Energies

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36 pages, 5440 KiB

Open AccessArticle

Compensation of Budeanu’s Reactive and Complemented Reactive Currents in Extended Budeanu Theory in 3-Phase 4-Wire Systems Powered by Symmetrical Nonsinusoidal Voltage Source

by Zbigniew Sołjan, Tomasz Popławski, Marek Kurkowski and Maciej Zajkowski

Energies 2024, 17(9), 2020; https://doi.org/10.3390/en17092020 - 25 Apr 2024

Viewed by 589

Abstract

The result of continuous efforts in the development of power theory, Budeanu’s power theory was successfully extended. The mathematical description that has been proposed is based on another concept, namely the Currents’ Physical Components (CPC) theory. With CPC theory, it was possible to [...] Read more.

The result of continuous efforts in the development of power theory, Budeanu’s power theory was successfully extended. The mathematical description that has been proposed is based on another concept, namely the Currents’ Physical Components (CPC) theory. With CPC theory, it was possible to describe, in the original Budeanu theory, the components of the load current, including the Budeanu distortion current. The Budeanu distortion current can have a maximum of five components associated with different physical phenomena and related to the equivalent parameters of the load. This article discusses passive compensation, which provides compensation for the Budeanu reactive current and the Budeanu complemented reactive current due to the known equivalent load parameters associated with the reactance elements. In addition, the article refers to a very important aspect when determining the parameters of a passive compensator, i.e., choosing parameters in such a way that the compensator simultaneously compensates for the reactive current and the unbalanced current. The article presents five methods relating to the determination of compensator parameters. Two methods are related to the reactive current compensation only for the first harmonic without affecting the unbalanced current. The next three methods relate to the compensation of the Budeanu reactive current and the consideration of the unbalanced current. Calculations and simulations were performed for all five methods, the results of which are presented and analyzed in this publication. The Matlab/Simulink R2023a environment was used as the calculation and simulation software. Full article

(This article belongs to the Special Issue Thermo-Mechanical and Electrical Measurements for Energy Systems)

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30 pages, 5026 KiB

Open AccessArticle

Budeanu’s Distortion Power Components Based on CPC Theory in Three-Phase Four-Wire Systems Supplied by Symmetrical Nonsinusoidal Voltage Waveforms

by Zbigniew Sołjan and Tomasz Popławski

Energies 2024, 17(5), 1043; https://doi.org/10.3390/en17051043 - 22 Feb 2024

Cited by 1 | Viewed by 719

Abstract

Budeanu’s power theory, in its fundamental version, describes single-phase sinusoidal and nonsinusoidal systems. Over time, this elementary description has been extended to three-phase three-wire and four-wire systems, regardless of power conditions. Initially, three-phase systems were considered as three independent single-phase systems. A distinct [...] Read more.

Budeanu’s power theory, in its fundamental version, describes single-phase sinusoidal and nonsinusoidal systems. Over time, this elementary description has been extended to three-phase three-wire and four-wire systems, regardless of power conditions. Initially, three-phase systems were considered as three independent single-phase systems. A distinct approach was introduced by Czarnecki in his power theory (Currents’ Physical Components—CPC). The energy description and reference of the equivalent parameters of the load are comprehensive in the context of three-phase systems; Czarnecki treats such systems as a whole. This paper introduces a mathematical model to expand the basic Budeanu theory for three-phase four-wire (3-p 4-w) systems powered by symmetrical and nonsinusoidal voltage sources. The proposed approach is based on mutual elements between the fundamental Budeanu theory and the CPC theory, treating the 3-p 4-w system as a whole. In the extended Budeanu theory model, equations for the Budeanu reactive current and the Budeanu complemented reactive current are derived. The article also demonstrates their orthogonality concerning the remaining components, indicating that each of the seven components can exist independently of the others. Furthermore, in the extended Budeanu theory, it is possible to identify which equivalent parameters of the load are responsible for the individual currents (powers) and which components are associated with the total distortion power proposed by Budeanu in 1927. All of the calculations were performed in Matlab/Simulink 2023b software. Full article

(This article belongs to the Special Issue Thermo-Mechanical and Electrical Measurements for Energy Systems)

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17 pages, 5485 KiB

Open AccessArticle

Determination of Changes in Flux Density of Transformer Steel Sheets

by Witold Mazgaj, Michal Sierzega and Marcin Tomczyk

Energies 2024, 17(1), 171; https://doi.org/10.3390/en17010171 - 28 Dec 2023

Viewed by 674

Abstract

Magnetic fields in transformer cores are typically assumed to be one-dimensional fields, thus allowing magnetization processes to be regarded as axial magnetization. However, in the core corners or T-joint points of medium- and high-power rating transformers, the magnetic lines have different directions with [...] Read more.

