performed. It included determination of the humidity and pH, electrical conductivity and redox potential, elemental composition of solid waste. According to the research of the humidity of solid waste samples, the percentage of humidity in the samples is high (in the range from 48.97 to 55.24%), which is caused by the lack of protection of solid waste from atmospheric moisture at the stage of their collection. Analysis pH of MSW samples determine that the average pH is 5.2, which corresponds to the moderately acidic reaction. Based on the nature of the electrical conductivity dependence on the frequency and chemical composition of the test MSW samples, we can say that the samples contain different types of conductivity, due to the multicomponent composition of the samples. According to the research of chemical composition of MSW, the share of heavy metals and chemical elements harmful to human health does not exceed the permissible limits. The chemical composition of MSW is a rather variable characteristic; therefore, it can be given only in the form of estimated values. The study of the energy potential of solid waste in Ivano-Frankivsk region showed that average Net Calorific Value is equal 8468.6 J/g, and energy potential of electricity and thermal energy in region per year is 254014.4 kWh/yr. Acknowledgements This research was co-financed by the European Union within the framework of Hungary-Slovakia-Romania-Ukraine ENI CBC Programme 2014-2021 under the project “Energy Recovery from Municipal Solid Waste by Thermal Conversion Technologies in Cross-border Region” HUSKROUA/1702/6.1/0015.

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References 1. The Ministry for Communities and Territories Development of Ukraine. https://www.minreg ion.gov.ua/ 2. EKOLOHICHNYY PASPORT IVANO-FRANKIVS' KOYI OBLASTI za 2017 rik. http:// www.if.gov.ua/files/uploads/%D0%95%D0%9A_2017.pdf 3. EKOLOHICHNYY PASPORT IVANO-FRANKIVS' KOYI OBLASTI za 2018 rik. https:// www.if.gov.ua/storage/app/sites/24/documentu-2021/pasport2018-2compressed.pdf 4. Lysychenko, G., Weber, R., Kovach, V., Gertsiuk, M., Watson, A., Krasnova, I.: Threats to water resources from hexachlorobenzene waste at Kalush City (Ukraine)—a review of the risks and the remediation options. Environ. Sci. Pollut. Res. 22(19), 14391–14404 (2015). https://doi. org/10.1007/s11356-015-5184-1 5. Orfanova, M.M., Ivanyk, O.I.: Improving the system of solid waste management in the city of Ivano-Frankivsk. Man Environ. Issues Neoecol. 3–4(26), 126–131 (2016) 6. Popov, O., Yatsyshyn, A.: Mathematical tools to assess soil contamination by deposition of technogenic emissions. In: Dent, D., Dmytruk, Y. (eds.) Soil Science Working for a Living: Applications of soil science to present-day problems, pp. 127–137. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-45417-7_11 7. Karpash, M., Voronych, A., Yatsysyn, T., Orfanova, M.: Analysis of the system of municipal solid waste management In Ivano-Frankivsk region (Ukraine). Sci. Bull. North Univ. Center of Baia Mare., Series D., XXXIII(2), 39–47 (2019) 8. Draft decision of the executive committee of 06/18/2020. No. 354 On the report of municipal entrepreneurship “MSW Landfill” for 2019 and approval of the development plan 2020. http:// www.namvk.if.ua/prdt/462069/ 9. Boychuk, V., Kotsyubynsky, V., Rachiy, B., Bandura, K., Hrubiak, A., Fedorchenko, S.: βNi (OH) 2/reduced graphene oxide composite as electrode for supercapacitors. Mater. Today: Proc. 6, 106–115 (2019). https://doi.org/10.1016/j.matpr.2018.10.082 10. Shyyko, L.O., Kotsyubynsky, V.O., Budzulyak, I.M., Sagan, P.: MoS 2/C multilayer nanospheres as an electrode base for lithium power sources. Nanoscale Res. Lett. 11, 243 (2016). https://doi.org/10.1186/s11671-016-1451-4 11. Kotsyubynsky, A.O., Moklyak, V.V., Fodchuk, I.M., Kotsyubynsky, V.O., Lytvyn, P.M., Grubyak, A.B.: Magnetic microstructure of epitaxial films of LaGa-substituted Yttrium Iron Garnet. Metallofiz. Noveishie Tekhnol. 41, 529–548 (2019) 12. Methodological Recommendations for determining the morphological composition of municipal solid waste, approved by the order of the Ministry of Housing and Communal Services of Ukraine dated 16.02.2010 № 39 13. Lutsak, D.L., Prysyazhnyuk, P., Karpash, M., Pylypiv, V., Kotsyubynsky, V.: Formation of structure and properties of composite coatings TiB2-TiC-Steel obtained by overlapping of electric-arc surfacing and self-propagating higherature synthesis. Metallofizika i Noveishie Tekhnologii. 38(9) (2016) 1265–1278. https://doi.org/10.15407/mfint.38.09.1265 14. ISO 1928:2009 Solid mineral fuels—Determination of gross calorific value by the bomb calorimetric method and calculation of net calorific value 15. Marinov, K.I., Gochev, Z., Lieskovský, M., Ferenˇcík, M.: Exploring the energy performance of wood chips from Salix Viminalis–klon Tordis. Innov. Woodworking Ind. Eng. Design. 6, 50–56 (2018) 16. Abbas, A.H.A., Al-Rekabi, W.S., Hamdan, A.N.: Prediction of potential electrical energy generation from MSW of Basrah Government. In: 5th International Conference on Waste Management, Ecology and Biological Sciences (WMEBS-2017), Istanbul, Turkey (2017). https://doi. org/10.15242/dirpub.er0517030

Renewable Power Engineering

Geothermal Heat Supply Development Pathways in Ukraine Yulia Shurchkova , Sergii Shulzhenko , Anna Pidruchna , Volodymyr Deriy , and Vitaly Dubrovsky

Abstract The chapter considers the trends in the development of geothermal heat in the world and the situation with the use of renewable energy sources in Ukraine. The reasons for the country’s lag in this area in the presence of resource and scientific base, experience in construction and operation of thermal geothermal stations are analyzed, as well as economic prerequisites for creating geothermal heat supply systems based on deep wells and near-surface geothermal resources. Keywords Geothermal energy · Heat supply technology · District heating · Economic feasibility · Geological wells

1 Introduction Since the world’s ecological challenges, the reduction of world reserves of fossil fuels, and the rising fuel prices, the question of the development of the alternative energy industry is acute. The world is moving from the traditional combustion of fossil fuels for heat supply to the use of energy-efficient technologies, including geothermal. Geothermal energy is developing in two main areas: electricity generation and heat production. Geothermal electricity is developing mainly in countries located in areas of modern volcanism, where the coolant has high parameters, available on the Earth’s surface, the cost of building geothermal power plants is minimal, and energy costs are competitive in the energy market. Geothermal heat is geographically more widespread, as it requires thermal resources with lower temperatures. Analysis of trends in the development of geothermal energy shows that in the coming decades, the most intensive development of geothermal heat supply. The production of geothermal heat accounts for 85% of the total capacity of the world’s geothermal energy by today. The total installed capacity of thermal geothermal plants in the world accounted for 107,727 MW at the end of 2019. According to WGC2015 [1], the increase in capacity in the period from 2010 to 2015 was about 45%, and in Y. Shurchkova · S. Shulzhenko · A. Pidruchna (B) · V. Deriy · V. Dubrovsky General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_23

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the period from 2015 to 2019—52%. In terms of volumes of all types of renewable energy sources for heat supply, geothermal energy ranks second in the world after solar [2]. Geothermal district heating currently is used in 28 countries in Europe, Asia and America. The leaders are China, Iceland, France and Germany. There are more than 5000 geothermal district heating systems in Europe, which is about 10% of the total heating market. The countries of Eastern and Central Europe—Hungary, Poland, Slovakia, Slovenia, the Czech Republic and Romania—are also active in developing geothermal heat supply. Ukraine is not still belonging to the countries that develop geothermal energy, despite the obvious urgency of the problems, both fuel and environmental, and despite the fact that the country has a fairly high geothermal potential. In terms of the scale of geothermal energy use, it is critically lagging behind not only the leading countries in this field, but also the neighboring countries that have similar or even less potential for geothermal resources. Table 1 shows the data for the use of geothermal energy in Ukraine’s neighboring countries in 2015 [3]. The use of geothermal energy for the purposes of heat supply, ventilation and air conditioning can reduce energy consumption by 25–50% compared to traditional systems [4]. According to the International Geothermal Agency, the use of geothermal heat in 2015 saved 52.5 million tons of oil equivalent per year and significantly reduces the consumption of traditional fuels and reduces environmental pollution. The study has been conducted by the US Department of Energy in the field of geothermal heating has shown that geothermal heating system to reduce carbon emissions by 46 million tons compared to the use of fuel oil. The intensive development of geothermal energy in the world is largely determined by the fact that a number of industrialized countries are investing heavily in this Table 1 The use of geothermal energy in Ukraine’s neighboring countries Country

Installed capacity, MW

Annual consumption TJ/yr

Coefficient GWh/yr

4.73

113.53

31.54

Hungary

905.58

10 268.06

2 852.47

Moldova

–

–

–

488.84

2 742.60

761.89

Belorussia

Poland

Load Factor* 0.76 0.36 – 0.18

Russia

308.20

6 143.50

1 706.66

0.63

Romania

245.13

1 905.32

529.30

0.25

Slovakia

149.40

2 469.60

686.05

0.52

10.90

118.80

33.00

0.35

** Ukraine (according to the statistical data for 2005) *

Load Factor—power factor: (annual energy consumption in TJ/year)/(installed capacity in MW) × 0.03171 ** data for 2005 are given for Ukraine, as they are not available for the following years

Geothermal Heat Supply Development Pathways in Ukraine

387

industry. Thus, in the period from 2010 to 2014, 49 countries invested about $20 billion in geothermal energy, which is twice as much as in 2005–2009. Turkey, Kenya, China, Thailand, the United States, Switzerland, New Zealand, Australia, Italy and South Korea have invested more than $500 million.

2 Ukraine’s Available Geothermal Energy Resources and Technologies The explored reserves of geothermal energy in Ukraine are about 200 GW. They are represented by thermal waters with a temperature from 50 to 220C and are located in almost all regions of the country. According to the State Energy Efficiency Agency of Ukraine, the long-term potential of geothermal energy is about 90 TWh/yr, which can provide annual fuel savings for heat production of about 10 billion cubic meter of natural gas. The Geothermal Atlas of Ukraine [5] presents temperature fields at depths from 0 to 75 km. According to these data, at a depth of 0.5 km temperatures vary widely: from 130C for the Ukrainian Shield (Fig. 1) to 19–320C for the Donbass and the Dnieper-Donetsk basin and up to 430C for the Transcarpathian Depression. At a depth of up to 1 km in the area of the Ukrainian Shield temperatures do not exceed 19–220 °C; in the Donetsk region—in the range of 23–500 °C; in the Carpathian region—30 to 500 °C; in the Transcarpathian depression from 70 to 1000 °C; in the Pre-Carpathian zone—from 45 to 700 °C. In the territory of Crimea in the central and western part, and also on the Kerch peninsula waters with a temperature of 60–900 °C could be found out. At depths of 3–3.5 km there is a higher background temperature with large differences. In the Donetsk region (in the extreme west of the country), and Crimea, temperatures reach 100–1400 °C, and in the Uzhgorod region—1600 °C. In the area of the Dnieper-Donetsk basin, which covers Chernihiv, Sumy, Kharkiv, Poltava, Luhansk regions, as well as in the Carpathians and Prykarpattia, the temperature of the overlying rocks is 70–900 °C. At a depth of 5 km there are large volumes of coolant with a temperature of 84–950 °C almost throughout the country. As can be seen, high-temperature waters at accessible depths are available in limited quantities in several small deposits. Mostly in most parts of the country there are waters with temperatures from 50 to 1000 °C. According to the calculations of the ITTF of the NAS of Ukraine [7], the technically available energy potential of geothermal energy sources in Ukraine is 51.14 million MWh/yr, which can provide annual fuel savings for heat production of 6.65 million tons per ton. Technologies for the use of geothermal energy for heat supply. Modern geothermal systems use the principle of forced circulation of the coolant through underground permeable layers, when heated geothermal water, which is in a natural or artificial underground permeable reservoir, is extracted to the surface through a production

388

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Fig. 1 State Geological Map of Ukraine [6]: 1—Ukrainian shield; 2—slopes of the Ukrainian Shield and the Voronezh Massif; 3—shield framing: Volyn-Podilsk and Scythian plates, DnieperDonetsk depression and Pripyat depression; 4—south-eastern outskirts of the Western European platform; 5—Black Sea basin; 6—Donetsk folded region; 7—folded systems of the Carpathians, Dobrudzha and Crimea; 8—Carpathian and Pre-Dobrudzha depressions

well, fed to the consumer and then pumped back into the downhole. This method of removing heat from the deep layers of the Earth—the creation of geothermal circulation systems (GCS)—was first proposed in the mid-50 s of the last century at the Institute of Heat Power Engineering of the Academy of Sciences of Ukraine by Academicians A. N. Scherban and O. O. Kremnev. In the scientific team under the leadership of Doctor of Technical Sciences AV Shurchkov, the scientific basis for the functioning of GCS systems was created, a large amount of research and development work was carried out. A number of technologies and installations, including for geothermal heat supply of settlements, industrial, agricultural, social, communal and other facilities, were brought to the research and industrial stage. The emergence of new technologies for the extraction and use of coolant, as well as methods for forecasting geothermal resources, have provided a significant increase in the last 25 years of consumption of thermal geothermal energy. In the world, a multivariate technology for the use of geothermal resources has been developed and millions of existing heat supply systems have been built [8]. A typical heat supply system consists of two main parts: an underground complex that includes production and injection wells, and a complex of ground structures that includes pumping stations, heat exchangers, heat transformers (heat pumps), heating

Geothermal Heat Supply Development Pathways in Ukraine

389

mains, water treatment and treatment plants, peak boilers. Schematic diagram of the station is shown in Fig. 2 [9]. For the conditions of Ukraine, several variants of schemes for creating geothermal heat supply systems are possible: 1. Based on specially drilled wells in the area of the geothermal field, when the water temperature exceeds 750 °C. The implementation of such technology is possible in some areas of the Carpathian region and the Donetsk-Dnieper Basin, in the Crimea at a depth of wells up to 3500 m. 2. On the basis of specially drilled wells with water temperature below 750 °C. The depth of wells, as a rule, does not exceed 2500 m. As the water temperature is

Fig. 2 Schematic diagram of a geothermal heat supply station: 1-injection well; 2-pump installation; 3-system of water and gas purification and water treatment; 4-heat exchangers; 5-peak heaters; 6-mains pump; 7-main heating mains; 8-12—potential heat consumers; 13-heat pump; 14-depth pumps; 15-production (water-lifting) well; 16-filter system

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insufficient for supply to the heat supply system, heat pumps are used to increase its temperature. 3. Based on existing wells. These can be spent and preserved wells of gas and oil fields or various types of exploratory wells containing thermal waters. There are more than 20,000 unused wells in Ukraine that could potentially be used for these purposes. The results of their survey are shown in Table 2. / 10 / The largest number of wells is located in densely populated regions in Donetsk, Chernihiv, Sumy, Poltava, Kharkiv regions. Depth of thermal waters from 3.5 to 5 km, temperature range from 35 to 1700 °C. 4. Based on near-surface heat resources. Due to the use of heat pump technologies, low-temperature near-surface geothermal resources at depths from a few meters to 100–300 m are becoming increasingly important. Despite the fact that the properties and processes occurring in the near-surface zone are currently insufficiently studied, there is no substantiated data for the selection of sites for geothermal systems, the existing recommendations are indicative and preliminary, world practice shows that the use of low-potential Geothermal resources are economically viable for heat supply of low power facilities. Shallow geothermal resources have a number of advantages, such as practical inexhaustibility, ubiquity, proximity to the consumer, safety, economic competition for traditional boilers, environmental friendliness. The essence of the technology of using the heat of the near-surface zone is to create a downhole or horizontally located underground heat exchanger connected to the heat pump. Figure 3 shows the schematic diagrams of heat supply systems using the heat of the surface layers of the earth [9]. The heat pumping equipment of most world companies is currently present on the Ukrainian market. We offer mainly systems for private homes and cottages. The payback period of such systems is from 2 to 5 years. Table 2 Lawn and oil wells suitable for thermal water production Regions Crimea

Zakarpattia

Dnieper-Donetsk Rift

Number of existing wells

36

14

141

Depth, m

1200…1600

1000…2000

3500…5000

Flow rate, m3/day

500…1200

500…1000

500…1200

Temperature, oC

50…70

55…75

90…170

Mineralization, g/l

10…20

15…25

150…200

The nature of productio

self-deprecation

pump

pump

Geothermal Heat Supply Development Pathways in Ukraine

391

Fig. 3 Geothermal system. A—with horizontal channels: 1–heat pump, 2–heat accumulator, 3– ground heat exchanger;B—with vertical wells: 1–heat accumulator, 2–heat pump, 3–columns of pipes

3 Geothermal Heat Supply Economic Feasibility Assessment for Ukraine The main consumers of thermal energy in Ukraine are households and communal services. The needs of households and communal services in the total energy balance of the country accounts about 55% of heat produced and more than 27% of fuel consumed. Heat is currently produced at 14 large coal-fired thermal power plants and 31,000 boilers, 24% of which are equipped with boilers operated for more than 20 years, with an efficiency of less than 82% and a low level of gas cleaning. Coal and gas for thermal energy production are largely imported from abroad. The difference between the needs of the industry and own resources exceeds 30%. The housing sector is considered to be technically backward with a number of economic and environmental problems. Large-scale use of geothermal energy for housing and the private sector could be a good alternative to partially replace traditional fuels, significantly reduce greenhouse gas emissions and improve the environment. The main advantage of geothermal energy compared to other renewable sources is that its use is possible around the clock, all year round, unlike, for example, solar or wind, which can generate energy only about one third of the time. In addition, the direct use of geothermal energy is one of the most environmentally friendly. The main disadvantage of the geothermal system is the need for significant investments at the initial stage of development, in the design and construction of stations in combination with a high level of risk. But the specifics of projects for the construction of geothermal stations is that with a fairly high capital investment, operating costs are sharply reduced. Total costs for the construction of a geothermal thermal power plant based on deep wells include costs for preparation for construction, preparation of design and

