The paper presents a comprehensive study of modern industrial battery monitoring systems with a focus on technological evolution, driven by the growing deployment of battery storage in critical infrastructures, data centers, renewable-energy installations, and microgrids. Ensuring reliable and safe operation of battery assets requires continuous monitoring not only of basic electrical parameters but also of internal degradation indicators that determine long-term performance and operational safety. The study reviews key directions including the adoption of IoT measurement clusters, cloud-enabled diagnostic platforms, digital-twin models, and machine-learning algorithms for the estimation of State of Charge, State of Health, and prediction of degradation trajectories. Additional attention is given to the increasing importance of time-series analytics and the use of large historical datasets for refining prognostic models and enhancing operational reliability in demanding industrial environments. A structured comparison of five industrial solutions— VIGILANT, Alpais, EverExceed, InfraSensing, and DFUN—is conducted to assess their sensing capabilities, modular architecture, data-processing methods, and communication interfaces. The results demonstrate that while these systems offer mature and robust hardware platforms, their analytical functions remain mostly reactive and do not fully exploit modern methods of predictive analytics. The paper concludes that future generations of battery monitoring systems should integrate cloud computing with machine learning to achieve reliable battery life prediction, improve maintainability, and support data-driven decision-making in complex energy systems, ultimately contributing to safer and more efficient deployment of energy storage systems.

Despite the many advantages of renewable energy sources, the stochastic nature of their generation creates a mismatch between electricity production and demand timing. Without appropriate storage solutions, surplus energy remains unused. Although battery energy storage systems are increasingly applied to improve the flexibility and reliability of power systems, there is still a research gap in forecasting the optimal power and storage capacity of solar power plant–battery energy storage system energy complexes operating in parallel with the grid under short-term forecasting conditions, particularly when economic aspects such as partial leasing of storage capacity are considered. Therefore, the development of energy complexes based on solar power plants with the integration of battery energy storage systems, as well as the development of corresponding computational models, becomes critical for ensuring the stability, flexibility, reliability, and efficiency of power systems. Battery energy storage systems are widely used due to their availability, high response speed, significant energy density, and sufficient power capacity; however, their cost remains relatively high. This paper proposes a methodology and a calculation model for determining the optimal forecasted capacity and the rational storage requirements of an energy complex consisting of a solar power plant and a battery energy storage system operating in parallel with the grid at constant power under short-term forecasting conditions (day-ahead or longer). The proposed approach makes it possible to minimise the costs of energy companies associated with the short-term lease of part of a battery energy storage system when they do not own one, or, if such a system is available, to lease out its unused capacity and obtain corresponding profits. The validation of the computational model uses a dataset of hourly daily power outputs of solar power plants in the Integrated Power System of Ukraine for 2018. Statistical analysis of the obtained results shows that the probability of occurrence of maximum deviations for the optimal capacity of the energy complex (5.4%), as well as for the power and capacity of the battery energy storage system (13% and 18%, respectively), does not exceed 0.05 during the year. The results confirm that the proposed methodology provides a reliable basis for determining optimal parameters of solar power plant–battery energy storage system energy complexes and enables economically efficient use of storage capacity through short-term leasing mechanisms. Although the proposed methodology is applied using solar power plant generation data for the national power system as a whole, it can also be used for individual solar power plants located in different regions and countries with different climatic conditions. Certainly, the calculated coefficients differ, but the methodology itself and the sequence of its application remain the same.

This paper examines an algorithm and evaluates the limit values of technical parameters for step-by-step management of the coverage of the forecast schedule for the aggregated generation of solar power plants (SPPs) in Ukraine, given the high share of renewable energy sources in the structure of the integrated power system of Ukraine. The relevance of the research is due to the growth in the installed capacity of SPPs, stricter requirements for forecasting accuracy, and the full financial responsibility of producers for imbalances in accordance with the current electricity market model. The problem is formulated as a special case of a hierarchically controlled quasi-dynamic power system, taking into account technological, energy and economic constraints. The objective function is defined as the minimisation of the total hourly measure of discrepancy between the forecast and actual volumes of electricity supplied, whilst ensuring power balance through energy storage systems and flexible generation. The numerical implementation was carried out using the "SOPS" software and information complex. The input data used were hourly indicators of the forecasted and actual generation of Ukraine’s solar power plants for 2021–2025, published by the state-owned enterprise "Guaranteed Buyer". Hourly, daily and monthly operating parameters for aggregated solar power generation in 2025 have been calculated. It is shown that, with an installed storage system capacity of 30,000 MWh and corresponding limitations on charge/discharge power, full coverage of the forecast schedule (IMB(t)=0) is ensured even on the day of maximum mismatch between forecast and actual generation. The required volumes of flexible generation and the operating parameters of the storage systems have been determined. The practical significance of the results lies in their potential use for operational planning of the operating modes of solar power plants, energy storage systems and flexible generation on a daily and hourly basis, as well as for justifying technical and economic decisions aimed at reducing imbalances. The results obtained confirm the effectiveness of the proposed step-by-step control algorithm and demonstrate the possibility of minimising imbalances through the rational coordination of solar power plants, energy storage systems and flexible generation capacities.

