Search Results (242)

This paper investigates the vibration suppression of cantilevered beams using nonlinear shunted piezoelectric circuits. The beam’s inertia and geometric nonlinearities are considered. A quadratic nonlinear piezoelectric capacitance is used such that there exists a two-to-one internal resonance between the mechanical and electrical modes. The internal resonance coupling is exploited to trigger the saturation phenomenon such that the beam’s vibration reaches a limit beyond an excitation amplitude threshold. The equations governing the nonlinear vibration of the beam coupled with the shunt circuit are derived, and modal analysis is used to obtain a system of two nonlinearly coupled modal equations. The equations are then numerically integrated to obtain the results. A parametric study is performed to assess the significance of system parameters, such as the location of the piezoelectric patch, its size, circuit resistance, and nonlinear gain, on the effectiveness of vibration suppression. The results show that the proposed design effectively suppresses the linear and nonlinear vibrations of the beam. The proposed absorber is space-efficient and does not add mass to the primary system, and hence, it has the potential in systems where the weight matters, such as aerospace applications. Full article

The electrodynamics of current provide much of our technology, from telegraphs to the wired infrastructure powering the circuits of our electronic technology. Current flow is analyzed by its own rules that involve the Maxwell Ampere law and magnetism. Electrostatics does not involve magnetism, and so current flow and electrodynamics cannot be derived from electrostatics. Practical considerations also prevent current flow from being analyzed one charge at a time. There are too many charges, and far too many interactions to allow computation. Current flow is essential in biology. Currents are carried by electrons in mitochondria in an electron transport chain. Currents are carried by ions in nerve and muscle cells. Currents everywhere follow the rules of current flow: Kirchhoff’s current law and its generalizations. The importance of electron and proton flows in generating ATP was discovered long ago but they were not analyzed as electrical currents. The flow of protons and transport of electrons form circuits that must be analyzed by Kirchhoff’s law. A chemiosmotic theory that ignores the laws of current flow is incorrect physics. Circuit analysis is easily applied to short systems like mitochondria that have just one internal electrical potential in the form of the Hodgkin Huxley Katz (HHK) equation. The HHK equation combined with classical descriptions of chemical reactions forms a computable model of cytochrome c oxidase, part of the electron transport chain. The proton motive force is included as just one of the components of the total electrochemical potential. Circuit analysis includes its role just as it includes the role of any other ionic current. Current laws are now needed to analyze the flow of electrons and protons, as they generate ATP in mitochondria and chloroplasts. Chemiosmotic theory must be replaced by an electro-osmotic theory of ATP production that conforms to the Maxwell Ampere equation of electrodynamics while including proton movement and the proton motive force. Full article

This paper presents a novel analytical model of a double-stator single-rotor (DSSR) ironless axial flux machine (IAFM), with no iron either in the rotor or in the stator, that has cylindrical magnets in the rotor. The model is based on sizing equations that include the peak no-load flux density as a determining parameter, and then static simulations using the finite element method show that the 3D magnetic field created by cylindrical magnets can be generally fitted with an empirical function. The analytical model is validated throughout this work with finite element simulations and experiments over a prototype, showing a good agreement. It is stated that the integration of the magnetic field for different rotor positions, using the empirical approach presented here, gives accurate results regarding the back-electromotive force waveform and harmonics, with a reduced computation time and effort compared to the finite element method and avoiding complex formulations of previous analytical models. Moreover, this straightforward approach facilitates the design and comparison of IAFMs with other machine topologies, as sizing equations and magnetic circuits developed for conventional electrical machines are not valid for IAFMs, because, here, the magnetic field circulates entirely through air due to the absence of ferromagnetic materials. Furthermore, the scope of this paper is limited to a DSSR-IAFM, but the method can be directly applied to single-sided IAFMs and could be refined to deal with single-stator double-rotor IAFMs. Full article

