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Keywords = RL electrical circuit

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44 pages, 5593 KB  
Review
Nanoscale Cross-Sectional Characterization of Thin Layers in Material Assemblies
by Frédéric Addiego, Rutuja Bhusari, Julien Bardon, Sascha Scholzen and Zainhia Kaidi
Nanomaterials 2025, 15(11), 840; https://doi.org/10.3390/nano15110840 - 30 May 2025
Cited by 2 | Viewed by 2970
Abstract
Thin-film assemblies containing an adhesion layer (AdL) or a release layer (RL) with nanoscale thickness are widely used in semiconductors, electrical circuit boards, optical and optoelectronic devices, photodiodes, and photonics applications. Current environmental concerns and technological demands necessitate continuous advancements in these nano-AdLs [...] Read more.
Thin-film assemblies containing an adhesion layer (AdL) or a release layer (RL) with nanoscale thickness are widely used in semiconductors, electrical circuit boards, optical and optoelectronic devices, photodiodes, and photonics applications. Current environmental concerns and technological demands necessitate continuous advancements in these nano-AdLs and nano-RLs in terms of formulation, design, functionality, and durability. Developing these nano-layers relies on understanding their structural properties, which is challenging because only characterization tools with nanoscale or sub-nanoscale lateral resolution can be employed. The aim of this review is to provide an overview of the current techniques and methods available for characterizing the structural properties of nano-layers in cross-section. Emphasis is placed on sample preparation methods, the fundamental principles, advantages, and limitations of various techniques, and examples from the existing literature. First, selecting the appropriate characterization technique depends on the required lateral resolution—it must be finer than the size of the structural feature of interest. A high lateral resolution relative to this structural feature translates to more accurate characterization, enabling effective profiling and mapping analysis. Subsequently, it is important to optimize sample preparation regarding shape, dimensions, and surface roughness, while minimizing artifacts. Combining techniques that offer complementary structural information—such as morphological, chemical, and nanomechanical data—is recommended to gain a comprehensive understanding of the nano-layer’s structure and properties. This is especially important when utilizing 3D characterization methods. It is worth noting that few examples of cross-sectional analysis for nano-AdLs and nano-RLs are available in the literature, highlighting the need for further nanoscale investigations. This review aims to serve as a practical guide for scientists, helping them identify suitable characterization procedures based on the specific structural information they seek to obtain. Full article
(This article belongs to the Section Synthesis, Interfaces and Nanostructures)
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22 pages, 677 KB  
Article
The LDG Finite-Element Method for Multi-Order FDEs: Applications to Circuit Equations
by Mohammad Izadi, Hari Mohan Srivastava and Mahdi Kamandar
Fractal Fract. 2025, 9(4), 230; https://doi.org/10.3390/fractalfract9040230 - 5 Apr 2025
Cited by 7 | Viewed by 1078
Abstract
The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the [...] Read more.
The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the Liouville–Caputo fractional derivative and upwind numerical fluxes to discretize governing equations while preserving stability. The method was validated through benchmark test cases, including comparisons with analytical solutions and established numerical techniques (e.g., Gegenbauer wavelets and Dickson collocation). The results demonstrate that the LDG method achieves high-accuracy solutions (e.g., with a relatively large time step size) and reduced computational costs, which are attributed to its element-wise formulation. These findings position LDG as a promising tool for complex scientific and engineering applications, particularly in modeling fractional-order systems such as RL, RLC circuits, and other electrical circuit equations. Full article
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18 pages, 3827 KB  
Article
Adaptive Joint Sigma-Point Kalman Filtering for Lithium-Ion Battery Parameters and State-of-Charge Estimation
by Houda Bouchareb, Khadija Saqli, Nacer Kouider M’sirdi and Mohammed Oudghiri Bentaie
World Electr. Veh. J. 2024, 15(11), 532; https://doi.org/10.3390/wevj15110532 - 18 Nov 2024
Viewed by 2044
Abstract
Precise modeling and state of charge (SoC) estimation of a lithium-ion battery (LIB) are crucial for the safety and longevity of battery systems in electric vehicles. Traditional methods often fail to adapt to the dynamic, nonlinear, and time-varying behavior of LIBs under different [...] Read more.
