Energy Systems Research http://esrj.ru/index.php/esr <p><em>Energy Systems Research</em> is an international peer-reviewed journal that addresses all facets of energy systems. It focuses on their sustainable development and efficient use; smart and reliable operation, control, and management; as well as integration and interaction in complex physical, technical, economic, and social contexts.</p> <p>Energy systems research methodology is based on a systems approach that views energy facilities as systems with intricate structure and external connections and encompasses the methods and technologies of systems analysis.</p> <p>Within this broad multi-disciplinary scope, topics of particular interest include the strategic development of energy systems at the international, regional, national, and local levels; energy supply reliability and security; energy markets, regulations, and policy; technological innovations with their implications and future-oriented transformations of energy systems.</p> <p>The journal welcomes articles on advances in heat and electric power industries, energy efficiency and conservation, renewable energy and clean fossil fuel generation, and other innovative energy technologies.</p> <p><em>Energy Systems Research</em> is also concerned with energy systems challenges related to the applications of information and communication technologies, including intelligent control and cyber security, modern approaches of systems analysis, modeling, forecasting, numerical computations, and optimization.</p> <p>The journal is published by <a title="Melentiev Energy Systems Institute of Siberian Branch of Russian Academy of Sciences" href="http://isem.irk.ru/en/" target="_blank" rel="noopener">Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences</a>.</p> <p>Editor-in-Chief: Valery Stennikov, academician of Russian Academy of Sciences.</p> <p>The journal's ISSN is 2618-9992. The publication features four issues annually, with special issues also available, all presented in English.</p> <p>All articles are available online as Open Access publications.</p> <p>The journal is indexed in the <strong>international database Scopus</strong> and included in the <strong>Unified Russian List of Scientific Journals ("White List") - level 2</strong>.</p> <p class="v1MsoNormal"><span lang="EN-US">The journal is included in the list of VAK-approved peer-reviewed scientific publications, where the main scientific findings of dissertations are to be published in the following scientific disciplines:</span></p> <p class="v1MsoNormal"><span lang="EN-US">1.2.2. Mathematical modeling, numerical methods, and software packages (engineering sciences),</span></p> <p class="v1MsoNormal"><span lang="EN-US">2.4.3. Electrical power engineering (engineering sciences),</span></p> <p class="v1MsoNormal"><span lang="EN-US">2.4.5. Energy systems and complexes (engineering sciences).</span></p> <p class="v1MsoNormal"><span lang="EN-US">In May 2024, the <em>Energy Systems Research </em> was classified as Category 2 (K2) journal. It is i</span><span lang="EN-US">ndexed by the platforms such as Scopus, RSCI, CyberLeninka, Google Scholar, and Crossref.</span></p> <p class="v1MsoNormal">The journal is registered with the Federal Service for Supervision of Communications, Information Technology, and Mass Media (Roskomnadzor). The registration certificate Эл № ФС77-84526 was issued on January 16, 2023.</p> en-US info@esrj.ru (Alexey Mikheev) info@esrj.ru (Alexey Mikheev) Tue, 31 Mar 2026 00:00:00 +0300 OJS 3.3.0.8 http://blogs.law.harvard.edu/tech/rss 60 Transformation of Natural-Technical Systems at the Initial Stage of the Syllakh Coal Deposit Development http://esrj.ru/index.php/esr/article/view/2026-01-0001 <p>A preliminary assessment of the transformation of the natural-technical system “Coal Complex – Natural Environment” was conducted for planning the development of the Syllakh coal deposit in South Yakutia. The assessment aimed to determine both the potential resilience of natural landscapes to anthropogenic pressure and the current state of technogenic disturbance. The methodology integrated landscape analysis, a score-based assessment of permafrost landscape resilience, and GIS techniques, including satellite imagery analysis. The potential landscape resilience was evaluated based on a combination of permafrost and bioclimatic indicators specific to each landscape. Remote sensing data analysis and the subsequent mapping of anthropogenic disturbance revealed a nonlinear relationship between the observed disturbance patterns and the assessed potential resilience. This finding suggests that the spatial distribution of the anthropogenic impact is driven primarily by infrastructural and techno-economic factors rather than the inherent resilience of the landscapes.