The no-insulation (NI) technique improves the stability and defect-tolerance of high-temperature superconducting (HTS) coils by enabling current redistribution, thereby reducing the risk of quenching. NI–HTS coils are widely applied in DC systems such as high-field magnets and superconducting field coils for electric machines. However, the presence of turn-to-turn contact resistance makes current distribution uneven, rendering traditional simulation methods unsuitable. To address this, a finite element method (FEM) based on the T–A formulation is proposed. This model solves coupled equations for the magnetic vector potential (A) and current vector potential (T), incorporating turn-to-turn contact resistance and anisotropic conductivity. The thin-strip approximation simplifies second-generation HTS materials as one-dimensional conductors, and a homogenization technique further reduces computational time by averaging the properties between turns, although it may limit the resolution of localized inter-turn effects. To verify the model’s accuracy, simulation results are compared against the H formulation, distributed circuit network (DCN) model, and experimental data. The proposed T–A model accurately reproduces key transient characteristics, including magnetic field evolution and radial current distribution, in both circular and racetrack NI coils. These results confirm the model’s potential as an efficient and reliable tool for transient electromagnetic analysis of NI–HTS coils. Full article

Due to the coupling of DC and AC components, the ion flow field of HVDC and HVAC transmission lines in the same corridor or even the same tower is complex and time-dependent. In order to effectively analyze the ground-level electric field of hybrid transmission lines, the Krylov subspace methods with pre-conditioning treatment are used to solve the discretization equations. By optimizing the coefficient matrix, the calculation efficiency of the iterative process of the electric field in the time domain is greatly increased. Based on the limit of electric field, radio interference and audible noise applied in China, the main factor influencing the design of hybrid transmission lines is determined in terms of electromagnetic environment. After the ground-level electric field of transmission lines with different configurations is analyzed, the minimum height and corridor width of double-circuit 500 kV HVAC lines and one-circuit ±800 kV HVDC lines in the same corridor are obtained. The research provides valuable practical recommendations for optimal tower configurations, minimum heights, and corridor widths under various electromagnetic constraints. Full article

The implementation of chaotic behavior and a sensitivity assessment of the newly developed M-fractional Kuralay-II equation are the foremost objectives of the present study. This equation has significant possibilities in control systems, electrical circuits, seismic wave propagation, economic dynamics, groundwater flow, image and signal denoising, complex biological systems, optical fibers, plasma physics, population dynamics, and modern technology. These applications demonstrate the versatility and advantageousness of the stated model for complex systems in various scientific and engineering disciplines. One more essential objective of the present research is to find closed-form wave solutions of the assumed equation based on the $({\displaystyle \frac{G^{\prime }}{G^{\prime }+G+A}})$-expansion approach. The results achieved are in exponential, rational, and trigonometric function forms. Our findings are more novel and also have an exclusive feature in comparison with the existing results. These discoveries substantially expand our understanding of nonlinear wave dynamics in various physical contexts in industry. By simply selecting suitable values of the parameters, three-dimensional (3D), contour, and two-dimensional (2D) illustrations are produced displaying the diagrammatic propagation of the constructed wave solutions that yield the singular periodic, anti-kink, kink, and singular kink-shape solitons. Future improvements to the model may also benefit from what has been obtained as well. The various assortments of solutions are provided by the described procedure. Finally, the framework proposed in this investigation addresses additional fractional nonlinear partial differential equations in mathematical physics and engineering with excellent reliability, quality of effectiveness, and ease of application. Full article

This paper presents an algorithm for the implementation of a model that calculates shunt currents in redox flow batteries. The formation patterns of the equivalent electrical circuit that models shunt currents in redox flow batteries are analyzed in such a way that the proposed algorithm is applicable for batteries with any number of cell stacks and any number of cells per stack. Linear algebra is applied to solve the equation system related to the equivalent electric circuit. The solution of such a system of equations is obtained by performing the inverse of a matrix and premultiplying that matrix on both sides of the equation system. This being rather trivial, the real problem lies in automating the generation of the matrices relative to the system of equations. For this reason, it is analyzed how to generate the matrixes in order to facilitate the implementation of their generation. Finally, the most important parts of the implementation of the resolution algorithm are shown. Full article