Precise modeling and state of charge (SoC) estimation of a lithium-ion battery (LIB) are crucial for the safety and longevity of battery systems in electric vehicles. Traditional methods often fail to adapt to the dynamic, nonlinear, and time-varying behavior of LIBs under different operating conditions. In this paper, an advanced joint estimation approach of the model parameters and SoC is proposed utilizing an enhanced Sigma Point Kalman Filter (SPKF). Based on the second-order equivalent circuit model (2RC-ECM), the proposed approach was compared to the two most widely used methods for simultaneously estimating the model parameters and SoC, including a hybrid recursive least square (RLS)-extended Kalman filter (EKF) method, and simple joint SPKF. The proposed adaptive joint SPKF (ASPKF) method addresses the limitations of both the RLS+EKF and simple joint SPKF, especially under dynamic operating conditions. By dynamically adjusting to changes in the battery’s characteristics, the method significantly enhances model accuracy and performance. The results demonstrate the robustness, computational efficiency, and reliability of the proposed ASPKF approach compared to traditional methods, making it an ideal solution for battery management systems (BMS) in modern EVs. Full article
(This article belongs to the Special Issue Lithium-Ion Battery Diagnosis: Health and Safety)
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21 pages, 10788 KB  
Article
Resilient Reinforcement Learning for Voltage Control in an Islanded DC Microgrid Integrating Data-Driven Piezoelectric
by Kouhyar Sheida, Mohammad Seyedi, Muhammad Ali Afridi, Farzad Ferdowsi, Mohammad J. Khattak, Vijaya K. Gopu and Tyson Rupnow
Machines 2024, 12(10), 694; https://doi.org/10.3390/machines12100694 - 1 Oct 2024
Cited by 10 | Viewed by 2222
Abstract
This research study presents a resilient control scheme for an islanded DC microgrid (DC MG) integrating solar photovoltaic (PV), battery storage (BESS), and piezoelectric (PE) energy harvesting modules. The microgrid (MG) case study represents an energy hub designed to provide electricity for lighting [...] Read more.
This research study presents a resilient control scheme for an islanded DC microgrid (DC MG) integrating solar photovoltaic (PV), battery storage (BESS), and piezoelectric (PE) energy harvesting modules. The microgrid (MG) case study represents an energy hub designed to provide electricity for lighting systems in transportation, roads, and other infrastructure. To enhance practicality, the PE is modeled using the real data captured from a traffic simulator. The proposed reinforcement learning (RL) method was tested against four severe and unexpected failure scenarios, including short circuit at the load side, sudden and severe change of load, open circuit, and converter failure. The performance of the controller was quantitatively compared with a conventional PI controller. The results show marginal improvement in one scenario and significant improvement in the other three, suggesting that the proposed scheme is a robust candidate for microgrids with high levels of uncertainty, such as those involving solar and PE harvesters. Full article
(This article belongs to the Special Issue Applications of Piezoelectric Devices and Materials)
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26 pages, 8471 KB  
Article
Impact of Data Corruption and Operating Temperature on Performance of Model-Based SoC Estimation
by King Hang Wu, Mehdi Seyedmahmoudian, Saad Mekhilef, Prashant Shrivastava and Alex Stojcevski
Energies 2024, 17(19), 4791; https://doi.org/10.3390/en17194791 - 25 Sep 2024
Viewed by 1419
Abstract
Electric vehicles (EVs) are becoming popular around the world. Making a lithium battery (LIB) pack with a robust battery management system (BMS) for an EV to operate under different complex environments is both a challenge and a requirement for engineers. A BMS can [...] Read more.