</p> D.D. Pinigin, N.A. Nikolaeva, L.P. Sergeeva, N.V. Pavlov, V.E. Zakharov, D.V. Prokhorov (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0001 Tue, 31 Mar 2026 00:00:00 +0300 The Irkutsk Region Gas Industry: Development Trends and Role within the Eastern Dimension of Russia’s Energy Strategy http://esrj.ru/index.php/esr/article/view/2026-01-0002 <p>The reorientation of natural gas export routes toward the East, the advantageous geographical location, and the substantial resource potential of the Irkutsk Region underscore the critical importance of defining priority areas for development of the regional gas industry and its role in the Eastern energy strategy of Russia over the coming decades. The driving and constraining factors that shape the evolution of the gas industry in the Irkutsk Region are analyzed. The study identifies long-term priority development areas, formulates an aggregated forecast natural gas balance for the Irkutsk Gas Production Center, and assesses a qualitative risk. Based on the natural gas balance, which reflects the resource base, regional specificities, and the eastward shift of Russian gas exports, the study evaluates the significance of the Irkutsk Region gas industry within the Eastern dimension of Russia’s energy strategy.</p> G.G. Lachkov, B.G. Saneev, A.E. Filippov (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0002 Tue, 31 Mar 2026 00:00:00 +0300 Composite Index for Managing Emergency Repair in Electrical Utilities under Heterogeneous Incident Data http://esrj.ru/index.php/esr/article/view/2026-01-0003 <p>The paper focuses on the management of emergency repair crews in distribution systems characterized by high emergency rates and heterogeneous incident data. The study examines the human-machine system, Human–Tools–Logistics, which necessitates a compact, interpretable, and data-resilient readiness indicator. The scientific novelty lies in the development of a non-compensatory composite operational readiness index for crews, based on the geometric aggregation of three sub-indices: Human, Tools, and Logistics.</p> <p>A two-stage methodology for constructing the composite operational readiness index is proposed. In the first stage, heterogeneous data and expert knowledge regarding personnel, equipment, logistics, and environmental conditions are integrated through a multi-agent data fusion framework. In the second stage, normalized sub-indices (<em>H</em>/<em>T/L</em>) are developed using fuzzy logic. Finally, the operational readiness index is aggregated as a normalized weighted geometric mean, ensuring its non-compensatory nature.</p> <table width="100%"> <tbody> <tr> <td> <p> </p> <p><sup>*</sup> Corresponding author.</p> <p>E-mail: <a href="mailto:starkcom8@mail.ru">starkcom8@mail.ru</a></p> <p> </p> <p>DOI: <a href="http://dx.doi.org/10.25729/esr.2026.01.0003">10.25729/esr.2026.01.0003</a></p> <p>Received December 7, 2025. Revised January 26, 2025. Accepted January 30, 2026. Available online March 31, 2026.</p> <p>This is an open-access article under a Creative Commons Attribution-NonCommercial 4.0 International License.</p> <p>© 2026 ESI SB RAS and authors. All rights reserved.</p> </td> </tr> </tbody> </table> <p><br />Simulation software was developed to model emergency scenarios in Moscow power grids. For a fixed point in time, the index values are calculated for multiple crews to match them with an incident and establish the most effective crew for that incident. The impact of temperature, traffic congestion, crew size, along with personnel experience and qualifications is analyzed. The analysis demonstrates diminishing returns on crew size and saturation of the experience curve, alongside the significant influence of adverse meteorological conditions and traffic congestion.</p> <p data-start="92" data-end="652">The proposed index is compared with existing simulation-based, probabilistic, and optimization-oriented models, as well as fuzzy-logic and decision support systems. The findings demonstrate that the proposed operational readiness index offers superior interpretability for dispatcher decision-making and can be seamlessly integrated into assignment and routing optimization tasks, facilitating bottleneck identification and dispatcher training.</p> <p>The paper focuses on the management of emergency repair crews in distribution systems characterized by high emergency rates and heterogeneous incident data. The study examines the human-machine system, Human–Tools–Logistics, which necessitates a compact, interpretable, and data-resilient readiness indicator. The scientific novelty lies in the development of a non-compensatory composite operational readiness index for crews, based on the geometric aggregation of three sub-indices: Human, Tools, and Logistics.</p> <p>A two-stage methodology for constructing the composite operational readiness index is proposed. In the first stage, heterogeneous data and expert knowledge regarding personnel, equipment, logistics, and environmental conditions are integrated through a multi-agent data fusion framework. In the second stage, normalized sub-indices (<em>H</em>/<em>T/L</em>) are developed using fuzzy logic. Finally, the operational readiness index is aggregated as a normalized weighted geometric mean, ensuring its non-compensatory nature.