The dielectric relaxation behavior of polymeric materials is critical to their performance in electronic, insulating, and energy storage applications. This study presents an electrical fractional model (EFM) based on fractional calculus and the complex electric modulus ($M^{*}\mathit{=}{M}^{\prime }\mathit{+}i{M}^{″}$) formalism to simultaneously describe two key relaxation phenomena: $\alpha$-relaxation and interfacial polarization (Maxwell–Wagner–Sillars effect). The model incorporates fractional elements (cap-resistors) into a modified Debye equivalent circuit to capture polymer dynamics and energy dissipation. Fractional differential equations are derived, with fractional orders taking values between 0 and 1; the frequency and temperature responses are analyzed using Fourier transform. Two temperature-dependent behaviors are considered: the Matsuoka model, applied to $\alpha$-relaxation near the glass transition, and an Arrhenius-type equation, used to describe interfacial polarization associated with thermally activated charge transport. The proposed model is validated using literature data for amorphous polymers, polyetherimide (PEI), polyvinyl chloride (PVC), and polyvinyl butyral (PVB), successfully fitting dielectric spectra and extracting meaningful physical parameters. The results demonstrate that the EFM is a robust and versatile tool for modeling complex dielectric relaxation in polymeric systems, offering improved interpretability over classical integer-order models. This approach enhances understanding of coupled relaxation mechanisms and may support the design of advanced polymer-based materials with tailored dielectric properties. Full article

Noise reduction is essential in analyzing electrochemical impedance spectroscopy (EIS) data for accurate parameter identification of models of electrochemical sources and interfaces. EIS is widely used to study the behavior of electrochemical systems as it provides information about the processes occurring at electrode surfaces. However, measurement noise can severely compromise the accuracy of parameter identification and the interpretation of EIS data. This paper presents methods for parameter identification of Randles (also known as R-RC or 2R-1C) equivalent electrical circuits and noise reduction in EIS data using recursive filtering. EIS data obtained at the estimated characteristic frequency is processed with three equations in the closed form for the parameter estimation of series resistance, charge transfer resistance, and double-layer capacitance. The proposed recursive filter enhances estimation accuracy in the presence of random noise. Filtering is embedded in the estimation procedure, while the optimal value of the recursive filter weighting factor is self-tuned based on the proposed search method. The distinguished feature is that the proposed method can process EIS data and perform estimation with filtering without any input from the user. Synthetic datasets and experimentally obtained impedance data of lithium-ion batteries were successfully processed using PC-based and microcontroller-based systems. Full article

This paper remedies the lack of comparison between studies specifically addressing partial discharge (PD) localization using electrical techniques. It identifies all the elements in need in each technique as well as the equations leading to a precise determination of the discharge site in a cable with a certain length and documents several circuit models set to simulate various types of PD. From the details in this paper, different detection methods can be combined based on the specific requirements of each method for detecting PD. This work thoroughly evaluates several electrical PD detection approaches, including time-based, frequency band, and electromagnetic time reversal (EMTR). Additionally, it gathers circuit modeling for various types of PD along cables to improve detection accuracy. It is evident that all time-dependent methods, despite their simplicity and requiring only a small number of components, face challenges when applied to long cables. This is primarily due to their reliance on signal propagation time. The authors provide profound insights into suggestions for future study areas. This review will provide essential insights and serve as a foundation for researchers to develop more effective methods for detecting PD in cables. Full article

