This paper presents an analysis of the instability of the electricity generation of renewable energy sources (RESs), specifically Digital Twins of RESs. The first part deals with the analysis of RES electricity generation around the world and Ukraine. The following chapter describes features of functioning power grids in modern conditions in Ukraine and ways to ensure the balance reliability in the power system for conditions of high-grade RES integration. The rapid increase in electricity generation RESs causes control problems of distributed power supply in the power grid. A mathematical model of the parameter controls in normal mode electric power systems for conditions with high integration of RESs is proposed in the second part. The study investigates components of the optimality criterion at the control of normal mode parameters of the electric power system with RESs. In general, digital transformation helps decarbonize the energy supply, decrease dependency on fossil fuels, and integrate renewables into power systems. A model Digital Twin (DT) of a photovoltaic system, or an exact 3D visualization, analyzing the accumulator system depending on load and generation, are presented. The problems of Digital Twin are very widely discussed, but many papers and studies are general without any practical implementations. The main part of this paper focuses on research and deals with daily electricity generation from different kinds of RESs, namely mini-hydropower stations, photovoltaic power stations, and wind power stations. Measured data of electricity generation from photovoltaic power plants, wind power plants, and mini-hydropower plants and obtained meteorological factors were used for the calculation of Spearman’s, Kendall’s, and Pearson’s correlation rank coefficients. The main contribution of this research is to determine the main metrological factors for each kind of studied RES. In the future, it will help to decide the task of forecasting power generation more presciently. Additionally, the presented model of DT RESs allows the installation and operation of grids with higher efficiency, because it can help to predict all influences, from shading up to the optimization of the battery storage system.

This study presents a comprehensive analytical framework for modeling electric vehicle (EV) charging infrastructures through a stochastic queueing-theoretic approach that explicitly incorporates critical customer behavioral dynamics. The proposed model addresses key phenomena often overlooked in classical frameworks, including customer impatience (reneging), balking behavior, feedback mechanisms, and state-dependent service threshold policies, within a finite-population, multiple-server environment. These behavioral elements reflect realistic operational scenarios in which users may opt not to join extended queues, abandon the system due to excessive delays, or return for service completion based on prior dissatisfaction. The system dynamics are formulated using a continuous-time Markov chain (CTMC), and the corresponding Chapman-Kolmogorov differential equations are derived to characterize state transitions. Employing a matrix-analytic solution technique, the steady-state probability distribution is obtained, enabling the computation of multiple performance metrics such as system occupancy, server utilization, abandonment rates, and throughput. Numerical simulations validate the model’s applicability and highlight intricate interdependencies among customer tolerance thresholds, service quality levels, and operational performance indicators. The findings offer valuable insights into capacity planning, congestion control, and service optimization, providing a rigorous decision-support framework for the design and management of EV charging networks under uncertain and dynamic user behavior. The study also outlines practical managerial implications and suggests directions for future research to enhance the adaptability and efficiency of smart charging infrastructures.

During the design of extra-high-voltage transmission lines, studies of the influence of asymmetry due to the phase difference of the parameters on its processes and the electrical network were performed. To compensate for this source of asymmetry for transmission lines longer than 100 km, a relatively simple technical means was proposed and implemented—phase transposition (change of the mutual location of phase wires in space). However, at the same time transposition causes additional capital costs in construction and reduces reliability during operation, so when designing a specific transmission line, extra-high-voltage is desirable to evaluate the effectiveness of the use of this measure in the real electricity network. Thus, under certain conditions, even for a transmission line 600 km in length, it was possible to perform either an incomplete transposition cycle, or abandon this measure altogether.

The problem of information support of the task of estimating the quality of functioning of the distribution power grids (DPG) with renewable energy sources (RES) is considered. The analysis of information support of this task is carried out. In this article is presented a two-levels monitoring and control system architecture, within the SmartGrid concept. This system implements active end-consumers behavior, optimum integration of distributed generation (DG), power storage systems of various types and capacities into electricity grids. Proposed two-levels monitoring and control system architecture will allow increasing the reliability and quality of electricity.

We showed an analysis of installed capacity and annual electricity generation of photovoltaic power stations in the world and Ukraine. The main focus of our research was on the analysis of the influence of meteorological factors on power generation. Two photovoltaic power stations of two types (terrestrial and rooftop) located in Ukraine were selected for the study. We used Spearman's rank correlation to estimate the impact of meteorological factors on solar power generation.

Magnetic levitation (maglev) systems are characterized by strong nonlinearities and inherent open-loop instability, making precise position regulation of levitating bodies exceptionally challenging. These systems are highly sensitive to model uncertainties, parameter variations, and external disturbances. This demands advanced control strategies beyond conventional PID techniques. To address these challenges, this study introduces a novel two-degree-of-freedom proportional-integral-derivative-acceleration (2-DOF PIDA) controller, specifically designed to stabilize and regulate ball position in magnetic levitation systems. The controller's structure is augmented with acceleration feedback and reference input weighting, enabling decoupled tuning for transient and steady-state performance and ensuring enhanced damping, disturbance rejection, and tracking accuracy. A core innovation of this work is integration of the controller with the enzyme action optimizer (EAO)-a recently developed bio-inspired metaheuristic algorithm that emulates adaptive catalytic behavior observed in enzymatic reactions. The EAO algorithm balances global exploration and local exploitation to efficiently optimize the 2-DOF PIDA controller parameters, minimizing the integral of absolute error (IAE) as the objective function. This optimization framework is evaluated against two recent metaheuristics: the horned lizard optimization algorithm (HLOA) and the sea-horse optimizer (SHO), using extensive time-domain simulations. Quantitative results confirm the superior performance of the proposed method, achieving 0% overshoot, a rise time of 0.0121 s, and a settling time of 0.0365 s the optimal response speed and stability among all tested algorithms. Additionally, robustness is rigorously validated under multiple scenarios of parameter perturbations, including variations in resistance and inductance, simulating real-world effects such as component aging and thermal drift. The EAO-tuned controller consistently maintains superior regulation and stability across all test cases, exhibiting high resilience to system uncertainties. Furthermore, a comprehensive comparative analysis involving 12 state-of-the-art control strategies, including PID, FOPID, and RPIDD² variants optimized via diverse evolutionary algorithms, confirms the proposed controller's dominance across all critical performance indices, including IAE, rise time, settling time, and overshoot. These findings underscore the effectiveness of combining 2-DOF control architectures with bio-inspired optimization algorithms for real-time implementation in nonlinear, unstable systems. Overall, the proposed EAO-optimized 2-DOF PIDA controller offers a computationally efficient, auto-tunable, and robust solution for high-precision maglev control.