The rapid development of Integrated Energy Systems (IES), which unify diverse energy technologies such as electricity, heat, cooling, and gas, has heightened the importance of optimizing their operational modes. This paper explores the application of ternary optimization in IES, a discrete optimization approach where variables are constrained to three values: {-1, 0, +1}. Ternary optimization offers a balanced trade-off between binary and full-precision optimization, providing significant advantages in computational efficiency, memory savings, and energy efficiency. The article covers: key concepts of ternary optimization, including ternary representation, sparsity, and quantization; advantages and challenges of ternary optimization, such as reducing computational complexity and potential loss of accuracy; the application of ternary optimization for the IES. The role of ternary optimization in simplifying energy flow management, reducing computational resources, and enabling faster decision-making in dynamic environments is emphasized. Examples of using ternary optimization for energy distribution, microgrid management, integration of renewable energy sources, and energy storage systems are provided. A practical example of transforming an optimization model for IES into a ternary model using GMPL (GNU MathProg Language) is provided, demonstrating how ternary variables, constraints, and objective functions can be adapted. The paper concludes by discussing promising directions for ternary optimization in IES, including integration with AI and machine learning, development of specialized algorithms, and hardware support for ternary computations. Research underscores the potential of ternary optimization to enhance the efficiency, resilience, and scalability of IES, particularly in the context of increasing renewable energy integration and the complexity of modern energy grids.

The paper studies the transformation of energy security of distributed energy systems in the context of growing uncertainty, geopolitical shocks and volatility of fuel markets in order to form theoretical and methodological foundations for increasing the resilience, adaptability and economic efficiency of energy systems in crisis conditions. In contrast to traditional approaches focused mainly on cost minimization, a multi-criteria risk-based optimization model is proposed, combining indicators of economic efficiency (LCOE, CAPEX, OPEX), reliability of the energy system and systemic risk, which is quantified using the notional cost at risk (CVaR). The empirical base of the study is based on the analysis of long-term data of the European electricity market for 2010–2025, supplemented by scenario modelling using simulation and stochastic modelling methods to reproduce exogenous shocks. The results of the analysis confirmed the presence of a structural fracture after 2021, characterized by a transition from a stable mode of operation to a highly volatile state with increased sensitivity of the system to fuel factors. It has been established that the elasticity of the transmission of fuel shocks to electricity prices increases significantly in crisis periods (from 0.21 in 2010–2016 to 0.62 in 2021–2025), which indicates the formation of a fuel-sensitive mode of functioning of energy markets. While increasing the share of renewable energy sources increases the economic efficiency and environmental sustainability of the energy system, it does not guarantee its stability without the introduction of system flexibility tools, such as energy storage and demand management mechanisms. The results of scenario modelling and risk assessment showed that the use of these tools can reduce the level of systemic risk (CVaR) by up to 35% in crisis conditions. In addition, the effect of risk inertia (risk hysteresis) was revealed, which is manifested in the maintenance of an increased level of risk (CVaR = 0.18 in 2024–2025 compared to 0.05 in 2010–2015) even after partial stabilization of the market. This indicates the long-term nature of the impact of crisis shocks on the functioning of energy systems. The obtained results expand scientific approaches to the interpretation of energy security as a dynamic multidimensional category and substantiate the need to transition to risk-based models of energy system management.

This paper presents a comprehensive assessment of the technical and economic performance of the Integrated Power System (IPS) of Ukraine under conditions of high penetration of wind and solar power generation. The relevance of the study is driven by the rapid expansion of renewable energy sources (RES), which introduces increased generation variability, amplifies power imbalances, and complicates real-time system operation and control. The study analyzes the current state of the Ukrainian power system, including structural changes in generation and consumption under wartime conditions and the associated reduction in available capacity. Particular attention is given to daily and seasonal load variability, the stochastic nature of wind and solar generation, and the limited operational flexibility of conventional generation assets. A quantitative assessment is conducted using an optimization framework based on an economic–technological forecasting methodology for determining optimal system development and operation parameters. The model explicitly incorporates battery energy storage systems (BESS), pumped storage power plants (PSPP), constraints on renewable generation curtailment, and balancing market mechanisms. Scenario-based simulations up to 2030, assuming an increase in the RES share to 45–50%, indicate that power imbalances may rise to 600–900 MW, while reserve requirements could reach 6–7 GW. The results demonstrate that the deployment of BESS with a capacity of 1.5–2 GW can reduce imbalances by 30–40%, significantly decrease RES curtailment, and yield annual savings of €80–120 million in balancing costs. The proposed approach enables a more robust evaluation of power system performance under high RES penetration and provides a methodological basis for enhancing system flexibility, reliability, and economic efficiency. The findings can support strategic decision-making regarding the modernization and sustainable development of the IPS of Ukraine. Keywords: renewable energy sources, Integrated Power Systems, grid stability and control, power regulators, mathematical models.