Electric vehicles (EVs) are becoming popular around the world. Making a lithium battery (LIB) pack with a robust battery management system (BMS) for an EV to operate under different complex environments is both a challenge and a requirement for engineers. A BMS can intelligently manage LIB systems by estimating the battery state of charge (SoC). Due to the nonlinear characteristics of LIB, influenced by factors such as the harsh environment and data corruption caused by electromagnetic interference (EMI) inside electric vehicles, SoC estimation should consider available capacity, model parameters, operating temperature and reductions in data sampling time. The widely used model-based algorithms, such as the extended Kalman filter (EKF) have limitations. Therefore, a detailed review of the balance between temperature, data sampling time, and different model-based algorithms is necessary. Firstly, a state of charge—open-circuit voltage (SoC-OCV) curve of LIB is obtained by the polynomial curve fitting (PCF) method. Secondly, a first-order RC (1-RC) equivalent circuit model (ECM) is applied to identify the battery parameters using a forgetting factor-based recursive least squares algorithm (FF-RLS), ensuring accurate internal battery parameters for the next step of SoC estimation. Thirdly, different model-based algorithms are utilized to estimate the SoC of LIB under various operating temperatures and data sampling times. Finally, the experimental data by dynamic stress test (DST) is collected at temperatures of 10 °C, 25 °C, and 40 °C, respectively, to verify and analyze the impact of operating temperature and data sampling time to provide a practical reference for the SoC estimation. Full article
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20 pages, 866 KB  
Article
Probabilistic Analysis of an RL Circuit Transient Response under Inductor Failure Conditions
by Muhammad Farooq-i-Azam, Zeashan Hameed Khan, Syed Raheel Hassan and Rameez Asif
Electronics 2022, 11(23), 4051; https://doi.org/10.3390/electronics11234051 - 6 Dec 2022
Cited by 2 | Viewed by 3504
Abstract
We apply probability theory for the analysis of the exponentially decaying transient response of a resistor inductor electric circuit with partially known value of the inductance due to its failure. The inductance is known to be within a continuous interval, and the exact [...] Read more.
We apply probability theory for the analysis of the exponentially decaying transient response of a resistor inductor electric circuit with partially known value of the inductance due to its failure. The inductance is known to be within a continuous interval, and the exact value is unknown, which may happen as a result of inductor faults due to a variety of factors—for example, when the circuit is deployed in an unusually harsh environment. We consider the inductance as a continuous uniform random variable for our analysis, and the transient voltage is treated as a derived random variable which is a function of the inductance random variable. Using this approach, a probability model of the transient voltage at the output terminals of the circuit is derived in terms of its cumulative distribution function and the probability density function. In our work, we further elaborate that the probability model of any other circuit parameter can also be obtained in a similar manner, or it can be derived from the transient voltage probability model. This is demonstrated by getting the model of a branch current from the probability distribution of the transient voltage. Usage of the probability model is demonstrated with the help of examples. The probability of the transient voltage falling in a certain interval at a given instant of time is evaluated. Similarly, the probability values of the branch current in different intervals are determined and analyzed. The derived probability model is checked for its validity and correctness as well. The model is found to be useful for probabilistic analysis of the circuit. Full article
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16 pages, 3005 KB  
Article
An Inline V-Band WR-15 Transition Using Antipodal Dipole Antenna as RF Energy Launcher @ 60 GHz for Satellite Applications
by Atul Varshney, Vipul Sharma, Issa Elfergani, Chemseddine Zebiri, Zoran Vujicic and Jonathan Rodriguez
Electronics 2022, 11(23), 3860; https://doi.org/10.3390/electronics11233860 - 23 Nov 2022
Cited by 19 | Viewed by 2957
Abstract
This article demonstrates the design and development of WR-15 transition using an antipodal microstrip dipole antenna at a frequency of 60 GHz for space applications. An inline microstrip line to rectangular waveguide (MS-to-RWG) transition is proposed for the V-band (50–75 GHz) functioning. The [...] Read more.