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estimate documentation, topographic and engineering surveys, construction of an underground complex, construction of surface structures. The largest capital expenditures are for the construction of an underground complex—for drilling exploration and production wells or reconstruction of existing ones. They account for 50–90% of the total investment, depending on the depth of the productive formation containing thermal water, its temperature, effective power, permeability and formation pressure [9]. According to [10] in Ukraine, the average cost of drilling 1 m of oil and gas wells on land is about 2000 USD/meter. The cost of drilling geothermal wells is within the same limits. A new gas well could cost up to $5.5 million USA. For comparison, in the USA the average cost of drilling of 1 m of wells depending on depth lies within the same limits—from 500 to 2000 dollars USA/m. When using existing wells, capital costs for the construction of an underground complex are significantly reduced. For example, according to [11], the amount of capital investment in the construction of the underground HRT complex in Beregovo in the Transcarpathian region on the basis of a specially drilled well with a depth of 1300 m amounted to 3.226 million US dollars, and capital expenditures for the reconstruction of canned wells of the same depth $57 million USA. The costs of construction or reconstruction of terrestrial infrastructure consist of the cost of pumping stations, heat exchangers, thermal transformers, heating mains. The total cost of building a ground complex depends on many factors and varies widely. The specific cost of construction of thermal power plants depends on the depth of wells, their type, the configuration of surface structures, the location of the station relative to the consumer and others. The expediency and efficiency of the use of geothermal heat supply systems are determined mainly by the amount of production profit and payback periods, which, in turn, depend on heat tariffs. In [11] the results of researches of dependence of payback period on heat tariffs on materials of 20 projects of geothermal thermal power plants developed in Institute of thermal physics of National Academy of Sciences of Ukraine during 1998–2003 are shown at Fig. 4. With existing tariff for the heat energy (14.1–15.91 USD/MWh), the payback period of the projects averaged about 15 years. Therefore, despite the high assessment of technical, environmental, social solutions, the projects were not implemented, as economic parameters made them unprofitable. Projects could be considered feasible at rates of $27/MWh and above, with a payback period of 7 years or less. During the period from 1998 to 2020 in Ukraine, tariffs for heat and electricity have increased many times, both in hryvnia and in dollar terms. It is of interest to compare the economic efficiency of these projects in terms of tariffs and prices in 2003 and 2020. For this purpose, 4 projects were selected, which passed the technical expert evaluation of foreign experts and were approved for implementation. Table 3 presents the technical parameters of these projects. While maintaining all the technical decisions made in these projects, calculations of economic indicators for the conditions of 2020 were made. The results of the calculations are presented in Table 4. The calculations showed that the specific capital investment in geothermal heating system for the conditions of 2020 compared to 2003

Geothermal Heat Supply Development Pathways in Ukraine

393

Fig. 4 The payback period depending on the value of tariff [11]

Table 3 The list of the projects and their technical characteristics Regions Lviv region, Mostyska

Chernihiv region

Crimea

Zakarpattia region, Beregovo

Depth of wells, m

3500

3500

2230

1300

Number of well

3 (2/1)*

2 (1/1)*

3 (2/1)*

5 (3/2)*

Type of wells

NW**

RW**

NW**

NW/RW**

Water temperature, °C 95

90

90

60

Heat load, MW

12.57

1.63

20

6

Annual heat consumption, MWh

42,075

7304.7

51,200

18,148

*

number of production / number of absorbing wells ** NW —new wells, RW —restored wells

increases by 42% for newly drilled wells and 40% for restored wells. The cost of heat production for systems based on newly drilled wells increased by an average of 62%, for restored wells—by 49.8%. But, at the same time, due to high tariffs for heat production profit increased by an average of 580%. Payback periods of projects have been reduced to 3–7 years. It is evident that the listed projects are feasible in modern conditions, and could be implemented with high economic benefits [12]. If we compare geothermal heat supply systems with fuel boilers, the analysis presented in [11] shows that in terms of profitability they correspond to the economic indicators of heat supply projects based on small fuel boilers. But environmental benefits and independence from fuel market conditions and pricing make geothermal heating systems more cost-effective than fuel boilers.

*30.6/26.9 _ Over 15

USD/kWyr

USD

Years

Cost

Production profit

Payback period

7/4

*614.8/584.5

*45.9/40.3

*702/365

2020

Over 15

366.0

9.5

460

3

5372212.8

19.5

519.7

2020

2003

*/ 261

1998

USD/kWyr

Chernihiv region

Lviv region. Mostyska

Regions

Specific capital expenditures

Units

Table 4 The financial efficiency of the projects

13

508.2

3.9

433

2003

Crimea

3

2737.6

5.9

872

2020

Over 15

39.8

7.7

625

2001

6

360.2

11.5

767

2020

Zakarpattia region Beregovo

394 Y. Shurchkova et al.

Geothermal Heat Supply Development Pathways in Ukraine

395

4 Ukrainian Legal Base and State Support In Ukraine, the main legal documents in the field of alternative energy sources are: Law of Ukraine «On Alternative Energy Sources», Law of Ukraine «On Energy Conservation», Code of Subsoil of Ukraine, Law of Ukraine «On Heat» Law of Ukraine «On Energy Lands and Legal Regime» special zones of energy facilities «and a number of others. The development of geothermal energy is envisaged by the National Renewable Energy Action Plan until 2020. According to Ukraine’s energy strategy in the field of geothermal energy, it is planned to reach 0.19 GW of installed capacity by 2020 and 0.7 GW by 2030. The Law of Ukraine on Heat Supply provides for the use of «non-traditional and renewable energy sources, including geothermal waters». A number of documents declare state support in accordance with the amount of funds provided by the law on the State Budget of Ukraine, as well as funds for research work to improve heat supply and energy saving systems. In 2015, a Memorandum of Cooperation and Understanding in the Development of Geothermal Energy was signed between Ukraine and Iceland. The Tax Code of Ukraine provides benefits for the taxation of energy-saving and energy-efficient projects, including those related to geothermal energy. It would seem that favorable conditions have been created for the development of geothermal heat supply. However, according to the State Agency for Energy Efficiency, as of the end of 2020, geothermal energy is not among the recently commissioned renewable energy facilities. World experience shows that the successful development of geothermal energy requires government support, detailed information on geothermal deposits, sufficient funding, and involvement of modern technologies.

5 Conclusions The analysis of trends in the development of geothermal energy in the world shows that in the coming decades, the most intensive development of geothermal heat supply. There is a transition from traditional combustion of organic fuels to the use of energy efficient technologies, including geothermal. In terms of volumes of all types of renewable energy sources for heat supply, geothermal energy ranks second in the world after solar. The use of geothermal energy can significantly reduce the cost of traditional fuels and reduce environmental pollution, ensures independence from the situation and pricing in the fuel market. The main advantage of geothermal energy compared to other renewable sources is that its use is possible around the clock all year round, unlike, for example, solar or wind, which can generate energy only about one third of the time. Ukraine is critically lagging behind not only the leading countries in this field in terms of the scale of geothermal energy use, but also the neighboring countries that have similar or even lower potential for geothermal resources.

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In the presence of fossil fuel shortages, low efficiency of most old boilers, high levels of greenhouse gas pollution, the development of geothermal energy in the field of housing and communal services may be an alternative to partial replacement of traditional fuels. Ukraine has all the prerequisites for the development of geothermal heat energy: there are significant reserves of geothermal energy of medium potential, spread almost throughout the territory; has scientific potential; scientific and technical experience in the design and implementation of geothermal thermal power plants. The country has extensive legislation regulating the use of alternative energy sources, declaring state support and allocating funds for research. Calculations show that geothermal projects of thermal power plants in the conditions of existing tariffs and prices can be economically feasible, they are highly profitable with short payback periods. In terms of profitability, they correspond to the economic indicators of heating projects based on small fuel boilers. But environmental benefits and independence from fuel market conditions and pricing make geothermal heating systems more cost-effective than fuel boilers. World experience shows that the successful development of geothermal energy requires government support, detailed information on geothermal deposits, sufficient funding, and involvement of modern technologies.

References 1. World Geothermal Congress, 2015, Melbourne, Australia, International Geothermal Association (2015). https://www.geothermal-energy.org/…/world-geothermal-co 2. International Energy Agency. Statistics. https://www.iea.org/ 3. Lund, J.W., Boyd, T.L.: Direct utilization of geothermal energy 2015 worldwide review. In: Boyd Geo-Heat Center, Oregon Institute of Technology, Klamath Falls, OR 97601, USA, retired (hidden) (Last Accessed 07 Aug 2020) 4. Geothermal Heating and Cooling Technologies. https://www.epa.gov/rhc/geothermal-heatingand-cooling-technologies. (Last Accessed 23 Apr 2020) 5. Geothermal Atlas of Ukraine. https://docplayer.ru/142360361-Geotermicheskiy-atlas-ukrainy. html. (Application date 25 Feb 2020) 6. State geological map of Ukraine. geoinf.kiev.ua/wp/kartograma_rep.php?listn=m35-4. (Application date 21 Feb 2020) 7. Zabarny, G.M., Shurchkov, A.V. (2002) Energy potential of non-traditional energy sources of Ukraine. K.: ITTF NAS of Ukraine, p. 211 (2002) 8. Geothermal heating systems. https://earthrivergeothermal.com/geothermal-heating-systems/. Accessed 19 Aug 2020 9. Boguslavsky, E.I.: Development of thermal energy of the subsoil. M.: Sputnik + Publishing House, p. 448 (2018) 10. Morozov Y.P.: Method of intensification of geothermal well flow. http://naukarus.com/metodintensifikatsii-debita-geotermalnyh-skvazhin 11. Zabarny, G.M., Shurchkov, A.V., Barilo, A.A.: Feasibility study of the feasibility of using heat pumps in geothermal heat supply systems using thermal waters of the Miocene thermal aquifer complex of the Transcarpathian region. Kyiv ITTF NAS of Ukraine, p. 230 (1999) 12. Kostyukovsky, B.A., Shulzhenko, S.V., Maksimets, E.A. A system of mathematical models for a comprehensive assessment of the prospects for the development of the fuel and energy complex. In: International Scientific and Practical Conference «Energy Efficiency-2008», p. 37–38. Gas Institute of the National Academy of Sciences of Kyiv, Ukraine, October 6–8 2008

Environmental Aspects of Geothermal Energy Anna Pidruchna

and Yulia Shurchkova

Abstract The chapter deals with the problems associated with the global environmental energy conservation, the causes of its occurrence and possible ways out of it. Issues of international cooperation in the field of development of renewable energy sources are discussed. An analysis of the life cycles of various types of renewable energy, features of the life cycle of geothermal stations, possible geological consequences of the impact on water and land resources, environmental problems and risks associated with the implementation of geothermal projects are given. The prospects of using geothermal energy in Ukraine are shown. Keywords Ecology · Renewable energy sources · Life cycle · Emissions · Greenhouse gases · Environment The average temperature on the planet in the period from 2008 to 2018 increased by 1.00 C. If this rate of temperature growth continues, then by 2050 global warming will reach the level of 1.50 C. The Nuclear Energy Agency of the Organization for Economic Co-operation and Development (OECD/NEA) has published a study «The Cost of Decarbonization: The Cost of Systems with a High Share of Nuclear and Renewable Generation», which showed that in order to prevent a rise in temperature by 2050, it is necessary to reduce CO2 emissions in electricity sector of the OECD countries by 90%. Currently, this figure averages 430 g/1 kWh, and by 2050 should be reduced to 50 g/1 kWh. The energy industry, which provides 40% of total atmospheric emissions and housing and communal services are the largest air polluters, since the main share of energy, both electrical and thermal, is produced by burning fossil fuels. Figure 1 shows the growth rate of emissions into the atmosphere by regions of the world over the past 50 years. As shown China, the USA, and India produce the largest volumes of CO2 emissions.

A. Pidruchna (B) · Y. Shurchkova General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_24

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Fig. 1 Emissions of fossil CO2 (CDIAC/GCP/BP/USGS data)

Developed countries currently spend approximately 1–2% of GDP on environmental protection, while the cost of environmental damage annually is 4–6% [1]. Against the backdrop of the environmental, with the reduction of world reserves of fossil fuels and rising prices for it, the question of developing the industry of alternative energy carriers has become acute. In the middle of the last century, broad international cooperation on environmental issues began, important environmental agreements were reached, and most countries adopted important environmental laws. In 2019, the European Commission launched the European Green Deal (EGD)—a roadmap to ensure the resilience of the EU economy by overcoming the climate crisis by reducing CO2 emissions, efficient use of resources, moving towards a clean economy and slowing climate change [2]. The main goal of the European Green Deal is to reduce emissions by 50–55% by 2030 and reduce greenhouse gas emissions to zero by 2050. It concerns all sectors of the economy, in particular, energy, metalworking, transport, construction, agriculture, chemical industry, etc. In 2020, the share of renewable energy sources (RES) in the generation of EU countries for the first time in history overtook all other energy sources: RES accounted for 38% of total generation against 37% of the share of traditional electricity. In March 2021, a historical maximum of electricity production from wind-based generation facilities was recorded in Europe. Renewable wind power provided 28.9% of daily electricity demand. The Government of Ukraine has announced its intention to join the Green Deal as it is a practical implementation of the European integration vector of the country’s development. The main advantage of using renewable energy sources in comparison with other types of energy carriers is their environmental friendliness and minimal impact on

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399

Table 1 Environmental parameters of power plants Type of power plant

Emissions in atmosphere m3 /MWh

Fresh water consumption m3 /MWh

Waste water discharge m3 /MWh

Volume of solid waste kg/MWh

Withdrawal lands ha/MWh

Conservation spending %total cost

solar

–

–

0.02

–

2–3

–

Wind

–

–

0.01

–

1–10

1

geothermal

1

–

–

–

0.2

1

biomass

2–10

20

0.2

0.2

0.2–0.3

–

TPP–coal

20–35

40–60

0.5

200–500

1.5

30

TPP–gas

2–15

2–5

0.2

0.2

0.5–0.8

10

HPP

–

–

–

–

100

2

NPP

–

70–90

0.2

0.2

2.0

50

the environment. The one option to compare the environmental impact of different power generation technologies is to analyze their environmental parameters, but it is necessary taking into account e.g. whole power system operational modes. Table 1 shows comparative data on the environmental performance of power plants operating on both renewable energy sources and conventional fuels [3]. In almost all most often, power plants operating on renewable energy sources have significant advantages over conventional fuel power plants, since energy generation in this case occurs without burning hydrocarbons and without emitting greenhouse gases into the atmosphere. However, if we consider from the standpoint of ecology not only the period of energy generation, but also the preparatory stages of project development, then it will be necessary to take into account the side effects accompanying these stages. To ensure the operation of stations on renewable energy sources, it is necessary to carry out a number of activities related to the operation of machine-building, metallurgical and other enterprises that use energy obtained from traditional sources that generate greenhouse gases and other pollution. If we consider the full period of the existence of a renewable energy facility project—from the idea to the disposal of used equipment (“from the cradle to the grave”), including preparation, exploration, infrastructure creation, equipment manufacturing, provision of raw materials and materials, construction work, waste and equipment disposal at the end of the life of the facility, it is no longer possible to speak of “zero CO2 emissions”. Therefore, the transition to renewable energy does not always give the effect that is determined only by the period of energy production. To assess the impact on the environment, it is necessary to take into account the impact of all stages of the object’s existence. Life cycle analysis takes into account the complete life cycle of the system, from the receipt of materials during construction to operation and end-of-life waste management, and helps to identify the key stages that affect the effectiveness of the chosen technology. Research on side effects from the creation and operation of renewable energy facilities is currently insufficient and they are often contradictory. In the work

400 Table 2 Indicators of CO2 emission in life cycles for various types of power plants

A. Pidruchna and Y. Shurchkova Technology

Life cycle emissions, gCO2 eq/kWh

Wind

12

Tidal

15

Hydraulic

20

Ocean Wave

22

Geothermal

35

Solar (photovoltaic) batteries

40

Solar Concentrators

10

Bioenergy

230

Coal

820

Gas

490

Atomic

12

of a researcher at the Western Norway Research Institute, WNRI Otto Andersen “Unintended consequences of renewable energy. Problems to be Solved” [4] provides the results of generalization of information on studies of the negative environmental impacts of renewable energy on various types of energy and regions of the world, considers the unintended impact of renewable energy sources on human health and the environment, and also provides an analysis of the full “life cycle” renewable energy facilities and assessment of the so-called «reverse effects» (rebound effects). According to Andersen, different types of renewable energy differ significantly in the intensity of green color, if they are evaluated from the standpoint of the entire life cycle. The indicator of the intensity of greenhouse gas emissions in the production of energy is the amount of gram-equivalent of CO2 per unit of energy produced, taking into account the time interval and the installed capacity utilization factor. The Intergovernmental Panel on Climate Change—IPCC—released a report in 2014 on climate change mitigation [5]. The energy systems chapter provides lifecycle emissions data for various types of power plants, both renewable and fossil fuels (Table 2). As can be seen, the total CO2 emissions of the life cycles of power plants operating on renewable energy sources are an order of magnitude lower compared to those operating on fossil raw materials. At the same time, it should be emphasized that the lowest emission rate for traditional plants is in the nuclear power industry−12—i.e. at the level of the lowest indicator of energy from renewable sources. It also provides data on the distribution of emissions over the life cycle, broken down by source (Fig. 2). It is obvious that the distribution of greenhouse gas emissions by stages of the life cycle of production for different types of energy is fundamentally different. In the case of wind, solar, geothermal and hydropower, the main environmental burden falls on the stage of production of materials, equipment and construction of stations. The nuclear power industry has a similar structure. Fossil fuel-based power generation

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401

Fig. 2 Own estimations according to cycle greenhouse gas emissions from electricity supplied using fossil fuels, renewable sources and nuclear power [5]

accounts for the bulk of emissions during the operation of the plant, which requires fuel combustion. The same is true for bioenergy. The reasons why greenhouse gas emissions can reach high values for the life cycles of hydroelectric, solar, bioenergy and geothermal plants are different, as much depends on the technologies used and the specific production conditions. Thus, the development of energy from renewable energy sources requires a simultaneous increase in fossil fuels for the operation of enterprises that produce materials and equipment for the creation and operation of these stations, i.e. Increasing the production of energy through renewable energy, respectively, leads to an increase in

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the consumption of traditional resources. And only when full production cycles are created that ensure the production of renewable energy without the participation of traditional fuels, it will be possible to talk about zero emissions and the bright green color of energy from renewable energy sources. Ecological problems of geothermal energy. The impact of geothermal energy on the environment depends on the form of its use or transformation: either directly in the form of heat production, or for the production of electricity in geothermal power plants. Power generation. Geothermal power plants differ in the type of technologies that are used to convert heat into electricity, such as direct steam, flash evaporation, binary technologies. Various cooling technologies are also used—water or air. The environmental impact will vary depending on the conversion and refrigeration technology used. The most significant possible adverse effects of geothermal energy on the environment include the following: discharge of waste water and condensate contaminated with chemical impurities; change in the level of groundwater, soil failures, waterlogging; gas emissions (methane, hydrogen, nitrogen, ammonia, hydrogen sulfide); pollution of groundwater and aquifers, soil salinization; brine emissions from pipeline ruptures; heat emissions into the atmosphere or surface water, which create a local increase in air humidity; change in temperature fields of underground horizons; land alienation. Impact on water systems. One of the serious problems in the use of underground thermal waters is their high mineralization, increased gas content, tendency to salt deposition when temperature and pressure conditions change, and high corrosive aggressiveness to structural materials. The discharge of such brines into natural water systems can lead to irreversible environmental consequences. In this regard, the waste thermal waters are in most cases pumped back into the underground aquifer. In such systems, wells for pumping water are equipped with steel casing pipes cemented with the surrounding rock [6], which reliably protects groundwater from pollution by geothermal objects [7]. But these measures significantly increase energy costs, capital investments for the construction of an injection well and additional costs for its operation. Re-injection of waste water is also necessary to maintain reservoir pressure in the aquifer, which otherwise can lead to a decrease in plant productivity and possible ground subsidence in the area of the geothermal field. Environmental damage could be high consumption of fresh water, which is used by geothermal power plants for cooling and re-injection. In most cases, when using a closed circulation system, not the entire volume of water pumped out of the underground horizon can be returned back due to the fact that part of the water is lost in the form of steam. To maintain reservoir pressure, it is necessary to use water from outside. The required amount of water depends on the capacity of the station and the technology used. Since there are no strict requirements for the composition of the injected water, clean water is not always used for this purpose. For example, in geothermal power plants in California, in the USA, on Geyser Square, non-potable treated wastewater is pumped.

