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A special issue of Energies (ISSN 1996-1073). This special issue belongs to the section "F1: Electrical Power System".

Deadline for manuscript submissions: closed (25 May 2026) | Viewed by 8205

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Dr. Konrad Zajkowski

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Department of Energy, Faculty of Mechanical and Energy Engineering, Koszalin University of Technology, Koszalin, Poland
Interests: practical and theoretical experience in the field of electronics; electrotechnics and energetics; artificial neural networks; technical diagnostics; power theory; energy systems; electric drives; reactive power compensation and overvoltage reduction
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Special Issue Information

Dear Colleagues,

The biggest problem of modern energy is activities that reduce its impact on the environment around us. New technologies for producing clean energy are being developed, but solutions to reduce energy consumption are also sought after.

Energy consumption should be understood as physical phenomena occurring in all elements of the power system. Therefore, this topic concerns the elements of generation, transmission, and reception. The efficiency of the total power system is influenced by the efficiency of the individual elements of the system. Improving the efficiency of the power system requires the use of mathematical models and analyses.

This Special Issue of Energies aims to collate papers on mathematical models and analyses of power system circuits. In particular, we aim to focus on the following problems:

Modeling and analysis of generating systems;
Modeling and analysis of distribution systems;
Mathematical description of the electrical energy receiver;
Improving the efficiency of electricity generation, transmission, and consumption;
Modeling of dispersed energy production systems;
Intelligent control of energy flow in a dispersed energy production system;
Modeling hybrid production systems;
Mathematical description of physical phenomena in three-phase lines in the case of non-symmetric sources, unbalanced, and non-linear load;
Power compensation for three- and four-wire lines.

Dr. Konrad Zajkowski
Guest Editor

Manuscript Submission Information

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Keywords

mathematical modeling
power grids
efficiency of the power system

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Published Papers (6 papers)

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Research

21 pages, 1133 KB

Open AccessArticle

Life-Cycle Analysis and Decision Model for Utilization of Distribution Transformers

by Velichko Tsvetanov Atanasov, Dimo Georgiev Stoilov, Nikolina Stefanova Petkova and Nikola Nedelchev Nikolov

Energies 2026, 19(8), 1858; https://doi.org/10.3390/en19081858 - 10 Apr 2026

Viewed by 523

Abstract

This paper presents a comprehensive life-cycle analysis of distribution transformers, based on realized measurements of the increased power losses as a result of their long-term service under real-world conditions. The study is based on aggregated measured data from extensive fleets of oil-immersed distribution transformers characterized by diverse designs, manufacturing vintages, and service lives. The evolution of no-load losses and short-circuit losses is analyzed as a function of operational duration, structural characteristics, and the specific technologies employed for windings and magnetic core construction. Statistical models describing the variation in these losses are presented, highlighting the limitations of the static assumptions commonly utilized in power distribution network planning. On this basis, an approximation of the time evolution of the transformer’s total power and energy losses is proposed as appropriate for implementation in a life-cycle analysis model. Furthermore, the impacts of thermal loading and abnormal operating conditions—such as unbalanced loads, frequent short circuits, and repeated overheating of the transformer oil—are analyzed as drivers of accelerated transformer aging. These effects are integrated into a unified life-cycle framework, enabling the quantitative assessment of loss variations and their associated operational expenditures (OPEX). A numerical example is provided to evaluate the cost-effectiveness of “repair vs. replacement” scenarios, utilizing a discounted cash flow analysis that incorporates a carbon component. The findings establish a methodological foundation for a broader assessment of technical condition and energy performance, identifying the optimal intervention point for repair or replacement to support decision-making for Distribution System Operators (DSOs) amidst increasing requirements for efficiency and decarbonization. Full article

(This article belongs to the Special Issue Modeling and Analysis of Power Systems)