This article demonstrates the design and development of WR-15 transition using an antipodal microstrip dipole antenna at a frequency of 60 GHz for space applications. An inline microstrip line to rectangular waveguide (MS-to-RWG) transition is proposed for the V-band (50–75 GHz) functioning. The RF energy is coupled and launched through an antipodal dipole microstrip antenna. Impedance matching and mode matching between the MS line and dipole are achieved by a quarter wave impedance transformer. This results in the better performance of transitions in terms of insertion loss (IL > −0.50 dB) and return loss (RL < −10 dB) for a 40.76% relative bandwidth from 55.57 GHz to 65.76 GHz. The lowest values of IL and RL at 60 GHz are −0.09 dB and −32.05 dB, respectively. A 50 μm thick double-sided etched InP substrate material is used for microstrip antipodal dipole antenna design. A back-to-back designed transition has IL > −0.70 dB and RL < −10 dB from 54.29 GHz to 64.07 GHz. The inline transition design is simple in structure, easy to fabricate, robust, compact, and economic; occupies less space because the transition size is exactly equal to the WR-15 length; and is prepared using an InP substrate with high permittivity of 12.4 and thickness of 50 μm. Thus, the devices have the lowest insertion loss value and lowest return loss (RL) value, of <−31 dB, as compared to earlier designs in the literature. Therefore, the proposed design has the lowest radiation loss (because of thickness) and highest transmission (about 97% power). Easy impedance matching using only a single-step quarter-wave transformer between the antipodal dipole antenna and 50 Ω microstrip line (avoiding the multi-sections’ demand and microstrip line’s tedious complexity) is needed. Since, when the InP dielectric substrate is inserted in WR-15, the waveguide becomes a dielectric-filled waveguide (DFWG), and its characteristics impedance reduces to 143 Ω from 505 Ω at an operating frequency of 60 GHz. In the proposed transition, no ridge waveguide or waveguide back-short is utilized in WR-15. The microstrip line did not contain any via, fence, window, screw, galvanic structure, post, etc. Hence, the transition is suitable for high-data-rate 5G communications, satellite remote sensing, missile navigation, MIC/MMIC circuits’ characterization, and mm-wave applications. The electrical equivalent model of the proposed design has been generated and validated using an RF circuit simulator and was found to have excellent matching. Full article
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21 pages, 3936 KB  
Article
Application of a Machine Learning Algorithm for Evaluation of Stiff Fractional Modeling of Polytropic Gas Spheres and Electric Circuits
by Fawaz Khaled Alarfaj, Naveed Ahmad Khan, Muhammad Sulaiman and Abdullah M. Alomair
Symmetry 2022, 14(12), 2482; https://doi.org/10.3390/sym14122482 - 23 Nov 2022
Cited by 17 | Viewed by 2869
Abstract
Fractional polytropic gas sphere problems and electrical engineering models typically simulated with interconnected circuits have numerous applications in physical, astrophysical phenomena, and thermionic currents. Generally, most of these models are singular-nonlinear, symmetric, and include time delay, which has increased attention to them among [...] Read more.
Fractional polytropic gas sphere problems and electrical engineering models typically simulated with interconnected circuits have numerous applications in physical, astrophysical phenomena, and thermionic currents. Generally, most of these models are singular-nonlinear, symmetric, and include time delay, which has increased attention to them among researchers. In this work, we explored deep neural networks (DNNs) with an optimization algorithm to calculate the approximate solutions for nonlinear fractional differential equations (NFDEs). The target data-driven design of the DNN-LM algorithm was further implemented on the fractional models to study the rigorous impact and symmetry of different parameters on RL, RC circuits, and polytropic gas spheres. The targeted data generated from the analytical and numerical approaches in the literature for different cases were utilized by the deep neural networks to predict the numerical solutions by minimizing the differences in mean square error using the Levenberg–Marquardt algorithm. The numerical solutions obtained by the designed technique were contrasted with the multi-step reproducing kernel Hilbert space method (MS-RKM), Laplace transformation method (LTM), and Padé approximations. The results demonstrate the accuracy of the design technique as the DNN-LM algorithm overlaps with the actual results with minimum percentage absolute errors that lie between 108 and 1012. The extensive graphical and statistical analysis of the designed technique showed that the DNN-LM algorithm is dependable and facilitates the examination of higher-order nonlinear complex problems due to the flexibility of the DNN architecture and the effectiveness of the optimization procedure. Full article
(This article belongs to the Special Issue Trends in Fractional Modelling in Science and Innovative Technologies)
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15 pages, 4499 KB  
Article
Study on Co-Estimation of SoC and SoH for Second-Use Lithium-Ion Power Batteries
by Nan Jiang and Hui Pang
Electronics 2022, 11(11), 1789; https://doi.org/10.3390/electronics11111789 - 5 Jun 2022
Cited by 24 | Viewed by 4164
Abstract
Lithium-ion batteries are an ideal power supplier for electric vehicles (EVs) due to their high-power density and wide operating voltage, but their performance decays to 80% before retirement from EVs. Nevertheless, they still have a particular use value after decommissioning, so recycling the [...] Read more.