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403

Fresh ground water in geothermal power plants is also used for cooling and condensation. In the USA, all geothermal power plants use wet recirculation technology with cooling towers [8]. The cooling water consumption of geothermal power plants per kWh of electricity produced is 4–5 times that of thermal power plants due to lower efficiency. Atmosphere. The volume of emissions of harmful gases into the atmosphere in geothermal power plants is much less than in thermal power plants. In terms of chemical composition, they differ from emissions from fossil fuel stations. The steam produced at geothermal stations is 80% water. Gas impurities consist mainly of carbon dioxide, a small part of methane, hydrogen, nitrogen, ammonia and hydrogen sulfide. The most dangerous and harmful is hydrogen sulfide (0.0225%). Once in the atmosphere, hydrogen sulfide turns into sulfur dioxide (SO2 ) and when combined with water, causes acid rain, which causes great damage to nature, and causes heart and lung disease in humans and animals. But it should be noted that SO2 emissions from geothermal power plants are about 30 times lower per 1 MWh than from coalfired power plants, which are the largest sources of SO2 . CO2 emissions per 1 MWh of generated energy at a geothermal plant are 0.45 kg, while at a thermal power plant operating on natural gas—464 kg, on fuel oil—720 kg, on coal—819 kg (thirteen) [9]. The amount of air emissions from geothermal plants depends on whether an open or closed fluid circuit is used. In systems with a closed loop, gases from the liquid practically do not enter the atmosphere, because. After use, they are pumped back into the aquifer and therefore emissions to the atmosphere are minimal. In open loop systems, air emissions are reduced by filter and scrubber technologies. But this produces a sludge consisting of trapped substances, which include sulfur, vanadium, silica compounds, chlorides, arsenic, mercury, nickel and other heavy metals. This toxic sludge must be disposed of in hazardous waste landfills [10]. Land use. The size of the land area required to accommodate a geothermal power plant depends on the properties of the underground collector, the capacity of the station, the energy conversion technology used, the type of cooling system, the layout of pipelines, and the area of auxiliary buildings. For example, one of the world’s largest geothermal stations Geysers, USA, has a capacity of 1517 MW, the station area is about 78 square kilometers. Large geothermal power plants are mainly located in fault zones, in zones of modern volcanism, in places with high geothermal gradient where seismic instability and earthquakes are observed. Earthquakes can occur when drilling deep wells, when hydraulically stimulating rocks to create additional fractures and increase the heat exchange surface for the coolant, as well as in the development of petrothermal systems, when high-pressure water is pumped into the underground formation of hot rocks to create fractures in the formation, similar to technology hydraulic fracturing of natural gas reservoir. These phenomena have been observed in different parts of the world. Seismic activity in this case is usually minor, but can lead to damage to buildings, injury and even death. For example, in 2006 a geothermal exploration project in Basel, Switzerland was charged with causing a series of earthquakes measuring up to 3.4 on the Richter scale. In 2011,

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scientists established a definite relationship between geothermal exploration and seismic activity. On November 15, 2017, a powerful earthquake of magnitude 5.5 on the Richter scale struck Pohang, South Korea, injuring 135 people and leaving 1700 homeless [11]. Certain problems arise when drilling deep wells during the construction of GeoPES and GeoTPP, when hydrogen, the reserves of which are quite large at depths of 2–3 km, is released, as a result of the combination of hydrogen with atmospheric oxygen, vacuum-type explosions can occur. Dozens of such cases are known in Russia and, according to unofficial data, happened in Ukraine. A serious environmental problem in the use of geothermal energy is also the potential instability of the surface of the geothermal field. This is because when water and steam are extracted from underground collectors, the ground above them may slowly sink over time. This risk is significantly reduced when using closed circulation systems, when the spent coolant is pumped into the aquifer and the formation pressure is maintained constant. Duration of operation of geothermal power plants. In world practice, it is believed that geothermal resources can be used for 20–30 years, although many of them work longer. After these periods, the volume of energy production decreases and their further operation becomes unprofitable. Geothermal resources can be exhausted even before certain deadlines if the rate of heat extraction exceeds the rate of its natural replenishment. The service life largely depends on the power of the heat source and the technologies for its use. For example, a geothermal power plant in Larderello, Italy, has been generating energy since the early 1900s, and at Geysers, USA, since 1960.The problem of reducing the decline in productivity was solved by drilling new wells and additional injection of treated wastewater into the aquifer [12]. Direct use of geothermal energy. The most common form of use of geothermal energy is its direct use without transformation—it is space heating and cooling, including district heating; balneology; pools for swimming and bathing; Agriculture; greenhouse heating; drying, etc. More than 80% of the total global geothermal energy capacity is used in heating and hot water supply systems. At the end of 2019, the total installed capacity of thermal geothermal plants in the world was 107,727 MW. According to WGC2015, the increase in capacity for the period from 2010 to 2015 was 52.0, or 8.7% per year. For district heating, geothermal energy is used in 28 countries. The leaders in district heating in terms of annual energy consumption are: China, Iceland, France and Germany. Individual heating is developed mainly in Turkey, USA, Italy, Slovakia and Russia. There are more than 5000 district heating systems in Europe, and the district heating market share is about 10% of the total heating market. In Iceland, more than 90% of the heat supply is based on geothermal heat. In Reykjavik, 99% of the needs are provided by geothermal heat. In France, the installed capacity of thermal geothermal plants, including geothermal heat pumps, is 2.3 thousand tons.MW, which reduces CO2 emissions by about 1.8 million tons. Around Paris, 33 geothermal plants heat 170,000 homes, saving the equivalent of 144.4 million m3 of natural gas. It is planned that geothermal thermal stations should provide 60% of the heat demand in Paris and its environs. The use of geothermal energy for heating needs has a number

Environmental Aspects of Geothermal Energy

405

of advantages compared to both fossil and renewable types of energy: year-round and 24 h availability, no fuel depots, no labor for loading fuel into boilers, no low chimneys, etc. Problems, which arise from the use of underground thermal waters in direct use, are similar to those that occur during the construction and operation of geothermal power plants, although to a lesser extent. Thermal waters for direct use tend to have a lower potential than geothermal power plants and require medium to shallow wells to extract them. In this regard, the concentration of impurities in the waters is much lower. But this does not exclude the need for re-injection of waste water into an underground aquifer. This makes it possible to protect surface natural water systems from pollution, from waterlogging of the area and soil salinization. In the case of systems with an open circuit, emissions of gases and heat into the atmosphere or surface water are possible. The use of low-grade water in combination with heat pumps in closed circulation systems can significantly reduce the risks of negative environmental impact. In systems using surface heat in combination with heat pumps, with shallow wells (up to 300 m) or heat exchangers, greenhouse gas emissions are practically absent and the environmental impact is minimized. In such systems, small changes in the temperature of groundwater or surrounding rocks are possible. The temperature around vertical wells may rise or fall slightly depending on the time of year and operating conditions. But with a balanced heating or cooling load, the ground temperature will remain stable. The size of the land areas required for the placement of thermal geothermal stations is determined by the type of hydraulic scheme used for the circulation of thermal waters in the ground complex; the number of production and absorbing wells; distances between production wells and the geothermal plant, between the thermal water intake circuit and the injection circuit; placement of peak boilers and geothermal installations, auxiliary facilities. Usually, station nodes fit into existing heating systems with boilers and do not occupy large areas. Near-surface geothermal systems also occupy relatively small areas. For example, according to the description, in Klamath Falls, Oregon, USA, (Klamath Falls (Oregon)—Wikipedia) a geothermal thermal plant that provides residential heating, district heating, a snowmelt system in the city center, heat supply to local industrial enterprises, has about 600 geothermal wells 100 m deep, almost invisible in the city. The lifetimes of geothermal thermal plants, if properly managed and operated properly, can be quite long. For example, the Reykjavik district heating system has been operating since the early 1930s with little change in performance, while the Oregon Institute of Technology geothermal heating system has been operating since the 1950s with no change in performance. Life cycle assessment studies for geothermal energy production are few and often conflicts depend on many factors, such as the specific characteristics of geothermal fields, the uncertainty of the terms of operation, the imperfection of the technologies used. Life cycle analysis of geothermal technologies includes the following main steps: [13]:

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. characteristics of wells: fluid temperature, depth and size of wells, number of exploration, injection and production wells, type and amount of materials for well construction; . characteristics of the power plant: plant capacity, type and quantity of materials for the construction of the ground part of the station, geothermal field capacity and net energy production; . operational characteristics: characteristics of the working fluid, requirements for make-up water; . comparison with the characteristics of other energy production systems. Environmental impact assessment is carried out taking into account from 1 to 18 indicators. According to the IPCC, 2011 IPCC Special Report on Renewable Energy and Climate Change Mitigation, greenhouse gas emissions from near-surface open-loop geothermal systems during operation are approximately 0.1 pounds (0.0454 kg) of carbon dioxide equivalent per 1 kWh in closed loop systems, the gases are not vented to the atmosphere. But in both cases, there are emissions associated with the construction of stations and service infrastructure. In geothermal systems, which include deep wells that require energy to drill and pump water into underground reservoirs to create a developed infrastructure, life cycle greenhouse gas emissions are approximately 0.2 pounds (0.091 kg) of carbon dioxide equivalent per kW hr. For comparison, data are provided to estimate life cycle greenhouse gas emissions for electricity generated from natural gas—from 0.6 to 2 pounds (0.2722–0.9072 kg) of carbon dioxide equivalent per 1 kWh, and for electricity, produced on coal—from 1.4 to 3.6 pounds (0.6350–1.6329 kg) of carbon dioxide equivalent per 1 kWh. However, in most countries, little attention is paid to the analysis of the life cycle of geothermal systems, while it allows for a deep analysis of the environmental impact of each stage of the life cycle and targeted management of geothermal energy production. Economic and environmental assessment of the use of geothermal energy. The economic assessment of the environmental benefits of developing geothermal resources is based on an assessment of the degree of interchangeability of traditional and geothermal energy sources. The economic effect of the use of geothermal energy is defined “as the prevented damage from the negative impact of the extraction of fossil fuels and the production of heat or electricity on natural resources and the environment” [14]. Mathematical dependence for assessing the economic efficiency of environmental benefits includes economic damage from the extraction and use of fossil fuels for the production of heat or electricity; economic damage from the generation of heat or electricity based on geothermal resources; economic effect from the additional environmental and social benefits of a geothermal energy source; unrealized income from the use of substituted conventional fuel for other purposes; expenses for the elimination of possible accidents and their consequences at power generating stations:

Environmental Aspects of Geothermal Energy

E g = U t − U g + E g + Dt + Ua ,

407

(1)

where U t —economic damage from the extraction and use of fossil fuels for the production of heat or electricity; U g —economic damage from the generation of heat or electricity based on geothermal resources; E g —economic effect of additional environmental and social benefits of a geothermal energy source; Dt —unrealized income from use of substituted traditional fuel for other purposes; U a —expenses for the elimination of possible accidents and their consequences at energy-producing stations. When designing geothermal plants, taking into account the amount of prevented economic damage can significantly affect the reduction of their payback periods. The design and technological parameters of geothermal systems are influenced by a large number of factors, such as the geological and geothermal conditions of the energy source, on the one hand, and a wide range of thermal loads and temperature conditions of consumers, on the other. Therefore, the assessment of the effectiveness and feasibility of creating each particular geothermal facility is possible only when determining its optimal parameters and indicators. The solution of such a problem is expedient with the use of economic and mathematical modeling of all stages of the creation of stations [15]. Geothermal energy in Ukraine. The main consumers of thermal energy in Ukraine are housing and communal services and the population (about 70%). More than 31 thousand boiler houses are operated in the country, 24% of which are equipped with boiler units that have been in operation for more than 20 years and have an efficiency below 82%. The total number of installed boilers is 75.8 thousand units. Among them are a significant number of small boiler houses with a heat output of up to 70 GJ/h, in which low-quality coals are burned, which leads to air pollution of cities and towns with a large amount of ash, dust and soot. Most small boiler houses operate without flue gas cleaning systems and ash collectors, since this increases the cost of heat generation by 10–25%. Given these circumstances, the development of geothermal heat can help the housing and communal services sector to get out of the energy conservation in terms of replacing traditional fuels and reducing the burden on the environment. Ukraine has all the prerequisites for the development of geothermal heat energy: there are significant reserves of geothermal energy of medium potential, spread almost throughout the territory; has scientific potential; scientific and technical experience in the design and implementation of geothermal thermal power plants. In 1996, the Institute of Technical Thermophysics developed the State Target Program “Environmentally friendly geothermal energy”, approved by the Cabinet of Ministers of Ukraine №100 on 17.01.1996 different regions of Ukraine. However, today in Ukraine there are no existing commercial projects to create electricity generation at the GeoPPP or heat supply stations. And this despite the fact that the annual technically achievable thermal potential of geothermal energy in the country is equivalent to about 90,000 million kWh/year (according to the State Energy Efficiency of Ukraine), and its use saves about 10 billion cubic meters. m of gas and significantly reduce emissions.

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The government periodically takes some measures to develop geothermal energy: in 2003 the Law of Ukraine “On Alternative Energy Sources” of 20.02 was adopted.2003 No. 555-1U; in March 2015, Iceland and Ukraine signed a memorandum of cooperation in the development of geothermal energy. As part of the Memorandum of Understanding in the fields of energy efficiency and renewable energy between the State Energy Efficiency and the National Energy Administration of Iceland (Orkustofnun), the parties agreed to implement joint projects to develop geothermal resources in Ukraine. Of course, the experience of Iceland, which heats about 93% of residential premises using this type of energy, is very important for Ukraine. However, this direction was frozen; The Ministry of Environmental Protection and Natural Resources plans to launch a monitoring, reporting and verification system for greenhouse gas emissions from 2021. (Law of Ukraine “On ambush monitoring, and verification of greenhouse gas emissions” dated April 29, 2019 No. 0875). However, according to the State Agency for Energy Efficiency, as of the end of 2020, geothermal energy is not among the recently commissioned renewable energy facilities, while the use of geothermal energy for heating, ventilation and air conditioning can reduce energy consumption by 25–50% comparable to traditional systems. According to the International Geothermal Agency, the use of geothermal heat in 2015 saved 52.5 million tons of oil equivalent per year and significantly reduces the consumption of traditional fuels and reduces environmental pollution. Studies by the US Department of Energy in the field of geothermal heating have shown that a geothermal heating system can reduce carbon dioxide emissions by 46 million tons compared to the use of fuel oil.

1 Conclusions The main advantage of using renewable energy sources in comparison with other types of energy carriers is their environmental friendliness and minimal impact on the environment. Comparison of the impact intensity of different energy production technologies is based on the analysis of their environmental parameters. For this purpose, life cycle analysis is used, which takes into account the entire life cycle of the analyzed system from the receipt of materials during construction to operation and disposal of waste at the end of its life, and helps to determine the key stages that affect the effectiveness of the selected technology. At present, it is impossible to talk about approaching zero greenhouse gas emissions when increasing the capacity of power stations using renewable energy sources, since this requires a simultaneous increase in fossil fuels for the operation of enterprises that produce materials and equipment for the creation and operation of these stations, which leads to an increase in pollution environment, including the atmosphere. Zero greenhouse gas emissions will be possible only when complete production cycles are created that ensure the production of renewable energy without the participation of traditional fuels at all stages of the life cycle. When creating

Environmental Aspects of Geothermal Energy

409

geothermal stations, it is necessary to take into account environmental problems, such as the discharge of waste water and condensate contaminated with chemical impurities; changes in the level of groundwater and soil failures; swamping and salinization of soils; gas emissions; pollution of groundwater and aquifers; heat emissions to the atmosphere or surface water; change in temperature fields of underground horizons; land alienation. Since the design and technological parameters of geothermal plants are influenced by a large number of factors, not only geological and geothermal, but also the operating modes of the consumer, the assessment of the effectiveness and feasibility of creating a particular geothermal facility is possible only when determining its optimal parameters and indicators. The solution of such a problem must be optimized using economic and mathematical modeling of all stages of the creation of stations. In Ukraine, due to the obvious shortage of hot water, the low efficiency of the old scorching boilers, the high level of pollution of the middle ground with greenhouse gases, the development of geothermal heat energy can be an alternative to modernizing the living room of the housing and communal state. In Ukraine p all changes of mind for the development of geothermal heat energy: p significant reserves of geothermal energy of the average potential, expanding practically throughout the territory; p scientific potential; scientific and technical report on the design and implementation of geothermal thermal stations. World experience shows that the construction of geothermal heat supply stations is economically feasible, and the replacement of boiler houses operating on traditional fuels with geothermal stations is beneficial not only from an environmental and economic point of view, but also has an important social aspect, because burning environmentally dirty fuel causes serious harm to the environment and human health.