The following article details a model predictive control (MPC) to improve grid resilience when faced with variable generation resources. This topic is of significant interest to utility power systems where distributed intermittent energy sources will increase significantly and be relied on for electric grid ancillary services. Previous work on MPCs has focused on narrowly targeted control applications such as improving electric vehicle (EV) charging infrastructure or reducing the cost of integrating Energy Storage Systems (ESSs) into the grid. In contrast, this article develops a comprehensive treatment of the construction of an MPC tailored to electric grids and then applies it integration of intermittent energy resources. To accomplish this, the following article includes a description of a reduced order model (ROM) of an electric power grid based on a circuit model, an optimization formulation that describes the MPC, a collocation method for solving linear time-dependent differential algebraic equations (DAEs) that result from the ROM, and an overall strategy for iteratively refining the behavior of the MPC. Next, the algorithm is validated using two separate numerical experiments. First, the algorithm is compared to an existing MPC code and the results are verified by a numerically precise simulation. It is shown that this algorithm produces a control comparable to existing algorithms and the behavior of the control carefully respects the bounds specified. Second, the MPC is applied to a small nine bus system that contains a mix of turbine-spinning-machine-based and intermittent generation in order to demonstrate the algorithm’s utility for resource planning and control of intermittent resources. This study demonstrates how the MPC can be tuned to change the behavior of the control, which can then assist with the integration of intermittent resources into the grid. The emphasis throughout the paper is to provide systematic treatment of the topic and produce a novel nonlinear control compatible design framework applicable to electric grids and the control of variable resources. This differs from the more targeted application-based focus in most presentations. Full article

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

Li ion batteries are emerging as the mainstream source for propulsion in the automotive industry. Subjecting a battery to extreme conditions of charging and discharging can negatively impact its performance and reduce its cycle life. Assessing a battery’s electrical and thermal behaviour is critical in the later stages of developing battery management systems (BMSs). The present study aims at the thermal modelling of a 3.3 Ah cylindrical 26650 lithium iron phosphate cell using ANSYS 2024 R1 software. The modelling phase involves iterating two geometries of the cell design to evaluate the cell’s surface temperature. The multi-scale multi-domain solution method, coupled with the equivalent circuit model (ECM) solver, is used to determine the temperature characteristics of the cell. Area-weighted average values of the temperature are obtained using a homogeneous and isotropic assembly. A differential equation is implemented to estimate the temperature due to the electrochemical reactions and potential differences. During the discharge tests, the cell is subjected to a load current emulating the Worldwide Harmonised Light Vehicles Test Procedure (WLTP). The results from the finite element model indicate strikingly similar trends in temperature variations to the ones obtained from the experimental tests. Full article

A coordinated control for the volt-var optimization (VVO) problem is presented using load tap changer transformers, voltage regulators, and capacitor banks with the integration of a PV-based microgrid. The harmony search (HS) algorithm, which is a metaheuristic-based optimization algorithm, was used to determine global optimum settings of related devices to operate efficiently under changing conditions. The major objectives of volt-var optimization were to reduce power losses, peak power demands, and voltage variations in the distribution circuit while maintaining voltages within the permitted range at all nodes and under all loading conditions. The problem was a mixed integer nonlinear problem with discrete integer variables; binary variables for the capacitor status on/off, voltage regulator taps as integers, and continuous variables; the current output of the microgrid; and nonlinear electric circuit equations. The simulations were verified using the IEEE 13-node test circuit. Daily load profiles of the main power system grid and the microgrid’s PV were used with a 15 min resolution. Power flow solutions were produced using the OpenDSS (version 9.5.1.1, year 2022) power distribution system solver. It can be applied to operational and planning purposes. The results showed that active power loss, peak power demand, and voltage fluctuation were significantly reduced by the coordinated control of the volt-var problem. Full article

Differential equations are frequently used to mathematically describe many problems in real life, but they are always subject to intrinsic phenomena that are neglected and could influence how the model behaves. In some cases like ecosystems, electrical circuits, or even economic models, the model may suddenly change due to outside influences. Occasionally, such changes start off impulsively and continue to exist for specific amounts of time. Non-instantaneous impulses are used in the creation of the models for this kind of scenario. In this paper, a new class of non-instantaneous impulsive $\psi$-Caputo fractional stochastic differential equations under integral boundary conditions driven by the Rosenblatt process was examined. Semigroup theory, stochastic theory, the Banach fixed-point theorem, and fractional calculus were applied to investigating the existence of piecewise continuous mild solutions for the systems under consideration. The impulsive Gronwall’s inequality was employed to establish the unique stability conditions for the system under consideration. Furthermore, we examined the controllability results of the proposed system. Finally, some examples were provided to demonstrate the validity of the presented work. Full article