</p> <table width="100%"> <tbody> <tr> <td> <p> </p> <p><sup>*</sup> Corresponding author.</p> <p>E-mail: <a href="mailto:starkcom8@mail.ru">starkcom8@mail.ru</a></p> <p> </p> <p>DOI: <a href="http://dx.doi.org/10.25729/esr.2026.01.0003">10.25729/esr.2026.01.0003</a></p> <p>Received December 7, 2025. Revised January 26, 2025. Accepted January 30, 2026. Available online March 31, 2026.</p> <p>This is an open-access article under a Creative Commons Attribution-NonCommercial 4.0 International License.</p> <p>© 2026 ESI SB RAS and authors. All rights reserved.</p> </td> </tr> </tbody> </table> <p><br />Simulation software was developed to model emergency scenarios in Moscow power grids. For a fixed point in time, the index values are calculated for multiple crews to match them with an incident and establish the most effective crew for that incident. The impact of temperature, traffic congestion, crew size, along with personnel experience and qualifications is analyzed. The analysis demonstrates diminishing returns on crew size and saturation of the experience curve, alongside the significant influence of adverse meteorological conditions and traffic congestion.</p> <p data-start="92" data-end="652">The proposed index is compared with existing simulation-based, probabilistic, and optimization-oriented models, as well as fuzzy-logic and decision support systems. The findings demonstrate that the proposed operational readiness index offers superior interpretability for dispatcher decision-making and can be seamlessly integrated into assignment and routing optimization tasks, facilitating bottleneck identification and dispatcher training.</p> L.A. Komarova, A.V. Timoshenko, A.A. Kochkarov (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0003 Tue, 31 Mar 2026 00:00:00 +0300 Impact of External Distortion Sources on Harmonic Voltage Profiles of Consumers http://esrj.ru/index.php/esr/article/view/2026-01-0004 <p>The study assesses how nonlinear electrical loads of external consumers connected at the point of common coupling impact the electrical installation of a small-scale enterprise. The nonlinear electrical load of the traction substation is considered as an external nonlinear load while the electrical installation of the enterprise represents a low-capacity consumer. The developed analytical expressions enable the assessment of external distortion impacts, considering the network short-circuit power at various points, along with the nonlinear and linear load of the low-capacity consumer represented by induction motors. The study reveals that the linear load of the consumer under study has a significant shunting effect, reducing voltage harmonics from the nonlinear electrical load of external consumers. The findings also indicate that the voltage harmonic distortion factor scales with the nonlinear load power of the traction substation, which can be determined using the derived analytical expressions. The introduced criterion enables a preliminary evaluation of the harmonic level, characterized by the ratio of the short-circuit power at the transformer secondary to the transformer capacity. The analytical calculation results showed strong agreement with the MATLAB/Simulink simulations.</p> A.N. Skamiyn, A.А. Sverbey, SV. Solovev (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0004 Tue, 31 Mar 2026 00:00:00 +0300 On Modern Approach to Assessing National Energy Security in Russia http://esrj.ru/index.php/esr/article/view/2026-01-0005 <p>The current approach for assessing national energy security is based on monitoring the state of the indicative analysis objects as established in the Energy Security Doctrine of the Russian Federation (2012). The limitation of this approach is that the critical aspects of certain objects exhibit significant overlap in their impact on the operability of energy systems and their facilities. Furthermore, there is no direct link between certain objects and the key priority of ensuring reliable fuel and energy supply to consumers. This study provides a rationale for adjusting the composition of the objects of indicative analysis to align integrated assessments with the goal to protect consumers from fuel and energy shortages at the national level. The paper presents the findings of the 2024 assessment regarding the state of the objects of indicative analysis within the national energy security framework.