The growing integration of variable renewable energy sources (VRES) challenges power system flexibility and may cause curtailment due to excess capacity, grid constraints, or operational and market factors. Power-to-Heat (PtH) technology can mitigate these issues by coupling electricity and district heating sectors, providing additional flexibility and supporting decarbonisation. This study develops a long-term generation capacity expansion model that integrates PtH and district heating system (DHS) operation to achieve balanced VRES penetration. The model includes DHS heat demand balances and links electricity and heat via thermal power plants, combined heat and power (CHP) plants, and PtH units. The methodology is applied to Ukraine’s Integrated Power System and district heating demand through 2040, employing typical daily load profiles discretised into six four-hour segments. Results demonstrate the feasibility of deploying PtH electric boilers during the non-heating season, when high RES and base load nuclear generation create surplus electricity. These boilers convert excess wind and solar power into thermal energy for district heating, displacing natural gas-fired technologies and simultaneously decarbonising electricity and heat supply.

The paper presents a comprehensive study of statistical algorithms for processing and analysing air pollution monitoring data, specifically focusing on regression and variance analysis techniques. Various methods are discussed, including the least squares method, Bartlett-Kenyon method, Kerrich method, and Fisher's criterion for assessing model adequacy. The significance of handling excessive measurement errors and identifying observations with such errors is also highlighted. The study elaborates on dispersion analysis, utilising variance array formation, calculation, and hypothesis testing with Bartlett's, Cochrane, and Neumann-Pearson criteria. A significant portion of the research is devoted to a matrix algorithm for air pollution data analysis, involving linear transformations and similarity measures. Additionally, the paper evaluates the air pollution monitoring system in Kyiv, Ukraine, comparing different observation posts and proposing visualisation techniques using numerical and colour matrices. The use of cluster analysis for system operation insights is suggested. While the regression and variance methods are presented primarily as a theoretical toolkit, the matrix-based comparison is demonstrated on real monitoring data from four Kyiv observation posts: the correct functioning of the selected posts, expressed as the share of days with a complete daily sampling programme, ranged from 56.6 to 76.3

Deterministic and probabilistic models of measured quantities, processes, and fields in production process control systems, as well as physical and probabilistic measures, enable the formation of measurement results and confer them the properties of objectivity and reliability. The issue of improving and developing models and measures in measurement methodology plays an increasingly important role in achieving high measurement accuracy in control systems and the reliability of decision-making by expert systems in production processes. The measurement result is formed by many factors, most of which are random in nature. The stochastic approach in measurement theory is particularly important for the measurement of probabilistic physical quantities and for the construction of decision rules for expert systems. Probabilistic measures play a key role in both the measurement of physical quantities and the construction of decision rules when using a stochastic approach. The main contribution of this paper is a measure-centred formulation of stochastic measurement and decision support, in which physical and probabilistic measures are treated as an explicit intermediate layer between the model and the algorithm. This is not presented as a new entropy or distance metric, but as a methodological integration that clarifies uncertainty handling, improves traceability of measurement results, and supports decision rules for production-process monitoring. The approach is illustrated on air-quality monitoring data from a real control system.

Introduction. The rapid expansion of electric vehicles (EVs) has raised pressing concerns about the disposal of lithium-ion batteries. Their repurposing for second-life applications has off ered a cost-eff ective and environmentally sound solution, contributing to grid stability and advancing the circular economy. In the Ukrainian context, second-life batteries have presented additional value by enhancing energy security and facilitating the integration of renewable energy sources. Problem Statement. Despite these advantages, the large-scale deployment of second-life EV batteries in Ukraine has faced signifi cant technical, economic, and regulatory challenges. The absence of standardized stateof-health assessment methods, well-defi ned integration strategies, and comprehensive market analysis has necessitated a structured SWOT analysis. Purpose. This study aims to evaluate the potential for deploying second-life EV batteries in Ukraine through a SWOT analysis and to determine their suitability for grid integration and energy storage applications. Materials and Methods. A SWOT analysis has been employed as the primary methodological framework, supplemented by market assessment, regulatory review, and economic feasibility evaluation. The analysis has drawn upon international case studies, policy documents, and empirical data on battery degradation, performance, and lifecycle extension.