References 1. Global Carbon Budget 2017. https://www.globalcarbonproject.org ›archive 2. Introduction to Europe’s Green Deal Presentation by Dr. Vladislav Bizek, WECOOP Key Expert on EU Legislation April 15, 2021. https://wecoop.eu/wp-content/uploads/2021/04/ Bizek_DKU_15_April.pdf 3. Bekirov, E., Fursenko, N.: Ecological characteristics of the operation of solar and wind power plants. Motrol 15(5), 147 (2013) 4. Andersen, O.: Unintended consequences of renewable energy: Problems to be solved. SpringerVerlag, London, vol XIII, p. 94. 16 illus (2013). https://www.twirpx.com › file 5. Energy Systems—IPCC. https://www.ipcc.ch/report/ar5/wg3/energy-systems/ 6. Kagel, A. The state of geothermal technology. Part II: Surface technology. Geothermal Energy Association, Washington DC (2008). http://www.earthpolicy.org/plan_b_updates/2008/upd ate74 7. Baldwin, S., DeMeo, E., Reilly, J.M., May, T., Arent, D., Porro, G., Sack, M., Sandor, D. (ed. 4 vols.): National renewable energy laboratory (NREL). In: Exploring the Future of Renewable Electricity. Hand, mm; NREL/TP-6A20-52409.National Renewable Energy Laboratory, Golden, CO (2012). https://www.nrel.gov/docs/fy12osti/52409-1.pdf

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8. McNick, J., et al.: Review of operational water consumption and withdrawal rates for power generation technologies. National Renewable Energy Laboratory, Golden, CO (2011). https:// www.nrel.gov/docs/fy11osti/50900. 9. John, W., Lund, T.: Direct utilization of geothermal energy 201worldwide review. Boyd GeoHeat Center, Oregon Ins. https://www.geothermal-energy.org/pdf/IGAstandard/WGC/2020/ 01018 10. Kagel, A.: Geothermal energy, defined as heat from the Earth, is a resource. The first U.S. geothermal power plant, opened at The Geysers in. https://www.osti.gov/servlets/purl/ 897425 11. Named the cause of a powerful earthquake in South Korea in 2017. https://rg.ru/2019/03/20/ nazvana-prichina-moshchnogo-zemletriaseniia-v-iuzhnoj-koree-v-2017-godu.html) 12. Sustainable operation of geothermal power plants. https://geothermal-energy-journal.springero pen.com/articles/https://doi.org/10.1186/s40517-021-00183-2 13. Life-Cycle Analysis of Geothermal Technologies. https://www.energy.gov/sites/default/files/ 2014/02/f7/analysis_wang_lifecycle_analysis.pdf 14. Boguslavsky, E.I.: Development of thermal energy of the bowels. M.: Sputnik + Publishing House, p. 448 (2018) 15. Shulzhenko, S., Turutiukov, O., Bilenko, M.: Mixed integer linear programming dispatch model for power system of Ukraine with large share of baseload nuclear and variable renewables. In: 2020 IEEE 7th International Conference on Energy Smart Systems (ESS), 2020, pp. 363– 368, (in Ukrainian)

Straw Pellets for Heat Supply in the Countryside: Economic, Environmental and Circular Economic Indicators Valerii Havrysh

and Vasyl Hruban

Abstract The country settlements of Ukraine use primarily natural gas for heating. Last year there was a drastic rise in natural gas prices. It burdens the budget of village councils. This state forces the local authorities to look for alternative energy resources. Currently, in Ukraine, large amounts of agricultural residues are left in the field. They can be used for heat generation. That is why the purpose of this paper is to make an assessment of economic viability for substitution of natural gas by straw pellet production and utilization. Renewable energy is a pillar of the circular economy. The circular economy is an alternative to the linear economy in solving global issues. This study determines some indicators which are improved by the straw-based heat supply system in the countryside. We have made a feasibility analysis (economic, energy, environmental, and sensitivity) for pellet heat supply in the Shevchenkovo village council (Mykolaiv province, Ukraine). Investment and operating costs were estimated at a pellet plant capacity of 590.27 t (annual pellet demand). Feedstock (straw) is the largest component (34.71%) in the production costs structure. The current energy prices at EUR37.98/GJ for natural gas and EUR11.98/GJ for straw pellets are favorable for biomass pellets to be competitive. The calculated straw pellet production cost is EUR172.87/t. The simple payback period is less than one year. Sensitivity analyses have shown that the project is most sensitive to investment costs and natural gas prices. Keywords Energy · Renewable · Biomass · Crop residue · Heating · Countryside · Circular economy · Emissions

1 Introduction Biomass, including agricultural residues, is a low-carbon energy source. Its use is important for the sustainable development of modern civilization [1]. Agricultural residues are one of the elements supporting the European Green Deal targets [2]. V. Havrysh (B) · V. Hruban Mykolayiv National Agrarian University, Mykolaiv, Ukraine e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_25

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The main disadvantages of biomass are low energy density and low yield. These factors result in a high cost of biomass delivery. That is why pellets have valueadded advantages over raw biomass, including straw. Pelletization reduces moisture content, increases energy density, and enhances combustion efficiency compared to raw biomass [3]. The bulk density of biomass pellets is almost ten times higher compared to straw [4]. It makes easier its handling and transport. For this reason, densification is the widely used method [5, 6]. Therefore, pellets are a more attractive form of biomass-based energy. Crop residues as renewable energy may be a pillar for the circular economy. The circular economy (CE) promotes the responsible and cyclical use of resources. In the recent decade, the idea of CE has been supported as an effective policy to stimulate further economic growth with minimum environmental impact [7]. This concept includes lowering material input and minimizing waste generation to decouple economic growth from natural resource use [8, 9]. In Ukraine, crop residues are the most abundant and cheapest biomass. They are the primary raw materials for pellet production. Ukraine is ranked first among pellet producers (934 thousand tonnes in 2016) [10]. The country settlements of Ukraine use primarily natural gas for heating. Its high price burdens the budget of village councils. Financial expenses, energy security, global warming, and exhaustibility of fossil fuels force using of biomass utilization. Biomass is, as a rule, a local energy resource. It is nearly carbon-neutral, hence its utilization helps to mitigate greenhouse gas emissions and strengthen energy security. Currently, in Ukraine, large amounts of agricultural residues are left in the field to rot. They could be used to produce pellets to be used as a natural gas substitution. An increase in European wholesale gas prices (Fig. 1) is encouraging utilities to use more cheap fuels electricity and heat generation. European coal prices have also resin too [11–13]. In December 2021, natural gas cost USD1488 per 1000 m3 . This cost included the transportation expenditure to the Ukrainian border. It was 52% higher compared to November 2021. In December 2020, import natural gas cost USD258 per 1000 m3 [14]. The high price is a result of the following reasons: • there are low reserves in European countries underground gas storage facilities; 200 180 160

Price, EUR/MWh

Fig. 1 Natural gas price history in the European Union and Ukraine

140 120 100 80 60 40 20 0 26-09-2020

04-01-2021

14-04-2021

23-07-2021

Period EU

Ukraine

31-10-2021

08-02-2022

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• there is Nord Stream 2 certification delay (the project does not comply with European legislation); • natural gas supply through Yamal gas pipeline has been suspended; • there has been a decrease in the gas supply from Norway. In Ukraine, natural gas price correlates with European trends. This European natural gas crisis is set to gain momentum. According to the international experience, the best solution is to support consumers to overcome this problem. Many European countries have taken steps to normalize the situation. Renewable energy may be a solution too. Many scientists have explored the use of biomass as an energy source. Economic and environmental analyzes are important elements for the development of pellet utilization. These problems are in the spotlight. Thomson and Liddel [15] studied the feasibility of biomass pellet-based heat supply systems. They paid attention to the advantages and barriers. The economic performance was analyzed by some scientists [16–19]. An environmental evaluation was done by Hendricks et al. [20–22]. Sunflower husk utilization for combined heat and power supply was studied too [23]. Environmental impacts of electricity from wheat straw pellets were investigated by Giuntoli et al. [24]. Li et al. [25] carried out a life cycle assessment of straw pellets in the Canadian Prairies. Kwasniewski and Kubon [26] studied the economic efficiency of straw pellet production. The purpose of the paper is to make an assessment of economic viability for substitution of natural gas by an alternative energy resource, namely of agricultural residue for pellet production and utilization on the example of Shevchenkovo village council (Mykolaiv region, Ukraine). To reach the aim, some objectives must be studied: • energy resource analysis; • availability of feedstock; • estimation of pellet production cost of agricultural biomass (e.g. wheat, barley, and oat straw) in the Shevchenko village council; • determination of the optimal location for the pellets plant; • carbon dioxide emission saving; • impact on circular economy indicators; • economic assessment. The scope of this research is to conduct a techno-economic assessment for developing a straw pellet plant operating for 20 years using wheat, barley and oats straw. This includes harvesting and collection, handling, storage, transportation, pellet production, pellet boiler installation.

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2 Methodology Data collection was carried out for the development of a techno-economic model of straw pellet production and its utilization. The determination of cost was based on data taken from the literature, statistical data, websites, personal communication with equipment suppliers, experts, and author developed data. System boundaries In this study, a life cycle analysis was applied. The production chain comprises all the stages from straw production to heat generation. The system boundaries are presented in Fig. 2. Economic indicators Technical, technological, agricultural, and economic factors were used in the study. Technical factors were: the efficiency of the boiler, the lower heating value of fuels or energy resources. The efficiency of the boiler and specific fuel consumption were used as technological factors. Crop straw yield variations were agricultural factors. Investment costs, payback period, the energy cost of fuel, the production cost of alternative fuel or energy resources were used as economic factors. The energy cost of fuel was determined as C E = F pr · (Q · ρ)−1 , EUR/GJ, where Fpr is the price of fuel, EUR/m3 ; Q is the lower heating value of the fuel, MJ/kg; ρ is the density of the fuel, t/m3 . Fig. 2 System boundaries for straw pellet pathway

Cultivating and harvesting of straw

Transport (straw)

Pellet mill

Transport (pellet)

Consumers

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The efficiency of the boiler depends on a number of factors, including the type of fuel used. Therefore, it is advisable to determine the energy cost that will be used for useful heating C E E = C E · η−1 = F pr · (η · Q · ρ)−1 , EUR/GJ, where η is the efficient of the boiler. The above for an electric boiler is equal to U ECe = 1000 · E pr · (3.6 · ηe )−1 , EUR/GJ, where ηe is the efficient of the electric boiler; Epr is the price of electricity, EUR/kWh. The same for a heat pump is equal to U ECe = 1000 · E pr · (3.6 · C O P)−1 , EUR/GJ, where COP is the coefficient of performance for a heat pump. The techno-economic model was developed for a straw pellet plant operating for 20 years. All life cycle costs of the pellet production and utilization were considered (the straw harvesting, transporting to the pellet plant, producing and utilization pellets). Capital cost, energy cost, employee cost, and consumable cost have been factored into the calculations. To develop the model, yields of wheat, barley, and oat straws were considered. The optimum location of the plant was determined by applying mathematical programming for average, maximum, and minimum biomass yields. Sensitivity analysis Sensitivity analysis investigates the impact of changes in project variables on the base indicators. As a rule, only adverse changes are assessed. The primary aim of sensitivity analysis is to identify the variables which have the greatest impact on the project performance. This analysis must be carried out systematically. We acted under the following recommendations [27]: • the identification of the key variables; • the calculation of the effect on the base project indicator (simple payback period); • the analysis of the direction and scale of changes in the project indicator for each key variable. The sensitivity variables are as follows: field costs, investment costs, employee costs, natural gas price, electricity price, and lifetime. For each variable, the base value was increased or decreased by 50% [28]. Available crop residues Crop residue potential was estimated for 30 years. We used Ukrainian official statistical reports. For this study, we selected three widespread crops: wheat, barley, and oats. We took into account crop harvest and a Residue-to-Crop Ratio (RCR)

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Table 1 Residue-to-crop ratios and calorific value of selected crops

Crop

Residue-to-crop ratio

Lower heating value of straw, MJ/kg

Wheat

0.8–1.8

15.0–18.1

Oats

1.0–2.0

15.0–18.1

Barley

0.9–1.8

15.0–18.1

to calculate the crop residue quantity MR =

n Σ

(Moi · RC Ri ), t,

i=1

where Moi is the average annual production of ith crop, t; RCPi is the Residue-to-Crop Ratio of ith crop; i is the crop number; n is the number of crops. Residue to crop ratios and calorific values for selected crops are shown in Table 1 [29–32]. Carbon dioxide emissions Lifecycle carbon dioxide emissions include several factors such as fuel combustion and well-to-tank emissions. Moreover, we took into account the emissions associated with electricity generation and associated with straw production. The carbon dioxide emission factor for electricity generation in Ukraine is equal to 323 g/kWh [33]. Natural gas has WTT carbon dioxide emissions of 56.38 gCO2 /MJ (0.203 kgCO2 /kWh) [34]. Well-to-wheel (WTW) emissions are equal to: W T W = BN G

) ( 11 + W T TN G , kg, · CC N G · 3

where CC NG is the carbon content in natural gas, CC NG = 0.75 kg/kg; WTT NG is the well-to-tank carbon dioxide emissions of natural gas, kg CO2 /kg; BNG is the natural gas combustion. Power generation results in the following carbon dioxide emissions [23]: C D E G = W · E Fe, kgCO2 , where EFe is the emission factor, kg CO2 /kWh; W is the electricity consumption, kWh. Optimal location of the pellet plant The optimal location of the pellet plant is the destination, when the pellet transportation work is minimized [35]. The objective function is || || S = ||di j · Gp j || → min,

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417

Table 2 Indicators for monitoring the circular economy transition Classification

Indicator

Footprint

Renewable energy share

Material and waste

Annual total waste generation

Aggregated GHG emissions (CO2 equivalents) Circular material use rate Socio-economic impact

Investment costs related to circular economy sectors Jobs related to circular economy sectors Number of new circular business created to implement the circular economy initiative

where d ij is the distance from ith destination to jth destination, km; Gpj is the annual consumption of pellets by jth destination, t. And for our case, the optimal location is Si =

6 Σ

Si, j , i ∗ = arg min Si ,

i=1

where i* is the optimal destination for the pellet plant location. Circular economy indicators Circular Economy is a major topic, especially in the European Union. For monitoring the Circular Economy transition, we selected the following indicators (Table 2) [36– 38]. The following sections demonstrate the application of this methodology of technical and economic assessment and optimization for agricultural pellet production in the Shevchenko village council (Mykolaiv province, Ukraine).

3 Initial Data In this study, we used prices which were set on February 2022. Electricity price in Mykolaiv oblast in 2021 (Fig. 3) [39]. From February 1, 2022, the price of natural gas for commercial consumers was set at UAH40500 per thousand m3 or EUR1276 per thousand m3 (EUR127.6/MWh) [7]. The Shevchenkovo village council has area of 296.81 km2 . Its farmers cultivate 20.5 thousand ha of arable land. We have determined the annual natural gas consumption of public buildings such as schools, kindergartens, and cultural institutions. According to our analysis, their annual consumption is 226.58 thousand m3 (Table 3). The village of Shevchenkovo has the highest gas consumption of 45.867 thousand m3 .

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V. Havrysh and V. Hruban 120

Fig. 3 Electricity price in Mykolaiv province in 2021

Price, EUR/MWh

100 80 60 40 20 0 1

2

3

4

5

6

7

8

9

10

11

12

Month

Table 3 Annual natural gas consumption, m3 Settlement

Schools

Kindergartens

Cultural institutions

Sum

Poligon

23,500

8128

6796

38,424

Kotlyareve

35,000

8672

0

43,672

Shevchenkovo

29,000

5702

11,165

45,867

Zarya

0

0

0

0

Luch

17,600

5702

0

23,302

Myrne

41,900

0

0

41,900

Zelenyy Hay

28,000

5417

0

33,417

Total

175,000

33,621

17,961

226,582

Public buildings are equipped by gas boilers. Their maximum power ranges from 16.96 to 99.17 kW (Table 4). Capacity of boilers were determined by the maximum gas consumption in the coldest month of the year. The school in the village of Myrne is equipped with a boiler with the highest capacity (99.17 kW). The kindergarten of the village of Zelenyy Hay has a boiler with the lowest capacity of 15.81 kW. Table 4 Maximum power of boilers, kW

Settlement

Schools

Kindergartens

Cultural institutions

Poligon

64

28.23

16.96

Kotlyarovo

87.5

33.88

0

Shevchenkovo

81

0

28.33

Zarya

0

0

0

Luch

46.67

22.59

0

Zelenyy Hay

72.33

15.81

0

Myrne

99.17

0

0

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Table 5 Distances between locations, km Settlement

Poligon

Kotlyareve

Shevchen-kovo

Zarya

Luch

Zelenyy Hay

Myrne

Poligon

0

16.5

19

22

22.8

16.2

29.7

Kotlyarovo

17.3

0

4.6

5.5

10.3

19.4

17.1

Shevchenkovo

19.7

3.3

0

8.6

12.7

21.9

19.6

Zarya

22.7

5.5

8.6

0

15.7

8.2

22.6

Luch

23.6

10.3

12.8

15.8

0

25.7

10

Zelenyy Hay

15.1

19.9

22.3

8.2

26.1

0

33

Myrne

29.7

17.1

19.6

22.6

10

33

0

To determine the optimal location of the pellet plant, it is necessary to minimize transport work. We used data on the distances between settlements to solve the optimization problem. The distance between settlements is presented in Table 5.

4 Alternatives In our case, there is possibility for some alternatives: • • • •

natural gas boiler; electric boiler; heat pump; solid biofuel boiler (pellet boilers).

Each alternative has its advantages and disadvantages (Table 6). Small-scale pellet combustion has been identified as one of the significant sources of particulate matter. Fine particles have an adverse effect on the environment. One way to solve this problem is to increase the efficiency of pellet boilers. There are a lot of investigations devoted to ensuring an energy-efficient of these boilers [40–42].

5 Straw Availability The annual potential volume of straw can be assessed. The actual amount depends on many factors (biomass species, biomass yield, location, climate, and technology). The yield of residue is an important parameter for a project. It affects the production cost of pellets. The lifespan of a typical bioenergy facility is 20–30 years. It requires a continuous and constant supply of feedstock. This is particularly true for facilities that depend on annual crop production. The total average yield of wheat, barley, and oats over the last 30 years (1990– 2020) has been 2941; 2239; and 1586 kg per ha respectively (Fig. 4) [43, 44].