Lithium-ion batteries are an ideal power supplier for electric vehicles (EVs) due to their high-power density and wide operating voltage, but their performance decays to 80% before retirement from EVs. Nevertheless, they still have a particular use value after decommissioning, so recycling the retired power battery in cascade can be considered. Therefore, accurate estimation of battery state-of-charge (SoC) and state-of-health (SoH) is crucial for extending the service life and echelon utilization of power lithium-ion battery packs. This paper proposes a comprehensive co-estimation scheme of battery SoC/SoH for the second-use of lithium-ion power batteries in EVs under different cycles using an adaptive extended Kalman filter (AEKF). First, according to the collected battery test data at different aging cycle levels, the external battery characteristics are analyzed, and then a cycle-dependent equivalent circuit model (cECM) is built up. Next, the parameter estimation of this battery model is performed via a recursive least square (RLS) algorithm. Meanwhile, the variations in internal battery parameters of the cycle numbers are fitted and synthesized. Moreover, validation of the estimated parameters is further carried out. Based on this enhanced battery model, the AEKF algorithm is utilized to fulfill battery SoC/SoH estimation simultaneously. The estimated results of SoC/SoH are obtained for a LiCoO2 cell in the case of CCC (constant current condition) under different cycle times. The results show that this proposed co-estimation scheme can predict battery SoC and SoH well, wherein the peak values of the SoC errors are less than 2.2%, and the peak values of SoH, calculated by the estimated capacity and internal resistance, are less than 1.7% and 2.2%, respectively. Hence, this has important guiding significance for realizing the cascade utilization of lithium-ion power batteries. Full article
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22 pages, 5834 KB  
Article
Online SoC Estimation of Lithium-Ion Batteries Using a New Sigma Points Kalman Filter
by Dongdong Ge, Zhendong Zhang, Xiangdong Kong and Zhiping Wan
Appl. Sci. 2021, 11(24), 11797; https://doi.org/10.3390/app112411797 - 12 Dec 2021
Cited by 21 | Viewed by 4408
Abstract
The accurate state of charge (SoC) online estimation for lithium-ion batteries is a primary concern for predicting the remaining range in electric vehicles. The Sigma points Kalman Filter is an emerging SoC filtering technology. Firstly, the charge and discharge tests of the battery [...] Read more.