Magnetic fields in transformer cores are typically assumed to be one-dimensional fields, thus allowing magnetization processes to be regarded as axial magnetization. However, in the core corners or T-joint points of medium- and high-power rating transformers, the magnetic lines have different directions with respect to the rolling direction. This paper describes a method that allows changes in the flux density of transformer steel sheets to be calculated for any magnetization direction. These changes are assumed to depend only on certain limiting hysteresis loops assigned separately to the rolling and transverse directions of a tested transformer sheet, where these loops depend on the magnetization direction on the sheet plane. The selection of coefficients that define the limiting hysteresis loops for several magnetization directions is described, and the condition for the flux density saturation is considered. The resultant flux density in a specified magnetization direction is the geometric sum of the corresponding flux densities assigned to both the rolling and transverse directions. The limiting and partial hysteresis loops determined based on the proposed method for several magnetization directions are compared with analogous measured loops. Additionally, a comparison of the calculated hysteresis loops with loops showing changes in the resultant flux density for several magnetization direction is presented. Full article

(This article belongs to the Special Issue Thermo-Mechanical and Electrical Measurements for Energy Systems)

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18 pages, 7024 KiB

Open AccessArticle

Direct Steady-State Calculation of Electromagnetic Devices Using Field-Circuit Models

by Marcin Jaraczewski, Tadeusz J. Sobczyk and Adam Warzecha

Energies 2023, 16(13), 4993; https://doi.org/10.3390/en16134993 - 27 Jun 2023

Viewed by 803

Abstract

Field-circuit models are very often used to model electromagnetic devices with conductive and non-linear magnetic materials. The numerical calculations of the field in the magnetic material must be combined with an equation of an external coil placed in the magnetic circuit. This means [...] Read more.

Field-circuit models are very often used to model electromagnetic devices with conductive and non-linear magnetic materials. The numerical calculations of the field in the magnetic material must be combined with an equation of an external coil placed in the magnetic circuit. This means that the partial differential equations of the electromagnetic field in non-linear conductive materials and the non-linear ordinary differential equations must be solved together. Effective algorithms for solving such problems are still being developed. The article presents an algorithm directly providing the steady state solution without the simulation of transients. The basic assumption is that the solution can be predicted as a periodic time and space function, which is represented by appropriate Fourier series. The developed algorithm uses discrete partial differential operators for time and space derivatives. It allows us to create finite difference equations directly from the field and circuit equations, which take the form of algebraic equations, generally non-linear. This is a unique approach developed by us, which till now did not exist (and is not mentioned) in the literature. That algorithm is tested on a simple case of a solenoid coil with a ferromagnetic and conductive cylindrical core, in 2D space of radius and time. The calculation results confirm the effectiveness of the proposed approach both qualitatively, with regard to physical phenomena in ferromagnetic and conductive material, and quantitatively, in comparison with the results from specialized commercial software. Full article

(This article belongs to the Special Issue Thermo-Mechanical and Electrical Measurements for Energy Systems)

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28 pages, 15827 KiB

Open AccessArticle

Medium-Voltage Testbed for Comparing Advanced Power Line Sensors vs. Measurement Transformers with Electrical Grid Events

by Emilio C. Piesciorovsky, R. J. Bruce Warmack and Yarom Polsky

Energies 2023, 16(13), 4944; https://doi.org/10.3390/en16134944 - 26 Jun 2023

Cited by 1 | Viewed by 1389

Abstract

Electrical utilities have relied upon potential transformers (PTs) and current transformers (CTs) for very accurate metering and to provide reliable signals for protective relays. Less expensive alternative sensing technologies offer the possibility of wider deployment, particularly in grids that employ distributed energy resources. [...] Read more.

Electrical utilities have relied upon potential transformers (PTs) and current transformers (CTs) for very accurate metering and to provide reliable signals for protective relays. Less expensive alternative sensing technologies offer the possibility of wider deployment, particularly in grids that employ distributed energy resources. In this work, the performance of an advanced medium-voltage sensor is compared with that of a reference PT and a CT and experimentally evaluated for different power grid scenarios on an advanced outdoor power line sensor testbed at the U.S. Department of Energy’s Oak Ridge National Laboratory. The sensor is based on a capacitive divider for voltage monitoring and a Rogowski coil with an integrator for current monitoring. The advanced outdoor power line sensor testbed has a real-time simulator that is used to generate transient scenarios (e.g., electrical faults, capacitor bank operation, and service restoration), while the analog signals are recorded by the same high-resolution power meter. The behaviors of analog signals, harmonic components, total harmonic distortion, and crest factors are assessed for this power line sensor and compared with those of the reference PT/CT because of the absence of testing standards for advanced outdoor power line sensors. Full article

(This article belongs to the Special Issue Thermo-Mechanical and Electrical Measurements for Energy Systems)

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19 pages, 4777 KiB

Open AccessFeature PaperArticle

Study and Analysis of Dynamics and Energy Efficiency of Arc Steelmaking Furnace Electrical Mode with a Fuzzy Control Algorithm

by Yaroslav Paranchuk, Daniel Jancarczyk and Pawel Falat

Energies 2023, 16(8), 3451; https://doi.org/10.3390/en16083451 - 14 Apr 2023

Cited by 2 | Viewed by 1233

Abstract

A review of the control laws (models) of alternating current arc steelmaking furnaces’ (ASF) electric modes (EM) is carried out. A phase-symmetric three-component additive fuzzy model of electrode movement control signal formation is proposed. A synthesis of fuzzy inference systems based on the [...] Read more.