This study presents a novel methodology for determining zonal electricity generation and capacity requirements corresponding to forecasted annual production in an integrated power system (IPS). The proposed model combines the statistical analysis of historical daily load patterns with a calibration technique to translate forecast total demand into zonal powers (base, semi-peak and peak). A representative reference daily electrical load graph (ELG) is selected from retrospective data using least squares criteria, and a calibration factor α = Wx/Wie scales its zonal outputs to match the forecasted annual generation Wx. The innovation lies in this combination of historical ELG identification and calibration for accurate zonal power prediction. Applying the model to Ukrainian IPS data yields high accuracy: a zonal power error below 1.02% and a generation error below 0.39%. Key contributions include explicitly stating the research questions and hypotheses, providing a schematic procedural description and discussing model limitations (e.g., treatment of renewable variability and omission of meteorological/astronomical factors). Future work is outlined to incorporate unforeseen factors (e.g., post-war demand shifts, electric vehicle adoption) into the forecasting framework.

The accurate forecasting of solar power generation is becoming increasingly important in the context of renewable energy integration and intelligent energy management. The variability of solar radiation, caused by changing meteorological conditions and diurnal cycles, complicates the planning and control of photovoltaic systems and may lead to imbalances in supply and demand. This study aims to identify the most effective exponential smoothing approach for real-world PV power forecasting using actual hourly generation data from a 9 MW solar power plant in the Kyiv region, Ukraine. Four exponential smoothing techniques are analysed: Classic, a Modified classic adapted to daily generation patterns, Holt’s linear trend method, and the Holt–Winters seasonal method. The models were implemented in Microsoft Excel (Microsoft 365, version 2408) using real measurement data collected over six months. Forecasts were generated one hour ahead, and optimal smoothing constants were identified via RMSE minimisation using the Solver Add-in. Substantial differences in forecasting accuracy were observed. The Classic simple exponential smoothing model performed worst, with an RMSE of 1413.58 kW and nMAE of 9.22%. Holt’s method improved trend responsiveness (RMSE = 1052.79 kW, nMAE = 5.96%), but still lacked seasonality modelling. Holt–Winters, which incorporates both trend and seasonality, achieved a strong balance (RMSE = 1031.00 kW, nMAE = 3.7%). The best performance was observed with the modified simple exponential smoothing method, which captured the daily cycle more effectively (RMSE = 166.45 kW, nMAE = 0.84%). These results pertain to a one-step-ahead evaluation on a single plant and an extended validation window; accuracy is dependent on meteorological conditions, with larger errors during rapid cloud transi. The study identifies forecasting models that combine high accuracy with structural simplicity, intuitive implementation, and minimal parameter tuning—features that make them well-suited for integration into lightweight real-time energy control systems, despite not being evaluated in terms of runtime or memory usage. The modified simple exponential smoothing model, in particular, offers a high degree of precision and interpretability, supporting its integration into operational PV forecasting tools.

The integration of distributed energy resources (DERs)—such as wind and solar power plants, cogeneration units, and energy-storage systems, can potentially reduce carbon emissions, improve power quality, and enhance both reliability and energy efficiency. While DER deployment may lessen the need for conventional grid expansion, managing a potentially large number of generation sources poses complex challenges for network operation and secure, efficient control. These challenges can be effectively addressed by microgrids. Microgrids are regarded as one of the most promising solutions for incorporating renewable-based distributed generation into the power system. They strengthen network reliability and resilience by ensuring uninterrupted electricity supply to consumers. The traditional model of energy production and use has evolved toward energy sharing, driven by the growing penetration of DERs. These changes transform passive consumers into active prosumers who not only consume but also exchange surplus electricity generated from DERs with the grid or with other consumers. Over the past decade the microgrid concept has been vigorously explored and developed, and it is now a practical reality. Several microgrids can operate in an interconnected mode, forming a microgrid cluster in which each individual microgrid (or the cluster as a whole) benefits from cooperation. In the coming years the existing power system is expected to transform into one comprising many microgrids. This study analyses scientific publications on microgrid clusters based on DERs, presents results of an assessment of possible cluster architectures, and focuses on control and communication structures and strategies, highlighting their advantages and drawbacks. Keywords: distributed energy resources, microgrid cluster, microgrid, control, monitoring, architecture, protocol, communication, network.