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Table 6 Advantages and disadvantages of fuels (energy resources) Fuel (energy resource)

Advantages

Disadvantages

Natural gas

Controllable Existing infrastructure

High price Instability of price Exhaustibility

Electric boiler

Controllable Ecologically clean

More expensive as compared to natural gas Additional investment costs

Heat pump

Low electricity consumption Controllable Ecologically clean

High investment costs High operating costs

Solid biofuel (pellets)

Renewable Ecologically clean

Additional investment costs in new boilers Additional investment costs in solid biofuel production Investment costs in warehouses Smoke control need Expensive transportation

4000

Fig. 4 Evolution of crop yields

3500

Yield, kg/ha

3000 2500 2000 1500 1000 500 0 1990

1995

2000

2005

2010

2015

2020

Period, year wheat

barley

oat

The available straw production volumes are typically determined by applying straw to grain mass ratios. After an analysis of technical charts and data, the ratios adopted in this study for estimating crop residue for wheat, barley, and oats are 1.1; 0.8 and 1.1, respectively. To determine the net yield of straw, additional factors have been taken into consideration: retained straw for soil conservations; organic fertilizer; some straw is left on the field in accordance with the efficiency of the combine harvesters; mulching; lost through handling, transport, and storage. The quantity of straw also depends on its moisture content. After the literature analysis, 0.75 t/ha was allocated to soil conservation. In this study, we assumed: • the moisture content of the straw—14%; • the harvest loss—30% [45–47];

Straw Pellets for Heat Supply in the Countryside: Economic, …

421

2250

Fig. 5 The evolution of straw yield for selected crops

2000 1750

Yield, kg/ha

1500 1250 1000 750 500 250 0 1990

1995

2000

2005

2010

2015

2020

Period, year wheat

barley

oat

• the storage and transportation loss—15% [46, 47]. The average yields of wheat, barley, and oats are 1480; 620 and 599 tons per ha, respectively in the Mykolaiv province (Fig. 5). A wide variability was observed in the net yields of straw over the years. To develop our techno-economic model, we have considered three cases: the average yield, the maximum yield, minimum yield, fuel and residue properties. The area needed for straw production can be calculated by the following formula Fs =

ξ·

Mp (1 − 0.01 · W p) , ha, · i=1 (Ui · εi ) (1 − 0.01 · W s)

Σn

where Mp is the annual pellet production, t; ξ is the arable area to total area ratio, ξ = 0,691; εi is the ith crop share; U i is the ith crop yield, t/ha; Wp is the moisture content of pellets, %; Ws is the moisture content of straw, %. We assumed the circular arrangement of the fields. In this case the radius is / R=

0.01 ·

Fs , km. π

The average distance of transportation is determined as Rt =

2 · R, km. 3

Values for radiuses of fields and distances of transportation for three scenarios are shown in Table 7. The pellet demand was calculated taking into account its lower heating value of 14.51 MJ/kg and pellet boiler efficiency—80%. It constitutes 590.27 tons per year (Table 8). To endow that mass of the pellet, it is necessary to have the corresponding crop area (Table 9).

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Table 7 Radiuses of fields and distances of transportation

Scenario

Radiuses of fields, km

Distances of transportation, km

556.43

2.45

1.63

Minimum yield

1528.36

4.06

2.71

Maximum yield

350.59

1.95

1.30

Average yield

Arable area needed, ha

Table 8 Annual pellet demand, tons Kindergartens

Cultural institutions

Sum, t

Poligon

61.22

21.17

17.70

100.10

Kotlyareve

91.18

22.59

0.00

113.77

Shevchenkovo

75.55

14.85

29.09

119.49

0.00

0.00

0.00

0.00

Settlement

Schools

Zarya Luch Zelenyy Hay Myrne

45.85

14.85

0.00

60.70

109.15

0.00

0.00

109.15

72.94

14.11

0.00

87.05

Total

Table 9 Needed crop area, ha

590.27

Crop species

Scenarios Average yield

Minimum yield

Maximum yield

wheat straw

422.72

996.59

292.18

barley straw

1008.66

4818.37

518.46

oat straw

1055.93

2909.71

605.07

The educational and cultural institutions of the village council own 200 ha of arable land. Thus, to ensure the need for biomass, it is necessary to use agricultural residues of the nearest farms.

6 Pellet Production Cost The production of pellets from agricultural residue involves harvesting, handling, storage, transportation and pellet production. Total production cost can be divided into four main components: • field cost (straw);

Straw Pellets for Heat Supply in the Countryside: Economic, …

423

7

Specific freighting cost, cent/(t*km)

Fig. 6 Freight cost

6 5 4 3

y = 7.4564e-0.047x R² = 0.9557

2 1 0 0

5

10

15

20

Carrying capacity, t Actual freight cost

Trend

• cost of transportation from field to pellet plant; • depreciation and maintenance; • salary of employees. Field cost was evaluated as follows. The estimated price of biomass can vary from a producer and crop species [48]. In our case, the field cost of agricultural residue was assumed from market prices of EUR37.5/t [49]. It includes storage cost. Transportation cost has two components. The fixed component of the cost is the cost of loading and unloading cost. The variable component includes wages, fuel, and maintenance. These variable costs are proportional to the distance traveled. Specific transportation cost depends on the carrying capacity of a truck (Fig. 6) [50]. When transporting straw, transportation costs increase by about 50%. The typical loading and unloading cost for truck transportation is around USD5.45/t [51, 52]. The transportation distance is proportional to the square root of the crop area needed for the pellets plant Fig. 8. The minimum yield scenario is based on yields obtained in the drought years. The straw-pellet plant has a capacity of 590.3 t/year. Pellet production cost is EUR172.87/t. In the European countries, bulk pellet prices are in the range of EUR150/t to EUR321/t. And the average prices ranged from EUR250/t to EUR270/t [53]. Therefore, the results of our calculations correspond to the European trends. The main components of pellet production cost are agricultural residue costs and salary costs (Fig. 7).

7 Economical Efficiency of the Project Existing natural gas boilers should be replaced by pellet boilers or dual fuel boilers. It needs EUR57,020.31 (Table 10). The above investment costs may be covered during 0.84 years (Table 11). In the previous study [54], the payback periods of

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Fig. 7 Production cost structure, %

depreciation&re pair 19% others 17% energy 7% salary 22% straw 35% depreciation&repair

Table 10 Investment costs for replacement of boilers

energy

straw

salary

others

Item

Price, EUR

Number

Sum, EUR

Boiler Kalvis (100 kW)

3437.50

4

13,750.00

Boiler Kalvis (70 kW)

2656.25

1

2656.25

Boiler Kalvis (50 kW)

1792.19

1

1792.19

Boiler Kalvis (40 kW)

1300.00

3

3900.00

Boiler Kalvis (25 kW)

1078.13

3

3234.38

Fuel supply system

390.63

12

4687.50

1562.50

12

18,750.00

Installation

156.25

12

1875.00

pellet warehouse

312.50

12

3750.00

transportation

156.25

12

1875.00

Other expenses

62.50

12

750.00

Project (design)

Total

57,020.31

similar projects were in the range of 0.57–5.2 years. In our study, the benefit of the straw project is the revenue from pellet production and utilization for a natural gas substitution in heat supply systems. Pellets need to compete with conventional sources of energy used for heating. The rise in natural gas prices makes these projects highly profitable (Fig. 8).

8 Sensitivity Analysis The sensitivity analysis was carried out for the average yield case by changing the values for different costs and technical factors from − 50% to + 50% in steps of 10% for each case. Cost factors (field, investment, employee, energy) and lifetime were included in the analysis. Figure 9 shows the results of the sensitivity analysis.

Straw Pellets for Heat Supply in the Countryside: Economic, … Table 11 Simple payback period

425 Unit

Item

Value

Annual natural gas consumption

Thousand

Annual pellet consumption

t

m3

226.58 590.27

m3

Natural gas price

EUR/1000

Pellet production cost

EUR/t

172.87

Total investment costs

Thousand EUR

156.42

Annual cost of natural gas

Thousand EUR

289.12

Annual cost of pellets

Thousand EUR

102.04

Return

EUR

187.08

Simple payback period

Years

0.84

Fig. 8 Energy cost

1276.00

Energy cost, EUR/GJ

40 30 20 10 0 Natural gas

Electricity (electric boiler)

Electricity (heat pump)

Pellet

It can be seen that the cost of pellet production is more sensitive to a decrease in natural gas price and an increase in investment costs. Lifetime and employee costs have a negligible impact on the project’s payback period. 250 Relative simple payback period, %

Fig. 9 Sensitivity analysis: relative simple payback period versus variables

225 200 175 150 125 100 75 50 -50

-40

-30

-20

-10

0

10

20

30

Change, % Field cost Employee costs electricity price

Investment costs Natural gas price Lifetime

40

50

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9 Carbon Dioxide Emissions Specific carbon dioxide emissions are a function of energy inputs (natural gas, electricity), the fuel carbon contents, the emission factors, well-to-tank emissions, and carbon dioxide emission associated with straw formation. For pellet production, specific carbon dioxide emission is equal to SC D E p =

V ngp ·

( 11 3

) · CCng + W T T ng + EC · E Fc + Ms · C DS F , kgCO2 /MJ, Ms · L H V s

where Vngp is the natural gas consumption for pellet production, m3 ; CC is the natural gas carbon content, CC = 0.75; WTTng is the well-to-tank carbon dioxide emissions for natural gas, WTTng = 2.03 kgCO2 /m3 ; EC is the electricity consumption, kWh; EFe is the emission factor for electricity, EFe = 0.365 kgCO2 /kWh; Ms is the annual straw consumption, kg; CDSF is the carbon dioxide emissions associated with straw production, kgCO2 /t; LHVs is the lower heating value of straw, MJ/kg. The same indicator for natural gas-based heat supply system is equal to SC D Eng =

11 3

· CCng + W T T ng , kgCO2 /MJ, L H V ng

The same indicator for electric heat supply system is calculated by the equation SC D Ee =

E Fe , kgCO2 /MJ. 3.6

The use of straw pellets emits the least carbon dioxide. Straw pellets have the lowest specific carbon dioxide emission for heat supply systems (Fig. 10). The carbon dioxide emissions in our study are comparable with available studies [24, 55, 56]. Therefore, the use of straw pellets to substitute natural gas can achieve high carbon dioxide emission savings.

10 Circular Economic Indicators Our civilization is extracting fossil resources to meet its requirements in energy and materials. Since 2017, the total annual extraction exceeded 100 billion tons [57]. A linear (traditional) economy is based on the use of natural resources. It generates a lot of waste and pollution [58]. The concept of the circular economy eliminates the disadvantages of the linear economy. The circular economy includes crop residue recycling too. Majeed and Luni underlined that renewable energy is an important pillar of the circular economy because it does not generate waste, reduces the use

Straw Pellets for Heat Supply in the Countryside: Economic, … 120

Specific carbon dioxide emissions, kgCO2/MJ

Fig. 10 Specific carbon dioxide emissions

427

100

80

60

40

20

0 Natural gas

Electricity

Heat pump

Pellet

Type of fuel

Table 12 Circular economy indicators Classification Footprint Material and waste

Indicator

Value

Renewable energy per capita

MJ per capita

726.86

Carbon dioxide emissions saving

kg per capita

82.51

Annual total waste generation

t

21,763

Circular material use rate (straw) Socio-economic impact

Unit

Investment costs related to circular economy sectors

t

590.27

%

2.7

Thousand EUR

156.42

Jobs related to circular economy sectors

3

Number of new circular business created to implement the circular economy initiative (pellet production)

1

of exhaustible resources and carbon dioxide emissions [59]. Table 12 presents the impact of a pellet-based heat supply system on the circular economy indicators.

11 Conclusions A techno-economic model was developed to estimate the pellet production cost and determine the optimum location of the pellet plant. Agricultural residues (wheat, barley and oat straw) were considered for average, maximum and minimum yield cases. The total cost was calculated from the harvest of straw to pellet production.

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The techno-economic model was applied to Shevchenko village council, Mykolaiv region, Ukraine. The use of crop residues for heat supply systems in the countryside has become more attractive due to drastically emerge of natural gas price. Currently, pellet energy cost is equal to around 41% of natural gas energy costs. Only heat pump systems can provide cheaper heat. However, they need higher investment costs. An investment project includes costs suck as a pellet mill and pellet boilers for consumers. The last item exceeds 50% of the total costs. Under current conditions, the payback period is less than one year. A decrease in natural gas price has the strongest impact on the project profitability. The sensitivity analysis has shown that the pellet production cost is more sensitive to the natural gas price decrease, and an increase in field costs. The use of straw pellet drastically reduces WTW carbon dioxide emissions. They are 20-fold less compared to natural gas-based heat supply systems. Electrical and heat pump heat supply systems are characterized by a large emission of carbon dioxide as well. Renewable energy for heat supply improve circular economy indicators. In this study, renewable energy and the circular economy were investigated. Crop residues as renewable energy may be the primary pillar of the circular economy. This study measured some indicators of the CE: carbon dioxide emissions savings, renewable energy per capita, circular material use rate (straw), investment costs in renewable energy, job creation, and a number of new circular businesses. Promotion of the circular economy, the use of waste biomass, and renewable energy are suggested to local and state authorities. Unlike fossil fuels, renewable energy does not harm the environment.

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Comparative Analysis of Energy-Economic Indicators of Renewable Technologies in Market Conditions and Fixed Pricing on the Example of the Power System of Ukraine Mykhailo Kulyk , Tetiana Nechaieva , Oleksandr Zgurovets , Sergii Shulzhenko , and Natalia Maistrenko Abstract World energy is currently experiencing a period of rapid development of wind (WPP) and solar (SPP) power plants in the structure of generating capacity of power systems. Back in 2016, the European Union (EU) recommended that EU member states in their energy policy on the development and use of WPP and SPP move to purely market relations. However, not all EU member states have taken advantage of these recommendations and continue to work in this area on the principles of fixed pricing with preferences for WPP and SPP owners. In Ukraine, such preferences are among the highest in Europe. This paper analyzes in detail and determines the factors and amounts of financial losses incurred by the IPS of Ukraine represented by NEC “Ukrenergo” and consumers of electricity generated by WPPs and SPPs. The consequences of such activities are projected both for NPC “Ukrenergo” and for the country’s economy and society. It is shown that such energy policy leads (paradoxically) to a significant deterioration of the environmental situation in the country. Recommendations have been developed for ways out of the critical state of the country’s energy in connection with the hypertrophied development of WPPs and SPPs in the structure of its power system. The obtained results and experience of the authors can be useful for specialists in countries with natural conditions comparable to Ukraine, and who carry out measures to decarbonize their own energy. Keywords Wind power plant · Solar power plant · Reserve power plant · Electricity production · Greenhouse gases · Electricity cost · Revenues · Profits

1 Introduction World energy is currently experiencing a period of rapid development and use of renewable energy sources (primarily wind (WPP) and solar (SPP) power plants) in M. Kulyk · T. Nechaieva (B) · O. Zgurovets · S. Shulzhenko · N. Maistrenko General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_26

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the generating capacity structure of power systems. This process has been developing for a long time without taking into account two extremely important factors, namely: (1) WPPs and SPPs are sources with zero guaranteed capacity; (2) due to their technological nature, WPPs and SPPs cannot ensure the normalized stability of the frequency and power of electricity which is supplied to the power system. At the same time, the relative share of WPP and SPP capacities in the initial period of their use in power systems were, firstly, insignificant, and, secondly, the required volumes of regulating capacities were forcibly attracted from primary and secondary regulation reserves provided in each power system in accordance with regulatory requirements for stabilization of normal and emergency modes of its (power system) operation. That is, to ensure the stable operation of wind and solar power plants as part of integrated power systems involved high-speed reserve capacity, designed for other purposes. This approach did not create problems in the power systems as long as the capacity of WPPs and SPPs (renewable energy sources—RES) was low. As their capacity increased significantly due to green tariff laws in many countries, severe systemic accidents began, all the way to blackouts (South Australia) and the disconnection of large regions with a total capacity of several thousand megawatts (Germany and other countries). At the same time, the rapid growth of the use of wind and solar power plants in integrated power systems (IPS) has been and is being carried out almost without proper scientific support, by trial and error. The IPS of Ukraine is no exception. As of October 2019, about 4000 MW of SPPs capacity and about 750 MW of WPPs capacity were commissioned. Two years later, the capacity of the SPPs was already about 6500 and the WPPs 1500 MW, that is, the total capacity of RES in the IPS of Ukraine has almost doubled. Additional highspeed capacities designed to stabilize the modes of operation of the IPS of Ukraine when using significant capacity of WPPs and SPPs, since the signing of the laws “On Alternative Energy Sources”, “On the Electricity Market” (hereinafter—the laws on “green tariff”) was not entered. Research by the Institute of General Energy (IGE) of the National Academy of Sciences of Ukraine has established that to ensure normalized frequency stability in a integrated power system with powerful RES requires high-speed electrical regulators such as batteries (AB), the total capacity of which must be not less than 30% of the operating capacity of RES. In addition, to ensure the continuous operation of the power system during weather shutdowns of RES, the reserve capacity of traditional power plants is required, which capacity practically coincides with the capacity of RES. Laws on “green” tariff exempt RES owners from construction in the power system adequate to them in terms of regulatory and reserve capacities. This provision of the law on “green” tariff grossly violates the principles of a market economy, which provides equal rights for market participants. All power plants with conventional technologies, according to the current regulations, must ensure the stability of the frequency and power of the electricity which is supplied to the power system. In addition to this unjustified and very significant benefit, the owners of WPPS and SPPs according to the mentioned laws till 2018 inclusive had even greater preferences for electricity sales tariffs, which are 2–3 times higher than the electricity tariffs of traditional power plants.

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In the current laws on the “green” tariff, the relations between the owners of WPPS and SPPs and NPC “Ukrenergo” are governed by the principle of “take or pay”. This is the most burdensome preference for the consumer, which these laws provide to the owner of WPP/SPP. According to this principle, with the functional ability of WPPs or SPPs, the dispatch control (DC) of the IPS of Ukraine is obliged to put them into operation regardless of the conditions in the power system. In case the DC is forced to restrictions these RES due to any factors (in particular, due to lack of current demand), the electricity market is obliged to pay the owners of WPPs and SPPs compensation for lost profits in the amount of electricity sold at a reduced rate. It is clear that the introduction of the declared SPP and WPP capacity in the structure of generating capacities of IPS of Ukraine will lead to its (power system) technological incapacity (blackout due to unacceptable frequency deviations), or to economic inability of the energy market to settle with WPP and SPP owners, since under such conditions all its total profit may be less than the total claims of the owners of WPP and SPP to compensate for their commercial benefits arising from the provisions of these laws.

2 Formation of Normative and Legal Legislation on the RES Operation as Part of the Integrated Power System of Ukraine The first “green” tariffs in Ukraine were introduced in 2008 [1]. The value of the “green” tariff was set annually at twice the weighted average electricity tariff for energy generating companies operating in the wholesale electricity market of Ukraine on price bids for the year preceding the year of tariff setting. Such incentives for RES producers were to last for 10 years from the date of its provision. In 2009, the conditions for providing “green” tariffs were significantly changed [2] with a breakdown by type of RES with a fixation in euros and lasting until January 1, 2030. The value of the “green” tariff was set at the level of the retail tariff for consumers of the second voltage class in January 2009, fixed in euros, multiplied by the “green” tariff coefficient determined for each type of alternative energy. As of January 2009, the retail price of electricity for second-class consumers was 58.46 kopecks/kWh [3], which was 5.4 eurocents/kWh in euros at the official exchange rate of the National Bank of Ukraine. For producers of electricity from solar radiation and hydropower in calculating the size of the “green” tariff used an additional multiplier—the increasing coefficient of peak load [3, 4]. The green tariff rate for terrestrial solar power plants was 46.5 eurocents/kWh, for wind farms from 2 MW to 11.3 eurocents/kWh. At the end of 2012, the coefficients of green tariffs were revised downwards from April 1, 2013 [5]. For power plants that were commissioned or significantly upgraded after 2014, 2020 and 2024, this coefficient was reduced by 10%, 20% and 30% relative to the 2013–2014 coefficients.