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17 pages, 2258 KB

Open AccessArticle

Modeling and Calibration Using Micro-Phasor Measurement Unit Data for Yeonggwang Substation

by Peng Li, Chung-Gang Kim, Sung-Hyun Choi, Kyung-Min Lee and Yong-Sung Choi

Energies 2026, 19(3), 834; https://doi.org/10.3390/en19030834 - 4 Feb 2026

Viewed by 514

Abstract

Against the backdrop of high-proportion renewable energy grid integration, modeling accuracy for substations incorporating wind and solar power is critical. Traditional modeling methods rely on theoretical parameters and lack sufficient accuracy. This study uses the 154 kV/23 kV Yeonggwang Substation in Jeollanam-do, South Korea (connected to three wind farms and three solar power plants, with 35 Micro-Phasor Measurement Unit (μPMU) measurement points deployed) as a case study. It investigates three-phase detailed modeling using Power System Computer Aided Design (PSCAD) and μPMU data-driven calibration. Based on substation topology and equipment parameters, a simulation model encompassing main transformers, transmission lines, renewable energy units, and loads was established. A hierarchical calibration system of “data preprocessing—parameter identification—iterative correction” was constructed, employing an iterative optimization strategy of “main grid layer—renewable energy layer—load layer.” A multi-objective optimization function centered on voltage, current, and power was developed. Verification results show that after calibration, the mean relative error rates (MRE) for voltage, current, active power and reactive power are 2.46%, 2.57%, 2.52% and 3.96% respectively, with mean error reduction rates (MERRs) of 80%, 82.75%, 81.33%, and 74.94% compared to pre-calibration values. The uniqueness of the calibration method proposed in this study lies in its use of actual μPMU measurement data to drive PSCAD model parameter calibration, achieving precise matching with the actual characteristics of the substation. This provides a reference method for modeling and digital twin construction of similar substations, demonstrating significant engineering application value. Full article

(This article belongs to the Special Issue Modeling and Analysis of Power Systems)

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21 pages, 1936 KB

Open AccessArticle

Technical and Economic Comparative Analysis of Nuclear Power Plants: AP1000 and SMR

by Natalia Kasińska, Agata Mielcarek, Jakub Sierchuła, Radosław Szczerbowski and Bartosz Ceran

Energies 2025, 18(17), 4749; https://doi.org/10.3390/en18174749 - 6 Sep 2025

Cited by 3 | Viewed by 2573

Abstract

Due to the necessity of decarbonising and transforming the Polish energy mix, topic of using nuclear power plants as one of the key low-carbon generation sources is returning to the public debate. This paper compares a large, system-wide AP1000 nuclear power plant with a new concept based on small modular reactors (SMRs), specifically NuScale 60 MW_e. Computer models of secondary loops of the generating units were used for the analysis, and basic operating parameters were determined. A consistent modelling approach was used to evaluate technical, thermodynamic, and economic indicators. As a result, a relationship between total capital expenditures and unit electricity generation cost was developed. For example, if the investment outlays, taking into account the freeze, for a large-scale nuclear power plant are USD 8 billion, then the investment outlays for an SMR power plant should be below USD 0.4 billion in order to ultimately ensure a lower or equal unit discounted cost of electric energy generation. Assuming stable power demand, the AP1000 reactor power plant remains the most cost-effective technology, offering favourable economies of scale. However, modular units are characterised by shorter lead times and greater flexibility of application in different areas of the energy industry. Therefore, in the decarbonisation process, it is essential to develop both analysed technologies in parallel. Full article

(This article belongs to the Special Issue Modeling and Analysis of Power Systems)

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18 pages, 603 KB

Open AccessEditor’s ChoiceArticle

Leveraging Dynamic Pricing and Real-Time Grid Analysis: A Danish Perspective on Flexible Industry Optimization

by Sreelatha Aihloor Subramanyam, Sina Ghaemi, Hessam Golmohamadi, Amjad Anvari-Moghaddam and Birgitte Bak-Jensen