</p> S.M. Senderov (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0005 Tue, 31 Mar 2026 00:00:00 +0300 A Method for Reducing Fluctuations in Total Power Generated by RES Plants in Localized Power Systems http://esrj.ru/index.php/esr/article/view/2026-01-0006 <p>In recent years, the total installed capacity of commissioned wind power plants (WPPs) and photovoltaic plants (PVPs) has exceeded that of all other types of power plants. The intermittency of primary energy resources determines the stochastic nature of wind and solar power output, complicating the management of localized power systems. Steam turbine plants in conventional thermal power plants (TPPs) lack the necessary operational flexibility to compensate for fluctuations in operating parameters, which are caused by the integration of WPPs and PVPs. Localized power systems, however, offer opportunities for constructing other types of power plants based on firm renewable energy sources (RES), enabling real-time operational management. These include small-scale hydropower plants (SHPPs), bio-thermal power plants (bioTPPs), waste-to-energy (WtE) plants, and others utilizing local energy resources. The paper proposes a method to reduce fluctuations in total power of firm RES plants in order to enhance the stability and management of localized power systems with a high penetration of WPPs and PVPs. The method is based on the coordinated power control of all firm RES plants and energy storage systems (ESS) integrated within WPPs and PVPs. This approach enables conventional TPPs to adhere to the dispatch load curve, mitigating the requirements for the flexibility of their generating equipment, the transfer capability of intersystem power transmission lines, and the power and energy capacity of the ESS.</p> P.V. Ilyushin, I.D. Georgievskiy (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0006 Tue, 31 Mar 2026 00:00:00 +0300 Development of Maintainability Metrics for Power Systems http://esrj.ru/index.php/esr/article/view/2026-01-0007 <p>This study focuses on developing methods to assess the optimality of maintenance campaign in terms of various criteria and the effect of maintenance on power system reliability. The assessment is based on a new set of metrics represented by power system maintainability indices. Adequacy metrics, in general, are ill-suited to deal with this problem: although the scope of power system adequacy assessment covers maintenance, the way it is done is either rudimentary or limited to a pre-specified list of maintenance requests. This study is centered on maintenance scheduling.</p> <p>Several metrics of power system maintainability are conceptualized, detailed, and tested. The analysis of the metrics employs Monte Carlo simulations. The metrics are tested by simulations on a modified standard test system to demonstrate that they are suitable for use in maintainability assessment of power systems. They perform best, however, when evaluating the criticality of generators and power transmission lines within the context of maintenance campaign. The findings from this study underscore the potential for further enhancement of the described procedures. Priority must be given to formulating indices and accelerating their calculation.</p> P.Yu. Gubin (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0007 Tue, 31 Mar 2026 00:00:00 +0300 Subsynchronous Oscillations in Inverter-Dominated Power Systems http://esrj.ru/index.php/esr/article/view/2026-01-0008 <p>The number of electric power conversion devices connected to AC grids of different voltages has markedly increased worldwide in recent years due to the steady growth in renewable power capacity. Unique features of power inverters (high performance, the dominant role of the automatic control system, etc.) modify dynamic properties of power systems, resulting in new operating states and processes. These are, most notably, broadband oscillations and subsynchronous oscillations (SSO) in particular. The latter are the subject of the present study. One of the causes of such oscillations is interaction between automatic control systems running inverters and the external grid. A comprehensive SSO analysis within the study involved frequency analysis of simplified models of the grid-tie inverter under different patterns of active and reactive power control, as well as the detailed modeling in the time domain. The findings of the above analysis served as a basis for a taxonomy of SSO causation mechanisms, which are related to the dynamics of inverter's automatic control system operation under various network topologies and operating conditions. Furthermore, the factors increasing the probability of SSO events in power grids with inverter-based generators are highlighted. Testing different designs of closed-loop automatic control systems provided evidence for the validity of the proposed taxonomy</p> А.