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Stimulating the introduction of renewable generation in Ukraine at the expense of “green” tariffs were important at the initial stage of their development. In particular, “green” tariffs were introduced to cover capital investment in RES, to promote investment in Ukrainian industry. The rates of the “green” tariff at the time of the adoption of the Law were focused on the cost of equipment at that time and the actual costs of implementing RES projects. The majority of the cost of RES projects is equipment. Thus, according to IRENA, 64% of the cost of a wind power plant are wind turbines. At the same time, most wind generation projects in Ukraine are implemented through wind turbines manufactured abroad. The situation is similar with solar panels. Despite the significant development of RES generation in recent years, most of the investments attracted have been used to support the economies of other countries by supplying imported equipment. At the same time, the experience of other countries shows that with “green” tariffs it is possible to develop industry and mechanical engineering. Thus, Germany and Denmark, through the production of wind turbines, ensured the development of the machine-building industry. China has taken a similar approach by localizing the production of RES equipment, in particular solar panels. According to NPC “Ukrenergo” [6], as of the end of 2020, 5360 MW of SPPs and 1110 MW of WPPs were installed in the IPS of Ukraine, which was more than 12% of the IPS total installed capacity. In fact, more than twice as much solar generation has been built, and wind generation is half as much as planned by the National Renewable Energy Action Plan [7], which envisages the introduction of 2280 MW of wind generation and 2300 MW of solar generation by the end of 2020. This rapid growth in solar energy is due to high tariffs for solar power plants, which has made them more attractive for investment than wind generation. Throughout the period of validity of the “green” tariffs, the issue of changing the amount of the “green” tariffs has been raised repeatedly. Thus, in September 2014, the National Commission for State Regulation of Energy and Utilities (NCRECP) stopped reviewing “green” tariffs, and in February and March 2015 it reduced “green” tariffs for RES producers. However, these reductions did not comply with the provisions of the Law “On Electricity” and were challenged in the courts by RES producers [8]. By the end of 2015, RES producers received compensation for unjustified revision and reduction of tariffs. This situation has contributed to a change in the order of revision of “green” tariffs and a partial reduction in tariffs for future projects. In June 2015, green tariff coefficients were revised downwards [9] to bring green tariff levels closer to the world average and to eliminate over-incentives for solar power plants. Also, for the SPPs, the coefficient for the peak period of time was excluded from the calculation of the value of the “green” tariff. The high level of the “green” tariff in Ukraine, especially for solar power plants, created an excessive price burden for consumers of electricity in Ukraine, which began to grow rapidly with the commissioning of new power plants. The transition from the “green” tariff to auctions announced in 2018 has intensified the activities of companies designing and commissioning new RES facilities, achieving the highest growth rates of installed capacity of the RES sector in 2019. In

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2019, 3.2 times more new RES capacity was built in Ukraine than in all the previous 10 years of the “green” tariff. With the launch of the new electricity market in 2019, a public service obligations mechanism (PSO) was introduced, which aims to provide affordable electricity to the households and pay a “green” tariff. Responsibility for the implementation of PSO rests with the Guaranteed Buyer, who is obliged to purchase all electricity generated from RES at a fixed “green” tariff. Part of the special responsibilities is assigned to the Transmission System Operator (Ukrenergo), which is obliged to send the funds received from the transmission tariff to the Guaranteed Buyer to pay the “green” tariff. The proposed PSO model created a payment crisis in the first months of the new electricity market, one of the reasons being the low transmission tariff, which led to Ukrenergo’s inability to meet its obligations. Guaranteed Buyer in 2020 almost completely stopped paying for electricity produced at the “green” tariff. Therefore, to resolve the situation on the electricity market, the Cabinet of Ministers, the European Energy Agency and the Ukrainian Wind Energy Association signed a “Memorandum of Understanding on June 10, 2020” (hereinafter—the Memorandum), in which producers voluntarily agreed to reduce the “green” tariff by 15% for existing SPPs and by 7.5% for existing WPPs. In addition, liability was introduced in the form of fines for imbalances in the deviation of the actual RES electricity production schedule from projected. In turn, the state has committed itself to resolving the payment of existing debts and ensuring the operation of the newly introduced auction model of RES support. The main provisions of the Memorandum were subsequently enshrined in law [10] by taking into account in the Law “On Alternative Energy Sources” [11] the peculiarities of the “green” tariff in the period from August 1, 2020 by introducing reduction factors. The current rates of “green tariffs” for WPP and SPP are given in Table 1.

3 Problem Statement In the period up to 2019, RES tariffs for energy in Ukraine were many times higher than market prices for electricity using traditional technologies. As proved in [12], this factor was one of the main factors that led to the loss of the Ukrainian electricity market and threatened it with bankruptcy. Since 2019, there have been radical changes in the tariff formation for electricity produced by both wind and solar power plants. The fixed tariffs established by law for wind farms are currently close to the tariffs of the Ukrainian electricity market. The current electricity tariffs of SPPs are even lower than market prices (Table 1). Annex 5 of the official document [13] defines the forecast estimates of the installed capacity of WPPs and SPPs in the IPS of Ukraine for the period up to 2030. In combination with the data in Table 1, this provides an opportunity to make a detailed analysis of the energy economic situation projected in the IPS of Ukraine and its energy

1.04.2021

9.41

16.96

WPP from 2000 kW

SPP from 10 MW

a From

01.01.2015 –30.06.2015

Date of commissioning 14.42

9.41

01.07.2015 –31.12.2015 13.60

9.41

2016 12.77

9.41

2017–2019

Table 1 Current rates of “green” tariffs, euro cents per kilowatt-hour in accordance with [11]

10.97

8.82

2020

8.82 4.20

8.82

2022

7.61/4.35a

2021

4.05

8.82

2023–2024

3.90

7.72

2025–2029

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market at 2030. This task is relevant both today and in the long run, as extremely negative forecasts made in [12] are already confirmed in the current state of Ukraine’s electricity sector in general, its power system and electricity market in particular. This is already manifested in the irrational use of existing generating capacity, especially high-economy nuclear generation, unreasonably high electricity prices in the domestic market, the associated significant imports of electricity with large excess capacity of its own generation and a number of other negative phenomena. Therefore, there is an opportunity and urgent need to develop reasonable, objective forecasts of the energy situation in the electricity sector of a country with a high level of RES development, its power system and electricity market, as well as to develop appropriate conclusions. This problem is relevant not only for the electricity industry of Ukraine, it is equally important for the energy complexes of most industrialized countries, which are moving to the principles of low-carbon development. The purpose and content of this publication are the development of directions and basic measures for solving the main tasks caused by this problem. At once it is necessary to note the main difficulty in the decision of problems associated with this problem. Availability of zero guaranteed power in RES leads to the need to use additional specific equipment in the structure of the IPS, which ensures the stability of the frequency and power supplied by RES to the system. In order to formulate technological requirements for this equipment, it is necessary to have the tools to analyze its operation within the IPS. It was necessary to develop specific mathematical models of frequency and power control in the IPS, and their (models) should have included mathematical blocks that reflect not only the characteristics (primarily frequency) of RES and traditional technologies, but also the characteristics of this additional technological equipment and interconnections between all IPS equipment, including RES, additional technological and traditional. An additional complication in such models is the synthesis of mathematical blocks that reflect the behavior of wind and solar radiation as a working fluid. Numerous specialized literature on RES usually examines the relationship and behavior between individual RES and additional equipment for this purpose. A fairly detailed analysis of these publications is given in [14]. Consideration of the problems of analysis of the functioning of RES in the IPS among the publications known to the authors was not found. Currently, a large number of studies on the functioning of RES as part of the IPS are conducted at the Institute of General Energy of the National Academy of Sciences of Ukraine. This uses a set of several mathematical models with different functionality. A model and software package for the study of the joint functioning of wind farms, solar power plants, hydroelectric power plants (HPPs) and battery energy storage (AB) in the IPS of Ukraine [14–16], which have passed various tests and applications on real data. A modification of the model and software package for forecasting the long-term development of power systems with wind and solar power plants using statistical information to increase the flexibility of the power system [17, 18]. Using the developed models and software complex, the role and mechanism of the influence of

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derivatives from control capacities on frequency stability in power systems with wind power plants have been studied [19]. For estimates the economic efficiency of joint operation of a RES power plant, a battery energy storage system and a conventional reserve power plant in conditions of ensuring a stable level of power developed an appropriate life cycle model of such a system [20]. An important result of the problem under study is the creation and study of an adaptive frequency and power control system in power systems with wind farms [21]. For forecasting the long-term development of the structure of generating capacity of the power system, taking into account the commissioning and decommissioning dynamics of capacities and changes in their technical and economic indicators during the forecast period, developed a partial integer mathematical model [22]. Due to the results presented, in particular, in publications [14–22], researchers have a reasonable opportunity to choose the types and power of regulators that provide the necessary frequency stability of IPS, in the structure of which operate RES of one nature or another. If, for example, high-capacity wind farms operate in the IPS, then frequency stabilization in it can be provided only by AB or high-power HPPs. Stable operation of IPS, in which mainly SPPs operates, can be ensured even by plain HPPs. However, neither in the first nor in the second case can thermal power plants of any physical nature be used to stabilize the frequency in the IPS. Taking into account, in particular, this information, energy and economic indicators of wind and solar power plants in the structure of the IPS of Ukraine at the level of 2030 were developed.

4 Energy and Economic Indicators of SPPs Operation in the IPS of Ukraine at the Level of 2030 According to the source [11] and Table 1, the electricity tariff of SPPs in Ukraine is legally established for 2030 in the amount of 3.9 eurocents per 1 kWh. This tariff is significantly lower than current prices on the Ukrainian electricity market [23]. This circumstance gives rise to possible estimates and claims that starting from 2023, solar energy will no longer have such a devastating impact on the state of the country’s energy complex, which is described in [12] and whose manifestations are observed in reality today. This situation and the above goal prompted the authors to conduct this study. Initial data for the study of energy efficiency indicators of SPP at the level of 2030 Solar power plants Installed SPP capacity—9947 MW; operating life of SPP—25 years;

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specific investments of SPP—$1000/kW; annual capacity factor of SPP—0.17; SPP electricity tariff (2029)—3.9 eurocents/kWh. Reserve power plants (modernized coal-fired thermal power plants) Installed reserve TPP capacity—9947 MW; specific investments—$400/kW; annual capacity factor (estimated)—0.63; specific fuel consumption—345 g sc/kWh; operating life—35 years; CO2 emissions payment—$3/ton. Energy-economic calculations of SPP indicators by processing large amounts of information (Appendix 1) according to known dependencies and algorithms. The exception is the value of the annual capacity factor of 0.63 instead of 0.83 due to the presence of sufficient intensity of solar radiation on average for 11 h a day. The results of calculations of energy-economic indicators of SPP in the structure of IPS of Ukraine at the level of 2030 are provided in two forms: Table 2, which shows the main indicators that determine the main conclusions and recommendations, and Annex 1, which contains all necessary basic and intermediate information in the form of numerical data and algorithms used to determine the required energy-economic indicators. Table 2 shows the energy-economic indicators of the SPP + reserve TPP complex for comparison with similar indicators of the alternative TPP (modernized coal-fired). For the purpose of objective comparison, the electricity production at the alternative TPP (ATPP) coincides with its production at the SPP (paragraph 3, Table 2). This makes it possible to compare the CO2 emissions from WPP + TPP complex (item 7) with emissions from ATPP (item 11). It can be seen that the CO2 emissions of the SPP + TPP complex are almost 4 times higher than the emissions made by ATPP. At the same time, the total costs of this complex are 14 times higher than the costs of ATPP. A similar pattern is maintained in the ratio of the cost of electricity production (for the consumer) by the SPP + TPP complex (item 9) to the cost of APEC (item 13, Table 2), which is equal to 3.

5 Energy and Economic Indicators of WPPs Operation in the IPS of Ukraine at the Level of 2030 The method of constructing this section is similar to that used in the previous section. According to the source [13] the WPP capacity at the level of 2030 is determined at 5033 MW. The reserve power plant identified a modernized coal-fired thermal power plant with a similar installed capacity.

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Table 2 Basic energy-economic indicators of solar power plants in the power system of Ukraine at the level of 2030 №

Indicator

Unit

Value

1

Installed SPP capacity

MW

9947

2

Electricity generation, total

kWh

55.77 × 109

3

of the SPP

kWh

11.85 × 109

4

at the reserve TPP

kWh

43.916 × 109

5

SPP owner costs (1 year of operation), total

$

457.72 × 109

6

Payback period of the SPPs owner’s capital

Year

8.87

7

CO2 emissions from the reserve TPP

Ton

55.55 × 106

8

Consumer costs for electricity generated $ by the SPP + TPP complex, total

9.411 × 109

9

Cost of electricity generated at the SPP + TPP complex (for the consumer)

$/kWh

0.169

Alternative TPPs (modernized coal-fired) 10

Installed power

kW

1.691 × 106

11

CO2 emissions alt. TPP

Ton

15 × 106

12

Total costs for alt. TPP (1 year of operation)

$

650.05 × 106

13

The cost of energy produced on alt. TPP $/kWh

0.0549

Initial data for the study Wind power plants Installed capacity—5033 MW; operating life—25 years; specific investments—$1400/kW; annual capacity factor—0.35; WPP electricity tariff—7.72 eurocents/kWh. Reserve power plants Installed capacity—5033 MW; specific investments—$400/kW; annual capacity factor—0.65; specific fuel consumption—345 g sc/kWh; operating life—35 years; CO2 emissions payment—$3/ton. Calculated basic energy efficiency indicators of wind farms in the IPS of Ukraine are given in Table 3, and their detailed description—in Annex 2.

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Table 3 Basic energy-economic indicators of wind power plants in the power system of Ukraine at the level of 2030 №

Indicator

Unit

Value

1

Installed WPP capacity

MW

5033

2

Electricity generation, total

kWh

35.27 × 109

3

of WPP

kWh

12.344 × 109

4

at the reserve TPP

kWh

22.926 × 109

5

WPP owner costs (1 year of operation), $ total

323.52 × 106

6

Payback period of the WPP owner’s capital

Year

0.535

7

CO2 emissions from the reserve TPP

Ton

29 × 106

8

Consumer costs for electricity generated by WPP + TPP

$

8.2475 × 109

9

Cost of electricity generated at the $/kWh WPP + TPP complex (in relation to the consumer)

0.234

Alternative TPP (modernized coal-fired) 10

Installed power

kW

1.761 × 106

11

CO2 emissions alt. TPP

ton

15.61 × 106

12

Total costs for alt. TPP

$

677.06 × 106

13

The cost of electricity alt. TPP

$/kWh

54.85 × 10−3

Table 3 and Annex 2 provide an opportunity to compare the main energy-economic indicators of the WPP + reserve TPP complex with similar indicators of the alternative coal-fired TPP, which produces the same amount of energy as the WPP (12,344 × 109 kWh) in 1 year. As in the previous case, the alternative TPP provides much better energy-economic indicators than the WPP + TPP complex. Carbon dioxide emissions (the main indicator that entitles to a number of large preferences of WPP) of this complex is almost twice the emissions of alternative thermal TPP. At the same time, the total costs of the WPP + TPP complex exceed the costs of the alternative TPP by more than 12 times, and the ratio of the cost of electricity production by the complex (item 9, Table 3) to the cost of alternative TPP (item 13) is 4.27.

6 Conclusions and Recommendations Of all the available power sources suitable for frequency balancing in IPS with WPP and SPP capacities, rechargeable batteries are the most efficient. To perform these functions, powerful HPPs can be used no less effectively, which Ukraine does not have and cannot have due to its natural conditions. It is advisable to use thermal (modernized coal-fired) TPPs as reserve capacities when working in complex with

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WPP (SPP) in Ukraine, as IPS of Ukraine has a surplus of sources of this type, and others either do not have the necessary maneuverability (NPP) or are too expensive to operate (gas reciprocating units) due to the use of large volumes of natural gas. Currently, the frequency stability in Ukraine’s UES is ensured by importing energy from Russia of powerful Volga Cascade HPPs on very favorable for Ukraine conditions of daily zero balance, when Ukraine imports very expensive high-speed hydropower energy and even has the right to pay for nuclear power electricity. However, such conditions threaten the country’s energy security, as Russia could cut off (and for a long time) its energy supply at any time, and then there will be a collapse of Ukraine’s IPS, which can be eliminated only by restriction of all WPP and SPP powers. Even if the import of regulatory powers from Russia is maintained, other arguments about the feasibility of using WPPs and WPPs in the conditions of Ukraine’s IPS remain irrefutable. The main political argument, which is primarily used to justify the need to use these technologies, is to reduce greenhouse gas emissions. However, as irrefutably proved above, in reality the opposite situation is true, namely, greenhouse gas emissions increase by 2–4 times compared to the emissions of alternative TPP, which produces the same amount of energy as WPP or SPP. It is also very important that the total consumer costs for the SPP + TPP complex are 14 times higher than its costs for the alternative TPP. For the WPP + TPP complex, these costs are 12 times higher. From this analysis it is irrefutably expedient in the conditions of Ukraine to refuse further new construction of WPP and SPP, freezing their installed capacity at the level of 2021. As shown in Sect. 4, further reductions in SPP electricity tariffs may bring their owners to the brink of bankruptcy, but the consumer’s costs remain sky-high, as the consumer reimburses the costs of frequency stabilization and redundancy. This situation will be observed with further reduction of tariffs for WPPs The requirement of the Law of Ukraine “On the Electricity Market”, which in practice is formed in the form of “Take or Pay”, is unfounded. It contradicts the Transmission System Code, which is a normative document of the National Commission of Ukraine for Energy Regulation and Public Utilities, which is not covered by the laws of the Verkhovna Rada of Ukraine in the field of energy. In addition, the application of this principle to the operation of wind farms and wind farms leads to additional losses to consumers and worsens the environmental situation in Ukraine. Therefore, this principle needs to be urgently removed from this law. The obtained results and experience of the authors can also be useful for specialists from countries with natural conditions comparable to Ukraine, and who carry out measures to decarbonize their own energy.