A review of the control laws (models) of alternating current arc steelmaking furnaces’ (ASF) electric modes (EM) is carried out. A phase-symmetric three-component additive fuzzy model of electrode movement control signal formation is proposed. A synthesis of fuzzy inference systems based on the Sugeno model for the implementation of the proposed additive three-component fuzzy law of arc length control is performed. A structural computer Simulink model of the EM control system in a high-power arc steelmaking furnace of the DSP-200 type with an ARDM-T-12 arcs power regulator is created. Computer research into control dynamics indicators under the influence of deterministic perturbations and also integral indicators of energy efficiency when handling stationary random arc lengths fluctuations (corresponding to various technological stages of melting) are carried out. A comparative analysis of dynamics indicators, energy efficiency, and electromagnetic compatibility of the proposed fuzzy and known differential model of ASF arc lengths control is carried out. The implementation of the proposed fuzzy three-component additive control model in comparison with the existing deterministic differential one reduces the dispersion of voltages, currents, and arcs powers, reduces electrical losses in an arc furnace high-power network by 10–22% and increases the average arc power by 0.9–1.5%. Full article

(This article belongs to the Special Issue Thermo-Mechanical and Electrical Measurements for Energy Systems)

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23 pages, 3823 KiB

Open AccessArticle

Sub-Optimal Stabilizers of the Pendubot Using Various State Space Representations

by Dariusz Pazderski, Paweł Parulski, Patryk Bartkowiak and Przemysław Herman

Energies 2022, 15(14), 5146; https://doi.org/10.3390/en15145146 - 15 Jul 2022

Cited by 2 | Viewed by 1170

Abstract

This paper considers the issue of linear-quadratic regulator (LQR) design for nonlinear systems with the use of smooth state and input transformations. The proposed design methodology is considered in the stabilisation task of the Pendubot, which is based on the concept of feedback [...] Read more.

This paper considers the issue of linear-quadratic regulator (LQR) design for nonlinear systems with the use of smooth state and input transformations. The proposed design methodology is considered in the stabilisation task of the Pendubot, which is based on the concept of feedback equivalent control systems. It turns out that it is possible to find a controller that ensures comparable dynamics of the closed-loop system in the vicinity of the set point regardless of the state-space representation adopted. In addition, the synthesis of suboptimal controllers according to the LQR strategy ensuring equal dynamics at the equilibrium point is presented. The properties of the studied controllers were investigated in a simulation environment and using experimental tests. The detailed forms of transformations and linear approximations given can be regarded as ready-made procedures that can be applied to stabilise similar mechanical systems in robotics. Full article

(This article belongs to the Special Issue Thermo-Mechanical and Electrical Measurements for Energy Systems)

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27 pages, 967 KiB

Open AccessArticle

Exploiting the Moth–Flame Optimization Algorithm for Optimal Load Management of the University Campus: A Viable Approach in the Academia Sector

by Ibrar Ullah, Irshad Hussain, Khalid Rehman, Piotr Wróblewski, Wojciech Lewicki and Balasubramanian Prabhu Kavin

Energies 2022, 15(10), 3741; https://doi.org/10.3390/en15103741 - 19 May 2022

Cited by 9 | Viewed by 1423

Abstract

Unbalanced load condition is one of the major issues of all commercial, industrial and residential sectors. Unbalanced load means that, when different loads are distributed on a three-phase four-wire system, unequal currents pass through the three phases. Due to it, a heavy current [...] Read more.

Unbalanced load condition is one of the major issues of all commercial, industrial and residential sectors. Unbalanced load means that, when different loads are distributed on a three-phase four-wire system, unequal currents pass through the three phases. Due to it, a heavy current flows in the neutral wire, which not only adds the losses, but also puts constraints on three phases’ loads. In this paper, we have presented a practical approach for load balancing. First, we have considered the existing three-phase load system where the supply is a three-phase unbalanced supply. Before balancing the load, it is necessary to compensate the current in neutral wire. A nature-inspired moth–flame optimization (MFO) algorithm is used to propose a scheme for balancing of current in neutral wire. The information of a distributed single-phase load was used to balance the currents in a three-phase system. The feeder phase and load profiles of each single-phase load are used to reconfigure the network using an optimization process. By balancing the current of three phases, the current of the neutral conductor in substation transformers was reduced to almost zero. Full article

(This article belongs to the Special Issue Thermo-Mechanical and Electrical Measurements for Energy Systems)

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