The accurate state of charge (SoC) online estimation for lithium-ion batteries is a primary concern for predicting the remaining range in electric vehicles. The Sigma points Kalman Filter is an emerging SoC filtering technology. Firstly, the charge and discharge tests of the battery were carried out using the interval static method to obtain the accurate calibration of the SoC-OCV (open circuit voltage) relationship curve. Secondly, the recursive least squares method (RLS) was combined with the dynamic stress test (DST) to identify the parameters of the second-order equivalent circuit model (ECM) and establish a non-linear state-space model of the lithium-ion battery. Thirdly, based on proportional correction sampling and symmetric sampling Sigma points, an SoC estimation method combining unscented transformation and Stirling interpolation center difference was designed. Finally, a semi-physical simulation platform was built. The Federal Urban Driving Schedule and US06 Highway Driving Schedule operating conditions were used to verify the effectiveness of the proposed estimation method in the presence of initial SoC errors and compare with the EKF (extended Kalman filter), UKF (unscented Kalman filter) and CDKF (central difference Kalman filter) algorithms. The results showed that the new algorithm could ensure an SoC error within 2% under the two working conditions and quickly converge to the reference value when the initial SoC value was inaccurate, effectively improving the initial error correction ability. Full article
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17 pages, 2315 KB  
Article
Modeling RL Electrical Circuit by Multifactor Uncertain Differential Equation
by Yang Liu and Lujun Zhou
Symmetry 2021, 13(11), 2103; https://doi.org/10.3390/sym13112103 - 5 Nov 2021
Cited by 9 | Viewed by 2711
Abstract
The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on multifactor [...] Read more.
The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on multifactor uncertain differential equation by considering the external noise and internal noise in an actual electrical circuit system. Then, the solution of uncertain RL circuit equation and the inverse uncertainty distribution of solution are derived. Some applications of solution for uncertain RL circuit equation are also investigated. Finally, the method of moments is used to estimate the unknown parameters in uncertain RL circuit equation. Full article
(This article belongs to the Special Issue Uncertainty Theory: Symmetry and Applications)
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15 pages, 3890 KB  
Article
New Equivalent Electrical Model of a Fuel Cell and Comparative Study of Several Existing Models with Experimental Data from the PEMFC Nexa 1200 W
by Fatima Zahra Belhaj, Hassan El Fadil, Zakariae El Idrissi, Abdessamad Intidam, Mohamed Koundi and Fouad Giri
Micromachines 2021, 12(9), 1047; https://doi.org/10.3390/mi12091047 - 30 Aug 2021
Cited by 41 | Viewed by 8847
Abstract
The present work investigates different models of polymer electrolyte membrane fuel cell. More specifically, three models are studied: a nonlinear state-space model, a generic dynamic model integrated into MATLAB/Simulink, and an equivalent RC electrical circuit. A new equivalent electrical RL model is proposed, [...] Read more.
The present work investigates different models of polymer electrolyte membrane fuel cell. More specifically, three models are studied: a nonlinear state-space model, a generic dynamic model integrated into MATLAB/Simulink, and an equivalent RC electrical circuit. A new equivalent electrical RL model is proposed, and the methodology for determining its parameters is also given. An experimental test bench, based on a 1200-W commercial PEMFC, is built to compare the static and dynamic behaviour of the existing models and the proposed RL model with the experimental data. The comparative analysis highlights the advantages and drawbacks of each of these models. The major advantages of the proposed RL model lie in both its simplicity and its ability to provide a similar transitory behaviour compared to the commercially manufactured PEMFC employed in this research. Full article
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15 pages, 1655 KB  
Article
An Accurate State of Charge Estimation Method for Lithium Iron Phosphate Battery Using a Combination of an Unscented Kalman Filter and a Particle Filter
by Thanh-Tung Nguyen, Abdul Basit Khan, Younghwi Ko and Woojin Choi
Energies 2020, 13(17), 4536; https://doi.org/10.3390/en13174536 - 1 Sep 2020
Cited by 19 | Viewed by 3985
Abstract
An accurate state of charge (SOC) estimation of the battery is one of the most important techniques in battery-based power systems, such as electric vehicles (EVs) and energy storage systems (ESSs). The Kalman filter is a preferred algorithm in estimating the SOC of [...] Read more.