Energies 2025, 18(15), 4116; https://doi.org/10.3390/en18154116 - 3 Aug 2025

Cited by 2 | Viewed by 1271

Abstract

Flexibility is advocated as an effective solution to address the growing need to alleviate grid congestion, necessitating efficient energy management strategies for industrial operations. This paper presents a mixed-integer linear programming (MILP)-based optimization framework for a flexible asset in an industrial setting, aiming to minimize operational costs and enhance energy efficiency. The method integrates dynamic pricing and real-time grid analysis, alongside a state estimation model using Extended Kalman Filtering (EKF) that improves the accuracy of system state predictions. Model Predictive Control (MPC) is employed for real-time adjustments. A real-world case studies from aquaculture industries and industrial power grids in Denmark demonstrates the approach. By leveraging dynamic pricing and grid signals, the system enables adaptive pump scheduling, achieving a 27% reduction in energy costs while maintaining voltage stability within 0.95–1.05 p.u. and ensuring operational safety. These results confirm the effectiveness of grid-aware, flexible control in reducing costs and enhancing stability, supporting the transition toward smarter, sustainable industrial energy systems. Full article

(This article belongs to the Special Issue Modeling and Analysis of Power Systems)

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18 pages, 5389 KB

Open AccessArticle

Novel Method of Estimating Iron Loss Equivalent Resistance of Laminated Core Winding at Various Frequencies

by Maxime Colin, Thierry Boileau, Noureddine Takorabet and Stéphane Charmoille

Energies 2025, 18(15), 4099; https://doi.org/10.3390/en18154099 - 1 Aug 2025

Viewed by 974

Abstract

Electromagnetic and magnetic devices are increasingly prevalent in sectors such as transportation, industry, and renewable energy due to the ongoing electrification trend. These devices exhibit nonlinear behavior, particularly under signals rich in harmonics. They require precise and appropriate modeling for accurate sizing. Identifying model-specific parameters, which depend on frequency, is crucial. This article focuses on a specific frequency range where a circuit model with series resistance and inductance, along with a parallel resistance to account for iron losses (

R_{iron}

), is applicable. While the determination of series elements is well documented, the determination of

R_{iron}

remains complex and debated, with traditional methods neglecting operating conditions such as magnetic saturation. To address these limitations, an innovative experimental method is proposed, comprising two main steps: determining the complex impedance of the magnetic device and extracting

R_{iron}

from the model. This method aims to provide a more precise and representative estimation of

R_{iron}

, improving the reliability and accuracy of electromagnetic and magnetic device simulations and designs. The obtained values of the iron loss equivalent resistance are different by at least 300% than those obtained by an impedance analyzer. The proposed method is expected to advance the understanding and modeling of losses in electromagnetic and magnetic devices, offering more robust tools for engineers and researchers in optimizing device performance and efficiency. Full article

(This article belongs to the Special Issue Modeling and Analysis of Power Systems)

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18 pages, 1407 KB

Open AccessArticle

Problems in Modeling Three-Phase Three-Wire Circuits in the Case of Non-Sinusoidal Periodic Waveforms and Unbalanced Load

by Konrad Zajkowski and Stanislaw Duer

Energies 2025, 18(12), 3219; https://doi.org/10.3390/en18123219 - 19 Jun 2025

Viewed by 970

Abstract

Asymmetry in the supply voltage in three-phase circuits disrupts the flow of currents. This worsens the efficiency of the distribution system and increases the problems in determining the mathematical model of the energy system. Among many power theories, the most accurate is the Currents’ Physical Components (CPC) power theory, which tries to justify the physical essence of each component. Such knowledge can be used to improve efficiency and reduce transmission losses in the power system. This article discusses the method of mathematical decomposition of current components in the case of a three-wire line connecting an asymmetric power source with linear time-invariant (LTI) loads. Special cases where irregularities appear in the results of calculations according to the CPC theory are discussed. The problem of equivalent conductance in the case of a non-zero value of the constant voltage component is discussed. The method of determining symmetrical components for periodic non-sinusoidal waveforms is also discussed. These considerations are supported by numerical examples. Full article

(This article belongs to the Special Issue Modeling and Analysis of Power Systems)

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