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Appendix 1 Energy-economic indicators of solar power plants as part of the energy system of Ukraine at the level of 2030 №

Indicator

Unit

Value

1

Installed SPP capacity

MW

9947

2

Operating capacity of SPP and reserve MW TPP (p.1 × 0.8)

3

Electricity generation:

3.1

of the SPP (p.2 × 0.17 × 8.76 × 103 )

kWh

11.85 × 109

3.2

at the reserve TPP (p.2 × 0.63 × 8.76 × 103 )

kWh

43.916 × 109

4

The cost of electricity:

7957.6

4.1

of SPP (p.3.1 × 0.039E)

$

522.2 × 106

4.2

at the reserve TPP (p.3.1 × 2.717₴)

$

4.143 × 109

5

SPP owner costs (for 1 year of operation)

5.1

Capital costs, taking into account the operating life (p.1 × 103 /25 × 1.112)

$

442.44 × 106

5.2

Staff salaries with accruals (820 persons)

$

7.321 × 106

5.3

Other costs (materials, etc.) (2% of item p.5.1)

$

7.958 × 106

5.4

Total SPP owner’s gross costs (p.5.1 + p.5.2 + p.5.3)

$

457.72 × 106

6

Gross revenue of the SPP owner (p.4.1)

$

522.2 × 106

7

Gross profit of the SPP owner (p.6 − p.5.4)

$

64.48 × 106

8

Net profit of the SPP owner (p.7 × 0.8)

$

51.58 × 106

9

Payback period of the owner’s capital (p.5.4/p.8)

year

8.87

10

CO2 emissions from the reserve TPP (p.3.2 × 0.345 × 10−3 × 44/12)

ton

55.55 × 106

11

Fee for CO2 emissions of the reserve TPP (p.10 × 3$/t)

$

166.66 × 106

12

Consumer costs for electricity generated by the SPP + TPP complex

12.1

The cost of electricity generated by SPPs itself (p.4.1)

$

522.2 × 106

12.2

Purchase of electricity for SPP reserve $

2.893 × 109 (continued)

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(continued) №

Indicator

12.3

Purchase of HPP electricity to $ stabilize the frequency (p.3.1 × 0.3 × 1.5$)

5.332 × 109

12.4

Fee for CO2 emissions of the reserve TPP (p.11)

166.66 × 106

12.5

Total consumer costs (p.12.1 + p.12.2 $ + p.12.3 + p.12.4)

9.411 × 109

13

Total produced electricity (SPP + TPP) (p.3.1 + p.3.2)

55.77 × 109

14

The cost of electricity generated at the $/kWh SPP + TPP complex (p.12.5/p.13)

15

Alternative TPP (modernized coal-fired)

15.1

Installed power (p.3.1/0.8(18.76 × 103 ))

kW

1.691 × 106

15.2

Capital expenditures for 1 year, including construction

$

21.49 × 106

15.3

Staff salaries with accruals (250 persons)

$

2.232 × 106

15.4

Other costs (materials, etc.) (2% of item p.15.2)

$

0.4298 × 106

15.5

Fuel consumption (p.3.1 × 0.345 × 10−3 )

ton

5.11 × 106

15.6

Fuel costs (p.15.5 × 3.274 × 103 ₴)

$

580.9 × 106

15.7

CO2 emissions alt. TPP (p.3.1 × 0.345 × 10−3 × 44/12)

ton

15 × 106

15.8

Fee for CO2 emissions of alt. TPP (p.15.7 × 3)

$

45 × 106

15.9

Total costs for alt. TPP (p.15.2 + p.15.3 + p.15.4 + p.15.6 + p.15.8)

$

650.05 × 106

15.10

Cost of electricity generated at alt. TPP (p.15.9/p.3.1)

$/kWh

0.0549

Unit

$

kWh

Value

0.169

Appendix 2 Energy-economic indicators of wind power plants as part of the energy system of Ukraine at the level of 2030

Comparative Analysis of Energy-Economic Indicators of Renewable … №

Indicator

447 Unit

Value

1

Installed WPP capacity

MW

5033

2

Working power (p.1 × 0.8)

MW

4026.4

3

Electricity generation kWh

12.344 × 109

kWh

22.926 × 109

3.1

of WPP (p.2 × 106 × 8.76 × 103 × 0.35)

3.2

at the reserve TPP (p.2 ×

4

106

× 8.76 ×

103

× 0.65)

The cost of electricity

4.1

of WPP (p.3.1 × 7.72 × 10−2 E)

$

1.0795 × 109

4.2

at the reserve TPP (p.3.2 × 2.717₴)

$

2.163 × 109

5

WPP owner costs (for 1 year of operation)

5.1

Capital expenditures taking into account construction

$

313.41 × 106

5.2

Staff salaries with accruals (430 persons)

$

3.839 × 106

5.3

Other costs (materials, etc.) (2% from p.5.1)

$

6.268 × 106

5.4

Total owner’s gross costs (p.5.1 + p.5.2 + p.5.3)

$

323.52 × 106

6

Gross revenue of the owner (p.4.1)

$

1.0795 × 109

7

Gross profit of the owner (p.4.1 − p.5.4)

$

755.98 × 106

8

Net profit of the owner (p.7 × 0.8)

$

604.78 × 106

9

Payback period of the owner’s costs (p.5.4/p.8)

year

0.535

ton

29 × 106

$

87 × 106

10−3

10

CO2 emissions from the reserve TPP (p.3.2 × 0.345 × × 44/12)

11

Fee for CO2 emissions of the reserve TPP (p.10 × 3$/t)

12

Consumer costs for electricity generated by WPP + TPP complex

12.1

Purchase of electricity generated by WPP (p.4.1)

$

1.0795 × 109

12.2

Purchase of electricity to reserve WPP

$

1.526 × 109

12.3

Purchase of HPP electricity to stabilize the frequency (p.3.1 × 0.3 × 1.5$)

$

5.555:109

12.4

Fee for CO2 emissions of the reserve TPP (p.11)

$

87 × 106

12.5

Total consumer costs (p.12.1 + p.12.2 + p.12.3 + p.12.4)

$

8.2475 × 109

13

Total electricity generated by the WPP + TPP complex (p.3.1 kWh + p.3.2)

35.27 × 109

14

The cost of electricity generated at the WPP + TPP complex (p.12.5/p.1.3)

$/kWh

0.234

15

Alternative TPP (modernized coal-fired)

15.1

Production of electricity on alt. TPP (p.3.1)

kWh

12.344 × 109

15.2

Installed power (p.3.1/0.8(18.76 ×

kW

1.761 × 106

15.3

Capital investment for 1 year, including construction

$

22.38 × 106

15.4

Staff salaries with accruals (250 persons)

$

2.232 × 106

15.5

Other costs (materials, etc.) (2% from p.15.3)

$

0.4476 × 106

15.6

Coal consumption (p.15.1 × 0.345 × 10−3 )

ton

5.323 × 106

103 ))

(continued)

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(continued) №

Indicator

Unit

Value

15.7

Fuel costs

$

605.16 × 106

15.8

CO2 emissions alt. TPP (p.15.1 × 0.345 × 10−3 × 44/12)

ton

15.61 × 106

15.9

Fee for CO2 emissions alt. TPP (p.15.8 × 3)

$

46.84 × 106

15.10

Total costs for alt. TPP (p.15.3 + p.15.4 + p.15.5 + p.15.7 + $ p.15.9)

677.06 × 106

15.11

Cost of electricity generated at alt. TPP (p.15.10/p.15.1)

54.85 × 10−3

$/kWh

References 1. Law of Ukraine of 25.09.2008 №601-VI: Pro vnesennia zmin do deiakykh zakoniv Ukrainy shchodo vstanovlennia «zelenoho» taryfu. https://zakon.rada.gov.ua/laws/show/601-17/ed2 0080925#Text (in Ukrainian) 2. Law of Ukraine of 01.04.2009 №1220-VI: Pro vnesennia zmin do deiakykh zakoniv Ukrainy shchodo vstanovlennia «zelenoho» taryfu. https://zakon.rada.gov.ua/laws/show/1220-17#Text (in Ukrainian) 3. Resolution of the National Electricity Regulatory Commission of Ukraine of 23.12.2008 N 1440: Shchodo zatverdzhennia na sichen 2009 rozdribnykh taryfiv na elektroenerhiiu z urakhuvanniam hranychnykh rivniv taryfiv pry postupo-vomu perekhodi do formuvannia yedynykh rozdribnykh taryfiv dlia spozhy-vachiv na terytorii Ukrainy. https://zakon.rada.gov.ua/rada/ show/v1440227-08#Text (in Ukrainian) 4. Stimulating renewable energy in Ukraine with a “green” tariff. A guide for investors. IFC Advisory Program in Europe and Central Asia (2012). https://saee.gov.ua/documents/greentariff.pdf (in Ukrainian) 5. Law of Ukraine of 20.11.2012 № 5485-VI: Pro vnesennia zmin do Zakonu Ukrainy «Pro elektroenerhetyku» shchodo stymuliuvannia vykorystannia alternatyvnykh dzherel enerhii. https://zakon.rada.gov.ua/laws/show/5485-17/ed20121120#Text (in Ukrainian) 6. Installed capacity of the IPS of Ukraine values as 12/2020. https://ua.energy/installed-capacityof-the-ips-of-ukraine/ 7. National Renewable Energy Action Plan until 2020. http://zakon.rada.gov.ua/laws/show/9022014-%D1%80 (in Ukrainian) 8. Gritsyshyna, M.: Shcho ne tak iz zelenym taryfom? Yurydychna Hazeta. https://yur-gaz eta.com/publications/practice/energetichne-pravo/shcho-ne-tak-iz-zelenim-tarifom.html (in Ukrainian) 9. Law of Ukraine of 04.06.2015 № 514-VIII: Pro vnesennia zmin do deiakykh zakoniv Ukrainy shchodo zabezpechennia konkurentnykh umov vyrobnytstva elektroenerhii z alternatyvnykh dzherel enerhii. https://zakon.rada.gov.ua/laws/show/514-19/ed20150604#Text (in Ukrainian) 10. Law of Ukraine of 21.07.2020 № 810-IX: Pro vnesennia zmin do deiakykh zakoniv Ukrainy shchodo udoskonalennia umov pidtrymky vyrobnytstva elektrychnoi enerhii z alternatyvnykh dzherel enerhii. https://zakon.rada.gov.ua/laws/show/810-20/ed20200721#Text (in Ukrainian) 11. Law of Ukraine № 555-IV: On alternative energy sources. https://zakon.rada.gov.ua/laws/show/ 555-15?lang=en#Text 12. Kulyk, M.M., Nechaieva, T.P., Zgurovets, O.V.: Prospects and problems of development of integrated power system of Ukraine in the conditions of its connection to the power system of the European Union and hypertrophied use in its composition of wind and solar power plants. Probl. Gen. Energy 4(59), 4–12 (2019). https://doi.org/10.15407/pge2019.04.004 (in Ukrainian)

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13. Draft regulation of the Cabinet of Ministers of Ukraine «Pro Natsionalnyi plan dii z rozvytku vidnovliuvanoi enerhetyky na period do 2030 roku». State Agency on Energy Efficiency and Energy Saving of Ukraine (SAEE), 20 Jan 2022. https://saee.gov.ua/sites/default/files/blocks/ 02_Proekt_NPDVE-10.01.2022.docx (in Ukrainian) 14. Kulyk, M., Zgurovets, O.: Modeling of power systems with wind, solar power plants and energy storage. In: Babak, V., Isaienko, V., Zaporozhets, A. (eds.) Systems, Decision and Control in Energy I. Studies in Systems, Decision and Control, vol. 298, pp. 231–245. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-48583-2_15 15. Zgurovets, O., Kulyk, M.: Comparative analysis and recommendations for theuse of frequency regulation technologies in integrated power systems with alarge share of wind power plants. In: Babak, V., Isaienko, V., Zaporozhets, A. (eds.) Systems, Decision and Control in Energy II. Studies in Systems,Decision and Control, vol. 346, pp. 81–99. Springer, Cham (2021). https:// doi.org/10.1007/978-3-030-69189-9_5 16. Kulyk, M.M., Kyrylenko, O.V.: The state and prospects of hydroenergy of Ukraine. Tech. Electrodyn. 4, 56–64 (2019). https://doi.org/10.15407/techned2019.04.056 (in Ukrainian) 17. Nechaieva, T.P.: Accounting for use of energy storage systems in the model of the long-term power system development forecasting. Probl. Gen. Energy 3(66), 14–22 (2021). https://doi. org/10.15407/pge2021.03.014 (in Ukrainian) 18. Shulzhenko, S.V.: Statistical processing of wind and solar PV generation variability for assessment of additional power system flexibility. Probl. Gen. Energy 1(64), 14–28 (2021). https:// doi.org/10.15407/pge2021.01.014 (in Ukrainian) 19. Kulyk, M.M., Zgurovets, O.V.: The role and mechanisms of influence of the deriva-tives of regulating capacities on frequency stability in power systems with wind power plants. Probl. Gen. Energy 1(60), 24–30 (2020). https://doi.org/10.15407/pge2020.01.024 (in Ukrainian) 20. Nechaieva, T.P.: Assessment of the joint work of battery energy storage systems with power plants on renewable energy sources. Probl. Gen. Energy 3(58), 11–16 (2019). https://doi.org/ 10.15407/pge2019.03.011 (in Ukrainian) 21. Kulyk, M.M., Zgurovets, O.V.: Adaptive model of frequency and power control in power systems with wind power plants. Probl. Gen. Energy 4(55), 5–10 (2018). https://doi.org/10. 15407/pge2018.04.005 (in Ukrainian) 22. Nechaieva, T.P.: Model and structure of the long-term development of generating capacities of a power system with regard for the commissioning and decommis-sioning dynamics of capacities and changing their technical-and-economic indices. Probl. Gen. Energy 3(54), 5–9 (2018). https://doi.org/10.15407/pge2018.03.005 (in Ukrainian) 23. Accents of DAM and IDM: Reviews. JSC «Market operator», Dec 2021. https://www.oree. com.ua/index.php/web/10317 (in Ukrainian)

Prospects and Energy-Economic Indicators of Heat Energy Production Through Direct Use of Electricity from Renewable Sources in Modern Heat Generators Volodymyr Derii , Oleksandr Teslenko , Eugene Lenchevsky , Viktor Denisov , and Natalia Maistrenko Abstract The chapter presents the results of research on the use of electric heat generators in district heating systems as consumers—regulators who can provide ancillary services to the Integrated Power System of Ukraine to regulate its load. Electric heat generators can use excess electricity from wind and solar power plants in the daytime and during the night “failure” of the daily schedule of electrical loads. Modes of their operation for balancing the power system are determined by dispatchers of the Ukrainian IPS. Calculations have shown the competitiveness of electric heat generators compared to gas boilers. Implementation of electric heat generators with aggregated capacity of about 2500 MW to regulate the power system load will make the structure of the Ukrainian IPS generation more effective by increasing the level of NPP basic generation, reduce the natural gas consumption by 604.5 million m3 per year and TPP coal used by 296.7 thousand tons per year, reduce greenhouse gas emissions by 1691.3 thousand tons per year. Also, the Ukrainian IPS become more resistant to load changes, which will increase the Ukraine energy security and independence. Keywords District heating system · Ukrainian integrated power system · Electric heat generators · Wind power plant · Solar power plant · Electric boiler · Thermal networks

1 Introduction Currently, the Integrated Power System (IPS) of Ukraine operates as part of the energy systems unification of Russia, Ukraine, Belarus and the Baltic states. The stability of this unification is ensured by Russian hydroelectric power plants, which provide system services to Ukraine. One of the significant problems of Ukrainian IPS is the lack of its own maneuverability to ensure the stability of the energy V. Derii (B) · O. Teslenko · E. Lenchevsky · V. Denisov · N. Maistrenko General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 A. Zaporozhets (ed.), Systems, Decision and Control in Energy IV, Studies in Systems, Decision and Control 454, https://doi.org/10.1007/978-3-031-22464-5_27

451

452

V. Derii et al.

system. Due to the objective factors, that have developed in the economy of Ukraine (the structure production change, increasing the population electricity consumption, etc.), this problem will only worsen [1]. Particularly significant is the lack of shunting (regulating) power during the night “failure” hours (23 p.m.–7 a.m.) of the daily electrical loads schedule (DSEL). During this time period, forced shutdowns of coal-fired power units 150, 200 and 300 MW of thermal power plants (TPP) are used to regulate the production-consumption ratio. According to the national operator NEC Ukrenergo report on conformity assessment of generating capacities [2], from 7 to 10 power units of coal-fired thermal power plants are disconnected daily, which leads to accelerated depletion of their resource, excess fuel consumption, increased maintenance and repair costs. In addition, due to a number of political, economic, technological and other factors, Russia may at any time stop providing system services, or significantly increase their cost and jeopardize Ukraine’s energy security. Therefore, research aimed at full or partial solution of the own maneuverability of the of Ukrainian IPS problem increasing, is appropriate and relevant today.

2 Basic Material To estimate the maximum value of the required regulating power during the nighttime “failure” of the electricity load schedule of Ukrainian IPS, the indicator “depth of nighttime failure” proposed, determined by formula (1) Δ P = P23 − Pmin ,

(1)

where Δ P depth of nighttime “failure” of DSEL (MW); Pmin minimum electrical load of DSEL (between 4 and 5 a.m.) (MW); P23 electrical load of the DSEL at 11 p.m. of the previous day (MW). The statistical study results of the DSEL nighttime “failure” depth for the period 2014–2021 are shown in Fig. 1. As can be seen from Fig. 1, the DSEL depths of night “failures” (both maximum and average values) during 2014–2018 tended to decrease. This indicates that the processes of changing the load at night and the mode of operation of consumers established. But in the period 2018–2021 depth of night “failures” began to increase due to the influence of wind (WPP) and solar (SPP) power plants, which generating power depends on weather conditions and is stochastic. According to the legislation of Ukraine, the purchase of the entire amount of electricity from SPP and WPP is guaranteed, which determines their operation at the basic level. In the spring–summer day periods, when the generation volumes from SPP and WPP are large, the system operator uses all available offers of TPP and HPP manufacturers for unloading within the balancing market. Further, in order to maintain the stability of the Ukrainian IPS, the system operator is forced to switch Hydro Power Pumping Station (HPPS) to

Prospects and Energy-Economic Indicators of Heat Energy Production …

453

Fig. 1 DSEL nighttime “failure” depth for 2014–2021

pump operation, which reduces their capacity to operate during the night “failure” of DSEL, as shown in Fig. 2 for 22.07.2021. If these measures are not enough, the SPP and WPP power limits of are applied, as shown in Table 1. Table 1 shows that the maximum total power limitation in 2020 reached 2178.86 MW (07.06.2020) due to a significant increase WPP and SPP power. The first restriction of renewable energy sources (RES) power in 2021 was already on March 11 at 12 p.m., when the RES generation power reached 4.46 GW. Given surplus power and exhausted unloading reserves to ensure the IPS operational safety, this necessitated 400 MW the SPP and WPP power total unloading. RES electricity generation restrictions in 2021 also occurred on March 28, 1, 3, 10 and 11 April (last two days the total unloading power of about 1.5 GW each day) [3].