А. Suvorov, A.B. Askarov, V.E. Rudnik, I.N. Gusarov (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0008 Tue, 31 Mar 2026 00:00:00 +0300 First- and Second-Order Sensitivity Matrices (Differential Models) of Electric Power Systems: Applicability for Post-Emergency Steady-State Analysis http://esrj.ru/index.php/esr/article/view/2026-01-0009 <p>Reliability assessment of electric power systems necessitates an analysis of numerous operating states involving potential equipment outages and stochastic events within the minimal time. The sensitivity matrix method enables the calculation of post-emergency steady states. This paper describes the first- and second-order differential models for electric power system steady-state analysis, representing the dependence of bus voltage variations on power fluctuations. These models are applied to simulate generator outages and consumer load fluctuations. The proposed differential models are validated on a test electric power system. The first- and second-order sensitivity matrices applied to the model of electric power system steady states in power balance form demonstrate accurate qualitative and quantitative approximation of operating parameters. Furthermore, the second-order sensitivity matrices markedly improve the calculation accuracy of post-emergency steady-states</p> D.S. Krupenev (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0009 Tue, 31 Mar 2026 00:00:00 +0300 Modeling the Angara-Yenisei Cascade Operations Based on Firm Winter Power Output Maximization http://esrj.ru/index.php/esr/article/view/2026-01-00010 <p>The study explores the current challenges and constraints in regulating the operations of the Angara-Yenisei cascade of hydroelectric power plants. An overview of modern approaches to hydropower plant operation modeling is provided. A mathematical formulation of maximizing of the firm winter power output of the Angara-Yenisei cascade is presented. The developed Garant-Cascade system is described highlighting the interaction of its primary modules. The Angara-Yenisei cascade operations and optimal firm winter power output under various scenarios and constraints were calculated using the Garant-Cascade system. A database of average monthly reservoir inflows for the 1903–2025 period served as the input data for modeling a continuous series of hydropower operating conditions. Two scenarios of the cascade operations with and without firm winter power were discussed. The first scenario involves maintaining the required cascade winter power by regulating discharge at the Bratsk hydropower plant. The second scenario utilizes the dispatch curve to set the discharge of the Bratsk hydropower plant according to the current reservoir water level. The five levels of the winter power (low, reduced, firm, increased, high) were identified depending on the reservoir water level at the beginning of the winter period. The modeling results for the hydropower plant operations during the extreme low-water period of 2014–2018 are presented, demonstrating the minimum cascade winter power.</p> E.N. Osipchuk, N.N. Abasov, V.M. Nikitin, V.M. Berdnikov (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-00010 Tue, 31 Mar 2026 00:00:00 +0300 Methodology for Comprehensive Hierarchical Reliability Assessment and its Application to Heating System Operation and Expansion http://esrj.ru/index.php/esr/article/view/2026-01-0011 <p>This paper highlights the importance of a comprehensive hierarchical approach to the heating system reliability analysis. The core idea behind it is to integrate the methods and models used to assess the reliability of individual subsystems constituting heating systems, such as thermal energy sources and heat networks. This assessment accounts for a range of significant internal (systemic) and external factors. The main principles, provisions, and components of the methodology for the comprehensive hierarchical reliability analysis of heating systems are given. The methodology is employed in the key tasks related to assessing and ensuring (synthesizing) the operation of the studied systems. Building on the methodological approaches, models, and algorithms designed for the said analysis, this study introduces formulations, methods, models, and computational tools for new tasks of the long-term advancement of modern heating systems. These systems encompass both district and distributed thermal energy generation, featuring prosumer subsystems. The paper synthesizes the findings from the recent studies conducted by the contributing authors</p> V.A. Stennikov, I.V. Postnikov (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0011 Tue, 31 Mar 2026 00:00:00 +0300 Ensuring Reliability of the Central Asian Power System Under High Penetration of Renewable Energy Sources http://esrj.ru/index.php/esr/article/view/2026-01-0012 <p>The plans for massive integration of renewable energy sources in country-specific power systems within the Central Asian Power System (CAPS) pose the research challenge of balancing generation and consumption of electric power and capacity. Intermittent nature of renewable energy output could seriously affect CAPS stability. This study considers modern systems of energy storage as a solution to address unresolved capacity imbalances and ensure the stable power supply to consumers. We also highlight the types of energy storage that are best suited for the geographical area. Finally, this study outlines how to eliminate capacity shortages by integrating renewables into the system</p> Sh.V. Khamidov, I.M. Buranov, R.M. Tanirbergenov (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0012 Tue, 31 Mar 2026 00:00:00 +0300 Estimation of Confidence Intervals for Power Distribution Reliability Indices (SAIFI and SAIDI) http://esrj.ru/index.php/esr/article/view/2026-01-013 <p>Power distribution reliability indices, system average interruption duration index (SAIDI) and system average interruption frequency index (SAIFI), depend on the number of service interruptions per year, the number of customers affected by each interruption, and power supply restoration time. All three factors are stochastic and can vary widely even when the network structure and the technical condition of the electrical equipment remain unchanged. This leads to random year-to-year fluctuations in SAIDI and SAIFI values. Determining the range of these stochastic variations is essential for comparing the indices and assessing their compliance with regulatory standards. Currently, formal methodologies for estimating confidence intervals for reliability indices remain underdeveloped both in Russia and internationally. This paper proposes an algorithm for calculating confidence intervals for SAIDI and SAIFI based on daily segmentation and numerical simulation. The proposed algorithm is validated using a case study of distribution systems in Moscow and the Moscow region.</p> A.S. Vanin, D.M. Gabdushev (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-013 Tue, 31 Mar 2026 00:00:00 +0300 New Gas Pipelines as a Tool for Enhancing Reliability of Gas Supply to Consumers http://esrj.ru/index.php/esr/article/view/2026-01-0014 <p>This paper presents a set of tools for analysis of measures to compensate for compromised operation of critical facilities by identifying and creating new transmission routes beyond the arcs of the existing gas network graph. This study details and compares algorithms for network segmentation into basic polygons with isolated elements. Possible options are explored to minimize gas shortages during incidents at critical facilities, considering the integration of new arcs. This approach assumes that the unit cost of constructing new arcs is one to two orders of magnitude higher than that of existing mainline pipelines. The proposed toolkit is validated using a case study of Russia’s Unified Gas Supply System, followed by an analysis of the findings.</p> G.K. Danilov, S.V. Vorobev (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0014 Tue, 31 Mar 2026 00:00:00 +0300 VSM-based Inverters within Automated Hybrid Energy Systems http://esrj.ru/index.php/esr/article/view/2026-01-0015 <p>The evolving isolated energy system technologies are based on grid inverters, which play an important role in the parallel operation of renewable and conventional generation facilities. Characterized by zero inertia, these inverters lack the capacity to participate in voltage and frequency regulation. Traditionally, grid inverters operate as current sources to ensure maximum possible power generation. This function requires a reference voltage source and cannot be performed if the source is disconnected. It should be noted that modern microgrids often utilize specially designed inverters that operate as a current source when an external voltage source is available, while when the reference voltage is lost, they start forming a network, which supplies the microgrid loads with energy from renewable energy sources and existing energy storage systems. Under these conditions, the network is typically formed when such an inverter switches to the voltage-source inverter (VSI) operation. It is important to note that a conventional VSI does not possess an inherent load regulating effect, unlike motor loads or other consumers, which exhibit load sensitivity to changes in voltage or frequency. This circumstance complicates the parallel operation of VSI in the network, since the VSI inverter outputs a strictly defined frequency disregarding its possible variations when the electrical loads in the electrical network change. For this reason, VSI cannot provide a regulating response to load changes. It is also crucial to note that when VSI operates in parallel with other inverters, the “primary-secondary” operation is also impractical. Instead, distributed regulation and proportional load sharing are required. One of the most promising solutions is the implementation of virtual synchronous machine (VSM) algorithms without a phase-locked loop in parallel-operating inverters connected to renewable energy sources. The paper focuses on the development of a VSM-based inverter and considers algorithms for its implementation for off-grid and grid-parallel operation. The study also analyzes network disturbances and provides a comparative analysis of the results.</p> R.N. Berdnikov, A.A. Achitaev, A.G. Vaskov (Author) Copyright (c) 2026 Energy Systems Research http://creativecommons.org/licenses/by-nc/4.0 http://esrj.ru/index.php/esr/article/view/2026-01-0015 Tue, 31 Mar 2026 00:00:00 +0300