An accurate state of charge (SOC) estimation of the battery is one of the most important techniques in battery-based power systems, such as electric vehicles (EVs) and energy storage systems (ESSs). The Kalman filter is a preferred algorithm in estimating the SOC of the battery due to the capability of including the time-varying coefficients in the model and its superior performance in the SOC estimation. However, since its performance highly depends on the measurement noise (MN) and process noise (PN) values, it is difficult to obtain highly accurate estimation results with the battery having a flat plateau OCV (open-circuit voltage) area in the SOC-OCV curve, such as the Lithium iron phosphate battery. In this paper, a new integrated estimation method is proposed by combining an unscented Kalman filter and a particle filter (UKF-PF) to estimate the SOC of the Lithium iron phosphate battery. The equivalent circuit of the battery used is composed of a series resistor and two R-C parallel circuits. Then, it is modeled by a second-order autoregressive exogenous (ARX) model, and the parameters are identified by using the recursive least square (RLS) identification method. The validity of the proposed algorithm is verified by comparing the experimental results obtained with the proposed method and the conventional methods. Full article
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12 pages, 10654 KB  
Article
Comparative Study of Integer and Non-Integer Order Models of Synchronous Generator
by Szymon Racewicz, Filip Kutt, Michał Michna and Łukasz Sienkiewicz
Energies 2020, 13(17), 4416; https://doi.org/10.3390/en13174416 - 26 Aug 2020
Cited by 9 | Viewed by 2919
Abstract
This article presents a comparison between integer and non-integer order modelling of a synchronous generator, in the frequency domain as well as in the time domain. The classical integer order model was compared to one containing half-order systems. The half-order systems are represented [...] Read more.
This article presents a comparison between integer and non-integer order modelling of a synchronous generator, in the frequency domain as well as in the time domain. The classical integer order model was compared to one containing half-order systems. The half-order systems are represented in a Park d-q axis equivalent circuit as impedances modelled by half-order transmittances. Using a direct method based on the approximation of the half-order derivatives by the Grünwald–Letnikov definition, a state-space equation system was solved. For both models, a computational program written in Matlab® software was used. For the purpose of time domain simulation, the machine models were connected to an electric load composed of an RL circuit. To validate and compare both models, simulation results of a three-phase short-circuit and a no-load voltage recovery were compared with corresponding measurements performed on a solid salient-pole synchronous generator of 125 kVA. Full article
(This article belongs to the Special Issue Design and Analysis of Electric Machines)
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16 pages, 2077 KB  
Article
Direct Consideration of Eddy Current Losses in Laminated Magnetic Cores in Finite Element Method (FEM) Calculations Using the Laplace Transform
by Marek Gołębiowski, Lesław Gołębiowski, Andrzej Smoleń and Damian Mazur
Energies 2020, 13(5), 1174; https://doi.org/10.3390/en13051174 - 4 Mar 2020
Cited by 5 | Viewed by 4045
Abstract
The following article presents a computation procedure that enables us to simulate the dynamic states of electric machines with a laminated magnetic core, with direct consideration of the eddy current losses. The presented approach enables a significant reduction of the simulation process computational [...] Read more.
The following article presents a computation procedure that enables us to simulate the dynamic states of electric machines with a laminated magnetic core, with direct consideration of the eddy current losses. The presented approach enables a significant reduction of the simulation process computational complexity. The verification of the obtained data correctness is based on a detailed balance of energy and power in the investigated system. The correctness of the obtained results was also confirmed by comparing them with the results included in norms that describe the losses in laminated sheets. The presented approach is based on expressing the equivalent permeability of transformer metal sheets by using RC or RL circuits. The impedances of these circuits are treated as the transmittance of Infinite Impulse Response filters (IIR) of the Laplace s variable. In this form they are implemented in direct calculations of the dynamics of electric machines based on field-circuital models, using the Finite Element Method (FEM). In this way, we present the method of including eddy current losses in laminated metal circuits of chokes or transformers, during calculations using the finite element method, with the IIR filter in the domain of the variable s of the Laplace transform. Eddy current losses are directly included in the calculation process. Therefore, they have a direct impact on the transient state waveforms. However, the use of the Laplace variable s caused an excessive increase in the number of state variables, and the overall computational efficiency of the presented method is sufficiently low so as to be used in the simulation process of electrical machine dynamic states with a relatively large number of elements in the FE Model. Full article
(This article belongs to the Special Issue Applied Energy System Modeling 2018)
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