Fig. 2 Power generation of renewable energy sources and electricity consumption of Hydro Power Pumping Station in the period 09 a.m–7 p.m. 22.07.2021

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V. Derii et al.

Table 1 Power limits of WPP and SPP in 2020 [3] #

Date

Total electric power limitation, MW

Type of generation

1

07.01

929.5

WPP, SPP

2

10.03

510

WPP

3

14.03

282.5

WPP

4

15.03

400

WPP, SPP

5

26.03

407

WPP, SPP

6

28.03

409

WPP, SPP

7

02.04

390.4

WPP, SPP

8

03.04

597.6

WPP, SPP

9

04.04

1363.4

WPP, SPP

10

05.04

1656.7

WPP, SPP

11

09.04

400

SPP

12

11.04

958.46

WPP, SPP

13

12.04

644.27

SPP

14

19.04

380

SPP

15

10.05

910

WPP, SPP

16

07.06

2178.86

WPP, SPP

17

13.08

350

WPP, SPP

18

28.08

300

WPP, SPP

19

09.09

498.1

WPP, SPP

20

04.10

1113.16

WPP, SPP

Due to the lack of market pricing mechanisms, the possibility of adjusting the rates of the “green” tariff and reducing price of the SPP and WPP electricity, in recent years there has been a rapid increase in their number and installed power. At the beginning of 2021, the installed power SES was 6.87 GW and WPP—1.31 GW, and by 2030 it is planned to increase their installed power to 10.5 GW and 5.0 GW, respectively [4]. Such plans cannot be implemented without providing the IPS of Ukraine with sufficient own maneuverability, which is currently insufficient. To provide IPS of Ukraine with balancing power, the system operator NEK Ukrenergo plans to introduce highly maneuverable gas power plants with a total capacity of 2 GW and battery energy storage systems with a total capacity of 700 MW [3]. Problem definition: significant imbalance of the power system is forecasted due to the increase in the share of RES generation with non-guaranteed electricity generation in the absence of the necessary shunting power of the Ukrainian IPS. The purpose of research: to determine the prospects and energy efficiency of thermal energy production through the direct use of electricity from renewable sources in modern heat generators.

Prospects and Energy-Economic Indicators of Heat Energy Production …

455

A much economically feasible solution to this problem may be the transformation of electricity into thermal energy using controlled electric heat generators (EHG): electric boilers, compression heat pumps with electric motors, dynamic cavitation heat generators and more. These EHGs are operated as consumers-regulators on the instructions of the IPS dispatcher with daily accumulation of thermal energy. The essence of the method is that the excess electrical energy in the power system is converted into thermal energy using EHG. In case of electricity shortage in the power system, the EHG is turned off by order of the IPS dispatcher. The main conditions for the use of this method are the presence of consumers of thermal energy from EHG and the possibility of its partial or complete accumulation. Consumption of all thermal energy from EHG should occur every day during the year. District heating systems (DHS) are best suited for the implementation of this method. DHSs have consumers of hot water (year-round consumption) and main networks, which allow the accumulation of thermal energy by current regulations of Ukraine [5]. To determine the needs for EPG control capacities, daily information on the power/load of the Ukrainian IPS for 2021 was collected and analyzed [6]. As a result of the statistical analysis, the probability (P) dependence of the load deficit coverage (Pl) of the Ukrainian IPS on the power of the electric load of the EHG was constructed, as shown in Fig. 3. As can be seen from Fig. 3, ENG with an electric load of about 3000 MW is able to eliminate the deficit of shunting power of the Ukrainian IPS with a high level of probability (P = 0.9). Thus, the need for regulatory capacity of EHG to cover the night “failure” of the Ukrainian IPS as of 2021 was 3000 MW. Ukraine is one of the countries with a high level of centralization of heating systems. The share of DHS in the total heat supply of urban settlements in Ukraine is about 52%. The main equipment of the DHS of Ukraine is physically worn out and technologically obsolete, which caused a number of significant problems for both consumers and heat supply companies. Today, the DHS of Ukraine needs to be renewed through mass reconstruction and modernization. When planning the reconstruction and modernization

Fig. 3 The probability (P) dependence of the load deficit coverage (Pl) of the Ukrainian IPS on the power of the electric load EHG

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V. Derii et al.

of the DHS, it is necessary to provide for the introduction of EHG for heat production and ancillary services to power systems, which will solve one of the urgent problems of the Ukrainian IPS—reducing the deficit of shunting power. To assess the possibility of the DHS to provide ancillary services to the Ukrainian IPS through the use of EHG, the heat supply systems of large cities with a population of over 100,000 inhabitants with boilers with a power of more than 20 Gcal/h (23.25 MW) were studied. Such DHSs have well-developed main networks and supply hot water to consumers all year round. The analysis of these DHSs determined that the average heat load for domestic hot water supply systems (DHWS) is 3012 MW. In fact, these are potential shunting capacities of EHG, which are able to replace the power of existing boilers in the mode of hot water. To determine the prospects for the use of EHG in DHS, the influencing factors were identified and the forecast changes in the load of hot water systems was built. The biggest influencing factors on the hot water system load are the population of Ukraine reduction and the DHS decentralization processes. The demographic scenario of the Institute of Economics and Forecasting of the National Academy of Sciences of Ukraine was used for the analysis. It predicts the average rate of change in birth rates, life expectancy and net migration in Ukraine [7]. Data on the processes of heat supply systems decentralization have been used from [8]. Decentralization processes are primarily due to the low quality of DHWS services and their high prices. Consumers massively refuse these services and use household electric water heaters [9]. When constructing the DHWS load forecast, it was assumed that in 2020–2035 large-scale reconstruction and modernization of DHS will be carried out, restored DHWS systems and their services will be cheaper than the use of domestic boilers and decentralization of heating systems will stop. The load of hot water systems by years was calculated by the formula [ p q ] hwl qthwl = q2000 × (1 − ∂t )(1 − ∂t ) ,

(2)

hwl where qthwl —heat load of domestic hot water systems per year t; q2000 —heat load of p d domestic hot water systems in 2000; ∂t , ∂t —the rate of change in the population of Ukraine and the rate of decentralization of DHS per year t, respectively, %. The results of calculations and assumptions are given in Table 2. Table 2 shows that under the influence of population decline and decentralization of DHS, the total heat load of domestic hot water systems for the period 2000–2050

Table 2 Forecast of changes in the load of hot water systems Indicator/Year

2020

2025

2030

2035

2040

2045

2050

The rate of change in the population of Ukraine, %

0

1.80

1.83

2.34

2.39

2.21

2.51

Rate of decentralization of 0 DHS, %

6

7

5

2

0

0

Heat load of domestic hot water systems, MW

2685.5

2451.7

2274.7

2175.8

2127.8

2074.5

3012.0

Prospects and Energy-Economic Indicators of Heat Energy Production …

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Table 3 Possibilities of accumulation of thermal energy in thermal networks, GJ [10] Appellation

Season period Heating

Not heated

Maximum power of thermal networks for the accumulation of thermal energy

Design temperature graph—237,471 Actual temperature graph—147,007

108,560

The need for accumulation of thermal energy

96,100

will decrease by 31% and reach 2074.5 MW in 2050. For the period up to 2040, the total electrical load (consumption) of EHG should be chosen about 2500 MW. One of the conditions for using ETGs is that all the heat energy they produce must be consumed during the day. This is due to the cyclic mode of operation of the ETG (during the night “failure” of the DSEL). But during the night “failure” in the non-heating season, the consumption of hot water is minimal, and the only way to ensure the operation of the EHG at this time is the accumulation of thermal energy produced by them. As an option that does not require large investments in the construction of heat accumulators, is the use of thermal networks for these purposes. Thus, according to the current regulations of Ukraine [5], the accumulation of thermal energy is possible only in the main networks. And according to the Law of Ukraine “On Heat Supply”, the main networks have boilers with a power of at least 20 Gcal/h (23.25 MW). This fact is an additional limitation on the power of boilers where ETG can be used. Therefore, it is necessary to investigate the technical possibilities of thermal networks for the accumulation of thermal energy from EHG in the absence of its consumption at night. It is necessary to take into account the fact that part of the main heating networks has exhausted its technical resource. To increase the reliability of heating networks, heat supply companies were forced to move from design temperature schedules of 150/70 °C to schedules with lower limit temperatures (about 120/70 °C). Such a study has already been conducted for the period of April 14, 2018 in [10], in which the magnitude of the night “failure” of DSEL was 3002 MW, and the need for thermal energy accumulation—22,953 Gcal (96,100 GJ). In [10], in addition to the needs for the accumulation of thermal energy from EHG, the maximum storage power of thermal networks of large cities of Ukraine was also assessed (Table 3). As seen from Table 3, the maximum storage power of thermal networks is sufficient for the accumulation of thermal energy in the design and actual temperature schedule in both the heating and non-heating periods.

3 Research Methodology When determining the feasibility of using EHG in the DHS, a comparative analysis of the use of traditional gas boilers (GB) and electric boilers (EB) was conducted.

458

V. Derii et al.

An indicator such as the Levelized weighted average cost of heat (LCOH) is used as a criterion. To compare the efficiency of different energy generation technologies in the world, the method of estimating the average cost of energy over the life cycle is used—LCOE/LCOHC (Levelized cost of energy/levelized cost of heat (cold)). This method is universal and convenient in the comparative analysis of different types of energy production technologies (electricity, heat and cold) and is used by many reputable organizations, including the International Energy Agency. According to the European Commission’s guidelines for the development of renewable energy support systems (SWD (2013)) [11], three steps are envisaged for determination tariffs: (1) determination of parameters and methodology for calculating direct costs; (2) forecasting costs and revenues; (3) conversion of LCOE to the appropriate level of support. The methodology for estimating the indicator depends on the degree of complexity of the assumptions (financial, economic and technical). LCOH is defined as the constant cost of generating one kWh of heat/cold, which is equal to the discounted costs spent throughout the life cycle [12–15]. The main calculation formula of this method is: Σ N (It +Mt +Ft ) LC O H =

(1+r )t Ht t=1 (1+r )t

t=1

ΣN

,

(3)

where LCOH—average cost of heat for the life cycle; t—current year of the system since the beginning of construction (index of component costs); N—the duration of the project; I t —annual investment; M t —annual conditionally fixed costs for maintenance and repair, Ft—conditionally variable costs (for fuel, electricity, materials, taxes due to emissions of pollutants and greenhouse gases); H t —annual heat production, r—discount rate (discount), which reflects the rate of decline in investment capital over the years. Initial data and results of calculations. Comparative analysis of LCOH was performed under the following conditions and initial data. The main technical and economic indicators of boilers are shown in Table 4. Table 4 The main technical and economic indicators of boilers Heat Thermal Electric Conversion Specific Operating costs Resource, generator power, power factor capital (conditionally-fixed) years MW consumption, expenditures MW [16], e/kW Electric boiler

50.0

Gas boiler

58.15

51.02 –

0.98

30.6

0.25 e/MW/year

25

0.93

26.3

3 e/kW/year

20

Prospects and Energy-Economic Indicators of Heat Energy Production …

459

Table 5 Prices for energy resources and emissions taxes Year

Indicator

2020 2025 Natural gas, e/1000

m3

250

Electricity (night “failure” and day surplus), 50.1 e/MWh

2030 2035

2040

2045

2050

291.1 292

311.1 320.3 329.8 339.5

63.9

63.9

62.5

63.8

63.9

63.3

Payments for CO2 emissions, e/t

0.3

2.1

8

15

22

27

34

Emission payments CO, e/t

3.1

4.6

6.1

7.9

12.6

19.2

25.7

Emission payments NOx , e/t

82.6

111

128

145

165

209

250

Forecasts of prices for electricity and natural gas, ancillary services, taxes on greenhouse gas emissions and pollutants are given in Table 5. According to current trends in the theory and practice of financial activities, the cost of capital of the enterprise is recommended to be calculated based on the use of the so-called model of weighted average cost of capital WACC (Weighted Average Cost of Capital) [17]: W ACC =

E D · i d · (1 − t) + · ie D+E D+E

(4)

where D—share of debt capital, accepted 15%; E—share of equity, accepted 85%; id —cost of debt capital (interest rate on the loan), accepted 6%; ie —cost of equity, accepted 10%; t—income tax rate accepted 0%. The discount rate was determined as the weighted average value of equity and borrowed capital was 6.6%. The share of borrowed funds is 85% of capital expenditures for the implementation of heat generating equipment (the cost of basic and auxiliary equipment, design, construction, installation and commissioning). Contingencies are assumed to be equal to 10% of the total project cost. Modeling of the GB life cycle was conducted for the mode of operation during the year. At the same time, the initial cost of natural gas was variable—(250, 450, 500, 550, 600) e/1000 m3 . At the same time, the tendencies of changes in natural gas prices by years (Table 5) remained unchanged. Modeling the use of EB was performed in the following modes of operation: . generation of thermal energy during the night “failure” of DSEL power systems; . generation of thermal energy during the night “failure” of DSEL with the provision of ancillary services to power systems. The following assumptions were also made: . thermal energy from the EB will be partially consumed, and the rest—accumulated by thermal networks; . during peak modes of operation of power systems, when the EB will be completely disconnected, the accumulated thermal energy from thermal networks will be supplied to consumers.

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In addition, the cost of connecting the EB to the electricity grid was taken into account when estimating investment costs. Fees for non-standard connection to the electricity grid were calculated for 24 large cities of Ukraine according to the methodology of the national regulator in the field of electricity generation and supply [18]. For further modeling, their average value was used, which is 87.4 e/kW of the installed electric power of the EB. The cost of ancillary services as of 2020 is assumed to be e9.48/MWh. Variables in the simulation were the initial cost of electricity: 29; 50.1 and 60 e/MWh. At the same time, the trends in changes in electricity prices over the years (Table 5) remained unchanged. The amount of electricity consumed by the electric boiler and the heat energy produced by it was determined by the formulas E E B = k f s · PL E B · tn f · n y ,

(5)

HE B = E E B · η E B ,

(6)

where E EB —amount of electricity consumed by the electric boiler; k f s —coefficient of filling the schedule of night failure of power system (0.733); PL E B —electric boiler load; tn f – duration of night failure (8 h); n y —number of days per year; H EB —the amount of thermal energy produced by the electric boiler; η E B —conversion factor of electric boiler. The reduction in natural gas consumption of DH system, which is due to the replacement of thermal energy produced by the EB, is determined based on the formula VG =

E E B ηE B , 9.42ηG B

(7)

where V G —reduction of natural gas consumption; E EB —electricity consumption by electric boiler; H EB —conversion factor of electric boiler (accepted 0.98); 9.42— calorific value of natural gas, MWh/1000 m3 . The results of modeling the use of an electric boiler with a thermal power of 50 MW showed that: . . . . . . . .

annual heat production will be 107 thousand MWh; annual electricity consumption—109.2 million kWh; shunting electric load—51.02 MW; specific investment costs are 120 e per 1 kW of installed power; annual savings of natural gas—12,622.6 thousand m3 ; annual reduction of thermal power plant coal consumption—6.06 thousand tons; annual reduction of greenhouse gas emissions: CO2 —24,528.6 tons; annual reduction of nitrogen oxide emissions: NOx —26.86 tons. The results of LCOH modeling are given in Table 6.

Prospects and Energy-Economic Indicators of Heat Energy Production …

461

Table 6 LCOH of gas and electric boilers Gas boiler 58.15 MW Gas cost, e/1000 m3

250

450

500

550

600

LCOH, e/MWh

29.8

53.6

59.5

65.4

71.4

29

50.1

60

Electric boiler 50 MW Electricity cost, e/MWh LCOH, e/MWh

Without payment for AS

40.3

66.9

79.4

With payment for AS

23.0

49.5

61.9

AS ancillary services

To determine the sustainability of EB implementation projects, their sensitivity analysis was performed. The key parameter in our case will be LCOH of thermal energy, which depends on a number of factors, the main of which are the price of energy resources, the amount of investment costs, discount rate and amount of energy produced during the year (installed power utilization). In fact, the procedure for determining sensitivity is nothing more than finding partial derivatives of the function of many variables. In the practice of preparation of investment projects, usually the change of the key parameter is determined by a consistent change of influential factors by 10%. This was done for LCOH of thermal energy, which is produced using GB and EB. The results of the sensitivity analysis are shown in Table 7. As seen from Table 7, projects for the introduction of GB in the DH system are quite resistant to influencing factors. The main influencing factor on the LCOH of thermal energy is the change in the price of natural gas, and on the EB is the change in the price of electricity and ancillary services. The significance of this impact is moderate and acceptable for their implementation projects. Table 7 The results of the sensitivity analysis of the introduction of gas and electric boilers Impact factor (change by + 10%)

Change of LCOH, % Gas boiler with a thermal power of 58.15 MW

Electric boiler with a thermal power of 50 MW

Investment costs

0.25

3.1

Discount rate

0.1

2.7

The price of natural gas

9.96

The price of electricity

–

36.6

Cost of ancillary services (− 10%)

–

10.1

The amount of heat produced per year (− 10%)

0.13

3.2

462

V. Derii et al.

4 Discussion of Research Results As a result of the analysis of simulation results, it was found that the EB can be used without the provision of ancillary services to the power system under the following conditions. With the cost of surplus electricity 29.0 and 50.1 e/MWh, the cost of natural gas should not be less than 350 and 600 e/1000 m3 , respectively. When providing ancillary services to the energy system with the help of the EB (cost of electricity 29.0; 50.1 and 60 e/MWh), the cost of natural gas should not be less than (250, 450 and 550 e/1000 m3 ), respectively. The results of modeling the use of EB with a consumed electrical power of 51.02 MW for the provision of ancillary services to power systems allow to determine the indicators of the use of EB with a total electrical power of 2500 MW: . . . . .

the amount of investment costs—e300 million; electricity consumption—5.35 billion kWh/year; natural gas savings—618.5 million m3 /year; reduction of coal consumption—573 thousand tons/year; reduction of greenhouse gas emissions—1691.3 thousand tons/year.

5 Conclusions Electric heat generators are used as consumers-regulators when there is an excess of electricity from non-guaranteed generators (solar and wind power plants) and during a nighttime “failure” of the daily schedule of electrical loads. The modes of their operation are determined by the dispatchers of the Ukrainian IPS for balancing the power system. Calculations have shown the competitiveness of such electric heat generators in comparison with gas boilers. The introduction of electric heat generators with a capacity of about 2500 MW to regulate the load of power systems will make the generation structure of Ukrainian nuclear power plants more efficient by increasing the level of nuclear power plants basic generation, reduce the consumption of natural gas by 604.5 million m3 per year and coal used by thermal power plants by 296.7 thousand tons per year, reduce greenhouse gas emissions by 1691.3 thousand tons per year. Also, the Integrated Power System of Ukraine will be more resistant to changes in its load, which will increase energy security and energy independence of Ukraine.

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